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In this article, we consider the estimation of exponential sums along the points of the reduction mod $p^{m}$ of a $p$-adic analytic submanifold of $ \mathbb{Z}_{p}^{n}$. More precisely, we extend Igusa's stationary phase method to this type of exponential sums. We also study the number of solutions of a polynomial congruence along the points of the reduction mod $% p^{m}$ of a $p$-adic analytic submanifold of $\mathbb{Z}_{p}^{n}$. In addition, we attach a Poincare series to these numbers, and establish its rationality. In this way, we obtain geometric bounds for the number of solutions of the corresponding polynomial congruences.
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arxiv:0910.1887
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We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. Here we treat systems with a convex slow curve. In this case there is a set of parameter values accumulating to zero for which the system has exactly one attracting and one repelling canard cycle. The basin of the attracting cycle is almost the whole torus.
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arxiv:0910.1888
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It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal invariance has ever been given, and even physics arguments support (a priori weaker) M\"obius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures.
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arxiv:0910.2045
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One would like an explanation of the provocative McKay and Glauberman-Norton observations connecting the extended $E_8$-diagram with pairs of 2A involutions in the Monster sporadic simple group. We propose a down-to-earth model for the 3C-case which exhibits a logic to these connections.
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arxiv:0910.2057
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We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Psi. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound "runaway effect". Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Psi(r) diverges at short distances like g r^{-a}, g,a>0, by showing that the runaway effect still occurs if a<2.
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arxiv:0910.2184
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Violent relaxation -- the protocluster dynamical response to the expulsion of its residual star forming gas -- is a short albeit crucial episode in the evolution of star clusters and star cluster systems. Because it is heavily driven by cluster formation and environmental conditions, it is a potentially highly rewarding phase in terms of probing star formation and galaxy evolution. In this contribution I review how cluster formation and environmental conditions affect the shape of the young cluster mass function and the relation between the present star formation rate of galaxies and the mass of their young most massive cluster.
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arxiv:0910.2228
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We consider II$_1$ factors $M$ which can be realized as inductive limits of subfactors, $N_n \nearrow M$, having spectral gap in $M$ and satisfying the bi-commutant condition $(N_n'\cap M)'\cap M=N_n$. Examples are the enveloping algebras associated to non-Gamma subfactors of finite depth, as well as certain crossed products of McDuff factors by amenable groups. We use deformation/rigidity techniques to obtain classification results for such factors.
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arxiv:0910.2241
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In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.
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arxiv:0910.2246
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We investigate frequency up-conversion of low power cw resonant radiation in Rb vapour as a function of various experimental parameters. We present evidence that the process of four wave mixing is responsible for unidirectional blue light generation and that the phase matching conditions along a light-induced waveguide determine the direction and divergence of the blue light. Velocity-selective excitation to the 5D level via step-wise and two-photon processes results in a Doppler-free dependence on the frequency detuning of the applied laser fields from the respective dipole-allowed transitions. Possible schemes for ultraviolet generation are discussed.
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arxiv:0910.2292
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We studied the magnetoresistance due to a spin spiral by solving the Boltzmann equation. The scattering rates of conduction electrons are calculated by using the non-perturbative wave function of the conduction electrons and the non-equilibrium distribution function is obtained by numerically solving the Boltzmann equation. These enable us to calculate the resistivity of a sufficiently thin spin spiral. A magnetoresistance ratio of more than 50% is predicted for a spin spiral with high spin polarization (>0.8) and a small period (about 1-2 nm).
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arxiv:0910.2308
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We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For definable ($\mathbf{\Pi}^1_1$ on $\mathbf{\Sigma}^1_1) $\sigma$-ideals we show that if a $\sigma$-ideal is generated by closed sets, then it is generated by closed sets in all forcing extensions. We also prove an infinite-dimensional version of the Solecki dichotomy for analytic sets. Among examples, we investigate the $\sigma$-ideal $\E$ generated by closed null sets and $\sigma$-ideals connected with not piecewise continuous functions.
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arxiv:0910.2318
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We present a versatile and highly configurable scanning acoustic platform. This platform, comprising of a high frequency transducer, bespoke positioning system and temperature-regulated sample unit, enables the acoustic probing of materials over a wide range of length scales and with minimal thermal aberration. In its bare form the platform acts as a reflection-mode acoustic microscope, while optical capabilities are readily incorporated to extend its abilities to the acousto-optic domain. Here we illustrate the capabilities of the platform through its incarnation as an acoustic microscope. Operating at 55 MHz we demonstrate acoustic imaging with a lateral resolution of 25 microns. We outline its construction, calibration and capabilities as an acoustic microscope, and discuss its wider applications.
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arxiv:0910.2323
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It is well-known that in bulk, the solution of the Bogoliubov-de Gennes equations is the same whether or not the Hartree-Fock term is included. Here the Hartree-Fock potential is position independent and, so, gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. It is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position dependent Hartree-Fock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubov-de Gennes equations with the Hartree-Fock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters.
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arxiv:0910.2352
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Reported observations in H-alpha, Ca II H and K or or other chromospheric lines of coronal rain trace back to the days of the Skylab mission. Offering a high contrast in intensity with respect to the background (either bright in emission if observed at the limb, or dark in absorption if observed on disk) these cool blobs are often observed falling down from high coronal heights above active regions. A physical explanation for this spectacular phenomenon has been put forward thanks to numerical simulations of loops with footpoint concentrated heating, a heating scenario in which cool condensations naturally form in the corona. This effect has been termed 'catastrophic cooling' and is the predominant explanation for coronal rain. In this work we further investigate the link between this phenomenon and the heating mechanisms acting in the corona. We start by analyzing observations of coronal rain at the limb in the Ca II H line performed by the SOT instrument on board of the Hinode satellite. We then compare the observations with 1.5-dimensional MHD simulations of loops being heated by small-scale discrete events concentrated towards the footpoints (that could come, for instance, from magnetic reconnection events), and by Alfven waves generated at the photosphere. It is found that if a loop is heated predominantly from Alfven waves coronal rain is inhibited due to the characteristic uniform heating they produce. Hence coronal rain may not only point to the spatial distribution of the heating in coronal loops but also to the agent of the heating itself. We thus propose coronal rain as a marker for coronal heating mechanisms.
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arxiv:0910.2383
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Recent surveys have revealed a lack of close-in planets around evolved stars more massive than 1.2 Msun. Such planets are common around solar-mass stars. We have calculated the orbital evolution of planets around stars with a range of initial masses, and have shown how planetary orbits are affected by the evolution of the stars all the way to the tip of the Red Giant Branch (RGB). We find that tidal interaction can lead to the engulfment of close-in planets by evolved stars. The engulfment is more efficient for more-massive planets and less-massive stars. These results may explain the observed semi-major axis distribution of planets around evolved stars with masses larger than 1.5 Msun. Our results also suggest that massive planets may form more efficiently around intermediate-mass stars.
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arxiv:0910.2396
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We present an analysis of the neutral hydrogen and stellar populations of elliptical galaxies in the Tal et al. (2009) sample. Our aim is to test their conclusion that the continuing assembly of these galaxies at z~0 is essentially gas-free and not accompanied by significant star formation. In order to do so, we make use of HI data and line-strength indices available in the literature. We look for direct and indirect evidence of the presence of cold gas during the recent assembly of these objects and analyse its relation to galaxy morphological fine structure. We find that >25% of ellipticals contain HI at the level of M(HI)>10^8 M(Sun), and that M(HI) is of the order of a few percent of the total stellar mass. Available data are insufficient to establish whether galaxies with a disturbed stellar morphology are more likely to contain HI. However, HI interferometry reveals very disturbed gas morphology/kinematics in all but one of the detected systems, confirming the continuing assembly of many ellipticals but also showing that this is not necessarily gas-free. We also find that all very disturbed ellipticals have a single-stellar-population-equivalent age <4 Gyr. We interpret this as evidence that ~0.5-5% of their stellar mass is contained in a young population formed during the past ~1 Gyr. Overall, a large fraction of ellipticals seem to have continued their assembly over the past few Gyr in the presence of a mass of cold gas of the order of 10% of the galaxy stellar mass. This material is now observable as neutral hydrogen and young stars.
