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The Coxeter lattices, which we denote $A_{n/m}$, are a family of lattices containing many of the important lattices in low dimensions. This includes $A_n$, $E_7$, $E_8$ and their duals $A_n^*$, $E_7^*$ and $E_8^*$. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity $O(n\log{n})$ and the other with worst case complexity O(n) where $n$ is the dimension of the lattice. We show that for the particular lattices $A_n$ and $A_n^*$ the algorithms reduce to simple nearest point algorithms that already exist in the literature.
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arxiv:0903.0673
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We define a problem "exact non-identity check": Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a sense of the strict equivalence condition, this problem is different from a QMA-complete problem, non-identity check defined by D. Janzing etc. As corollaries, it is derived that exact equivalence check is also NQP-complete and that it is hard to minimize quantum resources of a given quantum gate array without changing an implemented unitary operation.
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arxiv:0903.0675
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Upon application of a uniform strain, internal sub-lattice shifts within the unit cell of a non-centrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric tensor. Several recent studies suggest that strain-gradient induced polarization may be responsible for a variety of interesting and anomalous electromechanical phenomena in materials including electromechanical coupling effects in non-uniformly strained nanostructures, dead layer effects in nanocapacitor systems, and giant piezoelectricity in perovskite nanostructures among others. In this work, adopting a lattice dynamics based microscopic approach we provide estimates of the flexoelectric tensor for certain cubic ionic crystals, perovskite dielectrics, III-V and II-VI semiconductors. We compare our estimates with experimental and theoretical values wherever available, address the discrepancy that exists between different experimental estimates and also re-visit the validity of an existing empirical scaling relationship for the magnitude of flexoelectric coefficients in terms of material parameters.
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arxiv:0903.0684
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In this paper we study left and right 4-Engel elements of a group. In particular, we prove that $<a, a^b>$ is nilpotent of class at most 4, whenever $a$ is any element and $b^{\pm 1}$ are right 4-Engel elements or $a^{\pm 1}$ are left 4-Engel elements and $b$ is an arbitrary element of $G$. Furthermore we prove that for any prime $p$ and any element $a$ of finite $p$-power order in a group $G$ such that $a^{\pm 1}\in L_4(G)$, $a^4$, if $p=2$, and $a^p$, if $p$ is an odd prime number, is in the Baer radical of $G$.
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arxiv:0903.0691
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The classical Chung-Feller theorem [2] tells us that the number of Dyck paths of length $n$ with $m$ flaws is the $n$-th Catalan number and independent on $m$. L. Shapiro [9] found the Chung-Feller properties for the Motzkin paths. Mohanty's book [5] devotes an entire section to exploring Chung-Feller theorem. Many Chung-Feller theorems are consequences of the results in [5]. In this paper, we consider the $(n,m)$-lattice paths. We study two parameters for an $(n,m)$-lattice path: the non-positive length and the rightmost minimum length. We obtain the Chung-Feller theorems of the $(n,m)$-lattice path on these two parameters by bijection methods. We are more interested in the pointed $(n,m)$-lattice paths. We investigate two parameters for an pointed $(n,m)$-lattice path: the pointed non-positive length and the pointed rightmost minimum length. We generalize the results in [5]. Using the main results in this paper, we may find the Chung-Feller theorems of many different lattice paths.
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arxiv:0903.0705
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By a result of Klyachko the Euler characteristic of moduli spaces of stable bundles of rank two on the projective plane is determined. Using similar methods we extend this result to bundles of rank three. The fixed point components correspond to moduli spaces of the subspace quiver. Moreover, the stability condition is given by a certain system of linear inequalities so that the generating function of the Euler characteristic can be determined explicitly.
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arxiv:0903.0723
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We explore the hypothesis that some high-velocity runaway stars attain their peculiar velocities in the course of exchange encounters between hard massive binaries and a very massive star (either an ordinary 50-100 Msun star or a more massive one, formed through runaway mergers of ordinary stars in the core of a young massive star cluster). In this process, one of the binary components becomes gravitationally bound to the very massive star, while the second one is ejected, sometimes with a high speed. We performed three-body scattering experiments and found that early B-type stars (the progenitors of the majority of neutron stars) can be ejected with velocities of $\ga$ 200-400 km/s (typical of pulsars), while 3-4 Msun stars can attain velocities of $\ga$ 300-400 km/s (typical of the bound population of halo late B-type stars). We also found that the ejected stars can occasionally attain velocities exceeding the Milky Ways's escape velocity.
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arxiv:0903.0738
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We consider the Cauchy problem for the wave equation on a non-globally hyperbolic manifold of the special form (Minkowski plane with a handle) containing closed timelike curves (time machines). We prove that the classical solution of the Cauchy problem exists and is unique if and only if the initial data satisfy to some set of additional conditions.
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arxiv:0903.0741
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We consider the problem of privacy in direct communications, showing how quantum mechanics can be useful to guarantee a certain level of confidentiality. In particular, we review a continuous variable approach recently proposed by us [S. Pirandola et al., Europhys. Lett. 84, 20013 (2008)]. Here, we analyze the degree of privacy of this technique against a broader class of attacks, which includes non-Gaussian eavesdropping.
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arxiv:0903.0750
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Double porosity models for the liquid filtration in a naturally fractured reservoir is derived from the homogenization theory. The governing equations on the microscopic level consist of the stationary Stokes system for an incompressible viscous fluid, occupying a crack-pore space (liquid domain), and stationary Lame equations for an incompressible elastic solid skeleton, coupled with corresponding boundary conditions on the common boundary "solid skeleton-liquid domain". We suppose that the liquid domain is a union of two independent systems of cracks (fissures) and pores, and that the dimensionless size $\delta$ of pores depends on the dimensionless size $\varepsilon$ of cracks: $\delta=\varepsilon^{r}$ with $r>1$. The rigorous justification is fulfilled for homogenization procedure as the dimensionless size of the cracks tends to zero, while the solid body is geometrically periodic. As the result we derive the well-known Biot -- Terzaghi system of liquid filtration in poroelastic media, which consists of the usual Darcy law for the liquid in cracks coupled with anisotropic Lame's equation for the common displacements in the solid skeleton and in the liquid in pores and a continuity equation for the velocity of a mixture. The proofs are based on the method of reiterated homogenization, suggested by G. Allaire and M. Briane. As a consequence of the main result we derive the double porosity model for the filtration of the incompressible liquid in an absolutely rigid body.
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arxiv:0903.0797
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A simple hot electron thermocouple is realized in a two-dimensional electron system (2DES) and used to measure the diffusion thermopower of the 2DES at zero magnetic field. This hot electron technique, which requires no micron-scale patterning of the 2DES, is much less sensitive than conventional methods to phonon-drag effects. Our thermopower results are in good agreement with the Mott formula for diffusion thermopower for temperatures up to T ~ 2 K.
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arxiv:0903.0835
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We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its "boundary depth," and establish basic results about how the boundary depths of different Hamiltonians are related. As applications, we prove that certain Hamiltonian symplectomorphisms supported in displaceable subsets have infinitely many nontrivial geometrically distinct periodic points, and we also significantly expand the class of coisotropic submanifolds which are known to have positive displacement energy. For instance, any coisotropic submanifold of contact type (in the sense of Bolle) in any closed symplectic manifold has positive displacement energy, as does any stable coisotropic submanifold of a Stein manifold. We also show that any stable coisotropic submanifold admits a Riemannian metric that makes its characteristic foliation totally geodesic, and that this latter, weaker, condition is enough to imply positive displacement energy under certain topological hypotheses.
