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WEAKLY PERTURBED boundary-value problems FOR DIFFERENTIAL EQUATIONS IN A BANACH SPACE

NONLINEAR OSCILLATIONS 2011年第3期13卷 311-324页

作者： Boichuk, O. A. Panasenko, E. V. Ukrainian Natl Acad Sci Inst Math Kiev Ukraine Zaporizhzhya Natl Univ Zaporizhzhya Ukraine

We consider boundary-value problems for a system of ordinary differential equations with a small parameter epsilon in the equations and boundary conditions. We establish conditions for the bifurcation of solutions of ... 详细信息

关键词： PERTURBATION (Mathematics) boundary value problems -- numerical solutions LINEAR systems BANACH spaces PARAMETER estimation DIFFERENTIAL equations BIFURCATION theory

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Eigenmode analysis of the electromagnetic field scattered by an elliptic cone

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ADVANCES IN RADIO SCIENCE 2011年 9卷 31-37页

作者： Kijowski, M. Klinkenbusch, L. Christian Albrechts Univ Kiel Inst Elect & Informat Engn Kiel Germany

The vector spherical-multipole analysis is applied to determine the scattering of a plane electromagnetic wave by a perfectly electrically conducting (PEC) semi-infinite elliptic cone. From the eigenfunction expansion of the total field in the space outside the elliptic cone, the scattered far field is obtained as a multipole expansion of the free-space type by a single integration over the induced surface currents. As for the evaluation of the free-space-type expansion it is necessary to apply suitable series transformation techniques, a sufficient number of eigenfunctions has to be considered. The eigenvalues of the underlying two-parametric eigenvalue problem with two coupled Lame equations belong to the Dirichlet- or the Neumann condition and can be arranged as so-called eigenvalue curves. It has been observed that the eigenvalues are in two different domains. In the first one Dirichlet- and Neumann eigenvalues are either nearly coinciding, while in the second one they are strictly separated. The eigenfunctions of the first (coinciding) type look very similar to free-space modes and do not contribute to the scattered field. This observation allows to significantly improve the determination of diffraction coefficients.

关键词： ELECTROMAGNETIC waves ELECTROMAGNETIC theory EIGENFUNCTIONS boundary value problems -- numerical solutions EIGENvalueS

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Nonsmooth Eigenfunctions in problems of Mathematical Physics

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DIFFERENTIAL EQUATIONS 2011年第3期47卷 355-362页

作者： Lomov, I. S. Moscow MV Lomonosov State Univ Moscow Russia

We study whether V.A. Il'in's method for proving the uniqueness of the solution of a mixed problem for a hyperbolic equation applies to a problem with transmission conditions in the interior of the interval. We show that the system of eigenfunctions corresponding to this problem is complete in the space L(2)( 0, l) and is a Riesz basis in this space.

关键词： EXPONENTIAL functions EIGENFUNCTIONS RIESZ spaces boundary value problems -- numerical solutions DIFFERENTIAL equations -- numerical solutions

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The Slow Erosion Limit in a Model of Granular Flow

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ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 2011年第1期199卷 1-31页

作者： Amadori, Debora Shen, Wen Univ Aquila Dipartimento Matemat Pura & Appl I-67010 Coppito Laquila Italy Penn State Univ Dept Math University Pk PA 16802 USA

We study a 2 x 2 system of balance laws that describes the evolution of a granular material (avalanche) flowing downhill. The original model was proposed by Hadeler and Kuttler (Granul Matter 2:9-18, 1999). The Cauchy problem for this system has been studied by the authors in recent papers (Amadori and Shen in Commun Partial Differ Equ 34:1003-1040, 2009;Shen in J Math Anal Appl 339:828-838, 2008). In this paper, we first consider an initial-boundary value problem. The boundary condition is given by the flow of the incoming material. For this problem we prove the global existence of BV solutions for a suitable class of data, with bounded but possibly large total variations. We then study the "slow erosion (or deposition) limit". We show that, if the thickness of the moving layer remains small, then the profile of the standing layer depends only on the total mass of the avalanche flowing downhill, not on the time-law describing the rate at which the material slides down. More precisely, in the limit as the thickness of the moving layer tends to zero, the slope of the mountain is provided by an entropy solution to a scalar integro-differential conservation law.

关键词： GRANULAR materials MATERIALS -- Erosion MATERIALS -- Mechanical properties CAUCHY problem -- numerical solutions boundary value problems -- numerical solutions THICKNESS measurement INTEGRO-differential equations CONSERVATION laws (Mathematics)

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Universal amplitude ratios for scaling corrections on Ising strips

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Physical Review E 2011年第5期84卷 051109-051109页

作者： N. Sh. Izmailian []Yerevan Physics Institute Alikhanian Brothers 2 AM-375036 Yerevan Armenia

We study the (analytic) finite-size corrections in the Ising model on the strip with free, fixed (++), and mixed boundary conditions. For fixed (++) boundary conditions, the spins are fixed to the same values on two sides of the strip. We find that subdominant finite-size corrections to scaling should be to the form ap/N2p−1 for the free energy fN and bp/N2p−1 for inverse correlation length ξN−1, with integer value of p. We investigate the set {ap,bp} by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios bp/ap remain constant upon varying coupling anisotropy. Such universal behavior is correctly reproduced by the conformal perturbative approach.

