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We study complete noncompact long time solutions $(M, g(t))$ to the K\"ahler-Ricci flow with uniformly bounded nonnegative holomorphic bisectional curvature. We will show that when the Ricci curvature is positive and uniformly pinched, i.e. $ R_\ijb \ge cRg_\ijb$ at $(p,t)$ for all $t$ for some $c>0$, then there always exists a local gradient K\"ahler Ricci soliton limit around $p$ after possibly rescaling $g(t)$ along some sequence $t_i \to \infty$. We will show as an immediate corollary that the injectivity radius of $g(t)$ along $t_i$ is uniformly bounded from below along $t_i$, and thus $M$ must in fact be simply connected. Additional results concerning the uniformization of $M$ and fixed points of the holomorphic isometry group will also be established. We will then consider removing the condition of positive Ricci for $(M, g(t))$. Combining our results with Cao's splitting for K\"ahler Ricci flow \cite{Cao04} and techniques of Ni-Tam \cite{NiTam03}, we show that when the positive eigenvalues of the Ricci curvature are uniformly pinched at some point $p \in M$, then $M$ has a special holomorphic fiber bundle structure. We will treat a special cases, complete K\"ahler manifolds with non-negative holomorphic bisectional and average quadratic curvature decay as well as the case of steady gradient K\"ahler Ricci solitons.
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arxiv:0806.2457
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Rectangular cavities are solvable models that nevertheless touch on many of the controversial or mysterious aspects of the vacuum energy of quantum fields. This paper is a thorough study of the two-dimensional scalar field in a rectangle by the method of images, or closed classical (or optical) paths, which is exact in this case. For each point r and each specularly reflecting path beginning and ending at r, we provide formulas for all components of the stress tensor T_{\mu\nu}(r), for all values of the curvature coupling constant \xi and all values of an ultraviolet cutoff parameter. Arbitrary combinations of Dirichlet and Neumann conditions on the four sides can be treated. The total energy is also investigated, path by path. These results are used in an attempt to clarify the physical reality of the repulsive (outward) force on the sides of the box predicted by calculations that neglect both boundary divergences and the exterior of the box. Previous authors have studied "piston" geometries that avoid these problems and have found the force to be attractive. We consider a "pistol" geometry that comes closer to the original problem of a box with a movable lid. We find again an attractive force, although its origin and detailed behavior are somewhat different from the piston case. However, the pistol (and the piston) model can be criticized for extending idealized boundary conditions into short distances where they are physically implausible. Therefore, it is of interest to see whether leaving the ultraviolet cutoff finite yields results that are more plausible. We then find that the force depends strongly on a geometrical parameter; it can be made repulsive, but only by forcing that parameter into the regime where the model is least convincing physically.
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arxiv:0806.2468
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We present results from an extensive set of simulations of gravitational fragmentation in the presence of magnetic fields and ambipolar diffusion. The average fragmentation spacing in the nonlinear phase of evolution is in excellent agreement with the prediction of linear perturbation theory. The time scale for nonlinear growth and runaway of the first core is $\approx 10$ times the calculated growth time $\taugm$ of the eigenmode with minimum growth time, when starting from a uniform background state with small-amplitude white-noise perturbations. Subcritical and transcritical models typically evolve on a significantly longer time scale than the supercritical models. Infall motions in the nonlinear fully-developed contracting cores are subsonic on the core scale in subcritical and transcritical clouds, but are somewhat supersonic in supercritical clouds. Core mass distributions are sharply peaked with a steep decline to large masses, consistent with the existence of a preferred mass scale for each unique set of dimensionless free parameters. However, a sum total of results for various initial mass-to-flux ratios yields a broad distribution reminiscent of observed core mass distributions. Based on our results, we conclude that fragmentation spacings, magnitude of infall motions, core shapes, and, especially, the curvature of magnetic field morphology, may serve as indirect observational means of determining a cloud's ambient mass-to-flux ratio.
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arxiv:0806.2482
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Today, many network applications require shorter react time. Robotic field is an excellent example of these needs: robot react time has a direct effect on its task's complexity. Here, we propose a full deterministic medium access method for a wireless robotic application. This contribution is based on some low-power wireless personal area networks, like ZigBee standard. Indeed, ZigBee has identified limits with Quality of Service due to non-determinist medium access and probable collisions during medium reservation requests. In this paper, two major improvements are proposed: an efficient polling of the star nodes and a temporal deterministic distribution of peer-to-peer messages. This new MAC protocol with no collision offers some QoS faculties.
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arxiv:0806.2509
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Recent experiments with superconducting qubits are motivated by the goal of fabricating a quantum computer, but at the same time they illuminate the more fundamental aspects of quantum mechanics. In this paper we analyze the physics of switching current measurements from the point of view of macroscopic quantum mechanics.
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arxiv:0806.2524
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We present observable upper bounds of squared concurrence, which are the dual inequalities of the observable lower bounds introduced in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)] and [L. Aolita, A. Buchleitner and F. Mintert, Phys. Rev. A 78, 022308 (2008)]. These bounds can be used to estimate entanglement for arbitrary experimental unknown finite-dimensional states by few experimental measurements on a twofold copy $\rho\otimes\rho$ of the mixed states. Furthermore, the degree of mixing for a mixed state and some properties of the linear entropy also have certain relations with its upper and lower bounds of squared concurrence.
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arxiv:0806.2598
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We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schr\"odinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order-by-order.
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arxiv:0806.2659
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We have performed large-scale Monte Carlo simulations on a two-dimensional generalized Ashkin-Teller model to calculate the thermodynamic properties in the critical region near its transitions. The Ashkin-Teller model has a pair of Ising spins at each site which interact with neighboring spins through pair-wise and 4-spin interactions. The model represents the interactions between orbital current loops in $Cu O_2$-plaquettes of high-$T_c$ cuprates, which order with a staggered magnetization $\Mso$ inside each unit-cell in the underdoped region of the phase diagram below a temperature $T^*(x)$ which depends on doping. The pair of Ising spins per unit-cell represent the directions of the currents in the links of the current loops. The generalizations are the inclusion of anisotropy in the pair-wise nearest neighbor current-current couplings consistent with the symmetries of a square lattice and the next nearest neighbor pair-wise couplings. We use the Binder cumulant to estimate the correlation length exponent $\nu$ and the order parameter exponent $\beta$. Our principal results are that in a range of parameters, the Ashkin-Teller model as well as its generalization has an order parameter susceptibility which diverges as $T \to T^*$ and an order parameter below $T^*$. Importantly, however, there is no divergence in the specific heat. This puts the properties of the model in accord with the experimental results in the underdoped cuprates. We also calculate the magnitude of the "bump" in the specific heat in the critical region to put limits on its observability. Finally, we show that the staggered magnetization couples to the uniform magnetization $M_0$ such that the latter has a weak singularity at $T^*$ and also displays a wide critical region, also in accord with recent experiments.
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arxiv:0806.2665
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We carry out a theoretical investigation to clarify the dynamic property of photo-created nano-sized ferroelectric cluster observed in the paraelectric BaTiO3 as a real time correlation of speckle pattern between two soft X-ray laser pulses, at just above the paraelectric-ferroelectric phase transition temperature. Based on a model with coupled soft X-ray photon and ferroelectric phonon mode, we study the time dependence of scattering probability by using a perturbative expansion approach. The cluster-associated phonon softening as well as central peak effects are well reproduced in the phonon spectral function via quantum Monte Carlo simulation. Besides, it is found that the time dependence of speckle correlation is determined by the relaxation dynamics of ferroelectric clusters. Near the transition point, cluster excitation is stable, leading to a long relaxation time. While, at high temperature, cluster structure is subject to the thermal fluctuation, ending up with a short relaxation time.
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arxiv:0806.2701
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We study the SUSY/non-SUSY duality proposed by Aganagic et al. from Type IIA string and M-theory perspectives. We find that our brane configuration generalizes the so-called $extended$ Seiberg-Witten theory on the one hand, and provides a way to realize non-SUSY vacua by intersecting NS5-branes on the other hand. We also argue how the partial SUSY breaking from $\Ncal=2$ down to $\Ncal=1$ can be clearly visualized through the brane picture.