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arxiv:0903.0903
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In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically suffer from large renormalization scale uncertainties. I present an efficient implementation of an algorithm for the automated, Feynman diagram based calculation of one-loop corrections to processes with many external particles. This algorithm has been successfully applied to compute the virtual corrections of the process $u\bar{u}\to b\bar{b}b\bar{b}$ in massless QCD and can easily be adapted for other processes which are required for the LHC.
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arxiv:0903.0947
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At present the color-octet mechanism is still an important and debatable part in the non-relativistic QCD(NRQCD). We find in this work that the polarized double charmonium production at the LHC may pose a stringent test on the charmonium production mechanism. Result shows that the transverse momentum($p_T$) scaling behaviors of double $J/\psi$ differential cross sections in color-singlet and -octet production mechanisms deviate distinctively from each other while $p_T$ is larger than 7 GeV. In color-octet mechanism, the two $J/\psi$s in one pair are mostly transversely polarized when $p_T\gg 2 m_c$, as expected from the fragmentation limit point of view. In color-singlet mechanism, there is about one half of the charmonium pairs with at least one $J/\psi$ being longitudinally polarized at moderate transverse momentum. The energy dependence of the polarized $J/\psi$ pair production is found to be weak, and this process is found to be experimentally attainable in the early phase of the LHC operation.
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arxiv:0903.0954
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We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length $x$. This also gives the velocity structure functions. Next, for the case where the initial density is uniform, we obtain the distribution of the density, over any scale $x$, and we derive the density two-point correlation and power spectrum. Finally, we consider the Lagrangian displacement field and we derive the distribution of increments of the Lagrangian map. We check that this gives back the well-known mass function of shocks. For all distributions we describe the limiting scaling functions that are obtained in the large-scale and small-scale limits. We also discuss how these results generalize to other initial conditions, or to higher dimensions, and make the connection with a heuristic multifractal formalism. We note that the formation of point-like masses generically leads to a universal small-scale scaling for the density distribution, which is known as the ``stable-clustering ansatz'' in the cosmological context (where the Burgers dynamics is also known as the ``adhesion model'').
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arxiv:0903.0956
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We study the decay rate of process B->K l+ l- (l=e,mu) and some of its other related observables, like forward backward asymmetry (A_{FB}), polarization asymmetry (PA) and CP-asymmetry (A_{CP}) in R-parity violating (R_{p}) Minimal Supersymmetric Standard Model (MSSM). The analysis shows that R_{p}Yukawa coupling products contribute significantly to the branching fraction of B->K l+ l- within 1 sigma and 2 sigma. Study shows that PA and A_{FB} are sensitive enough to R_{p}Yukawa coupling products and turn out to be good predictions for measurement in future experiments.The CP-asymmetry calculated in this framework agrees well with the recently reported value(i.e. 7%).
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arxiv:0903.0969
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We discuss timelike and spacelike minimal surfaces in $AdS_n$ using a Pohlmeyer type reduction. The differential equations for the reduced system are derived in a parallel treatment of both type of surfaces, with emphasis on their characteristic differences. In the timelike case we find a formulation corresponding to a complete gauge fixing of the torsion. In the spacelike case we derive three sets of equations, related to different parameterizations enforced by the Lorentzian signature of the metric in normal space. On the basis of these equations, we prove that there are no flat spacelike minimal surfaces in $AdS_n, n\geq 4$ beyond the four cusp surfaces used in the Alday-Maldacena conjecture. Furthermore, we give a parameterization of flat timelike minimal surfaces in $AdS_5$ in terms of two chiral fields.
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arxiv:0903.0977
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In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
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arxiv:0903.1003
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Communities of vertices within a giant network such as the World-Wide Web are likely to be vastly smaller than the network itself. However, Fortunato and Barth\'{e}lemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than $\sqrt{L/2}$ edges, where $L$ is the number of edges in the entire network. This resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks. Fortunato and Barth\'{e}lemy's argument can be extended to networks with weighted edges as well, and we derive this corollary argument. We conclude that weighted modularity algorithms may fail to resolve communities with fewer than $\sqrt{W \epsilon/2}$ total edge weight, where $W$ is the total edge weight in the network and $\epsilon$ is the maximum weight of an inter-community edge. If $\epsilon$ is small, then small communities can be resolved. Given a weighted or unweighted network, we describe how to derive new edge weights in order to achieve a low $\epsilon$, we modify the ``CNM'' community detection algorithm to maximize weighted modularity, and show that the resulting algorithm has greatly improved accuracy. In experiments with an emerging community standard benchmark, we find that our simple CNM variant is competitive with the most accurate community detection methods yet proposed.
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arxiv:0903.1072
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The classical sampling theorem for bandlimited functions has recently been generalized to apply to so-called bandlimited operators, that is, to operators with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling versions of two of the most central extensions to the classical sampling theorem. In irregular operator sampling, the sampling set is not periodic with uniform distance. In multi-channel operator sampling, we obtain complete information on an operator by multiple operator sampling outputs.
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arxiv:0903.1082
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We have performed a detailed abundance analysis of the content of s-process elements of two dwarf stars with suspected overabundace of those elements. Such stars belong to a special kinematic sample of the solar neighborhood, with peculiar kinematics and different chemical abundances when compared to "normal" disk stars. We aim to define if those stars can be identified as barium stars, based on their s-process elements abundances, and their classification, i.e., if they share their chemical profile with strong or mild barium stars. We also intend to shed light on the possible origins of the different kinds of barium stars. Spectra have been taken by using the FEROS spectrograph at the 1.52m telescope of ESO, La Silla. Abundances have been derived for 18 elements, by matching the synthetic profile with the observed spectrum. We have found that HD 11397 shows a mild enhancement for most of the s-process elements as well as for some r-process elements. This star seems to share its abundance profile with the mild Ba-stars. Although showing some slight chemical anomalies for Y, Sr, Mo, and Pb, HD 14282 depicts a chemical pattern similar to the normal stars with slight s-process enhancements.
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arxiv:0903.1114
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Let $k\in\mathbb{N}$. Let $f(x)\in \Bbb{Z}[x]$ be any polynomial such that $f(x)$ and $f(x+1)f(x+2)... f(x+k)$ are coprime in $\mathbb{Q}[x]$. We call $$g_{k,f}(n):=\frac{|f(n)f(n+1)... f(n+k)|}{\text{lcm}(f(n),f(n+1),...,f(n+k))}$$ a Farhi arithmetic function. In this paper, we prove that $g_{k,f}$ is periodic. This generalizes the previous results of Farhi and Kane, and Hong and Yang.
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arxiv:0903.1162
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We present the self-consistent, non-perturbative analysis of isospin mixing using the nuclear density functional approach and the rediagonalization of the Coulomb interaction in the good-isospin basis. The largest isospin-breaking effects are predicted for N = Z nuclei and they quickly fall with the neutron excess. The unphysical isospin violation on the mean-field level, caused by the neutron excess, is eliminated by the proposed method. We find a significant dependence of the magnitude of isospin breaking on the parametrization of the nuclear interaction term. A rough correlation has been found between the isospin mixing parameter and the difference of proton and neutron rms radii. The theoretical framework described in this study is well suited to describe a variety of phenomena associated with isospin violation in nuclei, in particular the isospin symmetry-breaking corrections to superallowed Fermi beta decays.
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arxiv:0903.1182
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Exploiting an improved analysis of the electronic antineutrinos signal from the explosion of a galactic core collapse supernova, we show that it is possible to identify within about ten milliseconds the time of the bounce, which is strongly correlated to the time of the maximum amplitude of the gravitational signal. This allows to precisely identify the gravitational wave burst timing.