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arxiv:0910.2416
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We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real and shape-invariant, leading to translational shift in a suitable parameter by \textit{real} units. The case of two different superpotentials, leading to same potential, yields broken PT-symmetry, the energy spectra in the two phases being separated by a bifurcation. Interestingly, these two superpotentials generate the two disjoint sectors of the Hilbert space. In the broken case, shape invariance produces \textit{complex} parametric shifts.
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arxiv:0910.2423
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At the onset of X Chromosomes Inactivation, the vital process whereby female mammal cells equalize X products with respect to males, the X chromosomes are colocalized along their Xic (X-Inactivation Center) regions. The mechanism inducing recognition and pairing of the X's remains, though, elusive. Starting from recent discoveries on the molecular factors and on the DNA sequences (the so-called ``pairing sites'') involved, we dissect the mechanical basis of Xic colocalization by using a Statistical Physics model. We show that soluble DNA specific binding molecules, as those experimentally identified, can be indeed sufficient to induce the spontaneous colocalization of the homologous chromosomes, but only when their concentration, or chemical affinity, rises above a threshold value, as a consequence of a thermodynamic phase transition. We derive the likelihood of pairing and its probability distribution. Chromosome dynamics has two stages: an initial independent Brownian diffusion followed, after a characteristic time scale, by recognition and pairing. Finally, we investigate the effects of DNA deletion/insertions in the region of pairing sites and compare model predictions to available experimental data.
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arxiv:0910.2436
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We present an analysis of the X-ray properties of 35 submm galaxies(SMGs) in the CDF-N. Using a sample of robust 850micron-selected galaxies, with accurate positions from Spitzer and/or radio counterparts, we find 16 objects (45+/-8%) with significant X-ray detections in the 2Ms Chandra data. 6 of these SMGs (~17+/-6%) have measured X-ray luminosities or upper limits consistent with those expected based on the far-infrared (FIR) or radio-derived star formation rate (SFR), and hence with the X-rays coming solely from star formation. In another 7 sources (20+/-7%) a dominant AGN contribution to the X-ray emission is required, while in 3 more it is unclear whether stellar process or accretion are responsible. Stacking of the X-ray undetected SMGs reveals a highly significant detection. If due to star formation, this corresponds to an average X-ray derived SFR of ~150 Msun/yr. We deduce that the AGN fraction in SMGs based on X-ray observations is 20-29 (+/-7) %, which is towards the lower limit of previous estimates. Spectral analysis shows that in general the SMGs are not heavily obscured in the X-ray but most of the SMGs classfied as AGN show absorption with N_H in excess of 10^22 cm^-2. Of the secure AGN, the bolometric luminosity appears to be dominated by the AGN in only 3 cases. In ~85% of the SMGs, the X-ray spectrum effectively rules out an AGN contribution that dominates the bolometric emission, even if the AGN is Compton thick. The evidence therefore suggests that intense star formation accounts for both the FIR and X-ray emission in most SMGs. We argue that, rather than having an especially high AGN fraction or duty cycle, SMGs have a high X-ray detection rate at very faint fluxes partly because of their high star formation rates and, in rarer cases, because the submm emission is from an AGN.(abridged)
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arxiv:0910.2464
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Using total variation based energy minimisation we address the recovery of a blurred (convoluted) one dimensional (1D) barcode. We consider functionals defined over all possible barcodes with fidelity to a convoluted signal of a barcode, and regularised by total variation. Our fidelity terms consist of the L^2 distance either directly to the measured signal or preceded by deconvolution. Key length scales and parameters are the X-dimension of the underlying barcode, the size of the supports of the convolution and deconvolution kernels, and the fidelity parameter. For all functionals, we establish regimes (sufficient conditions) wherein the underlying barcode is the unique minimiser. We also present some numerical experiments suggesting that these sufficient conditions are not optimal and the energy methods are quite robust for significant blurring.
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arxiv:0910.2494
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The first goal of this paper is to show that discreteness, locality, and relativistic covariance can peacefully coexist if the ordinary spacetime (OST) is replaced with phase spacetime (PST) as a geometric background of a Poisson process, where PST is a spacetime generalization of a notion of phase space (this is a 7-dimensional version of the 8-dimensional structure proposed by Caianiello). Furthermore, Caianiello's idea of finite acceleration is implemented. After this is done, the paper then goes on to generalize the geometric notions obtained from the intuition of PST to a general discrete causal set, without any geometric background. It then takes advantage of the absence of lightcone singularity to attempt to tackle the definition of PST-like causal set; that is, a discrete system that approximates the geometrical properties that we would expect from continuum PST. Finally, the paper proceeds to introduce quantum field theory on a causal set, and shows that the locality gained by switching from OST to PST brings us one step closer to be able to treat quantum field theory on a causal set analytically rather than numerically.
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arxiv:0910.2498
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Very recently, the new 6K superconductor (SC) LiFeP, the first arsenic-free analogue of the family of the so-called "111" FeAs SCs, was discovered. Here, based on first-principle FLAPW-GGA calculations, the band structure, density of states, Fermi surface topology, electron density distribution and effective atomic charges for the new SC LiFeP are investigated and discussed in comparison with isostructural and isoelectronic LiFeAs.
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arxiv:0910.2550
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We engineer algorithms for sorting huge data sets on massively parallel machines. The algorithms are based on the multiway merging paradigm. We first outline an algorithm whose I/O requirement is close to a lower bound. Thus, in contrast to naive implementations of multiway merging and all other approaches known to us, the algorithm works with just two passes over the data even for the largest conceivable inputs. A second algorithm reduces communication overhead and uses more conventional specifications of the result at the cost of slightly increased I/O requirements. An implementation wins the well known sorting benchmark in several categories and by a large margin over its competitors.
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arxiv:0910.2582
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Consider the energy critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, under an appropriate smallness assumption, any type II blow-up radial solution is essentially the sum of a rescaled W concentrating at the origin and a small remainder which is continuous with respect to the time variable in the energy space. This is coherent with the solutions constructed by Krieger, Schlag and Tataru. One ingredient of our proof is that the unique radial solution which is compact up to scaling is equal to W up to symmetries.
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arxiv:0910.2594
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Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective integrals. Error bounds for the approximation error are derived and the approximations are used to simulate certain classes of infinitely divisible random fields.
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arxiv:0910.2625
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Suppose that $K$ is a field of characteristic 0, $p$ is an odd prime, $r$ a positive integer, $q=p^r$ a prime power. Suppose that $f(x)$ is a polynomial of degree $n > 4$ with coefficients in $K$ and without multiple roots. Let us consider the superelliptic curve $C: y^q=f(x)$ and its jacobian $J(C)$. Assuming that $K$ is a subfield of the field of complex numbers, we study the (connected reductive algebraic) Hodge group $Hdg$ of the corresponding complex abelian variety $J(C)$. In our previous paper (arXiv:0907.1563 [math.AG]) we studied the center of $Hdg. In this paper we study the semisimple part (commutator subgroup) of $Hdg$. Assuming that $p$ does not divide $n$ and $n-1$ is not divisible by $q$, the Galois group of $f(x)$ over $K$ is either the full symmetric group $S_n$ or the alternating group $A_n$, we prove that the semisimple part of $Hdg$ is "as large as possible".