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arxiv:0806.2705
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Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as will be the focus in this paper. We derive Palm distributions of several wave characteristics that can be related to steepness of waves for two different cases, namely for waves observed along a line at a fixed time point and for waves encountering a ship sailing on the ocean. The relation between the distributions obtained in the two cases is also given physical interpretation in terms of a ``Doppler shift'' that is related to the velocity of the ship and the velocities of the individual waves.
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arxiv:0806.2718
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A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures $M[0,t], 0\le t\le1$. In this paper we obtain an extension of this process, referred to as multifractal fractional random walk (MFRW), by considering the limit in distribution of a sequence of conditionally Gaussian processes. These conditional processes are defined as integrals with respect to fractional Brownian motion and convergence is seen to hold under certain conditions relating the self-similarity (Hurst) exponent of the fBm to the parameters defining the multifractal random measure $M$. As a result, a larger class of models is obtained, whose fine scale (scaling) structure is then analyzed in terms of the empirical structure functions. Implications for the analysis and inference of multifractal exponents from data, namely, confidence intervals, are also provided.
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arxiv:0806.2731
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Electron transport through multi-terminal rectangular arrays of quantum rings is studied in the presence of Rashba-type spin-orbit interaction (SOI) and of a perpendicular magnetic field. Using the analytic expressions for the transmission and reflection coefficients for single rings we obtain the conductance through such arrays as a function of the SOI strength, the magnetic flux, and of the wave vector $k$ of the incident electron. Due to destructive or constructive spin interferences caused by the SOI, the array can be totally opaque for certain ranges of $k$, while there are parameter values where it is completely transparent. Spin resolved transmission probabilities show nontrivial spin transformations at the outputs of the arrays. When point-like random scattering centers are placed between the rings, the Aharonov-Bohm peaks split, and an oscillatory behavior of the conductance emerges as a function of the SOI strength.
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arxiv:0806.2734
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The X-ray binary XTE J1817-330 was discovered in outburst on 26 January 2006 with RXTE/ASM. One year later, another X-ray transient discovered in 1996, XTE J1856+053, was detected by RXTE during a new outburst on 28 February 2007. We triggered XMM-Newton target of opportunity observations on these two objects to constrain their parameters and search for a stellar black holes. We summarize the properties of these two X-ray transients and show that the soft X-ray spectra indicate indeed the presence of an accreting stellar black hole in each of the two systems.
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arxiv:0806.2736
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We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving reflected BSDEs and the Snell envelope.
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arxiv:0806.2761
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In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost function. We focus on control systems such as nonholonomic control mechanical systems and the associated kinematic systems as long as they are equivalent. With all this in mind, first we study conditions to relate an optimal control problem for the mechanical system with another one for the associated kinematic system. Then, Pontryagin's Maximum Principle will be used to connect the abnormal extremals of both optimal control problems. An example is given to glimpse what the abnormal solutions for kinematic systems become when they are considered as extremals to the optimal control problem for the corresponding nonholonomic mechanical systems.
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arxiv:0806.2814
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Previous models of galactic disk heating in interactions invoke restrictive assumptions not necessarily valid in modern LCDM contexts: that satellites and orbits are rigid and circular, with slow decay over many orbital times from dynamical friction. This leads to a linear scaling of disk heating with satellite mass: disk heights and velocity dispersions scale ~M_sat/M_disk. In turn, observed disk thicknesses present strong constraints on merger histories: the implication for the Milky Way is that <5% of its mass could come from mergers since z~2, in conflict with cosmological predictions. More realistically, satellites merge on nearly radial orbits, and once near the disk, resonant interactions efficiently remove angular momentum while tidal effects strip mass, leading to rapid merger/destruction in a couple of free-fall plunges. Under these conditions the proper heating efficiency is non-linear in mass ratio, ~(M_sat/M_disk)^2. We derive the scaling of disk scale heights and velocity dispersions as a function of mass ratio and disk gas content in this regime, and show this accurately describes the results of simulations with proper 'live' halos and disks. Under realistic circumstances, disk heating in minor mergers is suppressed by an order of magnitude relative to expectations of previous models. We show that the Milky Way disk could have absorbed ~5-10 1:10 mass-ratio mergers since z=2, in agreement with cosmological models. These distinctions lead to dramatic differences in which mass ratios are most important for disk heating and in the isophotal shapes of disk+bulge systems.
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arxiv:0806.2861
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We show that every essentially small finitely semisimple k-linear additive spherical category in which k=End(1) is a field, is equivalent to its dual over the long canonical forgetful functor. This includes the special case of modular categories. In order to prove this result, we show that the universal coend of the spherical category with respect to the long forgetful functor is self-dual as a Weak Hopf Algebra.
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arxiv:0806.2903
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We study finite set-theoretic solutions $(X,r)$ of the Yang-Baxter equation of square-free multipermutation type. We show that each such solution over $\C$ with multipermutation level two can be put in diagonal form with the associated Yang-Baxter algebra $\Acal(\C,X,r)$ having a $q$-commutation form of relations determined by complex phase factors. These complex factors are roots of unity and all roots of a prescribed form appear as determined by the representation theory of finite abelian group $\Gcal$ of left actions on $X$. We study the structure of $\Acal(\C,X,r)$ and show that they have a $\bullet$-product form `quantizing' the commutative algebra of polynomials in $|X|$ variables. We obtain the $\bullet$-product both as a Drinfeld cotwist for a certain canonical 2-cocycle and as a braided-opposite product for a certain crossed $\Gcal$-module (over any field $k$). We provide first steps in the noncommutative differential geometry of $\Acal(k,X,r)$ arising from these results. As a byproduct of our work we find that every such level 2 solution $(X,r)$ factorises as $r=f\circ\tau\circ f^{-1}$ where $\tau$ is the flip map and $(X,f)$ is another solution coming from $X$ as a crossed $\Gcal$-set.
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arxiv:0806.2928
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A class of exact solutions of Einstein's equations is presented which describes accelerating photon rockets in de Sitter and anti-de Sitter universe. These are particular members of the Robinson-Trautman family of axially symmetric spacetimes with pure radiation. In particular, generalizations of (type D) Kinnersley's rockets and (type II) Bonnor's rockets to the case of a non-vanishing cosmological constant are given. Some of the main physical properties of these solutions are investigated, and their relation to the C-metric solution which describes uniformly accelerated black holes is also given.
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arxiv:0806.2966
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The need to regularize loop integrals in a manner that preserves gauge invariance, for example, using the Pauli-Villars method, requires a subtraction that in the large mass limit hides its high momentum origin. This gives rise to the illusion that only nonrelativistic kaon loop momenta are relevant, when in fact this is not the case, as we show.
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arxiv:0806.2993
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We show that if (u;K) is a minimizer of the Mumford-Shah functional in an open set of R^3, and if x, K and r > 0 are such that K is close enough to a minimal cone of type P (a plane), Y (three half planes meeting with 120 degrees angles) or T (cone over a regular tetrahedron centered at the origin) in terms of Hausdorff distance in B(x; r), then K is C^1,alpha equivalent to the minimal cone in B(x; cr) where c < 1 is an universal constant.
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arxiv:0806.2994
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We show that the secant variety of a linearly normal smooth curve of degree at least 2g+3 is arithmetically Cohen-Macaulay, and we use this information to study the graded Betti numbers of the secant variety.
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arxiv:0806.3056
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We provide computationally convenient expressions for all marginal distributions of the polarization CMB power spectrum distribution P(C_l|sigma_l), where C_l = {C_l^TT, C_l^TE, C_l^EE, C_l^BB} denotes the set of ensemble averaged polarization CMB power spectra, and sigma_l = {sigma_l^TT, sigma_l^TE, sigma_l^EE, sigma_l^BB} the set of the realization specific polarization CMB power spectra. This distribution describes the CMB power spectrum posterior for cosmic variance limited data. The expressions derived here are general, and may be useful in a wide range of applications. Two specific applications are described in this paper. First, we employ the derived distributions within the CMB Gibbs sampling framework, and demonstrate a new conditional CMB power spectrum sampling algorithm that allows for different binning schemes for each power spectrum. This is useful because most CMB experiments have very different signal-to-noise ratios for temperature and polarization. Second, we provide new Blackwell-Rao estimators for each of the marginal polarization distributions, which are relevant to power spectrum and likelihood estimation. Because these estimators represent marginals, they are not affected by the exponential behaviour of the corresponding joint expression, but converge quickly.