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arxiv:0903.1191
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We have studied the effect of non-magnetic Zn impurities in the coupled spin-ladder Bi(Cu1xZnx)2PO6 using 31P NMR, muSR and Quantum Monte Carlo simulations. Our results show that the impurities induce in their vicinity antiferromagnetic polarizations, extending over a few unit cells. At low temperature, these extended moments freeze in a process which is found universal among various other spin-gapped compounds: isolated ladders, Haldane or Spin-Peierls chains. This allows us to propose a simple common framework to explain the generic low-temperature impurity induced freezings observed in low dimensional spin-gapped materials.
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arxiv:0903.1234
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Deformations of liquid interfaces by the optical radiation pressure of a focused laser wave were generally expected to display similar behavior, whatever the direction of propagation of the incident beam. Recent experiments showed that the invariance of interface deformations with respect to the direction of propagation of the incident wave is broken at high laser intensities. In the case of a beam propagating from the liquid of smaller refractive index to that of larger one, the interface remains stable, forming a nipple-like shape, while for the opposite direction of propagation, an instability occurs, leading to a long needle-like deformation emitting micro-droplets. While an analytical model successfully predicts the equilibrium shape of weakly deformed interface, very few work has been accomplished in the regime of large interface deformations. In this work, we use the Boundary Integral Element Method (BIEM) to compute the evolution of the shape of a fluid-fluid interface under the effect of a continuous laser wave, and we compare our numerical simulations to experimental data in the regime of large deformations for both upward and downward beam propagation. We confirm the invariance breakdown observed experimentally and find good agreement between predicted and experimental interface hump heights below the instability threshold.
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arxiv:0903.1241
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A multivariate polynomial $p(x)=p(x_1,...,x_n)$ is sos-convex if its Hessian $H(x)$ can be factored as $H(x)= M^T(x) M(x)$ with a possibly nonsquare polynomial matrix $M(x)$. It is easy to see that sos-convexity is a sufficient condition for convexity of $p(x)$. Moreover, the problem of deciding sos-convexity of a polynomial can be cast as the feasibility of a semidefinite program, which can be solved efficiently. Motivated by this computational tractability, it has been recently speculated whether sos-convexity is also a necessary condition for convexity of polynomials. In this paper, we give a negative answer to this question by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos-convex. Interestingly, our example is found with software using sum of squares programming techniques and the duality theory of semidefinite optimization. As a byproduct of our numerical procedure, we obtain a simple method for searching over a restricted family of nonnegative polynomials that are not sums of squares.
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arxiv:0903.1287
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First-principles density functional theory calculations were carried out to determine the low energy geometries of anatase TiO$_2$(001) with Pt implants in the sublayers as substitutional and interstitial impurities as well as on the surface in the form of adsorbates. We investigated the effect of such a systematic Pt incorporation in the electronic structure of this surface for isolated and interacting impurities with an emphasis on the reduction in the band gap to visible region. Comprehensive calculations, for 1x1 surface, showed that Pt ions at interstitial cavities result in local segregation, forming metallic wires inside, while substitution for bulk Ti and adsorption drives four strongly dispersed impurity states from valence-bands up in the gap with a narrowing of ~1.5 eV. Hence, such a contiguous Pt incorporation drives anatase into infrared regime. Pt substitution for the surface Ti, on the other hand, metallizes the surface. Systematic trends for 2x2 surface revealed that Pt can be encapsulated inside to form stable structures as a result of strong Pt-O interactions as well as the adsorptional and substitutional cases. Dilute impurities considered for 2x2 surface models exhibit flat-like defect states driven from the valence bands narrowing the energy gap suitable to obtain visible light responsive titania.
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arxiv:0903.1362
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This paper explores the relationship between mirror symmetry for P^2, at the level of big quantum cohomology, and tropical geometry. The mirror of P^2 is typically taken to be ((C^*)^2,W), where W is a Landau-Ginzburg potential of the form x+y+1/xy. The complex moduli space of the mirror is the universal unfolding of W, and oscillatory integrals produce a Frobenius manifold structure on this universal unfolding. We show that W can be deformed by counting Maslov index two tropical disks, and the natural paramaters appearing in this deformation are then the flat coordinates on the moduli space. Furthermore, the oscillatory integrals are shown to read off directly tropical curve counts from the potential. Thus we show in fact that mirror symmetry for P^2 is equivalent in a strong sense to tropical curve counting formulas, including tropical formulas for gravitational descendent invariants.
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arxiv:0903.1378
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We prove that linear instability implies non-linear instability in the energy norm for the critically dissipative quasi-geostrophic equation.
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arxiv:0903.1391
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A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle only if the Lagrangian and the constraints are preserved not only by the gauge transformations but also by an additional family of transformations, called "pseudo-translations". Explicit expressions of pseudo-translations and of their action on gravitational gauge fields are given. They are expected to be useful for geometric interpretations of their analogues in supergravity theories.
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arxiv:0903.1446
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We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the Gamma-class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau-Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a root of unity in Y. Ruan's crepant resolution conjecture.
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arxiv:0903.1463
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New large deviations results that characterize the asymptotic information rates for general $d$-dimensional ($d$-D) stationary Gaussian fields are obtained. By applying the general results to sensor nodes on a two-dimensional (2-D) lattice, the asymptotic behavior of ad hoc sensor networks deployed over correlated random fields for statistical inference is investigated. Under a 2-D hidden Gauss-Markov random field model with symmetric first order conditional autoregression and the assumption of no in-network data fusion, the behavior of the total obtainable information [nats] and energy efficiency [nats/J] defined as the ratio of total gathered information to the required energy is obtained as the coverage area, node density and energy vary. When the sensor node density is fixed, the energy efficiency decreases to zero with rate $\Theta({area}^{-1/2})$ and the per-node information under fixed per-node energy also diminishes to zero with rate $O(N_t^{-1/3})$ as the number $N_t$ of network nodes increases by increasing the coverage area. As the sensor spacing $d_n$ increases, the per-node information converges to its limit $D$ with rate $D-\sqrt{d_n}e^{-\alpha d_n}$ for a given diffusion rate $\alpha$. When the coverage area is fixed and the node density increases, the per-node information is inversely proportional to the node density. As the total energy $E_t$ consumed in the network increases, the total information obtainable from the network is given by $O(\log E_t)$ for the fixed node density and fixed coverage case and by $\Theta (E_t^{2/3})$ for the fixed per-node sensing energy and fixed density and increasing coverage case.
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arxiv:0903.1496
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We study the phenomenology of supersymmetric models that explain neutrino masses through the spontaneous breaking of R-parity, finding strong correlations between the decays of the lightest neutralino and the neutrino mixing angles. In addition, the existence of a Goldstone boson, usually called Majoron ($J$), completely modifies the phenomenology with respect to the standard picture, inducing large invisible branching ratios and charged lepton decays, like $\mu \to e J$, interesting signals that can be used to constrain the model.
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arxiv:0903.1512
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We revisited a model for charmonium hybrid meson with a magnetic gluon [Yu. S. Kalashnikova and A. V. Nefediev, Phys. Rev. D {\bf 77}, 054025 (2008)] and improved the numerical calculations. These improvements support the hybrid meson interpretation of X(4260). Within the same model, we computed the hybrid meson mass with an electric gluon which is resolved to be lighter. Relativistic effects and coupling channels decreased also the mass.
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arxiv:0903.1547
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The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in cuprates, started in [Gh. Adam, S. Adam, J. Phys. A: Math. Theor., Vol.40, 11205 (2007)]. Discussion of the $(\delta, T)$ phase diagram of the model points to the divergence of the energy spectrum in the limit of vanishing doping $\delta$. Finite energy spectra at all possible doping rates $\delta$ are obtained provided the hopping part of the effective Hamiltonian is renormalized with an effective factor pointing to the site-pairs availability for fermion hopping processes.
