Date: Fri, 28 Oct 11 00:07:59 GMT Subject: math-ph daily 9 new + 5 crosses received by eprepget ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Send any comments regarding submissions directly to submitter. ------------------------------------------------------------------------------ Archives at http://arxiv.org/ To unsubscribe, e-mail To: math-ph@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received by eprepget from Wed 26 Oct 11 20:00:00 GMT to Thu 27 Oct 11 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1110.5921 Date: Wed, 26 Oct 2011 20:14:39 GMT (179kb,D) Title: Symmetry Preserving Numerical Schemes for Partial Differential Equations and their Numerical Tests Authors: Rapha\"el Rebelo and Francis Valiquette Categories: math-ph math.MP math.NA Comments: 18 pages, 9 figures MSC-class: 58J70, 68N06 \\ The method of equivariant moving frames on multi-space is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-dimensional symmetry groups. Invariant numerical schemes for a heat equation with a logarithmic source and the spherical Burgers equation are obtained. Numerical tests show how invariant schemes can be more accurate than standard discretizations on uniform rectangular meshes. \\ ( http://arxiv.org/abs/1110.5921 , 179kb) ------------------------------------------------------------------------------ \\ arXiv:1110.5940 Date: Wed, 26 Oct 2011 22:18:40 GMT (1121kb) Title: Unified Analytical Solution for Radial Flow to a Well in a Confined Aquifer Authors: Phoolendra Kumar Mishra and Velimir V. Vesselinov Categories: math-ph math.MP \\ Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper [1967]; Hantush [1964] when the pumping well has no wellbore storage; Theis [1935] when both conditions are fulfilled and Yang et.al. [2006] when the pumping well is partially penetrating, has finite radius but lacks storage. We use our solution to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells. \\ ( http://arxiv.org/abs/1110.5940 , 1121kb) ------------------------------------------------------------------------------ \\ arXiv:1110.5984 Date: Thu, 27 Oct 2011 04:57:28 GMT (2751kb,D) Title: An Immersed Boundary Fourier Pseudo-spectral Method for Simulation of Confined Two-dimensional Incompressible Flows Authors: Fereidoun Sabetghadam, Mehdi Badri, Shervin Sharafatmandjoor, Hosnieh Kor Categories: math-ph math.MP physics.flu-dyn \\ The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier--Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to many other similar methods, there is not an explicit external forcing function in the present formulation. The desired immersed boundary conditions are approximated on some regular grid points, using different orders (up to second-order) polynomial extrapolations. At the beginning of each timestep, the solenoidal velocities (also satisfying the desired immersed boundary conditions), are obtained and fed into a conventional pseudo-spectral solver, together with a modified vorticity. The zero-mean pseudo-spectral solution is employed, and therefore, the method is applicable to the confined flows with zero mean velocity and vorticity, and without mean vorticity dynamics. In comparison to the classical Fourier pseudo-spectral solution, the method needs ${\cal O}(4(1+\log N)N)$ more operations for boundary condition settings. Therefore, the computational cost of the method, as a whole, is scaled by ${(N \log N)}$. The classical explicit fourth-order Runge--Kutta method is used for time integration, and the boundary conditions are set at the beginning of each sub-step, in order to increasing the time accuracy. The method is applied to some fixed and moving boundary problems, with different orders of boundary conditions; and in this way, the accuracy and performance of the method are investigated and compared with the classical Fourier pseudo-spectral solutions. \\ ( http://arxiv.org/abs/1110.5984 , 2751kb) ------------------------------------------------------------------------------ \\ arXiv:1110.5987 Date: Thu, 27 Oct 2011 05:36:15 GMT (41kb) Title: Abrikosov Vortex Lattices at Weak Magnetic Fields Authors: I. M. Sigal, T. Tzaneteas Categories: math-ph math.MP Comments: 27 pages \\ We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field. \\ ( http://arxiv.org/abs/1110.5987 , 41kb) ------------------------------------------------------------------------------ \\ arXiv:1110.5988 Date: Thu, 27 Oct 2011 05:40:50 GMT (28kb) Title: Stability of Abrikosov lattices under gauge-periodic perturbations Authors: I. M. Sigal, T. Tzaneteas Categories: math-ph math.MP Comments: 18 pages \\ We consider Abrikosov-type vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, consisting of single vortices, for magnetic fields below but close to the second critical magnetic