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arxiv:0806.3074
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We construct stationary Ricci-flat inter-universe Lorentzian wormhole solutions in all D\ge 5 dimensions that connect two flat asymptotic spacetimes. Such a solution can be viewed as the gravity dual of a string tachyon state whose linear momentum is larger than its tension. We focus our analysis on the D=5 wormholes which are not traversable for the timelike and null geodesics; however, we demonstrate that there exist accelerated timelike trajectories that traverse from one asymptotic region to the other. We further study the minimally-coupled scalar wave equation and demonstrate that the quantum tunnelling between two worlds must occur. We also obtain charged wormholes in five-dimensional supergravities. With appropriate choice of parameters, these wormholes connect AdS$_3\times S^2$ in one asymptotic region to flat Minkowskian spacetime in the other.
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arxiv:0806.3111
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We give a necessary and sufficient condition for an MV polytope $P$ in a highest weight crystal to lie in an arbitrary fixed Demazure crystal (resp., opposite Demazure crystal), in terms of the lengths of edges along a path through the 1-skeleton of $P$ corresponding to a reduced word for the longest element of the Weyl group $W$. % Also, we give an explicit description as a pseudo-Weyl polytope for extremal MV polytopes in a highest weight crystal. % Finally, by combining the results above, we obtain a polytopal condition for an MV polytope $P$ to lie in an arbitrary fixed opposite Demazure crystal.
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arxiv:0806.3112
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We consider a discrete facility location problem with a new form of equity criterion. The model discussed in the paper analyzes the case where demand points only have strict preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the total envy felt by the entire set of demand points. We define this new total envy criterion and provide several integer linear programming formulations that reflect and model this approach. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances.
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arxiv:0806.3134
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Inspired by the obvious discrepancies between experiment and non-relativistic QCD (NRQCD) studies of $e^+ e^-\to J/\psi+\eta_c$ at $\sqrt{s}\simeq 10.6$ GeV, we investigate contributions from intermediate meson loops as long-range interaction transitions to this process. The intermediate meson loops include $D\bar D(\bar D^\ast)$, $D\bar D^\ast(D {or} D^\ast)$, $D^\ast \bar D^\ast(D)$ and corresponding $D_s$ intermediate mesons. With the constraints from experimental data on the vertex couplings, we find that the intermediate meson loops account for $2.7\sim 6.7 fb$ of the cross sections within a reasonable range of cut-off energies of the factor parameter. We also investigate contributions from the absorptive part and find that it accounts for approximately $0.58\sim 1.38 fb$. These results imply that contributions from long-range interaction transitions may still play a role in such an energy region.
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arxiv:0806.3140
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We study the problem of two superconducting quantum qubits coupled via a resonator. If only one quanta is present in the system and the number of photons in the resonator is measured with a null result, the qubits end up in an entangled Bell state. Here we look at one source of errors in this quantum nondemolition scheme due to the presence of more than one quanta in the resonator, previous to the measurement. By analyzing the structure of the conditional Hamiltonian with arbitrary number of quanta, we show that the scheme is remarkably robust against these type of errors.
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arxiv:0806.3148
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An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
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arxiv:0806.3163
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We prove that every complete Einstein (Riemannian or pseudo-Riemannian) metric $g$ is geodesically rigid: if any other complete metric $\bar g$ has the same (unparametrized) geodesics with $g$, then the Levi-Civita connections of $g$ and $\bar g$ coincide.
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arxiv:0806.3169
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Two path integral representations for the $T$-matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of "phantom" degrees of freedom which take away explicit phases that diverge for asymptotic times. In addition, energy conservation is enforced by imposing a Faddeev-Popov-like constraint in the velocity path integral. These expressions may be useful for attempts to evaluate the path integral in real time and for alternative multiple scattering expansions. Standard and novel eikonal-type high-energy approximations and systematic expansions immediately follow.
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arxiv:0806.3217
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(abridged) The Pierre Auger Collaboration has reported 27 Ultra-High Energy Cosmic Ray Events (UHECRs) with energies above 56 EeV and well determined arrival directions as of 2007 August 31. They find that the arrival directions are not isotropic, but instead appear correlated with the positions of nearby AGNs. Our aim was to determine the sources of these UHECRs by comparing their arrival directions with more comprehensive source catalogs. Four (eight) of the 27 UHECRs with energy >56EeV detected by the Pierre Auger Observatory have arrival directions within 1.5deg (3.5deg) of the extended (>180kpc) radio structures of nearby radiogalaxies or the single nearby BLLac with extended radio structure. Conversely the radio structures of three (six) of all ten nearest extended radiogalaxies are within 1.5deg (3.5deg) of a UHECR; three of the remaining four radiogalaxies are in directions with lower exposure times. This correlation between nearby extended radiogalaxies and a subset of UHECRs is significant at the 99.9% level. This is the first direct observational proof that radio galaxies are a significant source of UHECRs. For the remaining ~20 UHECRs, an isotropic distribution cannot be ruled out at high significance. The correlation found by the Auger Collaboration between the 27 UHECRs and AGNs in the Veron-Cetty & Veron catalog at D < 71Mpc has a much lower significance when one considers only the ~20 UHECRs not `matched' to nearby extended radiogalaxies. No correlation is seen between UHECRs and supernovae, supernova remnants, nearby galaxies, or nearby groups and clusters of galaxies. The primary difference between the UHECR detections at the Pierre Auger Observatory and previous experiments may thus be that the Southern Hemisphere is more privileged with respect to nearby extended radiogalaxies.
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arxiv:0806.3220
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A new type of simplified cloaks with matched exterior boundaries is proposed. The cloak uses non-magnetic material for the TM polarization and can function with a relatively thin thickness. It is shown that the $zero^{th}$ order scattering of such cloak is dominant among all cylindrical scattering terms. A gap is added at the cloak's inner surface to eliminate the zero-th order scattering, through the mechanism of scattering resonance. The reduction in scattering is relatively smooth, indicating that the proposed scattering reduction method has good tolerance to perturbations. Numerical simulations also confirm that the proposed structure has very low scattering.
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arxiv:0806.3226
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The statistics of catalogued quadruple stars consisting of two binaries (hierarchy 2+2) is studied in comparison with triple stars, with respective sample sizes of 81 and 724. Seven representative quadruple systems are discussed in greater detail. The properties of multiple stars do not correspond to the products of dynamical decay of small clusters, hence the N-body dynamics is not the dominant process of their formation. On the other hand, rotationally-driven (cascade) fragmentation possibly followed by migration of inner and/or outer orbits to shorter periods is a promising scenario to explain the origin of triple and quadruple stars. Our main results are: (i) Quadruple systems of Epsilon Lyr type with similar masses and inner periods are common. (ii) The distributions of the inner periods in triple and quadruple stars are similar and bimodal. The inner mass ratios do not correlate with the inner periods. (iii) The statistics of outer periods and mass ratios in triples and quadruples are different. The median outer mass ratio in triples is 0.39 independently of the outer period, which has a smooth distribution. In contrast, the outer periods of 25% quadruples concentrate in the narrow range from 10yr to 100yr, the outer mass ratios of these tight quadruples are above 0.6 and their two inner periods are similar to each other. (iv) The outer and inner mass ratios in triple and quadruple stars are not mutually correlated. (v) The inner and outer orbital angular momenta and periods in triple and quadruple systems with inner periods above 30d show some correlation, the ratio of outer-to-inner periods is mostly comprised between 5 and 10^4. In the systems with small period ratios the directions of the orbital spins are correlated, while in the systems with large ratios they are not.
