Date: Thu, 28 Jul 11 00:07:45 GMT Subject: math-ph daily 7 new + 6 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 Tue 26 Jul 11 20:00:00 GMT to Wed 27 Jul 11 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1107.5323 Date: Tue, 26 Jul 2011 20:24:44 GMT (675kb) Title: Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid Authors: Jordan Hristov Categories: math-ph math.MP Comments: 19 pages, 6 figures; in press Thermal Science, volume 16, 2012, issue 2 DOI: 10.2298/TSCI110401077H \\ Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes' first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a parabolic profile with an unspecified exponent allowing optimization through minimization of the norm over the domain of the penetration depth. The closed form solution explicitly defines two dimensionless similarity variables and, responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. The solution was developed with three forms of the governing equation through its two dimensional forms (the main solution and example 1) and the dimensionless version showing various sides of the flow field and how the dimensionless groups control it: mainly the effect of the Deborah number. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed have been performed. \\ ( http://arxiv.org/abs/1107.5323 , 675kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5341 Date: Tue, 26 Jul 2011 21:46:48 GMT (5718kb,D) Title: Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries Authors: Hui-Chia Yu, Hsun-Yi Chen, and K. Thornton Categories: math-ph math.MP physics.flu-dyn Comments: This document is the revised version of arXiv:0912.1288v1 \\ In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction-diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelled droplet. \\ ( http://arxiv.org/abs/1107.5341 , 5718kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5344 Date: Tue, 26 Jul 2011 21:52:21 GMT (20kb) Title: Extremum conditions for functionals involving higher derivatives of several variable vector valued functions Authors: Mahouton Norbert Hounkonnou and Pascal Dkengne Sielenou Categories: math-ph math.MP MSC-class: 49-01, 49J10, 49J40, 35A40, 35A15 \\ This paper addresses both necessary and relevant sufficient extremum conditions for a variational problem defined by a smooth Lagrangian, involving higher derivatives of several variable vector valued functions. A general formulation of first order necessary extremum conditions for variational problems with (or without) constraints is given. Global Legendre second order necessary extremum conditions are provided as well as new general explicit formula for second order sufficient extremum condition which does not require the notion of conjugate points as in the Jacobi sufficient condition. \\ ( http://arxiv.org/abs/1107.5344 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5465 Date: Wed, 27 Jul 2011 13:17:52 GMT (9kb) Title: On some mathematical model of turbulent flow with intensive selfmixing Authors: Marek Burnat Categories: math-ph math.MP MSC-class: 76F02, 76F25 \\ Paper contains description of a new non laminar mathematical model of turbulent flow. Equations of the model are given and main conservation laws for this model are proven. \\ ( http://arxiv.org/abs/1107.5465 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5516 Date: Wed, 27 Jul 2011 16:09:59 GMT (17kb) Title: Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials Authors: A.M. Gavrilik, A.M. Pavlyuk Categories: math-ph hep-th math.MP quant-ph Comments: 8 pages, two-column ujp style; http://www.ujp.bitp.kiev.ua Journal-ref: Ukr. J. Phys., 2011, Vol. 56, no. 7, pp. 680-687 \\ The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. Using this result and those from our previous papers, we express the Alexander polynomials \Delta_{n,3}(t) through Chebyshev polynomials. The latter result is extended to general torus knots T(n,l) with n and l coprime. \\ ( http://arxiv.org/abs/1107.5516 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5533 Date: Wed, 27 Jul 2011 16:48:51 GMT (15kb) Title: Geometrically relating momentum cut-off and dimensional regularization Authors: Susama Agarwala Categories: math-ph math.MP Comments: 11 pages MSC-class: 81R50, 16T05 \\ The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the $\beta$-functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories. \\ ( http://arxiv.org/abs/1107.5533 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5572 Date: Wed, 27 Jul 2011 19:50:01 GMT (21kb) Title: On Rigorous Derivation of the Enskog Kinetic Equation Authors: I.V. Gapyak, V.I. Gerasimenko Categories: math-ph