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arxiv:0910.2676
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We study the effect of magnetism and perpendicular external electric field strengths on the energy gap of length confined bilayer graphene nanoribbons (or nanoflakes) as a function of ribbon width and length using a \textit{first principles} density functional electronic structure method and a semi-local exchange-correlation approximation. We assume AB (Bernal) bilayer stacking and consider both armchair and zigzag edges, and for each edge type, we consider the two edge alignments, namely, $\alpha$ and $\beta$ edge alignment. For the armchair nanoflakes we identify three distinct classes of bilayer energy gaps, determined by the number of carbon chains in the width direction ({\it N} = 3{\it p}, 3{\it p}+1 and 3{\it p}+2, {\it p} is an integer), and the gaps decrease with increasing width except for class 3{\it p}+2 armchair nanoribbons. Metallic-like behavior seen in armchair bilayer nanoribbons are found to be absent in armchair nanoflakes. Class 3{\it p}+2 armchair nanoflakes show significant length dependence. We find that the gaps decrease with the applied electric fields due to large intrinsic gap of the nanoflake. The existence of a critical gap with respect to the applied field, therefore, is not predicted by our calculations. Magnetism between the layers plays a major role in enhancing the gap values resulting from the geometrical confinement, hinting at an interplay of magnetism and geometrical confinement in finite size bilayer graphene.
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arxiv:0910.2719
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We report on the experimental observation of vortex formation and production of tangled vortex distribution in an atomic BEC of Rb-87 atoms submitted to an external oscillatory perturbation. The oscillatory perturbations start by exciting quadrupolar and scissors modes of the condensate. Then regular vortices are observed finally evolving to a vortex tangle configuration. The vortex tangle is a signature of the presence of a turbulent regime in the cloud. We also show that this turbulent cloud has suppression of the aspect ratio inversion typically observed in quantum degenerate bosonic gases during free expansion.
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arxiv:0910.2729
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We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove "algebraic" analogs of classical results. Using a modified version of Quillen's small object argument, we show that every cofibrantly generated model structure in the usual sense underlies a cofibrantly generated algebraic model structure. We show how to pass a cofibrantly generated algebraic model structure across an adjunction, and we characterize the algebraic Quillen adjunction that results. We prove that pointwise natural weak factorization systems on diagram categories are cofibrantly generated if the original ones are, and we give an algebraic generalization of the projective model structure. Finally, we prove that certain fundamental comparison maps present in any cofibrantly generated model category are cofibrations when the cofibrations are monomorphisms, a conclusion that does not seem to be provable in the classical, non-algebraic, theory.
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arxiv:0910.2733
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We define a Regge limit for off-shell Green functions in quantum field theory, and study it in the particular case of conformal field theories (CFT). Our limit differs from that defined in arXiv:0801.3002, the latter being only a particular corner of the Regge regime. By studying the limit for free CFTs, we are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak coupling. The dominance of Feynman graphs where only two high momentum lines are exchanged in the t-channel, follows simply from the free field analysis. We can then define the BFKL kernel in terms of the two point function of a simple light-like bilocal operator. We also include a brief discussion of the gravity dual predictions for the Regge limit at strong coupling.
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arxiv:0910.2746
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Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication [1] advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset--quantum-state space--might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in [1], and all in conformity with quantum theory.
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arxiv:0910.2750
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We characterize a novel orthorhombic phase (gamma) of NaAlH4, discovered using first-principles molecular dynamics, and discuss its relevance to the dehydrogenation mechanism. This phase is close in energy to the known low-temperature structure and becomes the stabler phase above 320 K, thanks to a larger vibrational entropy associated with AlH4 rotational modes. The structural similarity of gamma-NaAlH4 to alpha-Na3AlH6 suggests it acts as a key intermediate during hydrogen release. Findings are consistent with recent experiments recording an unknown phase during dehydrogenation.
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arxiv:0910.2760
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It is shown that within a quantum system, the wave field has a (potential) energy content that can be exchanged with quantum particles. Energy conservation in quantum systems holds if potential energy is correctly taken to be a field attribute. From this perspective, a transfer of energy occurs on measurement from the wave field to a quantum particle and this provides a physical explanation of what is commonly referred to as the collapse of the wavefunction.
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arxiv:0910.2834
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We investigate the relationship between the linewidths of broad Mg II \lambda2800 and Hbeta in active galactic nuclei (AGNs) to refine them as tools to estimate black hole (BH) masses. We perform a detailed spectral analysis of a large sample of AGNs at intermediate redshifts selected from the Sloan Digital Sky Survey, along with a smaller sample of archival ultraviolet spectra for nearby sources monitored with reverberation mapping. Careful attention is devoted to accurate spectral decomposition, especially in the treatment of narrow-line blending and Fe II contamination. We show that, contrary to popular belief, the velocity width of Mg II tends to be smaller than that of Hbeta, suggesting that the two species are not cospatial in the broad-line region. Using these findings and recently updated BH mass measurements from reverberation mapping, we present a new calibration of the empirical prescriptions for estimating virial BH masses for AGNs using the broad Mg II and Hbeta lines. We show that the BH masses derived from our new formalisms show subtle but important differences compared to some of the mass estimators currently used in the literature.
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arxiv:0910.2848
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Densely-packed, all-digital aperture arrays form a key area of technology development required for the Square Kilometre Array (SKA) radio telescope. The design of real-time signal processing systems for digital aperture arrays is currently a central challenge in pathfinder projects worldwide. We describe interim results of such work; an heirarchical, frequency-domain beamforming architecture for synthesising a sky beam from the wideband antenna feeds of digital aperture arrays.
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arxiv:0910.2865
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Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum Mechanics. Such a complementarity is expressed as the impossibility of perform an exact simultaneous determination of the system energy and temperature by using an experimental procedure based on the thermal equilibrium with other system regarded as a measure apparatus (thermometer). In this work, we provide a simple generalization of this latter approach with the consideration of a thermodynamic situation with several control parameters.
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arxiv:0910.2867
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Inclined air showers - those arriving at ground with zenith angle with respect to the vertical theta > 60 deg - are characterised by the dominance of the muonic component at ground which is accompanied by an electromagnetic halo produced mainly by muon decay and muon interactions. By means of Monte Carlo simulations we give a full characterisation of the particle densities at ground in ultra-high energy inclined showers as a function of primary energy and mass composition, as well as for different hadronic models assumed in the simulations. We also investigate the effect of intrinsic shower-to-shower fluctuations in the particle densities.
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arxiv:0910.2873
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An extensive study of the alignment between the pump, the signal and the polarization dependent gain (PDG) vectors in stimulated Brillouin amplification in randomly birefringent fibers is realized by numerically integrating the equations governing the propagation. At the fiber output, the signal tends to align to the PDG vector for large pump power because of the nonlinear polarization pulling effect. The PDG vector, for large random birefringence, aligns to a state that has the same linear component of the pump but opposite circular component.
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arxiv:0910.2893
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We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices.
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arxiv:0910.2910
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We study integrations over light-cone momenta in the gauge invariant effective action of high energy QCD. A regularization mechanism which allows for the evaluation of the longitudinal integrations is presented. After a rederivation of the reggeized gluon and the BFKL-equation from the effective action, we study the 1-3 and 2-4 reggeized gluon transition vertex of QCD Reggeon field theory and discuss their connection with the usual triple Pomeron vertex of perturbative QCD.