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arxiv:0806.3263
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We theoretically study the magnetoresistance of a CPP-GMR system with current confined paths (CCP) in the framework of Valet-Fert theory. The continuity equations for charge and spin currents are numerically solved with the three-dimensional CCP geometry by use of finite element method. It is confirmed that the MR ratio is enhanced by the CCP structure, which is consistent with the experimental results. Moreover, we find that there exists a certain contact width which maximize the MR ratio. We show that the contact width which maximize the MR ratio is well described by the effective resistance matching.
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arxiv:0806.3314
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By using joint modulation and customized constellation set, we show that Quasi-Orthogonal Space-Time Block Code (QO-STBC) can be used to form a new differential space-time modulation (DSTM) scheme to provide full transmit diversity with non-coherent detection. Our new scheme can provide higher code rate than existing DSTM schemes based on Orthogonal STBC. It also has a lower decoding complexity than the other DSTM schemes, such as those based on Group Codes, because it only requires a joint detection of two complex symbols. We derive the design criteria for the customized constellation set and use them to construct a constellation set that provides a wide range of spectral efficiency with full diversity and maximum coding gain.
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arxiv:0806.3317
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We consider variation of energy of the light-like particle in Riemann space-time, find lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance with principles of the calculus of variations in mechanics. This method is shown to not lead to violation of conformity of varied curve to the null path in contradistinction of the interval variation. Though found equations are differ from standard form of geodesics equations, for the Schwarzschild space-time their solutions coincide with each other to within parameter of differentiation.
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arxiv:0806.3350
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This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to R^2 that is globally Holder continuous of exponent \alpha, and whose inverse is also globally Holder continuous of exponent \alpha can be approximated in the Holder norm of exponent \beta by piecewise affine homeomorphisms, for some \beta that only depends on \alpha. The proof is constructive. We adapt the proof of simplicial approximation in the supremum norm, and measure the side lengths and angles of the triangulation over which the approximating homeomorphism is piecewise affine. The approximation in the supremum norm, and a control on the minimum angle and on the ratio between the maximum and minimum side lengths of the triangulation suffice to obtain approximation in the Holder norm.
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arxiv:0806.3366
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We analyze macroscopic effects of TeV-scale black holes, such as could possibly be produced at the LHC, in what is regarded as an extremely hypothetical scenario in which they are stable and, if trapped inside Earth, begin to accrete matter. We examine a wide variety of TeV-scale gravity scenarios, basing the resulting accretion models on first-principles, basic, and well-tested physical laws. These scenarios fall into two classes, depending on whether accretion could have any macroscopic effect on the Earth at times shorter than the Sun's natural lifetime. We argue that cases with such effect at shorter times than the solar lifetime are ruled out, since in these scenarios black holes produced by cosmic rays impinging on much denser white dwarfs and neutron stars would then catalyze their decay on timescales incompatible with their known lifetimes. We also comment on relevant lifetimes for astronomical objects that capture primordial black holes. In short, this study finds no basis for concerns that TeV-scale black holes from the LHC could pose a risk to Earth on time scales shorter than the Earth's natural lifetime. Indeed, conservative arguments based on detailed calculations and the best-available scientific knowledge, including solid astronomical data, conclude, from multiple perspectives, that there is no risk of any significance whatsoever from such black holes.
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arxiv:0806.3381
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We present optical polarization maps of a sample of four interacting pairs at different phases of encounter, from nearly unperturbed galaxies to on-going mergers. Only the pair RR 24 shows a linear polarization pattern which extends in both galaxies for several kiloparsecs. The more perturbed member, RR 24b, is lineraly polarized up to the level of ~3%. No polarization is measured in the strongly perturbed late-type pair members of RR 23 and RR 99. Also, in the central part of the double nuclei shell galaxy ESO 2400100 there is no significant polarization. We use the ionized gas velocity field of RR 24 to interpret its linear polarization structure. In RR 24a the quite regular gas kinematics reflect the unperturbed spiral-like polarization structure. In RR 24b a strong velocity gradient in ionized gas could be associated with the polarization structure. We suggest that the large-scale magnetic field of the RR 24 pair members still plays a role in shaping the polarization pattern.
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arxiv:0806.3383
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We investigate the scattering of a quantum matter wave soliton on a barrier in a one dimensional geometry and we show that it can lead to mesoscopic Schr\"odinger cat states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition and we discuss in details the experimental feasibility.
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arxiv:0806.3395
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We introduce a new class of pseudoprimes-so called "overpseudoprimes" which is a special subclass of super-Poulet pseudoprimes. Denoting via h(n) the multiplicative order of 2 modulo n, we show that odd number n is overpseudoprime iff value of h(n) is invariant of all divisors d>1 of n. In particular, we prove that all composite Mersenne numbers 2^p-1,where p is prime, and squares of Wieferich primes are overpseudoprimes. We give also a generalization of the results on arbitrary base a>1 and prove that every overpseudoprime is strong pseudoprime of the same base.
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arxiv:0806.3412
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We give a geometric invariant theory (GIT) construction of the log canonical model $\bar M_g(\alpha)$ of the pairs $(\bar M_g, \alpha \delta)$ for $\alpha \in (7/10 - \epsilon, 7/10]$ for small $\epsilon \in \mathbb Q_+$. We show that $\bar M_g(7/10)$ is isomorphic to the GIT quotient of the Chow variety bicanonical curves; $\bar M_g(7/10-\epsilon)$ is isomorphic to the GIT quotient of the asymptotically-linearized Hilbert scheme of bicanonical curves. In each case, we completely classify the (semi)stable curves and their orbit closures. Chow semistable curves have ordinary cusps and tacnodes as singularities but do not admit elliptic tails. Hilbert semistable curves satisfy further conditions, e.g., they do not contain elliptic bridges. We show that there is a small contraction $\Psi: \bar M_g(7/10+\epsilon) \to \bar M_g(7/10)$ that contracts the locus of elliptic bridges. Moreover, by using the GIT interpretation of the log canonical models, we construct a small contraction $\Psi^+ : \bar M_g(7/10-\epsilon) \to \bar M_g(7/10)$ that is the Mori flip of $\Psi$.
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arxiv:0806.3444
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We present an integrated study of star formation and galactic stellar mass assembly from z=0.05-1.5 and galactic metallicity evolution from z=0.05-0.9 using a very large and highly spectroscopically complete sample selected by rest-frame NIR bolometric flux in the GOODS-N. We assume a Salpeter IMF and fit Bruzual & Charlot (2003) models to compute the galactic stellar masses and extinctions. We determine the expected formed stellar mass density growth rates produced by star formation and compare them with the growth rates measured from the formed stellar mass functions by mass interval. We show that the growth rates match if the IMF is slightly increased from the Salpeter IMF at intermediate masses (~10 solar masses). We investigate the evolution of galaxy color, spectral type, and morphology with mass and redshift and the evolution of mass with environment. We find that applying extinction corrections is critical when analyzing galaxy colors; e.g., nearly all of the galaxies in the green valley are 24um sources, but after correcting for extinction, the bulk of the 24um sources lie in the blue cloud. We find an evolution of the metallicity-mass relation corresponding to a decrease of 0.21+/-0.03 dex between the local value and the value at z=0.77 in the 1e10-1e11 solar mass range. We use the metallicity evolution to estimate the gas mass of the galaxies, which we compare with the galactic stellar mass assembly and star formation histories. Overall, our measurements are consistent with a galaxy evolution process dominated by episodic bursts of star formation and where star formation in the most massive galaxies (>1e11 solar masses) ceases at z<1.5 because of gas starvation. (Abstract abridged)
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arxiv:0806.3457
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We present the results of a numerical study on the effects of metal enrichment and metal cooling on galaxy formation and cosmic star formation (SF) history using cosmological hydrodynamic simulations. We find following differences in the simulation with metal cooling when compared to the run without it: (1) the cosmic star formation rate (SFR) is enhanced by about 50 & 20% at z=1 & 3, respectively; (2) the gas mass fraction in galaxies is lower; (3) the total baryonic mass function (gas + star) at z=3 does not differ significantly, but shows an increase in the number of relatively massive galaxies at z=1; (4) the baryonic mass fraction of intergalactic medium (IGM) is reduced at z<3 due to more efficient cooling and gas accretion onto galaxies. Our results suggest that the metal cooling enhances the galaxy growth by two different mechanisms: (1) increase of SF efficiency in the local interstellar medium (ISM), and (2) increase of IGM accretion onto galaxies. The former process is effective throughout most of the cosmic history, while the latter is effective only at z<3 when the IGM is sufficiently enriched by metals owing to feedback.