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arxiv:0903.1563
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Real and momentum space spectrally resolved images of microcavity polariton emission in the regime of condensation are investigated under non resonant excitation using a laser source with reduced intensity fluctuations on the timescale of the exciton lifetime. We observe that the polariton emission consists of many macroscopically occupied modes. Lower energy modes are strongly localized by the photonic potential disorder on a scale of few microns. Higher energy modes have finite k-vectors and are delocalized over 10-15 microns. All the modes exhibit long range spatial coherence comparable to their size. We provide a theoretical model describing the behavior of the system with the results of the simulations in good agreement with the experimental observations. We show that the multimode emission of the polariton condensate is a result of its nonequilibrium character, the interaction with the local photonic potential and the reduced intensity fluctuations of the excitation laser.
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arxiv:0903.1570
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A Monte Carlo simulation is performed in a cubic lattice of interacting identical Stoner-Woldfarth nanoparticles. The model system is a randomly-anisotropic Heisenberg spin system with a small anisotropy-to-exchange ratio D/J = 3.5. The dc susceptibility, chi(dc)(T), shows a Curie-Weiss-like transition at a temperature T-C/J approximate to 1.5, followed by a low-temperature glassy behavior manifested by cusps in both the zero-field-cooled and the field-cooled curves. The ac susceptibility, chi(ac) (T, omega), at various frequencies, w, shows that with decreasing temperature, a non-Arrhenius dispersive peak occurs at T-b(omega), succeeded by another dispersionless peak at T-g/J approximate to 1.20 in the in-phase part, chi'(T, omega), of chi (T, omega) while the out-of-phase part, chi '' (T, omega), shows only one peak. A dynamic scaling analysis shows that the system exhibits a critical slowing-down at T-g with a quite small exponent zv approximate to 1.65. However, no universal collapse is seen for the fully-scaled data of chi '' (T, omega). These observed behaviors are interpreted under the droplet-like hypothesis that the formation and development of exchange-induced correlated clusters drive ensembles of nanoparticles undergoing a transition from a paramagnetic order to a short-range order (SRO) at T-C, followed by a transition at T-g to the magnetic state in which a magnetic glassy order and a magnetic quasi-long-range order (QLRO) coexist. In addition, our simulation shows that the onset of the latter transition, which is peculiarly manifested by the dispersionless peak, occurs only for those ensembles possessing the anisotropy strength in the region 1.0 <= D/J <= 5.0.....
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arxiv:0903.1571
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In 1938, Morse and Hedlund proved that the subword complexity function of an infinite word is either bounded or at least linearly growing. In 1982, Ehrenfeucht and Rozenberg proved that this gap property holds for the subword complexity function of any language. The aim of the present paper is to present a self-contained, compact proof of Ehrenfeucht and Rozenberg's result.
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arxiv:0903.1627
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We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation of the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occur. We fill this gap by perturbatively incorporating classes of spatially-varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity and apply the method to the spherical pore with a simple hemi-spherical binary distribution of the depletion strength and obtain bounds for the induced change in the slowest relaxation mode.
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arxiv:0903.1655
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Star formation is thought to be triggered by the gravitational collapse of the dense cores of molecular clouds. Angular momentum conservation during the collapse results in the progressive increase of the centrifugal force, which eventually halts the inflow of material and leads to the development of a central mass surrounded by a disc. In the presence of an angular momentum transport mechanism, mass accretion onto the central object proceeds through this disc, and it is believed that this is how stars typically gain most of their mass. However, the mechanisms responsible for this transport of angular momentum are not well understood. The most promising are turbulence viscosity driven by the magnetorotational instability (MRI), and outflows accelerated centrifugally from the surfaces of the disc. Both processes are powered by the action of magnetic fields and are, in turn, likely to strongly affect the structure, dynamics, evolutionary path and planet-forming capabilities of their host discs. The weak ionization of protostellar discs, however, may prevent the magnetic field from effectively coupling to the gas and drive these processes. Here I examine the viability and properties of these magnetically driven processes in protostellar discs. The results indicate that, despite the weak ionization, the field is able to couple to the gas and shear for fluid conditions thought to be satisfied over a wide range of radii in these discs.
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arxiv:0903.1673
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This paper analyzes a broadcasting technique for wireless multi-hop sensor networks that uses a form of cooperative diversity called opportunistic large arrays (OLAs). We propose a method for autonomous scheduling of the nodes, which limits the nodes that relay and saves as much as 32% of the transmit energy compared to other broadcast approaches, without requiring Global Positioning System (GPS), individual node addressing, or inter-node interaction. This energy-saving is a result of cross-layer interaction, in the sense that the Medium Access Control (MAC) and routing functions are partially executed in the Physical (PHY) layer. Our proposed method is called OLA with a transmission threshold (OLA-T), where a node compares its received power to a threshold to decide if it should forward. We also investigate OLA with variable threshold (OLA-VT), which optimizes the thresholds as a function of level. OLA-T and OLA-VT are compared with OLA broadcasting without a transmission threshold, each in their minimum energy configuration, using an analytical method under the orthogonal and continuum assumptions. The trade-off between the number of OLA levels (or hops) required to achieve successful network broadcast and transmission energy saved is investigated. The results based on the analytical assumptions are confirmed with Monte Carlo simulations.
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arxiv:0903.1675
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We experimentally verified the phenomena of photonic jets generated by plane-electromagnetic-wave-illuminated dielectric micro-cylinders with diameter comparable to the corresponding wavelength at microwave frequencies. Using a home-made 2D spatial field mapping system, we carried out a point-by-point measurement of both phase and intensity of spatial electric field distribution inside and around scattering cylinders, providing a clear complete electromagnetic field picture for these phenomena. Correspondingly, the theoretically predicted super-enhancement of the backscattering induced by small particles of deeply-subwavelength size located within the photonic jets was also confirmed. Our measurements agreed well with the numerical simulations, indicating that the photonic jets indeed can provide a promising powerful way for deeply subwavelength detection and imaging.
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arxiv:0903.1693
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We construct families of pairs of Heegaard splittings that must be stabilized several times to become equivalent. The first such pair differs only by their orientation. These are genus n splittings of a closed 3-manifold that must be stabilized at least n-2 times to become equivalent. The second is a pair of genus n splittings of a manifold with toroidal boundary that must be stabilized at least n-4 times to become equivalent. The last example is a pair of genus n splittings of a closed 3-manifold that must be stabilized at least ${1/2}n -3$ times to become equivalent, regardless of their orientations. All of these examples are splittings of manifolds that are obtained from simpler manifolds by gluing along incompressible surfaces via "sufficiently complicated" maps.
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arxiv:0903.1695
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Motivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced order as well as that of original order and its fluctuation. It is also found that the induced order decreases with increasing the magnitude of the original order. Implications to the multilayered system are discussed.
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arxiv:0903.1697
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It was recently observed in a numerical study on a high order perturbation method under heavy fluid loading that a loaded vibrating plate results, not only in the classical frequency shift of the in vacuo single resonance (in both the real part because of the fluid added mass and the imaginary part because of energy lost by radiation), but also in an increase in the number of the resonance. As a result of the loading, a single in vacuo resonance of the structure is transformed into a multiple resonance. Here we show that this phenomenon is a refinement of the Sanchez's classical result where it was established, using asymptotic analysis, that in the case of a light loading conditions " the scattering frequencies of a fluid loaded elastic structure (ie the resonance frequencies) are nearly the real eigenfrequencies of the elastic body alone and the complex scattering frequencies of the fluid with a rigid solid ". A theoretical explanation of the multiple resonances is given using classical results on theory of entire functions. It is established that every single in vacuo resonance of a simply supported rectangular plate is transformed into an infinite number of resonances under fluid-loading condition.