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arxiv:0910.2981
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Understanding the nature of neutrino masses will require physics beyond the long-standing Standard Model of particle physics. Neutrinoless double beta decay experiments like the Cryogenic Underground Observatory for Rare Events (CUORE) are uniquely suited for probing the remaining mysteries of neutrino mass, particularly the question of the neutrino's Majorana nature. CUORE will be a next-generation experiment at the Laboratori Nazionali del Gran Sasso in Italy; it will consist of an array of 988 TeO2 detector crystals operated at ~10 mK, following the bolometric technique established by the Cuoricino experiment. It will look for the energy signal produced by the theoretically-predicted neutrinoless double beta decay in Te-130, and therefore reliable energy calibration of the detector is crucial to the experiment's success. We will present the most recent results from Cuoricino and discuss the current status of the CUORE project, with a particular emphasis on the development of the calibration system.
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arxiv:0910.2994
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Let $(F_t)$ be a continuous flow on a topological manifold M. For every open $V \subset M$ denote by P(V) the set of all continuous functions $\alpha:V \to R$ such that $F_{\alpha(z)}(z)=z$ for all $z\in V$. Such functions vanish at non-periodic points and their values at periodic points are equal to the corresponding periods (in general not minimal). They can be used for reparametrizations of flows to circle actions. In this paper P(V) is described for connected open subsets V, which extends previous results of the author. It is also shown that there is a difference between the sets P(V) for $C^{0}$ and $C^1$ flows.
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arxiv:0910.2995
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The Bc meson is composed of two heavy quarks of distinct flavor. Measurements of its lifetime and production properties have been made based on semileptonic Bc to J/psi+l+X decays using data collected with the CDF II detector corresponding to an integrated luminosity of 1 fb-1. The Bc average lifetime ctau is measured to be 142.5+15.8-14.8(stat) 5.5(syst) mum. The measurements of the ratio of the production cross section times branching ratio of Bc to J/psi+mu+nu relative to B+ to J/psi+K were done for two pT(B) thresholds: for pT(B) greater 4 GeV/c as 0.295+/-0.040(stat)+0.033-0.026(syst.)0.036(pT spectrum) and for pT(B) greater 6 GeV/c as 0.227+/-0.033(stat)+0.024-0.017(syst.)+/-0.014(pT spectrum).
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arxiv:0910.3013
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Using scanning tunneling microscopy and Ginzburg-Landau simulations we explore vortex configurations in magnetically coupled NbSe$_2$-Permalloy superconductor-ferromagnet bilayer. The Permalloy film with stripe domain structure induces periodic local magnetic induction in the superconductor creating a series of pinning-antipinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-1D arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the system becomes non-linear due to a change in both the number of vortices and the confining potential. The longitudinal instabilities of the resulting vortex structures lead to vortices `levitating' in the anti-pinning channels.
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arxiv:0910.3030
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We present the geometry of pure states of an ensemble of N spin-J systems using a generalisation of the Majorana representation. The approach is based on Schur-Weyl duality that allows for simple interpretation of the state transformation under the action of general linear and permutation groups. We show an exemplary application in theory of decoherence free subspaces and noiseless subsystems.
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arxiv:0910.3075
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The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.
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arxiv:0910.3220
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A new class of solutions to the coupled, spherically symmetric Einstein-Maxwell equations for a compact material source is constructed. Some of these solutions can be made to satisfy a number of requirements for being physically relevant, including having a causal speed of sound. In the case of vanishing charge these solutions reduce to those found by Bayin and Tolman. Only the latter can be considered as having physically realistic properties.
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arxiv:0910.3230
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When micrometric drops coalesce in-plane on a superhydrophobic surface, a surprising out-of-plane jumping motion was observed. Such jumping motion triggered by drop coalescence was reproduced on a Leidenfrost surface. High-speed imaging revealed that this jumping motion results from the elastic interaction of the bridged drops with the superhydrophobic/Leidenfrost surface. Experiments on both the superhydrophobic and Leidenfrost surfaces compare favorably to a simple scaling model relating the kinetic energy of the merged drop to the surface energy released upon coalescence. The spontaneous jumping motion on water repellent surfaces enables the autonomous removal of water condensate independently of gravity; this process is highly desirable for sustained dropwise condensation.
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arxiv:0910.3238
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On the basis of a moment method, general solutions of a linearized Boltzmann equation for a normal Fermi system are investigated. In particular, we study the sound velocities and damping rates as functions of the temperature and the coupling constant. In the extreme limits of collisionless and hydrodynamic regimes, eigenfrequency of sound mode obtained from the moment equations reproduces the well-known results of zero sound and first sound. In addition, the moment method can describe crossover between those extreme limits at finite temperatures. Solutions of the moment equations also involve a thermal diffusion mode. From solutions of these equations, we discuss excitation spectra corresponding to the particle-hole continuum as well as collective excitations. We also discuss a collective mode in a weak coupling case.
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arxiv:0910.3283
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A concept of the total velocity that contains velocity and oscillatory velocity is proposed for the velocity solution of Dirac equation. It is shown that the electronic rest energy all comes from the oscillation of the electron itself. For this reason, the velocity solution of Dirac equation is taken as the definition of elementary particles. Leptons, mesons and baryons appear in results as the newly defined elementary particles, but the particle that consists of more than three quarks is ruled out. The results also show that a quark is not a particle, but part of the hadron or a partial particle and that quark confinement may serve as an evidence of this conclusion.
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arxiv:0910.3286
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We present results on the electromagnetic and axial nucleon form factors using two degenerate flavors of twisted mass fermions on lattices of spatial size 2.1 fm and 2.7 fm and a lattice spacing of about 0.09 fm. We consider pion masses in the range of 260-470 MeV. We chirally extrapolate results on the nucleon axial ch arge, the isovector Dirac and Pauli root mean squared radii and magnetic moment to the physical point and co mpare to experiment.
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arxiv:0910.3309
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We studied how the intergalactic magnetic field (IGMF) affects the propagation of super-GZK protons that originate from extragalactic sources within the local GZK sphere. Toward this end, we set up hypothetical sources of ultra-high-energy cosmic-rays (UHECRs), virtual observers, and the magnetized cosmic web in a model universe constructed from cosmological structure formation simulations. We then arranged a set of reference objects mimicking active galactic nuclei (AGNs) in the local universe, with which correlations of simulated UHECR events are analyzed. With our model IGMF, the deflection angle between the arrival direction of super-GZK protons and the sky position of their actual sources is quite large with the mean value of $<\theta > \sim 15^{\circ}$ and the median value of $\tilde \theta \sim 7 - 10^{\circ}$. On the other hand, the separation angle between the arrival direction and the sky position of nearest reference objects is substantially smaller with $<S > \sim 3.5 - 4^{\circ}$, which is similar to the mean angular distance in the sky to nearest neighbors among the reference objects. This is a direct consequence of our model that the sources, observers, reference objects, and the IGMF all trace the matter distribution of the universe. The result implies that extragalactic objects lying closest to the arrival direction of UHECRs are not necessary their actual sources. With our model for the distribution of reference objects, the fraction of super-GZK proton events, whose closest AGNs are true sources, is less than 1/3. We discussed implications of our findings for correlation studies of real UHECR events.
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arxiv:0910.3361
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Shack Hartmann wavefront sensor is a two dimensional array of lenslets which is used to detect the incoming phase distorted wavefront through local tilt measurements made by recording the spot pattern near the focal plane. Wavefront reconstruction is performed in two stages - (a) image centroiding to calculate local slopes, (b) formation of the wavefront shape from local slope measurement. Centroiding accuracy contributes to most of the wavefront reconstruction error in Shack Hartmann sensor based adaptive optics system with readout and background noise. It becomes even more difficult in atmospheric adaptive optics case, where scintillation effects may also occur. In this paper we used a denoising technique based on thresholded Zernike reconstructor to minimize the effects due to readout and background noise. At low signal to noise ratio, this denoising technique can be improved further by taking the advantage of the shape of the spot. Assuming a Gaussian pattern for individual spots, it is shown that the centroiding accuracy can be improved in the presence of strong scintillations and background.