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arxiv:0806.3460
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We report on the high resolution photoassociation spectroscopy of a $^{87}$Rb spin-1 Bose-Einstein condensate to the $1_\mathrm{g} (P_{3/2}) v = 152$ excited molecular states. We demonstrate the use of spin dependent photoassociation to experimentally identify the molecular states and their corresponding initial scattering channel. These identifications are in excellent agreement with the eigenvalues of a hyperfine-rotational Hamiltonian. Using the observed spectra we estimate the change in scattering length and identify photoassociation laser light frequency ranges that maximize the change in the spin-dependent mean-field interaction energy.
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arxiv:0806.3464
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Suppression of fluctuations of normally perturbed magnetic fields in dynamo waves and slow dynamos along curved (folded), torsioned (twisted) and non-stretched, diffusive filaments are obtained. This form of fluctuations suppression has been recently obtained by Vainshtein et al [PRE 56, (1997)] in nonlinear ABC and stretch-twist-fold (STF) dynamos by using a magnetic Reynolds number of the order of $Rm\approx{10^{4}}$. Here when torsion does not vanish an expression between magnetic Reynolds number and length scale L as with constant torsion ${\tau}_{0}$ itself is obtained, such as $Rm\approx{\frac{{\tau}_{0}L}{\eta}}$ is obtained. At coronal loops $Rm\approx{10^{12}}$ and torsion of the twisted structured loop from astronomical data by Lopez-Fuentes et al [Astron. and Astrophys. (2003)] of ${\tau}\approx{9.0{\times}10^{-10}}cm^{-1}$ is used to compute a very slow magnetic diffusion of ${\eta}\approx{10^{-8}}$. The slow dynamo obtained here is in agreement with Vishik arguement that fast dynamo cannot be obtained in non-stretched dynamo flows. When torsion vanishes helical turbulence is quenched and but ${\alpha}$-dynamos cannot be maintained since exponential stretching depends on torsion. This is actually Zeldovich antidynamo theorem for torsion-free or planar filaments which has been discussed by the other also recently in another context [Astr Nach. (2008)]. The suppression of magnetic field fluctuations is actually a result of the coupling of the magnetic diffusion and Frenet torsion of helical turbulence.
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arxiv:0806.3476
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Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is built. It is therefore imperative to find other means of implementing secure protocols. This thesis aims to contribute to the understanding of both the physical limitations, as well as the possibilities of cryptography in the quantum setting. In particular, we investigate several questions that are crucial to the security of quantum protocols: How can we find good uncertainty relations for a large number of measurement settings? How does the presence of entanglement affect classical protocols? And, what limitations does entanglement impose on implementing quantum protocols? Finally, can we circumvent some of those limitations using realistic assumptions?
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arxiv:0806.3483
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We study a deformation of the Cuntz-Toeplitz $C^*$-algebra determined by the relations $a_i^*a_i=1+q a_ia_i^*, a_i^*a_j=0$. We define well-behaved unbounded *-representations of the *-algebra defined by relations above and classify all such irreducible representations up to unitary equivalence.
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arxiv:0806.3503
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We demonstrate in a superconducting qubit the conditional recovery ("uncollapsing") of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a non-unitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, effectively canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6.
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arxiv:0806.3547
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We show that failure of local realism can be revealed to observers for whom only extremely coarse-grained measurements are available. In our instances, Bell's inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. Furthermore, we can observe failure of local realism when an inequality enforced by non-local realistic theories is satisfied. This suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. Small-scale experimental demonstration of our examples may be possible in the foreseeable future.
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arxiv:0806.3558
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In this note we establish the positivity of Green's functions for a class of elliptic differential operators on closed, Riemannian manifolds.
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arxiv:0806.3587
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We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds, according to which the mean volume gradually increases with particle number, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We thereby indicate when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions are supported by Monte Carlo simulations of two particle-encapsulating model systems -- a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. In the former the particle-induced swelling is thermodynamically equivalent to the pressure-induced one whereas in the latter it is not.
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arxiv:0806.3618
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Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can identify low-lying minima for the corresponding mildly frustrated energy landscapes. For small systems the basin-hopping algorithm succeeds in locating both lower minima and conformations closer to the experimental structure than does molecular dynamics with simulated annealing. For large systems the efficiency of basin-hopping decreases for our initial implementation, where the steps consist of random perturbations to the Cartesian coordinates. We implemented umbrella sampling using basin-hopping to further confirm when the global minima are reached. We have also improved the energy surface by employing bioinformatic techniques for reducing the roughness or variance of the energy surface. Finally, the basin-hopping calculations have guided improvements in the excluded volume of the Hamiltonian, producing better structures. These results suggest a novel and transferable optimization scheme for future energy function development.
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arxiv:0806.3652
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Interaction of the superconducting condensate with deformations of the crystal lattice is formulated assuming the electrostatic potential of Bernoulli type and the effect of strain on material parameters. In the isotropic approximation it is shown that within the Ginzburg-Landau theory both contributions can be recast into the local but non-linear interaction term of the free energy.
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arxiv:0806.3660
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In this paper it has been shown that the neutrino bulk viscous stresses can give rise to the late time acceleration of the universe. It is found that a number of spatially flat FRW models with a negative deceleration parameter can be constructed using neutrino viscosity and one of them mimics a $\Lambda$CDM model. This does not require any exotic dark energy component or any modification of gravity.
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arxiv:0806.3666
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We formulate a quantum group analogue of the group of orinetation-preserving Riemannian isometries of a compact Riemannian spin manifold, more generally, of a (possibly $R$-twisted in the sense of a paper of one of the authors, and of compact type) spectral triple. The main advantage of this formulation, which is directly in terms of the Dirac operator, is that it does not need the existence of any `good ' Laplacian as in our previous works on quantum isometry groups. Several interesting examples, including those coming from Rieffel-type deformation as well as the equivariant spectral triples on $SU_\mu(2)$ and $S^2_{\mu 0}$ are dicussed.
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arxiv:0806.3687
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Meaning cannot be based on dictionary definitions all the way down: at some point the circularity of definitions must be broken in some way, by grounding the meanings of certain words in sensorimotor categories learned from experience or shaped by evolution. This is the "symbol grounding problem." We introduce the concept of a reachable set -- a larger vocabulary whose meanings can be learned from a smaller vocabulary through definition alone, as long as the meanings of the smaller vocabulary are themselves already grounded. We provide simple algorithms to compute reachable sets for any given dictionary.
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arxiv:0806.3710
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The mid- to far-infrared emission of the outbursting FU Orionis objects has been attributed either to a flared outer disk or to an infalling envelope. We revisit this issue using detailed radiative transfer calculations to model the recent, high signal-to-noise data from the IRS instrument on the {Spitzer Space Telescope}. In the case of FU Ori, we find that a physically-plausible flared disk irradiated by the central accretion disk matches the observations. Building on our previous work, our accretion disk model with outer disk irradiation by the inner disk reproduces the spectral energy distribution between ~4000 angstroms to ~40 microns. Our model is consistent with near-infrared interferometry but there are some inconsistencies with mid-infared interferometric results. Including the outer disk allows us to refine our estimate of the outer radius of the outbursting, high mass accretion rate disk in FU Ori as ~ 0.5 AU, which is a crucial parameter in assessing theories of the FU Orionis phenomenon. We are able to place an upper limit on the mass infall rate of any remnant envelope infall rate to ~ 7e-7 Msun/yr assuming a centrifugal radius of 200 AU. The FUor BBW 76 is also well modelled by a 0.6 AU inner disk and a flared outer disk. However, V1515 Cyg requires an envelope with an outflow cavity to adequately reproduce the IRS spectrum. In contrast with the suggestion by Green et al., we do not require a flattened envelope to match the observations; the inferred cavity shape is qualitatively consistent with typical protostellar envelopes. This variety of dusty structures suggests that the FU Orionis phase can be present at either early or late stages of protostellar evolution.