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arxiv:0903.1704
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The development of microfluidic devices is still hindered by the lack of robust fundamental building blocks that constitute any fluidic system. An attractive approach is optical actuation because light field interaction is contactless and dynamically reconfigurable, and solutions have been anticipated through the use of optical forces to manipulate microparticles in flows. Following the concept of an 'optical chip' advanced from the optical actuation of suspensions, we propose in this survey new routes to extend this concept to microfluidic two-phase flows. First, we investigate the destabilization of fluid interfaces by the optical radiation pressure and the formation of liquid jets. We analyze the droplet shedding from the jet tip and the continuous transport in laser-sustained liquid channels. In the second part, we investigate a dissipative light-flow interaction mechanism consisting in heating locally two immiscible fluids to produce thermocapillary stresses along their interface. This opto-capillary coupling is implemented in adequate microchannel geometries to manipulate two-phase flows and propose a contactless optical toolbox including valves, droplet sorters and switches, droplet dividers or droplet mergers. Finally, we discuss radiation pressure and opto-capillary effects in the context of the 'optical chip' where flows, channels and operating functions would all be performed optically on the same device.
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arxiv:0903.1739
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Let $G$ be a graph each edge $e$ of which is given a length $\ell(e)$. This naturally induces a distance $d_\ell(x,y)$ between any two vertices $x,y$, and we let $\ell-TOP$ denote the completion of the corresponding metric space. It turns out that several well studied topologies on infinite graphs are special cases of $\ell-TOP$. Moreover, it seems that $\ell-TOP$ is the right setting for studying various problems. The aim of this paper is to introduce $\ell-TOP$, providing basic facts, motivating examples and open problems, and indicate possible applications.
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arxiv:0903.1744
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The AdS(4)/CFT(3) duality is a new example of an integrable and exactly solvable AdS/CFT system. There is, however, a puzzling mismatch between the number of degrees of freedom used in the exact solution (4B+4F scattering states) and 8B+8F transverse oscillation modes of critical superstring theory. We offer a resolution of this puzzle by arguing that half of the string modes dissolve in the continuum of two-particle states once alpha' corrections are taken into account. We also check that the conjectured exact S-matrix of AdS(4)/CFT(3) agrees with the tree-level worldsheet calculation.
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arxiv:0903.1747
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Macroscopic systems are described most completely by local densities (particle number, momentum and energy) yet the superposition states of such physical variables, indicated by the Everett interpretation, are not observed. In order to explain this, it is argued that histories of local number, momentum and energy density are approximately decoherent when coarse-grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally-induced decoherence. We discuss the approach to local equilibrium and the subsequent emergence of hydrodynamic equations for the local densities. The results are general but we focus on a chain of oscillators as a specific example in which explicit calculations may be carried out. We discuss the relationships between environmentally-induced and conservation-induced decoherence and present a unified view of these two mechanisms.
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arxiv:0903.1802
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First-principles calculations of the electronic structure of members of the $R$NiC$_2$ series are presented, and their Fermi surfaces investigated for nesting propensities which might be linked to the charge-density waves exhibited by certain members of the series ($R$ = Sm, Gd and Nd). Calculations of the generalized susceptibility, $\chi_{0}({\bf q},\omega)$, show strong peaks at the same ${\bf q}$-vector in both the real and imaginary parts for these compounds. Moreover, this peak occurs at a wavevector which is very close to that experimentally observed in SmNiC$_2$. In contrast, for LaNiC$_2$ (which is a superconductor below 2.7K) as well as for ferromagnetic SmNiC$_2$, there is no such sharp peak. This could explain the absence of a charge-density wave transition in the former, and the destruction of the charge-density wave that has been observed to accompany the onset of ferromagnetic order in the latter.
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arxiv:0903.1814
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We present the SINS survey with SINFONI of high redshift galaxies. With 80 objects observed and 63 detected, SINS is the largest survey of spatially resolved gas kinematics, morphologies, and physical properties of star-forming galaxies at z~1-3. We describe the selection of the targets, the observations, and the data reduction. We then focus on the "SINS Halpha sample" of 62 rest-UV/optically-selected sources at 1.3<z<2.6 for which we targeted primarily the Halpha and [NII] emission lines. Only 30% of this sample had previous near-IR spectroscopic observations. As a whole, the SINS Halpha sample covers a reasonable representation of massive log(M*/Msun)>~10 star-forming galaxies at z~1.5-2.5, with some bias towards bluer systems compared to pure K-selected samples due to the requirement of secure optical redshift. The sample spans two orders of magnitude in stellar mass and in absolute and specific star formation rates, with median values of approximately log(M*/Msun) = 10.5, 70 Msun/yr, and 3/Gyr. The ionized gas distribution and kinematics are spatially resolved on scales ranging from 1.5 kpc for adaptive optics assisted observations to typically 4-5 kpc for seeing-limited data. The Halpha morphologies tend to be irregular and/or clumpy. About one-third are rotation-dominated yet turbulent disks, another third comprises compact and velocity dispersion-dominated objects, and the remaining galaxies are clear interacting/merging systems; the fraction of rotation-dominated systems increases among the more massive part of the sample. The Halpha luminosities and equivalent widths suggest on average roughly twice higher dust attenuation towards the HII regions relative to the bulk of the stars, and comparable current and past-averaged star formation rates. [Abridged]
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arxiv:0903.1872
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The general linear model (GLM) is a well established tool for analyzing functional magnetic resonance imaging (fMRI) data. Most fMRI analyses via GLM proceed in a massively univariate fashion where the same design matrix is used for analyzing data from each voxel. A major limitation of this approach is the locally varying nature of signals of interest as well as associated confounds. This local variability results in a potentially large bias and uncontrolled increase in variance for the contrast of interest. The main contributions of this paper are two fold (1) We develop a statistical framework called SMART that enables estimation of an optimal design matrix while explicitly controlling the bias variance decomposition over a set of potential design matrices and (2) We develop and validate a numerical algorithm for computing optimal design matrices for general fMRI data sets. The implications of this framework include the ability to match optimally the magnitude of underlying signals to their true magnitudes while also matching the "null" signals to zero size thereby optimizing both the sensitivity and specificity of signal detection. By enabling the capture of multiple profiles of interest using a single contrast (as opposed to an F-test) in a way that optimizes for both bias and variance enables the passing of first level parameter estimates and their variances to the higher level for group analysis which is not possible using F-tests. We demonstrate the application of this approach to in vivo pharmacological fMRI data capturing the acute response to a drug infusion, to task-evoked, block design fMRI and to the estimation of a haemodynamic response function (HRF) response in event-related fMRI. Our framework is quite general and has potentially wide applicability to a variety of disciplines.
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arxiv:0903.1880
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A model is proposed to study the possible pairing structures of N-boson systems with nonzero spin. Analytical solutions have been obtained. The emphasis is placed on the spin-structures of ground states with attractive or repulsive pairing force, and with or without the action of a magnetic field. A quantity (an analogue of the two-body density function) is defined to study the spin-correlation between two bosons in N-body systems. The excitation of the system has also been studied.
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arxiv:0903.1902
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The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition, and show that superfluidity is even more sensitive to imbalance than for three dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allow to identify a phase separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime.
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arxiv:0903.1931
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Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper. Capitalizing on prior research where the minimum mean square error and Fisher information matrices were linked to information-theoretic quantities through differentiation, closed-form expressions for the Hessian of the mutual information and the differential entropy are derived. These expressions are then used to assess the concavity properties of mutual information and differential entropy under different channel conditions and also to derive a multivariate version of the entropy power inequality due to Costa.