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arxiv:0910.3386
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Liquid Argon Time Projection Chamber detectors are ideally suited for studying neutrino interactions and probing the parameters that characterize neutrino oscillations. The ability to drift ionization particles over long distances in purified argon and to trigger on abundant scintillation light allows for excellent particle identification and triggering capability. In these proceedings the details of the ArgoNeuT test-beam project will be presented after a brief introduction to the detector technique. ArgoNeuT is a 175 liter detector exposed to Fermilab's NuMI neutrino beamline. The first neutrino interactions observed in ArgoNeuT will be presented, along with discussion of the various physics analyses to be performed on this data sample.
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arxiv:0910.3433
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How to find "best rational approximations" of maximal commutative subgroups of GL(n,R)? In this paper we pose and make first steps in the study of this problem. It contains both classical problems of Diophantine and simultaneous approximations as a particular subcases but in general is much wider. We prove estimates for n=2 for both totaly real and complex cases and write the algorithm to construct best approximations of a fixed size. In addition we introduce a relation between best approximations and sails of cones and interpret the result for totally real subgroups in geometric terms of sails.
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arxiv:0910.3482
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In this contribution we review recent efforts on investigations of the effect of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We demonstrate the applicability of the method to treat fundamental questions in microfluidics by investigating fluid flow in hydrophobic and rough microchannels as well as over surfaces covered by nano- or microscale gas bubbles.
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arxiv:0910.3492
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The limits placed by the non-measurement of atomic and neutron electric dipole moments on CP violating phases beyond the SM are found to be not fully justified since the calculations of the expected EDMs lack the full understanding of the connection between perturbative and nonperturbative regimes of QCD for the measured boundstates. As a consequence rather old subroutines for the evaluation of EDMs are still usable.
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arxiv:0910.3512
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We use Halpha and FUV GALEX data for a large sample of nearby objects to study the high mass star formation activity of normal late-type galaxies. The data are corrected for dust attenuation using the most accurate techniques at present available, namely the Balmer decrement and the total far-infrared to FUV flux ratio. The sample shows a highly dispersed distribution in the Halpha to FUV flux ratio indicating that two of the most commonly used star formation tracers give star formation rates with uncertainties up to a factor of 2-3. The high dispersion is due to the presence of AGN, where the UV and the Halpha emission can be contaminated by nuclear activity, highly inclined galaxies, for which the applied extinction corrections are probably inaccurate, or starburst galaxies, where the stationarity in the star formation history required for transforming Halpha and UV luminosities into star formation rates is not satisfied. Excluding these objects we reach an uncertainty of ~50% on the SFR. The Halpha to FUV flux ratio increases with their total stellar mass. If limited to normal star forming galaxies, however, this relationship reduces to a weak trend that might be totally removed using different extinction correction recipes. In these objects the Halpha to FUV flux ratio seems also barely related with the FUV-H colour, the H band effective surface brightness, the total star formation activity and the gas fraction. The data are consistent with a Kroupa and Salpeter initial mass function in the high mass stellar range and imply, for a Salpeter IMF, that the variations of the slope cannot exceed 0.25, from g=2.35 for massive galaxies to g=2.60 in low luminosity systems. We show however that these observed trends, if real, can be due to the different micro history of star formation in massive galaxies with respect to dwarf.
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arxiv:0910.3521
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The suppression of high transverse momentum P_T hadron production in ultrarelativistic heavy-ion (A-A) collisions as compared to the scaled expectation from proton-proton (p-p) collisions expressed as the nuclear modification factor R_AA is experimentally well established and can be traced back to interactions between the hard parton shower and the soft bulk matter. Physical intuition suggests that the medium modification should cease to be important when the hard scale of parton production is much larger than the typical momentum scale in the medium (e.g. the temperature T) and that consequently R_AA(P_T) -> 1 for P_T >> T. However, R_AA is not a 'simple' observable, but rather results from many different mechanisms which influence what happens when P_T increases. In particular, R_AA does not necessarily approch unity even if the hadron momentum is probed at the kinematic limit of the reaction. The aim of this work is to identify and discuss such mechanisms and to present different model expectations of what one would find if one could measure suppression out to the kinematic limit for hard hadron production and give predictions for the P_T dependence at both RHIC and LHC.
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arxiv:0910.3528
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Inspired by recent activities on Whittaker modules over various (Lie) algebras we describe some general framework for the study of Lie algebra modules locally finite over a subalgebra. As a special case we obtain a very general setup for the study of Whittaker modules, which includes, in particular, Lie algebras with triangular decomposition and simple Lie algebras of Cartan type. We describe some basic properties of Whittaker modules, including a block decomposition of the category of Whittaker modules and certain properties of simple Whittaker modules under some rather mild assumptions. We establish a connection between our general setup and the general setup of Harish-Chandra subalgebras in the sense of Drozd, Futorny and Ovsienko. For Lie algebras with triangular decomposition we construct a family of simple Whittaker modules (roughly depending on the choice of a pair of weights in the dual of the Cartan subalgebra), describe their annihilators and formulate several classification conjectures. In particular, we construct some new simple Whittaker modules for the Virasoro algebra. Finally, we construct a series of simple Whittaker modules for the Lie algebra of derivations of the polynomial algebra, and consider several finite dimensional examples, where we study the category of Whittaker modules over solvable Lie algebras and their relation to Koszul algebras.
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arxiv:0910.3540
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We provide an example of a spectrum over S^0 with an H_\infty structure which does not rigidify to an E_3 structure. It follows that in the category of spectra over S^0 not every H_\infty ring spectrum comes from an underlying E_\infty ring spectrum. After comparing definitions, we obtain this example by applying \Sigma^\infty_+ to the counterexample to the transfer conjecture constructed by Kraines and Lada.
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arxiv:0910.3566
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The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlinearity is "supercritical" in the case of two and three space dimensions. Thus the standard methods used for studying semilinear hyperbolic equations are not very effective in the present case. Nevertheless, we have recently proven the global existence and dissipativity of strong solutions in the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case with small inertial coefficient and arbitrary growth rate of the nonlinearity. The present contribution studies the long-time behavior of rather weak (energy) solutions of that equation and it is a natural complement of the results of our previous papers. Namely, we prove here that the attractors for energy and strong solutions coincide for both the cases mentioned above. Thus, the energy solutions are asymptotically smooth. In addition, we show that the non-smooth part of any energy solution decays exponentially in time and deduce that the (smooth) exponential attractor for the strong solutions constructed previously is simultaneously the exponential attractor for the energy solutions as well.
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arxiv:0910.3583
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We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and $\Lambda > 0$, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations (due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive.
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arxiv:0910.3637
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We present results of variability search in the field of the young open cluster NGC 1502. Eight variable stars were discovered. Of six other stars in the observed field that were suspected for variability, we confirm variability of two, including one beta Cep star, NGC 1502-26. The remaining four suspects were found to be constant in our photometry. In addition, UBVI photometry of the well-known massive eclipsing binary SZ Cam was obtained. The new variable stars include: two eclipsing binaries of which one is a relatively bright detached system with an EA-type light curve, an alpha2 CVn-type variable, an SPB candidate, a field RR Lyrae star and three other variables showing variability of unknown origin. The variability of two of them is probably related to their emission in Halpha, which has been measured by means of the alpha index obtained for 57 stars brighter than V=16 mag in the central part of the observed field. Four other non-variable stars with emission in Halpha were also found. Additionally, we provide VI photometry for stars down to V=17 mag and UB photometry for about 50 brightest stars in the observed field. We also show that the 10-Myr isochrone fits very well the observed color-magnitude diagram if a distance of 1 kpc and mean reddening, E(V-I)=0.9 mag, are adopted.