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arxiv:0806.3715
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We calculate the full $I-V$ characteristics at vanishing temperature in the self-dual interacting resonant level model in two ways. The first uses careful time dependent DMRG with large number of states per block and a representation of the reservoirs as leads subjected to a chemical potential. The other is based on integrability in the continuum limit, and generalizes early work of Fendley Ludwig Saleur on the boundary sine-Gordon model. The two approaches are in excellent agreement, and uncover among other things a power law decay of the current at large voltages when $U>0$.
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arxiv:0806.3731
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We perform a general analysis of the R-parity conserving dimension-five operators that can be present beyond the Minimal Supersymmetric Standard Model. Not all these operators are actually independent. We present a method which employs spurion-dependent field redefinitions that removes this "redundancy" and establishes the minimal, irreducible set of these dimension-five operators. Their potential effects on the MSSM Higgs sector are discussed to show that the tree level bound $m_h\leq m_Z$ cannot be easily lifted within the approximations used, and quantum corrections are still needed to satisfy the LEPII bound. An ansatz is provided for the structure of the remaining couplings in the irreducible set of D=5 operators, which avoids phenomenological constraints from flavor changing neutral currents. The minimal set of operators brings new couplings in the effective Lagrangian, notably "wrong"-Higgs Yukawa couplings and contact fermion-fermion-scalar-scalar interactions, whose effects are expected to be larger than those generated in the MSSM at loop or even tree level. This has implications in particular for LHC searches for supersymmetry by direct squark production.
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arxiv:0806.3778
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In this paper it is hown that given any smooth, positive function f on a closed, smooth manifold of dimension greater than four and with positive Paneitz invariant, there exists a metric on M such that $Q_g$ = f.
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arxiv:0806.3790
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A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.
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arxiv:0806.3833
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The notion of `Pseudo Algebraically Closed (PAC) extensions' is a generalization of the classical notion of PAC fields. It was originally motivated by Hilbert's tenth problem, and recently had new applications. In this work we develop a basic machinery to study PAC extensions. This machinery is based on a generalization of embedding problems to field extensions. The main goal is to prove that the Galois closure of any proper separable algebraic PAC extension is its separable closure. This vastly generalizes earlier works of Jarden-Razon, Jarden, and Jarden and the author. This also leads to a classification of all finite PAC extensions which in turn proves the `bottom conjecture' for finitely generated infinite fields. The secondary goal of this work is to unify proofs of known results about PAC extensions and to establish new basic properties of PAC extensions, e.g.\ transitiveness of PAC extensions.
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arxiv:0806.3851
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We present three dimensional hydrodynamical simulations aimed at studying the dynamical and chemical evolution of the interstellar medium (ISM) in isolated dwarf spheroidal galaxies (dSphs). This evolution is driven by the explosion of Type II and Type Ia supernovae, whose different contribution on both the dynamics and chemical enrichment is taken into account. Radiative losses are effective in radiating away the huge amount of energy released by SNe explosions, and the dSph is able to retain most of the gas allowing a long period (>2-3 Gyr) of star formation, as usually observed in this kind of galaxies. We are able to reproduce the stellar metallicity distribution function (MDF) as well as the peculiar chemical properties of strongly O-depleted stars observed in several dSphs. The model also naturally predicts two different stellar populations, with an anti-correlation between [Fe/H] and velocity dispersion, similarly to what observed in the Sculptor and Fornax dSphs. These results derive from the inhomogeneous pollution of the SNe Ia, a distinctive characteristic of our model. We also applied the model to the peculiar globular cluster (GC) Omega Cen in the hypothesis that it is the remnant of a formerly larger stellar system, possibly a dSph.
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arxiv:0806.3856
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We optimize number squeezing when splitting a mesoscopic Bose Einstein condensate. Applying optimal control theory to a realistic description of the condensate allowed us to identify a form of the splitting ramp which drastically outperforms the adiabatic splitting. The results can be interpreted in terms of a generic two-mode model mapped onto a parametric harmonic oscillator. This optimal route to squeezing paves the way to a much longer phase coherence and atom interferometry close to the Heisenberg limit.
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arxiv:0806.3877
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We calculate the thermal Euclidean correlators and the spectral functions of the energy-momentum tensor for pure gauge theories, including at non-zero spatial momentum, at leading order in perturbation theory. Our goal is to improve the extraction of transport properties from Euclidean correlators that are computable in lattice QCD. Based on our results and the predictions of hydrodynamics for the structure of the spectral functions at low frequencies, we show that the shear and bulk viscosities can advantageously be extracted from the Euclidean correlators of the conserved charges, energy and momentum, at small but non-vanishing spatial momentum. The spectral functions in these channels are free of the ultraviolet $\omega^4$ term which represents a large background to the thermal physics encoded in the correlators of the fluxes.
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arxiv:0806.3914
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The following work presents a generalized (extended) finite element formulation for the advection-diffusion equation. Using enrichment functions that represent the exponential nature of the exact solution, smooth numerical solutions are obtained for problems with steep gradients and high Peclet numbers (up to Pe = 25) in one and two-dimensions. As opposed to traditional stabilized methods that require the construction of stability parameters and stabilization terms, the present work avoids numerical instabilities by improving the classical Galerkin solution with an enrichment function. To contextualize this method among other stabilized methods, we show by decomposition of the solution (in a multiscale manner) an equivalence to both Galerkin/least-squares type methods and those that use bubble functions. This work also presents a strategy for constructing the enrichment function for problems with complex geometries by employing a global-local approach.
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arxiv:0806.3963
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Models of generalized parton distributions at zero skewness are used to relate the behavior of deep inelastic scattering quark distributions, evaluated at high x, to the transverse charge density evaluated at small distances. We obtain an interpretation of the recently obtained negative central charge density of the neutron. The d quarks dominate the neutron structure function for large values of Bjorken x, where the large momentum of the struck quark has a significant impact on determining the center of momentum, and thus the ``center'' of the nucleon in the transverse position plane.
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arxiv:0806.3977
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We study the interaction between several fields initially in coherent states. The solution allows us to explain why coherent states remain coherent states when subject to non-Markovian dissipation. We first study the interaction between two fields and show that this is the building block of the total interaction. We give a completely algebraic solution of this system.
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arxiv:0806.3997
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We prove two theorems which allow one to recognize indecomposable subcontinua of closed surfaces without boundary. If $X$ is a subcontinuum of a closed surface $S$, we call the components of $S \setminus X$ the complementary domains of $X$. We prove that a continuum is either indecomposable or the union of two indecomposable continua whenever it has a sequence of distinct complementary domains whose boundaries limit to the continuum in the Hausdorff metric. We define a slightly stronger condition on the complementary domains of a continuum, called the double-pass condition, which we conjecture is equivalent to indecomposability of the continuum. We prove that this is so for continua which are not the boundary of one of their complementary domains.
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arxiv:0806.4009
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The work presented here extends upon the best known universal quantum circuit, the Quantum Shannon Decomposition proposed in [Vivek V. Shende, Stephen S. Bullock and Igor Markov, Synthesis of Quantum Logic Circuits, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 25 (6): 1000-1010 (2006)]. We obtain the basis of the circuit's design in a pair of Cartan decompositions. This insight gives a simple constructive algorithm for obtaining the Quantum Shannon Decomposition of a given unitary matrix in terms of the corresponding Cartan involutions.
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arxiv:0806.4015
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A rotorcraft-based unmanned aerial vehicle exhibits more complex properties compared to its full-size counterparts due to its increased sensitivity to control inputs and disturbances and higher bandwidth of its dynamics. As an aerial vehicle with vertical take-off and landing capability, the helicopter specifically poses a difficult problem of transition between forward flight and unstable hover and vice versa. The LPV control technique explicitly takes into account the change in performance due to the real-time parameter variations. The technique therefore theoretically guarantees the performance and robustness over the entire operating envelope. In this study, we investigate a new approach implementing model identification for use in the LPV control framework. The identification scheme employs recursive least square technique implemented on the LPV system represented by dynamics of helicopter during a transition. The airspeed as the scheduling of parameter trajectory is not assumed to vary slowly. The exclusion of slow parameter change requirement allows for the application of the algorithm for aggressive maneuvering capability without the need of expensive computation. The technique is tested numerically and will be validated in the autonomous flight of a small scale helicopter.