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arxiv:0903.1945
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Recent radiative lifetime measurements accurate to +/- 5% using laser-induced fluorescence (LIF) on 43 even-parity and 15 odd-parity levels of Ce II have been combined with new branching fractions measured using a Fourier transform spectrometer (FTS) to determine transition probabilities for 921 lines of Ce II. This improved laboratory data set has been used to determine a new solar photospheric Ce abundance, log epsilon = 1.61 +/- 0.01 (sigma = 0.06 from 45 lines), a value in excellent agreement with the recommended meteoritic abundance, log epsilon = 1.61 +/- 0.02. Revised Ce abundances have also been derived for the r-process-rich metal-poor giant stars BD+17 3248, CS 22892-052, CS 31082-001, HD 115444 and HD 221170. Between 26 and 40 lines were used for determining the Ce abundance in these five stars, yielding a small statistical uncertainty of 0.01 dex similar to the Solar result. The relative abundances in the metal-poor stars of Ce and Eu, a nearly pure r-process element in the Sun, matches r-process only model predictions for Solar System material. This consistent match with small scatter over a wide range of stellar metallicities lends support to these predictions of elemental fractions. A companion paper includes an interpretation of these new precision abundance results for Ce as well as new abundance results and interpretations for Pr, Dy and Tm.
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arxiv:0903.1982
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Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordstr\"{o}m black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordstr\"{o}m black hole spacetime. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.
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arxiv:0903.1983
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Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates.
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arxiv:0903.1999
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Monovalent impurities on graphene can be divided into ionically and covalently bond impurities. The covalent impurities cause universal midgap states as the carbon atom next to the impurity is effectively decoupled from the graphene pi-bands. The electronic structure of graphene suppresses migration of these impurities and making the universal midgap very stable. This effect is strongest for neutral covalently bond impurities. The ionically bond impurities have migration barriers of typically less than 0.1eV. An asymmetry between anions and cations regarding their adsorption sites and topology of their potential energy landscape is predicted.
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arxiv:0903.2006
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This paper has been withdrawn by the author for further investigation.
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arxiv:0903.2033
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We derive a sharp bound on the location of non-positive eigenvalues of Schroedinger operators on the halfline with complex-valued potentials.
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arxiv:0903.2053
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Recent investigations have revealed a surprising lack of close binaries among extreme horizontal branch (EHB) stars in the globular cluster NGC6752, at variance with the analogous sdB field stars. Another puzzling result concerns the derived spectroscopic masses for some EHB stars. The present paper extends our study of NGC6752 to M80 and NGC5986. Twenty-one horizontal branch stars (out of which 5 EHBs) in NGC5986 and 31 in M80 (11 EHBs) were observed during four consecutive nights. We measured radial velocity variations, temperatures, gravities, and helium abundances. By means of a statistical analysis, we detected one EHB close binary candidate per cluster. In M80, the best estimate of the close binary EHB fraction is f=12%, and even the lowest estimate of the binary fraction among field sdB stars can be ruled out within a 90% confidence level. Because of the small observed sample, no strong conclusions can be drawn on the close EHB binary fraction for NGC5986, although our best estimate is rather low (f=25%). For the discrepancy in spectroscopic derived masses with theoretical models observed in NGC6752, our analysis of M80 EHB stars shows a similar trend. For the first time, we report a clear trend in surface helium abundance with temperature. Our results show that the deficiency of close binaries among EHB stars is now confirmed in two, and possibly three, globular clusters. This feature is therefore not a peculiarity of NGC6752. Our analysis also proves that the strangely high spectroscopic masses among EHB stars are now confirmed in at least a second cluster. Our results confirm that f could be a function of the age of the sdB star population, but we find that recent models have some problem reproducing all observations.
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arxiv:0903.2072
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We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location---inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable $\epsilon$-optimal stopping time. The paper is illustrated by a numerical example.
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arxiv:0903.2114
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In this paper we show how to extend the known algorithm of nodal analysis in such a way that, in the case of circuits without nullors and controlled sources (but allowing for both, independent current and voltage sources), the system of nodal equations describing the circuit is partitioned into one part, where the nodal variables are explicitly given as linear combinations of the voltage sources and the voltages of certain reference nodes, and another, which contains the node variables of these reference nodes only and which moreover can be read off directly from the given circuit. Neither do we need preparational graph transformations, nor do we need to introduce additional current variables (as in MNA). Thus this algorithm is more accessible to students, and consequently more suitable for classroom presentations.
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arxiv:0903.2158
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We investigate gauge-Higgs unification models in eight-dimensional spacetime where extra-dimensional space has the structure of a four-dimensional compact coset space. The combinations of the coset space and the gauge group in the eight-dimensional spacetime of such models are listed. After the dimensional reduction of the coset space, we identified $\mathrm{SO}(10)$, $\mathrm{SO}(10) \times \mathrm{U}(1)$ and $\mathrm{SO}(10) \times \mathrm{U}(1) \times \mathrm{U}(1)$ as the possible gauge groups in the four-dimensional theory that can accomodate the Standard Model and thus is phenomenologically promising. Representations for fermions and scalars for these gauge groups are tabulated.
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arxiv:0903.2164
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Exact solutions of the dispersive and modified equations are expressed in terms of special polynomials associated with rational solutions of the fourth Painleve equation, which arises as generalized scaling reductions of these equations. Generalized solutions that involve an infinite sequence of arbitrary constants are also derived which are analogues of generalized rational solutions for the Korteweg-de Vries, Boussinesq and nonlinear Schrodinger equations
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arxiv:0903.2192
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We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes a canonical ensemble such as the reciprocal temperature $\beta$ or any variable that the Hamiltonian explicitly depends on. The partition function is determined by minimizing the difference of the thermal conjugates of $\lambda$ (the energy in the case of $\lambda=\beta$), defined as the difference between the value from the dynamically updated derivatives of the partition function and the value directly measured from simulation. Higher-order derivatives of the partition function are included to enhance the Brownian motion in the $\lambda$ space. The method is much less sensitive to the system size, and the size of $\lambda$ window than other methods. On the two dimensional Ising model, it is shown that the method asymptotically converges the partition function, and the error of the logarithm of the partition function is much smaller than the algorithm using the Wang-Landau recursive scheme. The method is also applied to off-lattice model proteins, the $AB$ models, in which cases many low energy states are found in different models.
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arxiv:0903.2195
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It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions. The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions.
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arxiv:0903.2231
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One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by existence of a border between the phases and the fact that only in the vicinity of that border it is possible for molecules to change their phase. Not only the model is introduced and theoretical analysis of its properties is made but also the results of Monte Carlo simulations are presented together with the results of numerical calculation of the distribution of energy levels of the system.
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arxiv:0903.2249
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The safety of our day-to-day life depends crucially on the correct functioning of embedded software systems which control the functioning of more and more technical devices. Many of these software systems are time-critical. Hence, computations performed need not only to be correct, but must also be issued in a timely fashion. Worst case execution time (WCET) analysis is concerned with computing tight upper bounds for the execution time of a system in order to provide formal guarantees for the proper timing behaviour of a system. Central for this is to compute safe and tight bounds for loops and recursion depths. In this paper, we highlight the TuBound approach to this challenge at whose heart is a constraint logic based approach for loop analysis.
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arxiv:0903.2251
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We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles have to be packed non-overlapping and orthogonal, i.e., axis-parallel. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P != NP.