关键词： ISING model boundary value problems -- numerical solutions PERTURBATION (Mathematics) SCALING laws (Statistical physics) ELECTRON spin

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Universal Scaling Law for Jets of Collapsing Bubbles

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Physical Review Letters 2011年第20期107卷 204501-204501页

作者： D. Obreschkow M. Tinguely N. Dorsaz P. Kobel A. de Bosset M. Farhat Laboratoire des Machines Hydrauliques EPFL 1007 Lausanne Switzerland Department of Chemistry University of Cambridge Cambridge CB2 1EW United Kingdom Max-Planck-Institut für Sonnensystemforschung 37191 Katlenburg-Lindau Germany

Cavitation bubbles collapsing and rebounding in a pressure gradient ∇p form a “microjet” enveloped by a “vapor jet.” This Letter presents unprecedented observations of the vapor jets formed in a uniform gravity-induced ∇p, modulated aboard parabolic flights. The data uncover that the normalized jet volume is independent of the liquid density and viscosity and proportional to ζ≡|∇p|R0/Δp, where R0 the maximal bubble radius and Δp is the driving pressure. A derivation inspired by “Kelvin-Blake” considerations confirms this law and reveals its negligible dependence of surface tension. We further conjecture that the jet only pierces the bubble boundary if ζ≳4×10−4.

关键词： CAVITATION VISCOSITY MATHEMATICAL models BUBBLE dynamics SURFACE tension boundary value problems -- numerical solutions

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Hierarchy of boundary-driven phase transitions in multispecies particle systems

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Physical Review E 2011年第1期83卷 011130-011130页

作者： Vladislav Popkov Mario Salerno Dipartimento di Fisica “E. R. Caianiello” and Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia (CNISM) Università di Salerno Fisciano Italy

Interacting systems with K driven particle species on an open chain or chains that are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions that are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary-driven phase transition (BDPT) is observed and we reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths, one generically encounters Z discontinuous and 2(K−Z) continuous BDPT’s, with Z taking values 0⩽Z⩽K depending on the path. As model examples, we consider solvable exclusion processes with product measure states and K=1,2,3 particle species and a nonsolvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.

关键词： PHASE transformations (Physics) ADIABATIC processes boundary value problems -- numerical solutions MONTE Carlo method numerical analysis

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Quantum solution for the one-dimensional Coulomb problem

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Physical Review A 2011年第6期83卷 064101-064101页

作者： H. N. Núñez-Yépez A. L. Salas-Brito Didier A. Solis Departamento de Física Universidad Autónoma Metropolitana Unidad Iziapalapa Apartado Postal 55-534 Iztapalapa CP 09340 D. F Mexico Departamento de Ciencias Básicas Universidad Autónoma Metropolitana Unidad Azcapotzalco Apartado Postal 21-267 Coyoacán CP 04000 D. F Mexico Facultad de Matemáticas UniversidadAutónoma de Yucatan Per~férico Norte Tablaje C. 13615 Mérida Yucatan Mexico

The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct—such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.

关键词： NONMETALS HYDROGEN boundary value problems -- numerical solutions EIGENFUNCTIONS NUCLEAR forces (Physics)

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NON-UNIQUE solutions TO boundary value problems FOR NON-SYMMETRIC DIVERGENCE FORM EQUATIONS

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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 2010年第2期362卷 661-672页

作者： Axelsson, Andreas Stockholms Univ Inst Matemat S-10691 Stockholm Sweden

We calculate explicitly solutions to the Dirichlet and Neumann boundary value problems in the upper half plane, for a family of divergence form equations having non-symmetric coefficients with a jump discontinuity. It is shown that the boundary equation method and the Lax-Milgram method for constructing solutions may give two different solutions when the coefficients are sufficiently non-symmetric.

关键词： boundary value problems -- numerical solutions SYMMETRY (Mathematics) NEUMANN problem numerical calculations MATHEMATICAL analysis DIRICHLET problem

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Noncommutativity in weakly curved background by canonical methods

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Physical Review D 2011年第6期83卷 066014-066014页

作者： Lj. Davidović B. Sazdović []Institute of Physics University of Belgrade 11001 Belgrade P.O. Box 57 Serbia

Using the canonical method, we investigate the Dp-brane world-volume noncommutativity in a weakly curved background. The term “weakly curved” means that, in the leading order, the source of nonflatness is an infinitesimally small Kalb-Ramond field Bμν, linear in coordinate, while the Ricci tensor does not contribute, being an infinitesimal of the second order. On the solution of boundary conditions, we find a simple expression for the space-time coordinates in terms of the effective coordinates and momenta. This basic relation helped us to prove that noncommutativity appears only on the world sheet boundary. The noncommutativity parameter has a standard form, but with the infinitesimally small and coordinate-dependent antisymmetric tensor Bμν. This result coincides with that obtained on the group manifolds in the limit of the large level n of the current algebra. After quantization, the algebra of the functions on the Dp-brane world volume is represented with the Kontsevich star product instead of the Moyal one in the flat background.

关键词： D-branes boundary value problems -- numerical solutions RICCI flow MATHEMATICAL models ALGEBRAIC functions

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