field H_{c2} = kappa^2 and for superconductors filling the entire R^2. Here kappa is the Ginzburg-Landau parameter. The lattice shape, parameterized by tau, is allowed to be arbitrary (not just triangular or rectangular). Within the context of the time-dependent Ginzburg-Landau equations, called the Gorkov-Eliashberg-Schmidt equations, we prove that such lattices are asymptotically stable under gauge periodic perturbations for kappa^2 > (1/2)(1 - (1/beta(tau)) and unstable for kappa^2 < (1/2)(1 - (1/beta(tau)), where beta(tau) is the Abrikosov constant depending on the lattice shape tau. This result goes against the common belief among physicists and mathematicians that Abrikosov-type vortex lattice solutions are stable only for triangular lattices and kappa^2 > 1/2. (There is no real contradiction though as we consider very special perturbations.) \\ ( http://arxiv.org/abs/1110.5988 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6066 Date: Thu, 27 Oct 2011 12:34:48 GMT (43kb,D) Title: Kinematic reduction and the Hamilton-Jacobi equation Authors: Mar\'ia Barbero-Li\~n\'an and Manuel de Le\'on and Juan Carlos Marrero and David Mart\'in de Diego and Miguel C. Mu\~noz-Lecanda Categories: math-ph math.DG math.MP math.OC Comments: 33 pages \\ A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces. \\ ( http://arxiv.org/abs/1110.6066 , 43kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6147 Date: Thu, 27 Oct 2011 18:11:46 GMT (17kb) Title: An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor Authors: R. Mehrem Categories: math-ph math.MP nucl-th Comments: 7 Pages \\ The integrals $\threej{\Llo}{\Llt}{\Llth} {0}{0}{0}\,\int_0^\infty \,r^{\Llth+1}\,e^{-\alpha r}\,j_\Llo(k_1r)\, j_\Llt(k_2r)\,dr$ and $\threej{\Llo}{\Llt}{\Llth} {0}{0}{0}\,\int_0^\infty \,r^{\Llth+2}\,e^{-\alpha r}\,j_\Llo(k_1r)\, j_\Llt(k_2r)\,dr$ are evaluated analytically. The result is a finite sum over the associated Legendre function of the second kind. \\ ( http://arxiv.org/abs/1110.6147 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6164 Date: Thu, 27 Oct 2011 19:42:33 GMT (35kb) Title: Noncommutative geometry of the Moyal plane: translation isometries and spectral distance between coherent states Authors: Pierre Martinetti, Luca Tomassini Categories: math-ph hep-th math.MP math.OA \\ We compute Connes' spectral distance in the Moyal plane, showing that the distance between any state of the Moyal algebra and any of its translated is the amplitude of translation. As a particular case, we obtain the spectral distance between coherent states of the quantum harmonic oscillator. This is the Euclidean distance on the plane, multiplied by the Planck length. We apply this result to the Doplicher-Fredenhagen-Roberts model of quantum spacetime [DFR], showing that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization. Although selfcontained, this paper can be viewed as a continuation of both arXiv:0912.0906 and arXiv:1106.0261. \\ ( http://arxiv.org/abs/1110.6164 , 35kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6165 Date: Thu, 27 Oct 2011 19:42:47 GMT (26kb) Title: Bi-Darboux Theorem and Para-Hypercomplex Geometry Authors: Igor A. Batalin and Klaus Bering Categories: math-ph hep-th math.MP Comments: 28 pages, LaTeX MSC-class: 37J99, 53D99, 55R10, 57R30, 58C50, 70S05 \\ We provide necessary and sufficient conditions for a version of Darboux Theorem on an even or odd bi-Poisson supermanifold, i.e., for the existence of common Darboux coordinates for two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with ranks equal to 2/3 of the dimension of the supermanifold. This is, e.g., relevant for Sp(2)-symmetric field-antifield formulation. We demonstrate a one-to-one correspondence to para-hypercomplex geometry. \\ ( http://arxiv.org/abs/1110.6165 , 26kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1110.5944 (*cross-listing*) Date: Wed, 26 Oct 2011 23:09:03 GMT (210kb) Title: Communication cost of classically simulating a quantum channel with subsequent rank-1 projective measurement Authors: Alberto Montina Categories: quant-ph cs.IT math-ph math.IT math.MP \\ A process of preparation, transmission and subsequent projective measurement of a qubit can be simulated by a classical model with only two bits of communication and some amount of shared randomness. However no model for n qubits with a finite amount of classical communication is known at present. A lower bound for the communication cost can provide useful hints for a generalization. It is known for example that the amount of communication must be greater than c 2^n, where c~0.01. The proof uses a quite elaborate theorem of communication complexity. Using a mathematical conjecture known as the "double cap conjecture", we strengthen this result by presenting a geometrical