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arxiv:0903.2265
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We show that the nonlinear response of a driven circuit quantum electrodynamics setup displays antiresonant multiphoton transitions, as recently observed in a transmon qubit device. By including photon leaking, we explain the lineshape by a perturbative and a semiclassical analysis. We derive a bistable semiclassical quasienergy surface whose lowest quasienergy eigenstate is squeezed, allowing for a squeezing-dependent local effective temperature. We study the escape dynamics out of the metastable state and find signatures of dynamical tunneling, similar as for the quantum Duffing oscillator.
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arxiv:0903.2338
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Honorable Rector, Honorable Professors, and Students of this University: In these times of political and economic struggle and nationalistic fragmentation, it is a particular joy for me to see people assembling here to give their attention exclusively to the highest values that are common to us all. I am glad to be in this blessed land before a small circle of people who are interested in topics of science to speak on those issues that, in essence, are the subject of my own meditations.. [abridged].
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arxiv:0903.2401
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The spectral energy distributions for pure-hydrogen (DA) hot white dwarfs can be accurately predicted by model atmospheres. This makes it possible to define spectrophotometric calibrators by scaling the theoretical spectral shapes with broad-band photometric observations -- a strategy successfully exploited for the spectrographs onboard the Hubble Space Telescope (HST) using three primary DA standards. Absolute fluxes for non-DA secondary standards, introduced to increase the density of calibrators in the sky, need to be referred to the primary standards, but a far better solution would be to employ a network of DA stars scattered throughout the sky. We search for blue objects in the sixth data release of the Sloan Digital Sky Survey (SDSS) and fit DA model fluxes to identify suitable candidates. Reddening needs to be considered in the analysis of the hottest and therefore more distant stars. We propose a list of nine pure-hydrogen white dwarfs with absolute fluxes with estimated uncertainties below 3%, including four objects with estimated errors <2%, as candidates for spectrophotometric standards in the range 14<g<18, and provide model-based fluxes scaled to match the SDSS broad-band fluxes for each. We apply the same method to the three HST DA standards, linking the zero point of their absolute fluxes to ugr magnitudes transformed from photometry obtained with the USNO 1-m telescope. For these stars we estimate uncertainties of <1% in the optical, finding good consistency with the fluxes adopted for HST calibration.
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arxiv:0903.2420
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For a prime power $q$, we study the distribution of determinent of matrices with restricted entries over a finite field $\mathbbm{F}_q$ of $q$ elements. More precisely, let $N_d (\mathcal{A}; t)$ be the number of $d \times d$ matrices with entries in $\mathcal{A}$ having determinant $t$. We show that \[ N_d (\mathcal{A}; t) = (1 + o (1)) \frac{|\mathcal{A}|^{d^2}}{q}, \] if $|\mathcal{A}| = \omega(q^{\frac{d}{2d-1}})$, $d\geqslant 4$. When $q$ is a prime and $\mathcal{A}$ is a symmetric interval $[-H,H]$, we get the same result for $d\geqslant 3$. This improves a result of Ahmadi and Shparlinski (2007).
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arxiv:0903.2508
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We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al., 2008) are also sufficient for sparse structure estimation.
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arxiv:0903.2515
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This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. We notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. We investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited.
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arxiv:0903.2530
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This paper explores integrable structures of a generalized melting crystal model that has two $q$-parameters $q_1,q_2$. This model, like the ordinary one with a single $q$-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions. The partition function is thereby a function of an infinite number of coupling constants $t_1,t_2,...$ and an extra one $Q$. There is a compact expression of this partition function in the language of a 2D complex free fermion system, from which one can see the presence of a quantum torus algebra behind this model. The partition function turns out to be a tau function (times a simple factor) of two integrable structures simultaneously. The first integrable structure is the bigraded Toda hierarchy, which determine the dependence on $t_1,t_2,...$. This integrable structure emerges when the $q$-parameters $q_1,q_2$ take special values. The second integrable structure is a $q$-difference analogue of the 1D Toda equation. The partition function satisfies this $q$-difference equation with respect to $Q$. Unlike the bigraded Toda hierarchy, this integrable structure exists for any values of $q_1,q_2$.
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arxiv:0903.2607
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Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an {\it exact} analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a ``Michaelis-Menten-like'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.
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arxiv:0903.2608
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Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on the set of isotopy classes of certain subsurfaces of (\Sigma). We then construct such additive functions, and thus isotopy-invariant topological measures, from probability measures on (\Sigma) together with some additional data. The map associating topological measures to probability measures is affine and continuous. Certain Dirac measures map to simple topological measures, while the topological measures due to Py and Rosenberg arise from the normalized Euler characteristic.
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arxiv:0903.2659
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We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are analyzed. We show that the particle composite nature reduces the anti-bunching effect predicted for elementary bosons. Furthermore, the probability distribution exhibits a dispersion which is greater for composite bosons than for elementary bosons. This dispersion corresponds to the one of sub-Poissonian processes, as for a quantum state, but, unlike its elementary boson counterpart, it is not minimum. In general, our work shows that it is necessary to take into account the Pauli exclusion principle which takes place between fermionic components of composite bosons - along the line here used - to possibly extract statistical properties in a precise way.
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arxiv:0903.2664
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The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a metod due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density matrix renormalization group result is obtained.
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arxiv:0903.2707
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We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability is not well understood. We provide several mathematical answers, with discrimination between approximate and exact controllability, and between finite time or infinite time controllability: this system is not exactly controllable in finite time $T$ with bounded controls in $L^2(0,T)$, but it is approximately controllable in $L^\infty$ in finite time with unbounded controls in $L^{\infty}_{loc}([0,+\infty))$. Moreover, we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin +1/2 or -1/2.
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arxiv:0903.2720
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We consider a simple model of partially expanding map on the torus. We study the spectrum of the Ruelle transfer operator and show that in the limit of high frequencies in the neutral direction (this is a semiclassical limit), the spectrum develops a spectral gap, for a generic map. This result has already been obtained by M. Tsujii (05). The novelty here is that we use semiclassical analysis which provides a different and quite natural description. We show that the transfer operator is a semiclassical operator with a well defined "classical dynamics" on the cotangent space. This classical dynamics has a "trapped set" which is responsible for the Ruelle resonances spectrum. In particular we show that the spectral gap is closely related to a specific dynamical property of this trapped set.
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arxiv:0903.2747
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We introduce a general model for a lossy bosonic memory channel and calculate the classical and the quantum capacity, proving that coherent state encoding is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels.
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arxiv:0903.2764
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We give analytic methods for nonparametric bias reduction that remove the need for computationally intensive methods like the bootstrap and the jackknife. We call an estimate {\it $p$th order} if its bias has magnitude $n_0^{-p}$ as $n_0 \to \infty$, where $n_0$ is the sample size (or the minimum sample size if the estimate is a function of more than one sample). Most estimates are only first order and require O(N) calculations, where $N$ is the total sample size. The usual bootstrap and jackknife estimates are second order but they are computationally intensive, requiring $O(N^2)$ calculations for one sample. By contrast Jaeckel's infinitesimal jackknife is an analytic second order one sample estimate requiring only O(N) calculations. When $p$th order bootstrap and jackknife estimates are available, they require $O(N^p)$ calculations, and so become even more computationally intensive if one chooses $p>2$. For general $p$ we provide analytic $p$th order nonparametric estimates that require only O(N) calculations. Our estimates are given in terms of the von Mises derivatives of the functional being estimated, evaluated at the empirical distribution. For products of moments an unbiased estimate exists: our form for this "polykay" is much simpler than the usual form in terms of power sums.