cond-mat.stat-mech math.AP math.MP Comments: 28 pages MSC-class: 35Q20, 35Q82, 47J35, 82C05, 82C40 \\ We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear kinetic Enskog equation and its generalizations are justified. It is established that for initial states which are specified in terms of one-particle distribution functions the description of the evolution by the Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the generalized Enskog kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is an equivalent. For the initial-value problem of the generalized Enskog equation the existence theorem is proved in the space of integrable functions. \\ ( http://arxiv.org/abs/1107.5572 , 21kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1104.2289 (*cross-listing*) Date: Tue, 12 Apr 2011 18:04:25 GMT (28kb) Title: Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state Authors: Elena R. Loubenets Categories: quant-ph math-ph math.MP math.PR \\ We introduce for a general correlation scenario the notion of a local quasi hidden variable (LqHV) model where locality inherent to an LHV model is preserved but one of hidden variables attributes is dropped. We prove the basic statement on LqHV modelling and show that every S_{1}x...xS_{N}-setting correlation scenario on an N-partite quantum state admits an LqHV simulation. Via the LqHV approach, we construct analogs of Bell-type inequalities for an N-partite quantum state and find a new analytical upper bound on violation by an N-partite state of any S_{1}x...xS_{N}-setting Bell-type inequality - either on correlation functions or on joint probabilities and for outcomes of any spectral type, discrete or continuous. This analytical upper bound is expressed in terms of the new state dilation characteristics introduced in the present paper and not only traces states admitting an S_{1}x...xS_{N}-setting LHV description but also specifies a new exact numerical upper estimate on Bell violations by an arbitrary N-partite state. We, in particular, prove that violation by an N-partite quantum state of any Bell-type inequality for S settings per site cannot exceed (2S-1)^{N-1} even in case of an infinite dimensional state and infinitely many outcomes. \\ ( http://arxiv.org/abs/1104.2289 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5305 (*cross-listing*) Date: Mon, 25 Jul 2011 23:02:59 GMT (1219kb,D) Title: Universal constants and equations of turbulent motion Authors: Helmut Z. Baumert Categories: physics.flu-dyn math-ph math.MP nlin.CD Comments: 18 pages, 8 figures, 63 references submitted to physics.fllu-dyn \\ In the spirit of Prandtl [1926], for turbulence at high Reynolds number we present an analogy with the kinetic theory of gases, with dipoles made of Thorpe's [1977] quasi-solid vortex tubes as frictionless, incompressible but deformable quasi-particles. Their movements are governed by Helmholtz' elementary vortex rules applied locally. A contact interaction or 'collision' leads either to random scatter of a trajectory or to the formation of two likewise rotating, fundamentally unstable whirls forming a dissipative patch slowly rotating around its center of mass which is almost at rest. This approach predicts von Karman's constant as 1/sqrt(2 pi) = 0.399 and the spatio-temporal dynamics of energy-containing time and length scales controlling turbulent mixing Baumert [2009]. A link to turbulence spectra was missing so far. In the present paper it is shown that the above image of random vortex-dipole movements is compatible with Kolmogorov's turbulence spectra if dissipative patches, beginning as two likewise rotating eddies, evolve locally into a space-filling bearing in the sense of Herrmann [1990], i.e. into an "Apollonian gear". Its parts and pieces are incompressible and flexibly deformable vortex tubes which are frictionless, excepting the dissipative scale of size zero. For steady and locally homogeneous conditions our approach predicts the dimensionless pre-factor in the 3D Eulerian wavenumber spectrum as [(4 pi)^2/3]/3 = 1.8, and in the Lagrangian frequency spectrum as 2. Our derivations rest on geometry, methods from many-particle physics, and on elementary conservation laws. \\ ( http://arxiv.org/abs/1107.5305 , 1219kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5308 (*cross-listing*) Date: Tue, 26 Jul 2011 20:00:03 GMT (30kb) Title: Fractional and noncommutative spacetimes Authors: Michele Arzano, Gianluca Calcagni, Daniele Oriti, Marco Scalisi Categories: hep-th gr-qc math-ph math.MP Comments: 15 pages \\ We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the non-rotation-invariant but