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arxiv:0806.4021
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Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.
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arxiv:0806.4024
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Atomic scale computer simulations on structures and photo induced volume changes of flatly and obliquely deposited amorphous selenium films have been carried out in order to understand how the properties of chalcogenide glasses are influenced by their preparation method. Obliquely deposited a-Se thin films contain more coordination defects, larger voids than the flatly deposited ones. To model the photo induced volume changes the electron excitation and hole creation were treated independently within the framework of tight-binding formalism. Covalent and interchain bond breakings and formations were found. The obliquely deposited samples containing voids showed a wide spectrum of photo induced structural changes in microscopic and volume changes in macroscopic levels.
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arxiv:0806.4066
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We give a definition of the spectral flow for paths of bounded essentially hyperbolic operators on a Banach space. The spectral flow induces a group homomorphism on the fundamental group of every connected component of the space of essentially hyperbolic operators. We prove that this homomorphism completes the exact homotopy sequence of a Serre fibration. This allows us to characterise its kernel and image and to produce examples of spaces where it is not injective or not surjective, unlike what happens for Hilbert spaces. For a large class of paths, namely the essentially splitting, the spectral flow of $ A $ coincides with $ -\ind(F_A) $, the Fredholm index of the differential operator $ F_A (u) = u' - A u $.
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arxiv:0806.4094
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We apply a semiclassical approach to express finite temperature dynamical correlation functions of gapped spin models analytically. We show that the approach of [A. Rapp, G. Zarand, Phys. Rev. B 74, 014433 (2006)] can also be used for the S=1 antiferromagnetic Heisenberg chain, whose lineshape can be measured experimentally. We generalize our calculations to O(N) quantum spin models and the sine-Gordon model in one dimension, and show that in all these models, the finite temperature decay of certain correlation functions is characterized by the same universal semiclassical relaxation function.
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arxiv:0806.4107
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Formation of massive stars by accretion requires a high accretion rate of > 10^-4 M_sun/yr to overcome the radiation pressure barrier of the forming stars. Here, we study evolution of protostars accreting at such high rates, by solving the structure of the central star and the inner accreting envelope simultaneously. The protostellar evolution is followed starting from small initial cores until their arrival at the stage of the Zero-Age Main Sequence (ZAMS) stars. An emphasis is put on evolutionary features different from those with a low accretion rate of 10^-5 M_sun/yr, which is presumed in the standard scenario for low-mass star formation. With the high accretion rate of 10^-3 M_sun/yr, the protostellar radius becomes very large and exceeds 100 R_sun. It is not until the stellar mass reaches 40 M_sun that hydrogen burning begins and the protostar reaches the ZAMS phase, and this ZAMS arrival mass increases with the accretion rate. At a very high accretion rate of > 3 x 10^-3 M_sun/yr, the total luminosity of the protostar becomes so high that the resultant radiation pressure inhibits the growth of the protostars under steady accretion before reaching the ZAMS stage. Therefore, the evolution under the critical accretion rate 3 x 10^-3 M_sun/yr gives the upper mass limit of possible pre-main-sequence stars at 60 M_sun. The upper mass limit of MS stars is also set by the radiation pressure onto the dusty envelope under the same accretion rate at 250 M_sun. We also propose that the central source enshrouded in the Orion KL/BN nebula has effective temperature and luminosity consistent with our model, and is a possible candidate for such protostars growing under the high accretion rate. (abridged)
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arxiv:0806.4122
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We show that the whole range of RHIC data for hadron production in d-Au collisions is compatible with geometric scaling. To establish the scaling violations expected from small-x evolution a larger kinematic range in transverse momentum and rapidity would be needed. We point out that the fall-off of the p_t distribution of produced hadrons at large p_t is a sensitive probe of small-x evolution especially at the LHC.
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arxiv:0806.4126
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We show that if a flavour-less vector meson remains bound after deconfinement, and if its limiting velocity in the quark-gluon plasma is subluminal, then this meson produces a distinct peak in the spectrum of thermal photons emitted by the plasma. We also demonstrate that this effect is a universal property of all strongly coupled, large-Nc plasmas with a gravity dual. For the J/psi the corresponding peak lies between 3 and 5 GeV and could be observed at LHC.
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arxiv:0806.4172
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The aim of this paper is to compare three regularized particle filters in an online data processing context. We carry out the comparison in terms of hidden states filtering and parameters estimation, considering a Bayesian paradigm and a univariate stochastic volatility model. We discuss the use of an improper prior distribution in the initialization of the filtering procedure and show that the regularized Auxiliary Particle Filter (APF) outperforms the regularized Sequential Importance Sampling (SIS) and the regularized Sampling Importance Resampling (SIR).
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arxiv:0806.4242
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We experimentally observe the two-photon interference of multimode photon pairs produced by an optical parametric oscillator far below threshold via a michelson interferometer, which shows a multipeaked structure. We find that the correlation function when the interferometer is unbalanced is clearly dependent on the path difference and phase between two interfering beams, but the shape of correlation function in balanced case is independent on the small path difference and phase beside the height. All experimental results are well agreed with the theoretical prediction.
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arxiv:0806.4260
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It is widely accepted that the progenitors of core collapse SNe are young massive stars and therefore their host galaxies are mostly spiral or irregular galaxies dominated by a young stellar population. Surprisingly, among morphologically classified hosts of core collapse SNe, we find 22 cases where the host has been classified as an Elliptical or S0 galaxy. To clarify this apparent contradiction, we carry out a detailed morphological study and an extensive literature search for additional information on the sample objects. Our results are as follows: 1. Of 22 "early type" objects, 17 are in fact misclassified spiral galaxies, one is a misclassified irregular, and one is a misclassified ring galaxy. 2. Of the 3 objects maintaining the early type classification, one (NGC2768) is a suspected merger remnant, another (NGC4589) is definitely a merger, and the third (NGC2274) is in close interaction. The presence of some amount of young stellar population in these galaxies is therefore not unexpected. These results confirm the presence of a limited, but significant, number of core collapse SNe in galaxies generally classified of early type. In all cases, anyway, there are independent indicators of the presence in host galaxies of recent star formation due to merging or gravitational interaction.
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arxiv:0806.4269
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Consider the following stochastic graph process. We begin with the empty graph on n vertices and add edges one at a time, where each edge is chosen uniformly at random from the collection of potential edges that do not form triangles when added to the graph. The process terminates at a maximal traingle-free graph. Here we analyze the triangle-free process, determining the likely order of magnitude of the number of edges in the final graph. As a corollary we show that the triangle-free process is very likely to produce a Ramsey R(3,t) graph; that is, our analysis of the triangle-free process gives a new proof of the lower bound on R(3,t) previously established by Jeong Han Kim. The techniques introduced extend to the K_4-free process thereby establishing a small improvement in the best known lower bound on the Ramsey number R(4,t).
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arxiv:0806.4375
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A generic `chirp' of the form h(t) = A(t) cos(phi(t)) can be closely approximated by a connected set of multiscale chirplets with quadratically-evolving phase. The problem of finding the best approximation to a given signal using chirplets can be reduced to that of finding the path of minimum cost in a weighted, directed graph, and can be solved in polynomial time via dynamic programming. For a signal embedded in noise we apply constraints on the path length to obtain a statistic for detection of chirping signals in coloured noise. In this paper we present some results from using this test to detect binary black hole coalescences in simulated LIGO noise.
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arxiv:0806.4417
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We review empirical and theoretical findings concerning white dwarfs in Galactic globular clusters. Since their detection is a critical issue we describe in detail the various efforts to find white dwarfs in globular clusters. We then outline the advantages of using cluster white dwarfs to investigate the formation and evolution of white dwarfs and concentrate on evolutionary channels that appear to be unique to globular clusters. We also discuss the usefulness of globular cluster white dwarfs to provide independent information on the distances and ages of globular clusters, information that is very important far beyond the immediate field of white dwarf research. Finally, we mention possible future avenues concerning globular cluster white dwarfs, like the study of strange quark matter or plasma neutrinos.