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arxiv:0903.2889
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The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips. These strips can have either one or three half-twists, and can be either right- or left-handed. The normals to the surrounding ellipses generate cone-like structures. Two special projections, one new geometrical, and seven new topological indices are developed to characterize the rather complex structures of the Mobius strips and cones. These eight indices, together with the two well-known indices used until now to characterize singular lines of circular polarization, could, if independent, generate 16,384 geometrically and topologically distinct lines. Geometric constraints and 13 selection rules are discussed that reduce the number of lines to 2,104, some 1,150 of which have been observed in practice; this number of different C lines is ~ 350 times greater than the three types of lines recognized previously. Statistical probabilities are presented for the most important index combinations in random fields. It is argued that it is presently feasible to perform experimental measurements of the Mobius strips and cones described here theoretically.
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arxiv:0903.2927
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A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p_z and can become larger than the former's growth rate which decreases with increasing p_z. These features may explain the interplay between the primary and secondary instabilities observed in the real-time simulation of a non-expanding glasma, i.e., stochastically generated anisotropic Yang-Mills fields without expansion.
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arxiv:0903.2930
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Just fourteen years ago the Solar System represented the only known planetary system in the Galaxy, and conceptions of planet formation were shaped by this sample of one. Since then, 320 planets have been discovered orbiting 276 individual stars. This large and growing ensemble of exoplanets has informed theories of planet formation, placed the Solar System in a broader context, and revealed many surprises along the way. In this review I provide an overview of what has been learned from studies of the occurrence, orbits and physical structures of planets. After taking a look back at how far the field has advanced, I will discuss some of the future directions of exoplanetary science, with an eye toward the detection and characterization of Earth-like planets around other stars.
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arxiv:0903.3059
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We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of many potentials which are involved (donor - bridge - acceptor) in the process. The coupling between these potentials are assumed to be represented by Dirac Delta functions. The diffusive motion in this paper is represented by the Smoluchowski equation. Our solution requires the knowledge of the Laplace transform of the Green's function for the motion in all the uncoupled potentials.
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arxiv:0903.3069
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Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable `matrix' quantum mechanics, which is recently proposed by Odake and the author. The ($q$-)Askey-scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of $q^x$ ($x$ being the population) corresponding to the $q$-Racah polynomial.
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arxiv:0903.3097
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We investigate the total effect of correlations on photoionization of atomic shells with nonzero orbital momentum, in the nonrelativistic high energy asymptotic limit, considering the exclusive case of the dominant final state of an initial neutral atom. We find that the substantial cancellation of the dominant intra-shell carrelations, which had been reported earlier, can be understood utilizing the closure properties satisfied by the eigen functions of the nonrelativistic Hamiltonian. Considering the sum of correlations with all states, occupied or not, we show that complete sum is equal to the contribution of the high energy part of the continuum. Consequently there is a total cancellation between the contributions of the bound states and the low energy part of the continuum states. This means that the real correlations in the physical atom can be obtained as the negative of the total contribution of low energy states and continuum unoccupied states. We calculate this in framework of the quantum defect number. The approach allows us to see that the dominant intrashell correlation is going to be cancelled. We can also obtain some limits on the correlation effects by considering calculations with the screened Coulomb functions. The role of correlations in the exclusive photoionization processes is discussed.
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arxiv:0903.3294
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The relation between isoenergetic and Hamiltonian thermostats is studied and their equivalence in the thermodynamic limit is proved in space dimension $d=1,2$. v.2: W_n and x_n replace W and x where needed
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arxiv:0903.3316
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Method for detection and visualization of trends, periodicities, local peculiarities in measurement series (dL-method) based on DFA technology (Detrended fluctuation analysis) is proposed. The essence of the method lies in reflecting the values of absolute deviation of measurement accumulation series points from the respective values of linear approximation. It is shown that dL-method in some cases allows better determination of local peculiarities than wavelet-analysis. Easy-to-realize approach that is proposed can be used in the analysis of time series in such fields as economics and sociology.
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arxiv:0903.3328
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(Abridged) A consequence of the Earth's motion with respect to the CMB is that over a 10 year period it will travel a distance of ~800 AU. As first noted by Kardashev in 1986, this baseline can be used to carry out astrometric measurements of quasar parallaxes, so that only microarcsecond precision is necessary to detect parallax shifts of objects at gigaparsec distances. Such precision will soon be approached with the launch of the astrometric satellites Gaia and SIM. We use a Fisher matrix formalism to investigate the constraints that these and future missions may be able to place on the cosmological distance scale and dark energy. We find that by observing around a million quasars as planned, an extended 10 year Gaia mission could detect quasar parallax shifts at the 2.8 sigma level and so measure the Hubble constant to within 25 km/s. For the interferometer SIMLite, a Key Project using 2.4 % of the total mission time to observe 750 quasars could detect the effect at the 2 sigma level. Gaia and a dedicated SIMLite only weakly constrain the presence of a cosmological constant at the ~1 sigma levels. We also investigate future mission concepts, such as an interferometer similar in scope and design to NASA's Terrestrial Planet Finder. This could in principle measure the dark energy parameters w_0 and w_a with high precision, yielding a Figure of Merit larger than the stage IV experiments considered by the the Dark Energy Task Force. Unlike perhaps all other probes of dark energy there appear to be no obvious astrophysical sources of systematic error. There is however uncertainty regarding the statistical errors. As well as measurement error, there will be small additional contributions from image centroiding of variable sources, quasar peculiar motions and weak microlensing by stars along the line of sight.
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arxiv:0903.3402
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One puzzling observed property of coronal loops is that they are of roughly constant thickness along their length. Various studies have found no consistent pattern of width variation along the length of loops observed by TRACE and SOHO. This is at odds with expectations of magnetic flux tube expansion properties, which suggests that loops are widest at their tops, and significantly narrower at their footpoints. Coronal loops correspond to areas of the solar corona which have been preferentially heated by some process, so this observed property might be connected to the mechanisms that heat the corona. One means of energy deposition is magnetic reconnection, which occurs along field lines called separators. These field lines begin and end on magnetic null points, and loops forming near them can therefore be relatively wide at their bases. Thus, coronal energization by magnetic reconnection may replicate the puzzling expansion properties observed in coronal loops. We present results of a Monte Carlo survey of separator field line expansion properties, comparing them to the observed properties of coronal loops.
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arxiv:0903.3430
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The origin of the Martian moons Deimos and Phobos is controversial. One hypothesis for their origin is that they are captured asteroids, but the mechanism requires an extremely dense martian atmosphere, and the mechanism by which an asteroid in solar orbit could shed sufficient orbital energy to be captured into Mars orbit has not been well elucidated. Since the discovery by the space probe Galileo that the asteroid Ida has a moon "Dactyl", a significant number of asteroids have been discovered to have smaller asteroids in orbit about them. The existence of asteroid moons provides a mechanism for the capture of the Martian moons (and the small moons of the outer planets). When a binary asteroid makes a close approach to a planet, tidal forces can strip the moon from the asteroid. Depending on the phasing, the asteroid can then be captured. Clearly, the same process can be used to explain the origin of any of the small moons in the solar system.
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arxiv:0903.3434
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The authors apply the generalized master equation to analyze time-dependent transport through a finite quantum wire with an embedded subsystem. The parabolic quantum wire and the leads with several subbands are described by a continuous model. We use an approach originally developed for a tight-binding description selecting the relevant states for transport around the bias-window defined around the values of the chemical potential in the left and right leads in order to capture the effects of the nontrivial geometry of the system in the transport. We observe a partial current reflection as a manifestation of a quasi-bound state in an embedded well and the formation of a resonance state between an off-set potential hill and the boundary of the system.
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arxiv:0903.3491
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The purpose of this paper is to present a simple and explicit construction of the Bokstedt-Hsiang-Madsen cyclotomic trace relating algebraic K-theory and topological cyclic homology. Our construction also incorporates Goodwillie's idea of a global cyclotomic trace.
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arxiv:0903.3495
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