cyclicity-preserving measure of \kappa-Minkowski. At scales larger than the log-period, the fractional measure is averaged and becomes a power-law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between \kappa-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra. \\ ( http://arxiv.org/abs/1107.5308 , 30kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5328 (*cross-listing*) Date: Tue, 26 Jul 2011 20:53:28 GMT (33kb) Title: Inelastic character of solitons of slowly varying gKdV equations Authors: Claudio Mu\~noz Categories: math.AP math-ph math.MP Comments: 27 pp., submitted \\ In this paper we describe the inelastic character of solitons of some slowly varying gKdV equations. We give precise lower bounds, in the energy space, of the defect induced by the potential on the solution as time goes to infinite. For the proof, we consider suitable Lyapunov functionals that propagate the defect along the dynamics in a non trivial fashion, in the spirit of the recent breakthroughs made by Martel and Merle in the case of the two soliton collision for non integrable gKdV equations. In addition, we also consider a special, degenerate case, where the defect is formally of second order. \\ ( http://arxiv.org/abs/1107.5328 , 33kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5417 (*cross-listing*) Date: Wed, 27 Jul 2011 09:05:35 GMT (5kb) Title: Pfaffian-type Sugawara operators Authors: A. I. Molev Categories: math.RT math-ph math.MP Comments: 4 pages \\ We show that the Pfaffian of a generator matrix for the affine Kac--Moody algebra hat o_{2n} is a Segal--Sugawara vector. Together with our earlier construction involving the symmetrizer in the Brauer algebra, this gives a complete set of Segal--Sugawara vectors in type D. \\ ( http://arxiv.org/abs/1107.5417 , 5kb) ------------------------------------------------------------------------------ \\ arXiv:1107.5460 (*cross-listing*) Date: Wed, 27 Jul 2011 12:54:42 GMT (52kb) Title: The Smooth Entropy Formalism on von Neumann Algebras Authors: Mario Berta, Fabian Furrer, Volkher B. Scholz Categories: quant-ph math-ph math.MP \\ We discuss quantum information theoretical concepts on von Neumann algebras and lift the smooth entropy formalism to the most general quantum setting. For the smooth min- and max-entropies we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and sketch possible applications to continuous variable quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra. From this we generalize the formula of Renes and Renner characterizing the optimal length of a distillable secure finite-key. We also elaborate on the question when the formalism of von Neumann algebras is of advantage in the description of quantum systems with an infinite number of degrees of freedom. \\ ( http://arxiv.org/abs/1107.5460 , 52kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:1101.3690 (*cross-listing*) replaced with revised version Wed, 27 Jul 2011 10:48:05 GMT (28kb) Title: Large Deviation Strategy for Inverse Problem Authors: Izumi Ojima and Kazuya Okamura Categories: quant-ph math-ph math.MP math.ST stat.TH \\ ( http://arxiv.org/abs/1101.3690 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1107.0663 (*cross-listing*) replaced with revised version Wed, 27 Jul 2011 09:13:16 GMT (15kb) Title: Nonstandard Parafermions and String Compactification Authors: Andrei Babichenko and Doron Gepner Categories: hep-th hep-ph math-ph math.MP Comments: 28 pages; typos corrected \\ ( http://arxiv.org/abs/1107.0663 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1107.1374 replaced with revised version Wed, 27 Jul 2011 13:17:06 GMT (46kb) Title: The holistic structure of causal quantum theory, its implementation in the Einstein-Jordan conundrum and its violation in more recent particle theories Authors: Bert Schroer Categories: math-ph hep-th math.MP Comments: 41 pages, expansion of conceptual content and addition of references \\ ( http://arxiv.org/abs/1107.1374 , 46kb) ------------------------------------------------------------------------------ \\ arXiv:1107.2525 replaced with revised version Wed, 27 Jul 2011 12:20:56 GMT (20kb) Title: Generic matrix superpotentials Authors: Anatoly G. Nikitin and Yuri Karadzhov Categories: math-ph math.MP quant-ph Comments: Ref. 17 is added MSC-class: 81Qxx, 81Rxx \\ ( http://arxiv.org/abs/1107.2525 , 20kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- 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. Author self-submissions are exceedingly preferred. E-mail submissions have been discontinued in favor of better support for Web submissions. See http://arXiv.org/help/uploads