and extremely simple derivation of the lower bound 2^n-1. Only rank-1 projective measurements are involved in the derivation. \\ ( http://arxiv.org/abs/1110.5944 , 210kb) ------------------------------------------------------------------------------ \\ arXiv:1110.5948 (*cross-listing*) Date: Wed, 26 Oct 2011 23:46:49 GMT (639kb,D) Title: Momentum Operators in Two Intervals: Spectra and Phase Transition Authors: Palle E. T. Jorgensen, Steen Pedersen, Feng Tian Categories: math.SP math-ph math.AP math.CA math.FA math.MP Comments: 35 pages, 20 figures MSC-class: 47L60, 47A25, 47B25, 35F15, 42C10 \\ We study the momentum operator defined on the disjoint union of two intervals. Even in one dimension, the question of two non-empty open and non-overlapping intervals has not been worked out in a way that extends the cases of a single interval and gives a list of the selfadjoint extensions. Starting with zero boundary conditions at the four endpoints, we characterize the selfadjoint extensions and undertake a systematic and complete study of the spectral theory of the selfadjoint extensions. In an application of our extension theory to harmonic analysis, we offer a new family of spectral pairs. Compared to earlier studies, it yields a more direct link between spectrum and geometry. \\ ( http://arxiv.org/abs/1110.5948 , 639kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6025 (*cross-listing*) Date: Thu, 27 Oct 2011 09:35:15 GMT (16kb) Title: Explicit Thin-Lens Solution for an Arbitrary Four by Four Uncoupled Beam Transfer Matrix Authors: Vladimir Balandin and Sergey Orlov Categories: physics.acc-ph math-ph math.MP Comments: 10 pages, no figures Report-no: DESY 11-192 \\ In the design of beam transport lines one often meets the problem of constructing a quadrupole lens system that will produce desired transfer matrices in both the horizontal and vertical planes. Nowadays this problem is typically approached with the help of computer routines, but searching for the numerical solution one has to remember that it is not proven yet that an arbitrary four by four uncoupled beam transfer matrix can be represented by using a finite number of drifts and quadrupoles (representation problem) and the answer to this questions is not known not only for more or less realistic quadrupole field models but also for the both most commonly used approximations of quadrupole focusing, namely thick and thin quadrupole lenses. In this paper we make a step forward in resolving the representation problem and, by giving an explicit solution, we prove that an arbitrary four by four uncoupled beam transfer matrix actually can be obtained as a product of a finite number of thin-lenses and drifts. \\ ( http://arxiv.org/abs/1110.6025 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6114 (*cross-listing*) Date: Thu, 27 Oct 2011 15:24:23 GMT (16kb) Title: Effective action for EPRL/FK spin foam models Authors: Aleksandar Mikovic and Marko Vojinovic Categories: gr-qc hep-th math-ph math.MP Comments: 4 pages, proceedings of Loops 11 conference, Madrid; to appear in Journal of Physics: Conference Series (JPCS) \\ We show that a natural modification of the EPRL/FK vertex amplitude gives a finite spin foam model whose effective action gives the Einstein-Hilbert action in the limit of large spins and arbitrarily fine spacetime triangulations. The first-order quantum corrections can be easily computed and we show how to calculate the higher-order corrections. \\ ( http://arxiv.org/abs/1110.6114 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6132 (*cross-listing*) Date: Thu, 27 Oct 2011 16:14:07 GMT (1175kb) Title: Internal gravity waves in a stratified medium of non-uniform depth Authors: Vitaly V. Bulatov (1), Yuriy V. Vladimirov (1) ((1) Institute for Problems in Mechanics of the Russian Academy of Sciences) Categories: physics.flu-dyn math-ph math.MP physics.ao-ph Comments: 33 pages, 18 figures \\ The problem of reconstructing non-harmonic internal gravity wave packets generated by a source moving in a stratified ocean is considered. The uniform asymptotic form of the internal gravity waves field generated by a source moving above the smoothly varying floor is constructed. The solution is proposed in terms of wave modes, propagating independently at the adiabatic approximation, and described as a non-integral degree series of a small parameter characterizing the stratified medium. A specific form of the wave packets, which can be parameterized in terms of model functions (Airy functions), depends on a local behavior of the dispersion curves of individual wave mode. A modified space-time ray method was proposed, which belongs to the class of geometrical optics methods. The key point of the proposed technique is the possibility to derive the asymptotic representation of the solution in terms of a non-integral degree series of the some small parameter. \\ ( http://arxiv.org/abs/1110.6132 , 1175kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:1103.4986 replaced with revised version Thu, 27 Oct 2011 09:59:57 GMT (12kb) Title: Nahm's conjecture and coset models Authors: Sin\'ead Keegan and Werner Nahm Categories: math-ph hep-th math.MP \\ ( http://arxiv.org/abs/1103.4986 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1105.3935 replaced with revised version Thu, 27 Oct 2011 14:09:15 GMT (17kb) Title: Dolbeault complex on S^4\{.