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arxiv:0910.3672
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These are notes associated with three lectures given at the 49th Cracow School of Theoretical physics where a pedagogical explanation of the Gross-Witten transition, Eguchi-Kawai reduction and continuum reduction were given, followed by a description of the numerical computation of fermionic observables in the 't Hooft limit of large N gauge theory.
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arxiv:0910.3711
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We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we obtain free of eigenvalues regions. As an application, we get exponential decay of the energy of the solutions of the correpsonding mixed boundary value problems.
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arxiv:0910.3778
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We propose near-infrared colour selection criteria to extract Active Galactic Nuclei (AGNs) using the near-infrared Colour-Colour Diagram (CCD) and predict near-infrared colour evolution with respect to redshift. First, we cross-identify two AGN catalogues with the 2MASS Point Source Catalogue, and confirm both the loci of quasars/AGNs in the near-infrared CCD and redshift-colour relations. In the CCD, the loci of over 70 - 80% of AGNs can be distinguished from the stellar locus. To examine the colours of quasars, we simulate near-infrared colours using Hyperz code. Assuming a realistic quasar SED, we derive simulated near-infrared colours of quasars with redshift (up to z ~ 11). The simulated colours can reproduce not only the redshift-colour relations but also the loci of quasars/AGNs in the near-infrared CCD. We finally discuss the possibility of contamination by other types of objects. We compare the locus of AGNs with the other four types of objects (namely, microquasars, CVs, LMXBs, and MYSOs) which have a radiation mechanism similar to that of AGNs. In the near-infrared CCD, each type of object is located at a position similar to the stellar locus. Accordingly, it is highly probable that the four types of objects can be distinguished on the basis of the locus in a near-infrared CCD. We additionally consider contamination by distant normal galaxies. The near-infrared colours of several types of galaxies are also simulated using the Hyperz code. Although galaxies with z ~ 1 have near-infrared colours similar to those of AGNs, these galaxies are unlikely to be detected because they are very faint. In other words, few galaxies should contaminate the locus of AGNs in the near-infrared CCD. Consequently, we can extract reliable AGN candidates on the basis of the near-infrared CCD.
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arxiv:0910.3804
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Recent results on pion physics from lattice QCD are reviewed. We discuss quark mass dependences of pion mass and decay constant and compare them with the predictions from chiral perturbation theory. In particular we focus on the convergence of chiral perturbation theory around strange quark mass region. We also consider quark mass as well as momentum dependences of pion form factors in recent full QCD simulations.
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arxiv:0910.3806
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We consider the effects of material flows on the dynamics of toroidal magnetic flux tubes located close to the base of the solar convection zone, initially within the overshoot region. The problem is to find the physical conditions in which magnetic flux can be stored for periods comparable to the dynamo amplification time, which is of the order of a few years. We carry out nonlinear numerical simulations to investigate the stability and dynamics of thin flux tubes subject to perpendicular and longitudinal flows. We compare the simulations with the results of simplified analytical approximations. We determine ranges of the flow parameters for which a linearly Parker-stable magnetic flux tube is stored in the middle of the overshoot region for a period comparable to the dynamo amplification time. The residence time for magnetic flux tubes with fluxes of 2x10^{21} Mx in the convective overshoot layer is comparable to the dynamo amplification time, provided that the average speed and the duration of the downflow do not exceed about 50 m/s and 100 days, respectively, and that the lateral extension of the flow is smaller than about 10 degrees.
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arxiv:0910.3858
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We propose that Kibble-Zurek scaling can be studied in optical lattices by creating geometries that support, Dirac, Semi-Dirac and Quadratic Band Crossings. On a Honeycomb lattice with fermions, as a staggered on-site potential is varied through zero, the system crosses the gapless Dirac points, and we show that the density of defects created scales as $1/\tau$, where $\tau$ is the inverse rate of change of the potential, in agreement with the Kibble-Zurek relation. We generalize the result for a passage through a semi-Dirac point in $d$ dimensions, in which spectrum is linear in $m$ parallel directions and quadratic in rest of the perpendicular $(d-m)$ directions. We find that the defect density is given by $ 1 /{\tau^{m\nu_{||}z_{||}+(d-m)\nu_{\perp}z_{\perp}}}$ where $\nu_{||}, z_{||}$ and $\nu_{\perp},z_{\perp}$ are the dynamical exponents and the correlation length exponents along the parallel and perpendicular directions, respectively. The scaling relations are also generalized to the case of non-linear quenching.
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arxiv:0910.3896
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We derive analytical forms for non-flow contributions from cluster correlation to two-particle elliptic flow (v2{2}) measure. We also derive an analytical form for jet-correlation flow-background with the same cluster approach. We argue that the elliptic flow v2 parameter to be used in jet-correlation background is that from two-particle method excluding non-flow correlations unrelated to the reaction plane, but including cross-terms between cluster correlation and cluster flow. We verify our result with Monte Carlo simulations. We discuss how one may obtain the v2 parameter for jet-correlation background experimentally.
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arxiv:0910.3902
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We present time-dependent density matrix renormalization group (DMRG) results for strongly interacting one dimensional fermionic systems at finite temperature. When interactions are strong the characteristic spin energy can be greatly suppressed relative to the characteristic charge energy, allowing for the possibility of spin-incoherent Luttinger liquid physics when the temperature is high compared to the spin energy, but small compared to the charge energy. Using DMRG we compute the spectral properties of the $t-J$ model at arbitrary temperatures with respect to both spin and charge energies. We study the full crossover from the Luttinger liquid regime to the spin-incoherent regime,focusing on small $J/t$, where the signatures of spin-incoherent behavior are more manifest. Our method allows us to access the analytically intractable regime where temperature is of the order of the spin energy, $T\sim J$. Our results should be helpful in the interpretation of experiments that may be in the crossover regime, $T\sim J$, and apply to one-dimensional cold atomic gases where finite-temperature effects are appreciable. The technique may also be used to guide the development of analytical approximations for the crossover regime.
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arxiv:0910.3957
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Long, stable and free-standing linear atomic carbon wires have been carved out from graphene recently [Meyer et al: Nature (London) 2008, 454, 319; Jin et al: Phys: Rev: Lett: 2009, 102, 205501]. They can be considered as the extremely narrow graphene nanoribbons or extremely thin carbon nanotubes. It might even be possible to make use of high strength and identical (without charity) carbon wires as a transport channel or on-chip interconnects for field-effect transistors. Here we investigate electron transport properties of linear atomic carbon wire-graphene junctions by nonequilibruim Green's function combined with density functional theory. For short wires, linear ballistic transport is observed in odd-numbered wire but destroyed by Peirerls distortion in even-numbered wire. For wires longer than 2.1 nm as fabricated above, however, the ballistic conductance of carbon wire-graphene junctions is remarkably robust against the Peierls distortion, structural imperfections, and hydrogen impurity adsorption of the linear carbon wires except oxygen impurities. As such, the epoxy groups might be the origin of low conductance experimentally observed in carbon wires. Moreover, double atomic carbon wires exhibit negative differential resistance (NDR) effect.
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arxiv:0910.4006
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When studying the information leakage in programs or protocols, a natural question arises: "what is the worst case scenario?". This problem of identifying the maximal leakage can be seen as a channel capacity problem in the information theoretical sense. In this paper, by combining two powerful theories: Information Theory and Karush-Kuhn-Tucker conditions, we demonstrate a very general solution to the channel capacity problem. Examples are given to show how our solution can be applied to practical contexts of programs and anonymity protocols, and how this solution generalizes previous approaches to this problem.