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arxiv:0806.4456
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I propose an extension to Boltzmann BGK equation for Hard Spheres. The present model has an $H$-theorem and it allows choice of Prandtl number as an independent parameter. I show that similar to Enskog equation this equation can reproduce dynamics of hard spheres in dense systems.
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arxiv:0806.4479
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A characterisation of scintillating fibres with silicon photomultiplier read-out was performed in view of their possible application in fibre tracking detector systems. Such a concept is being considered for the Kaos spectrometer at the Mainz Microtron MAMI and as a time-of-flight start detector for the hypernuclear physics programme at the PANDA experiment of the FAIR project. Results on particle detection effciency and time resolution are discussed. In summary, the silicon devices are very suitable for the detection of the low light yield from scintillating fibres insofar a trigger scheme is found to cope with the noise rate characteristics.
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arxiv:0806.4483
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To a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables defined by the orders of a function on irreducible components of the curve. The Poincare series of this filtration turnes out to coincide with the Alexander polynomial of the curve germ. For a finite set of divisorial valuations on the ring corresponding to some components of the exceptional divisor of a modification of the plane, in a previous paper there was obtained a formula for the Poincare series of the corresponding multi-index filtration similar to the one associated to plane germs. Here we show that the Poincare series of a set of divisorial valuations on the ring of germs of functions of two variables defines "the topology of the set of the divisors" in the sense that it defines the minimal resolution of this set up to combinatorial equivalence. For the plane curve singularity case, we also give a somewhat simpler proof of the statement by Yamamoto which proves that the Alexander polynomial is equivalent to the embedded topology.
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arxiv:0806.4492
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Using tools from algebraic geometry and Groebner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.
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arxiv:0806.4510
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To a proper inclusion N\subset M of II_1 factors of finite Jones index [M:N], we associate an ergodic C*-action of the quantum group S_\mu U(2). The deformation parameter is determined by -1<\mu<0 and [M:N]=|\mu+\mu^{-1}|. The higher relative commutants can be identified with the spectral spaces of the tensor powers of the defining representation of the quantum group. This ergodic action may be thought of as a virtual subgroup of S_\mu U(2) in the sense of Mackey arising from the tensor category generated by M regarded as a bimodule over N. \mu is negative as M is a real bimodule.
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arxiv:0806.4519
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We study quantitative asymptotics of planar random walks that are spatially non-homogeneous but whose mean drifts have some regularity. Specifically, we study the first exit time $\tau_\alpha$ from a wedge with apex at the origin and interior half-angle $\alpha$ by a non-homogeneous random walk on the square lattice with mean drift at $x$ of magnitude $O(1/|x|)$ as $|x| \to \infty$. This is the critical regime for the asymptotic behaviour: under mild conditions, a previous result of the authors (see arXiv:0910.1772) stated that $\tau_\alpha < \infty$ a.s. for any $\alpha$ (while for a stronger drift field $\tau_\alpha$ is infinite with positive probability). Here we study the more difficult problem of the existence and non-existence of moments $E[\tau_\alpha^s]$, $s>0$. Assuming (in common with much of the literature) a uniform bound on the walk's increments, we show that for $\alpha < \pi/2$ there exists $s_0 \in (0,\infty)$ such that $E[\tau_\alpha^s]$ is finite for $s < s_0$ but infinite for $s > s_0$; under specific assumptions on the drift field we show that we can attain $E[\tau_\alpha^s] = \infty$ for any $s > 1/2$. We show that for $\alpha \leq \pi$ there is a phase transition between drifts of magnitude $O(1/|x|)$ (the critical regime) and $o(1/|x|)$ (the subcritical regime). In the subcritical regime we obtain a non-homogeneous random walk analogue of a theorem for Brownian motion due to Spitzer, under considerably weaker conditions than those previously given (including work by Varopoulos) that assumed zero drift.
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arxiv:0806.4561
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The Lempel-Ziv universal coding scheme is asymptotically optimal for the class of all stationary ergodic sources. A problem of robustness of this property under small violations of ergodicity is studied. A notion of deficiency of algorithmic randomness is used as a measure of disagreement between data sequence and probability measure. We prove that universal compressing schemes from a large class are non-robust in the following sense: if the randomness deficiency grows arbitrarily slowly on initial fragments of an infinite sequence then the property of asymptotic optimality of any universal compressing algorithm can be violated. Lempel-Ziv compressing algorithms are robust on infinite sequences generated by ergodic Markov chains when the randomness deficiency of its initial fragments of length $n$ grows as $o(n)$.
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arxiv:0806.4572
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We prove that the weakly damped cubic Schr\"odinger flow in $L^2(\T)$ provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak $ L^2(\T) $-convergence inspired by a previous work of the author. Combining the compactness in $ L^2(\T) $ of the attractor with the approach developed by Goubet, we show that the attractor is actually a compact set of $ H^2(\T) $. This asymptotic smoothing effect is optimal in view of the regularity of the steady states.
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arxiv:0806.4578
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Sharpening (a particular case of) a result of Szemeredi and Vu and extending earlier results of Sarkozy and ourselves, we find, subject to some technical restrictions, a sharp threshold for the number of integer sets needed for their sumset to contain a block of consecutive integers of length, comparable with the lengths of the set summands. A corollary of our main result is as follows. Let $k,l\ge 1$ and $n\ge 3$ be integers, and suppose that $A_1,...,A_k\subset[0,l]$ are integer sets of size at least $n$, none of which is contained in an arithmetic progression with difference greater than 1. If $k\ge 2\lceil(l-1)/(n-2)\rceil$, then the sumset $A_1+...+A_k$ contains a block of consecutive integers of length $k(n-1)$.
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arxiv:0806.4580
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We examine CP violation in the Delta S=0 decays tau -> omega pi nu_tau and tau -> a_1 pi nu_tau and the Delta S=1 decay tau -> K pi pi nu_tau. We assume that the new physics is a charged Higgs. We show that sizeable CP-violating effects are possible in tau -> a_1 pi nu_tau (polarization-dependent rate asymmetry) and tau -> omega pi nu_ tau (triple-product asymmetry). The Delta S=1 decay tau -> K pi pi nu_tau can proceed via several resonances. We construct two modified rate asymmetries and a triple product asymmetry for this decay and discuss the potential sensitivities of these asymmetries.
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arxiv:0806.4585
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The subject of particle-antiparticle mixing in the neutral B meson systems is reviewed. The formalism of B0-B0bar mixing is recalled and basic Standard Model predictions are given, before experimental issues are discussed and the latest combinations of experimental results on mixing parameters are presented, including those on mixing-induced CP violation, mass differences, and decay-width differences. Finally, time-integrated mixing results are used to improve our knowledge on the fractions of the various b-hadron species produced in Z decays and at high-energy colliders.
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arxiv:0806.4634
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In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constitutive relation C of a balance system is realized as a mapping between a (partial) k-jet bundle and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system corresponding to a constitutive relation C is studied. Special cases of balance systems -Lagrangian systems of order 1 with arbitrary sources and RET (Rational Extended Ther- modynamics) systems are characterized in geometrical terms. Action of auto- morphisms of the configurational bundle on the constitutive mappings C is studied and it is shown that the symmetry group Sym(C) of C acts on the sheaf of solutions Sol(C) of he balance system. Suitable version of Noether Theorem for an action of a symmetry group is presented together with the special forms for semi- Lagrangian and RET balance systems and examples of energy momentum and gauge symmetries balance laws.
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arxiv:0806.4636
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We investigate the equations of anisotropic incompressible viscous fluids in $\R^3$, rotating around an inhomogeneous vector $B(t, x_1, x_2)$. We prove the global existence of strong solutions in suitable anisotropic Sobolev spaces for small initial data, as well as uniformlocal existence result with respect to the Rossby number in the same functional spaces under the additional assumption that $B=B(t,x_1)$ or $B=B(t,x_2)$. We also obtain the propagation of the isotropic Sobolev regularity using a new refined product law.
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arxiv:0806.4658
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