} and S^6\{.} through supersymmetric glasses Authors: A. V. Smilga Categories: math-ph hep-th math.MP Comments: 17 pages. The analysis of the twisted Dolbeault complex added. The index section is rewritten \\ ( http://arxiv.org/abs/1105.3935 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1106.3197 replaced with revised version Thu, 27 Oct 2011 14:49:11 GMT (61kb) Title: Clifford Algebras and Spinors Authors: Ivan Todorov Categories: math-ph math.HO math.MP physics.hist-ph Comments: Lecture notes prepared together with Dimitar Nedanovski (e-mail: dnedanovski@inrne.bas.bg), 32 pages. References added; footnote amended Report-no: CERN-PH-TH/2011-050 Journal-ref: Bulg.J.Phys.38:3-28,2011 \\ ( http://arxiv.org/abs/1106.3197 , 61kb) ------------------------------------------------------------------------------ \\ arXiv:1106.3297 (*cross-listing*) replaced with revised version Thu, 27 Oct 2011 16:06:21 GMT (11kb) Title: Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel Authors: M. E. Shirokov Categories: quant-ph math-ph math.MP Comments: 15 pages, generalizations to infinite dimensions including the case of continuous ensembles have been added \\ ( http://arxiv.org/abs/1106.3297 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1107.0058 (*cross-listing*) replaced with revised version Wed, 26 Oct 2011 20:17:00 GMT (11kb) Title: Coherent vortex structures and 3D enstrophy cascade Authors: R. Dascaliuc and Z. Gruji\'c Categories: math.AP math-ph math.MP physics.flu-dyn Comments: 12 pages; corrected some typos and updated the references MSC-class: 35Q30, 76D05, 76D02 \\ ( http://arxiv.org/abs/1107.0058 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1107.4156 replaced with revised version Thu, 27 Oct 2011 16:29:00 GMT (27kb) Title: CPT groups of higher spin fields Authors: V. V. Varlamov Categories: math-ph hep-th math.MP quant-ph Comments: 30 pages \\ ( http://arxiv.org/abs/1107.4156 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:1108.2985 (*cross-listing*) replaced with revised version Thu, 27 Oct 2011 09:00:12 GMT (19kb) Title: Convergence to equilibrium under a random Hamiltonian Authors: Fernando G.S.L. Brand\~ao, Piotr \'Cwikli\'nski, Micha{\l} Horodecki, Pawe{\l} Horodecki, Jaros{\l}aw Korbicz, Marek Mozrzymas Categories: quant-ph cond-mat.stat-mech math-ph math.MP Comments: 7 pages + appendix; comments welcome; results for a degenerate energy spectrum added \\ ( http://arxiv.org/abs/1108.2985 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1109.2862 replaced with revised version Thu, 27 Oct 2011 18:01:52 GMT (3kb) Title: The p7 term in the new Expansion for Lambda2(p) of the Monomer-Dimer Problem Authors: Paul Federbush Categories: math-ph cond-mat.stat-mech math.MP Comments: 3 pages, correction to p^7 term \\ ( http://arxiv.org/abs/1109.2862 , 3kb) ------------------------------------------------------------------------------ \\ arXiv:1110.0684 replaced with revised version Thu, 27 Oct 2011 17:59:23 GMT (3kb) Title: For the Monomer-Dimer Problem on Triangular and Hexagonal Lattices, the New p-Expansion Authors: Paul Federbush Categories: math-ph cond-mat.stat-mech math.MP Comments: 3 pages, a correction to p^7 term \\ ( http://arxiv.org/abs/1110.0684 , 3kb) ------------------------------------------------------------------------------ \\ arXiv:1110.3495 (*cross-listing*) replaced with revised version Wed, 26 Oct 2011 21:56:09 GMT (18kb) Title: Solution of the KdV equation using evolutionary vessels Authors: Andrey Melnikov Categories: math.AP math-ph math.FA math.MP math.SP MSC-class: 35Q53, 37K10, 37K35, 93A10, 46C20 \\ ( http://arxiv.org/abs/1110.3495 , 18kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For subscribe options to combined physics archives, e-mail To: physics@arXiv.org, Subject: subscribe ----------------------------------------------------------------------------- For help on viewing and making submissions, see http://arXiv.org/help/ For a list of archive mirror sites, see http://arXiv.org/servers.html ----------------------------------------------------------------------------- Third-party submissions cause excessive problems. 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