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arxiv:0910.4033
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We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the germs is a rational homology sphere. In the case of several sub-families we provide explicit formulas in terms of the Seifert invariants (generalizing results of Wagreich and VanDyke), and we also provide key examples showing that, in general, these invariants are not topological. We extend the discussion to the case of splice--quotient singularities with star--shaped graph as well.
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arxiv:0910.4035
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Since the first reports of oscillations in prominences in 1930s there have been major theoretical and observational advances to understand the nature of these oscillatory phenomena leading to a whole new field of so called "prominence seismology". There are two types of oscillatory phenomena observed in prominences; "small amplitude oscillations" (~2-3 km s$^{-1}$) which are quite common and "large amplitude oscillations" ($>$20 km s$^{-1}$) for which observations are scarce. Large amplitude oscillations have been found as "winking filament" in H$\alpha$ as well as motion in the sky plane in H$\alpha$, EUV, micro-wave and He 10830 observations. Historically, it was suggested that the large amplitude oscillations in prominences were triggered by disturbances such as fast-mode MHD waves (Moreton wave) produced by remote flares. Recent observations show, in addition, that near-by flares or jets can also create such large amplitude oscillations in prominences. Large amplitude oscillations, which are observed both in transverse as well as longitudinal direction, have a range of periods varying from tens of minutes to a couple of hours. Using the observed period of oscillation and simple theoretical models, the obtained magnetic field in prominences has shown quite a good agreement with directly measured one and therefore, justifies prominences seismology as a powerful diagnostic tool. On rare occasions, when the large amplitude oscillations have been observed before or during the eruption, the oscillations may be applied to diagnose the stability and the eruption mechanism. Here we review the recent developments and understanding in the observational properties of large amplitude oscillations and their trigger mechanisms and stability in the context of prominence seismology.
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arxiv:0910.4059
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Let S1(Gamma,Gamma) be the statement: For each sequence of point-cofinite open covers, one can pick one element from each cover and obtain a point-cofinite cover. b is the minimal cardinality of a set of reals not satisfying S1(Gamma,Gamma). We prove the following assertions: (1) If there is an unbounded tower, then there are sets of reals of cardinality b, satisfying S1(Gamma,Gamma). (2) It is consistent that all sets of reals satisfying S1(Gamma,Gamma) have cardinality smaller than b. These results can also be formulated as dealing with Arhangel'skii's property alpha_2 for spaces of continuous real-valued functions. The main technical result is that in Laver's model, each set of reals of cardinality b has an unbounded Borel image in the Baire space w^w.
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arxiv:0910.4063
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In this paper, we consider lower order eigenvalues of Laplacian operator with any order in Euclidean domains. By choosing special rectangular coordinates, we obtain two estimates for lower order eigenvalues.
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arxiv:0910.4101
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We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly used in mathematical finance for modelling asset prices, market indices, and interest rates. We show how the probability distributions of a squared Bessel bridge and a squared Bessel process with or without absorption at zero are reduced to randomized gamma distributions. Moreover, for absorbing stochastic processes, we develop a new bridge sampling technique based on conditioning on the first hitting time at zero. Such an approach allows us to simplify simulation schemes. New methods are illustrated with pricing path-dependent options.
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arxiv:0910.4177
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Given a flag in each of the vertex-transitive tessellations of the Euclidean plane by regular polygons, we determine the flag stabilizer under the action of the automorphism group of a regular cover. In so doing we give a presentation of these tilings as quotients of regular (infinite) polyhedra.
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arxiv:0910.4207
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We show that 3-fold terminal flips and divisorial contractions to a curve may be factored by a sequence of weighted blow-ups, flops, blow-downs to a locally complete intersection curve in a smooth 3-fold or divisorial contractions to a point.
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arxiv:0910.4209
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We provide sufficient conditions which ensure that the intrinsic martingale in the supercritical branching random walk converges exponentially fast to its limit. The case of Galton-Watson processes is particularly included so that our results can be seen as a generalization of a result given in the classical treatise by Asmussen and Hering. As an auxiliary tool, we prove ultimate versions of two results concerning the exponential renewal measures which may be interesting on its own and which correct, generalize and simplify some earlier works.
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arxiv:0910.4246
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We present results of the Suzaku observation of the dipping, periodically bursting low mass X-ray binary XB 1323-619 in which we concentrate of the spectral evolution in dipping in the energy range 0.8 - 70 keV. It is shown that spectral evolution in dipping is well-described by absorption on the bulge in the outer accretion disk of two continuum components: emission of the neutron star plus the dominant, extended Comptonized emission of the accretion disk corona (ADC). This model is further supported by detection of a relatively small, energy-independent decrease of flux above 20 keV due to Thomson scattering. It is shown that this is consistent with the electron scattering expected of the bulge plasma. We address the recent proposal that the dip sources may be explained by an ionized absorber model giving a number of physical arguments against this model. In particular, that model is inconsistent with the extended nature of the ADC for which the evidence is now overwhelming.
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arxiv:0910.4258
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We explore radio and spectroscopic properties of a sample of 14 miniature radio galaxies, i.e. early-type core galaxies hosting radio-loud AGN of extremely low radio power, 10^(27-29) erg s^(-1) Hz^(-1) at 1.4 GHz. Miniature radio galaxies smoothly extend the relationships found for the more powerful FRI radio galaxies between emission line, optical and radio nuclear luminosities to lower levels. However, they have a deficit of a factor of ~100 in extended radio emission with respect to that of the classical example of 3CR/FRI. This is not due to their low luminosity, since we found radio galaxies of higher radio core power, similar to those of 3CR/FRI, showing the same behavior, i.e. lacking significant extended radio emission. Such sources form the bulk of the population of radio-loud AGN in the Sloan Digital Sky Survey. At a given level of nuclear emission, one can find radio sources with an extremely wide range, a factor of >~100, of radio power. We argue that the prevalence of sources with luminous extended radio structures in flux limited samples is due to a selection bias, since the inclusion of such objects is highly favored. The most studied catalogues of radio galaxies are thus composed by the minority of radio-loud AGN that meet the physical conditions required to form extended radio sources, while the bulk of the population is virtually unexplored.
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arxiv:0910.4261
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The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale R^{-1}, where R is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order R^{-2}, and it is carried out through order R^{-4}. The metric is parameterized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning: The advanced-time coordinate $v$ is constant on past light cones that converge toward the black hole; the angles theta and phi are constant on the null generators of each light cone; and the radial coordinate r is an affine parameter on each generator, which decreases as the light cones converge toward the black hole. The coordinates are well-behaved on the black-hole horizon, and they are adjusted so that the coordinate description of the horizon is the same as in the Schwarzschild geometry: r = 2M. At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry and dynamics of the horizon, and calculate the rate at which the black-hole surface area increases as a result of the tidal interaction.
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arxiv:0910.4311
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In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses a question of K. Grove's about Riemannian submersions from Lie groups.
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arxiv:0910.4344
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We present the calculations of the complete next-to-leading order (NLO) QCD effects on the single top productions induced by model-independent $tqg$ flavor-changing neutral-current couplings at hadron colliders. Our results show that, for the $tcg$ coupling the NLO QCD corrections can enhance the total cross sections by about 60% and 30%, and for the $tug$ coupling by about 50% and 20% at the Tevatron and LHC, respectively, which means that the NLO corrections can increase the experimental sensitivity to the FCNC couplings by about 10%$-$30%. Moreover, the NLO corrections reduce the dependence of the total cross sections on the renormalization or factorization scale significantly, which lead to increased confidence on the theoretical predictions. Besides, we also evaluate the NLO corrections to several important kinematic distributions, and find that for most of them the NLO corrections are almost the same and do not change the shape of the distributions.
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arxiv:0910.4349
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We demonstrate the existence of superscarring in the LiNC=LiCN isomerization reaction described by a realistic potential interaction in the range of readily attainable experimental energies. This phenomenon arises as the effect of two periodic orbits appearing "out of the blue"in a saddle--node bifurcation taking place in the dynamics of the system. Potential practical consequences of this superlocalization in the corresponding wave functions are also considered.
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arxiv:0910.4365
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We report the discovery of radio afterglow emission from the gamma-ray burst GRB 090423, which exploded at a redshift of 8.3, making it the object with the highest known redshift in the Universe. By combining our radio measurements with existing X-ray and infrared observations, we estimate the kinetic energy of the afterglow, the geometry of the outflow and the density of the circumburst medium. Our best fit model is a quasi-spherical, high-energy explosion in a low, constant-density medium. \event had a similar energy release to the other well-studied high redshift GRB 050904 ($z=6.26$), but their circumburst densities differ by two orders of magnitude. We compare the properties of \event with a sample of GRBs at moderate redshifts. We find that the high energy and afterglow properties of \event are not sufficiently different from other GRBs to suggest a different kind of progenitor, such as a Population III star. However, we argue that it is not clear that the afterglow properties alone can provide convincing identification of Population III progenitors. We suggest that the millimeter and centimeter radio detections of \event at early times contained emission from a reverse shock component. This has important implications for the detection of high redshift GRBs by the next generation of radio facilities.
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arxiv:0910.4367
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We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion.
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arxiv:0910.4369
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High-beta superconducting radiofrequency (SRF) elliptical cavities are being developed for several accelerator projects including Project X, the European XFEL, and the International Linear Collider (ILC). Fermilab has recently established an extensive infrastructure for SRF cavity R&D for future accelerators, including cavity surface processing and testing and cavity assembly into cryomodules. Some highlights of the global effort in SRF R&D toward improving cavity performance, and Fermilab SRF cavity R&D in the context of global projects are reviewed.
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arxiv:0910.4384
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Experiments have shown that the tunneling current in a Co/Al$_2$O$_3$ magnetic tunneling junction (MTJ) is positively spin polarized, opposite to what is intuitively expected from standard tunneling theory which gives the spin polarization as exclusively dependent on the density of states (DOS) at $E_F$ of the Co layers. Here we report theoretical results that give a positive tunneling spin polarization and tunneling magnetoresistance (TMR) that is in good agreement with experiments. From density functional theory (DFT) calculations, an Al-rich interface MTJ with atomic-level disorder is shown to have a positively polarized DOS near the interface. We also provide an atomic model calculation which gives insights into the source of the positive polarization. A layer and spin dependent effective mass model, using values extracted from the DFT results, is then used to calculate the tunneling current, which shows positive spin polarization. Finally, we calculate the TMR from the tunneling spin polarization which shows good agreement with experiments.
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arxiv:0910.4415
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Syntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Having defined syntomic cohomology with compact supports of an abelian sheaf G on a k-scheme X, we show that it coincides with etale cohomology with compact supports when G is a lisse sheaf. If moreover the convergent F-isocrystal associated to G comes from an overconvergent isocrystal E, then the rigid cohomology of E expresses as a limit of syntomic cohomologies: then the etale cohomology with compact supports of G is the fixed points of Frobenius acting on the rigid cohomology of E.
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arxiv:0910.4436
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We consider spectroscopies of strongly interacting atomic gases, and we propose a model for describing the coupling between quasiparticles and gapless phonon-like modes. Our model explains features in a wide range of different experiments in both fermionic and bosonic atom gases in various spectroscopic methods.
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arxiv:0910.4447
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For a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the (non)binary Hamming cube, and algebras arising in SDP-hierarchies for coding bounds using moment matrices. We give a computationally efficient block diagonalization of A in terms of a given block diagonalization of B, and work out some examples, including the Terwilliger algebra of the binary- and nonbinary Hamming cube. As a tool we use some basic facts about representations of the symmetric group.
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arxiv:0910.4515
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Motivated by the phenomenological scenario of the chiral magnetic effect that can be possibly found in high-energy heavy ion collisions, we study the role of very intense magnetic fields and strong CP violation in the phase structure of strong interactions and, more specifically, their influence on the nature of the chiral transition. Direct implications for the dynamics of phase conversion and its time scales are briefly discussed. Our results can also be relevant in the case of the early universe.
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arxiv:0910.4525
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We report on two different manipulation procedures of a tunable rf SQUID. First, we operate this system as a flux qubit, where the coherent evolution between the two flux states is induced by a rapid change of the energy potential, turning it from a double well into a single well. The measured coherent Larmor-like oscillation of the retrapping probability in one of the wells has a frequency ranging from 6 to 20 GHz, with a theoretically expected upper limit of 40 GHz. Furthermore, here we also report a manipulation of the same device as a phase qubit. In the phase regime, the manipulation of the energy states is realized by applying a resonant microwave drive. In spite of the conceptual difference between these two manipulation procedures, the measured decay times of Larmor oscillation and microwave-driven Rabi oscillation are rather similar. Due to the higher frequency of the Larmor oscillations, the microwave-free qubit manipulation allows for much faster coherent operations.
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arxiv:0910.4562
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I discuss a family of statistical-mechanics models in which (some classes of) elements of a finite group $G$ occupy the (directed) edges of a lattice; the product around any plaquette is constrained to be the group identity $e$. Such a model may possess topological order, i.e. its equilibrium ensemble has distinct, symmetry-related thermodynamic components that cannot be distinguished by any local order parameter. In particular, if $G$ is a non-abelian group, the topological order may be non-abelian. Criteria are given for the viability of particular models, in particular for Monte Carlo updates.
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arxiv:0910.4574
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The centers of bulges are formed dissipationally via gas inflows over short timescales: the 'starburst' mode of star formation (SF). Recent work has shown that detailed observations can be used to separate the stellar mass profile of these 'burst relic' components in local systems. Together with the assumption that some Kennicutt-Schmidt law holds, and that the burst was indeed a dissipational gas-rich event, we show that the observed profiles can be inverted to obtain the time and space-dependent SF history of each burst. Performing this with a large sample of well-studied spheroids, we show that the implied bursts scale in magnitude, mass, peak SFR, and spatial extent with galaxy mass in simple manner, and provide fits to these correlations. Burst masses are ~10% the total spheroid mass; timescales a mass-independent ~10^8 yr; peak SFR ~M_burst/t_burst; and they decay in power-law fashion ~t^-2.4. Sizes are ~0.1 R_e(spheroid), but grow with time. Combined with measurements of the nuclear stellar population ages of these systems (i.e. burst times), it is possible to re-construct the burst contribution to the distribution of SFRs and IR luminosity functions at all redshifts. The burst LF agrees well with observed IR LFs at the brightest luminosities, at z=0-2. At low-L, bursts are always unimportant; the transition to their importance increases from ULIRG luminosities at z~0 to HyLIRG luminosities at z~2. At all redshifts, bursts are a small fraction (~5-10%) of the total SFR density. We discuss possible implications of tension between maximum relic stellar mass densities in massive systems, and estimated number counts of brightest sub-millimeter galaxies.
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arxiv:0910.4582
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We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as \delta_l ~ \pi/\gamma_max, where \gamma_max is the effective maximum extent of the partial spherical maps. We propose a correction algorithm to reduce systematic effects on the estimated C_l, as obtained from the partial map projection on the spherical harmonic Ylm(l,m) basis. We have derived near optimal bands and weighting functions in l-space for power spectrum calculation using small maps, and a correction algorithm for partially masked spherical maps that contain information on the angular correlations on all scales.
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arxiv:0910.4623
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