Vortices in the three-dimensional thin-film Ginzburg�CLandau model of superconductivity

Building on the results of Chapman et?al. (Z Angew Math Phys 47:410?C431, 1996) on the behavior of minimizers in the Ginzburg?CLandau thin-film model, we show that the vortices in the three-dimensional superconducting thin films are located in the cylinders whose cross sections coincide with the disks that contain the vortices in the two-dimensional model. To arrive at this conclusion, we prove that the three-dimensional minimizers converge to the two-dimensional counterparts in H ¹ and in C ^?? . We also give examples of regimes in which the vortex structure of the two-dimensional minimizers is well understood. Our results, in particular, provide insight into the behavior of the three-dimensional vortices in these regimes.     

Quantum Problem of Polaron Localization and Justification of the Su—Schrieffer—Heeger Approximation

Theoretical and Mathematical Physics - We consider a polaron localized on a trap in a one-dimensional lattice with a harmonic potential of nearest-neighbor interaction. We study the lattice...     

Asymptotics of the Riemann–Hilbert Problem for the Somov Model of Magnetic Reconnection of Long Shock Waves

Mathematical Notes - We consider the Riemann–Hilbert problem in a domain of complicated shape (the exterior of a system of cuts), with the condition of growth of the solution at infinity....     

Long Time Behavior of Difference Approximations for the Two-Dimensional Complex Ginzburg–Landau Equation

The finite difference approximations of the dynamical systems governed by two-dimensional complex Ginzburg–Landau equation was considered. For a fully discrete scheme, the solvability, stability and convergence are proved in discrete Sobolev spaces. Furthermore, the existence of global attractors 𝒜 _{h, τ} of the discrete system and the upper semicontinuity dist(𝒜 _{h, τ}, 𝒜) → 0 are obtained.     

The Error in the Approximation

In applying any numerical method such as the bisection method to determine a root, it is important to realize that the best we can usually achieve is an approximation ofthe exact root. At each iteration of the method,we obtain a better estimate of the root. Thus it becomes desirable that we be able to estimate how accurate the approximation is at each stage so that we know when to stop the process.With the bisection method,suppose we know that there is a root in some interval [a,b], where a and b are successive integers, say 2 and 3. If we select the midpoint M1 of this interval, then it is obvious that the root R is     

Stable transmission of solitons in the complex cubic–quintic Ginzburg–Landau equation with nonlinear gain and higher-order effects

In this paper, a complex cubic–quintic Ginzburg–Landau equation (CCQGLE) is investigated. Using the asymmetric method, the analytic one-soliton solution of the CCQGLE is obtained for the first time. Through analyzing the solutions obtained, the transmission of the soliton is controlled by changing the values of related parameters. Results of this paper contribute to obtain the analytic soliton solution of the higher-order CCQGLE.     

On the Simultaneous Approximation in Lp-norm

Let C_[-1,1]~(N) be the class of N-th continuously differentiable functions on [-1,1], denote by L_(p[-1,1]) the class of L_p-integrable functions on [-1,1], E_n(f)_p is thebest approximation of f∈L_(p[-1,1]) by nth algebraic polynomials, and C(·) is a positive constant only depending upon the quantities in the brackets. In Theorem 1, the condition that f(x)∈C_([-1,1])~((N-1)), f~((N-1))(x) is absolutely continuous, and f~((N))(x)∈L_(p[-1,1]) for N=O equals that f(x)∈L_(p[-1,1]).     

Stability of Planar Waves in the Allen–Cahn Equation

We study the asymptotic stability of planar waves for the Allen–Cahn equation on ? ⁿ , where n ≥ 2. Our first result states that planar waves are asymptotically stable under any—possibly large—initial perturbations that decay at space infinity. Our second result states that the planar waves are asymptotically stable under almost periodic perturbations. More precisely, the perturbed solution converges to a planar wave as t → ∞. The convergence is uniform in ? ⁿ . Lastly, the existence of a solution that oscillates permanently between two planar waves is shown, which implies that planar waves are not asymptotically stable under more general perturbations.     

On the Rabbinical Approximation of π

We discuss the Rabbinical tradition of geometry concerning circular shapes, as it appears in the Babylonian Talmud and in later commentaries. Three explanations of the difference between π and the Rabbinical value for it, so far not widely known among the scientific community, are given.Copyright 1998 Academic Press.Nous discutons ici la tradition rabbinique en géométrie à propos des figures circulaires, telle qu'elle apparaı̂t dans le Talmud babylonien et dans des commentaires ulterieurs. Trois explications sont proposées pour la différence entre π et la valeur donnée dans la littérature rabbinique. Ces explications semblent peu connues dans la communauté scientifique.Copyright 1998 Academic Press.Wir diskutieren die rabbinische Tradition der Geometrie der kreisförmigen Formen, wie sie im babylonischen Talmud und in späteren Kommentaren erscheint. Wir geben drei Erklärungen für den Unterschied zwischen π und seinem rabbinischen Wert, die unter Wissenschaftlern noch nicht weit bekannt sind.Copyright 1998 Academic Press.MSC 1991 subject classifications: 01A35, 01A17     

Topological transformations of three-dimensional dissipative solitons in the framework of the generalized Ginzburg—Landau equation

Theoretical and Mathematical Physics - We classify and analyze transformations of three-dimensional dissipative tangle-solitons, i.e., solitons with closed and nonclosed vortex lines, under smooth...     

Existence of Dyons in the Coupled Georgi�CGlashow�CSkyrme Model

We prove the existence of a continuous family of finite-energy particle-like solutions in the coupled Georgi–Glashow–Skyrme model carrying both electric and magnetic charges, known as dyons. Due to the presence of electricity and the Minkowski spacetime signature, we need to solve a variational problem with an indefinite action functional. Our results show that, while the magnetic charge is uniquely determined by the topological monopole number, the electric charge of a solution can be arbitrarily prescribed in an open interval.     

Mathematical Simulation of Superinertial Free Oscillations of the Black Sea in the β-Plane Approximation

New results on the numerical simulation of superinertial fee oscillations of the Black Sea for a variable Coriolis coefficient are presented.     

On the Order of Best Approximation by Polynomials in H_q~p Spaces

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Approximation Characteristics of the Spaces S p ϕ in Different Metrics

We continue the investigation of the approximation characteristics of the spaces introduced earlier. In particular, we establish direct and inverse theorems on the approximation of elements of these spaces. We also determine the exact values of upper bounds of m-term approximations of q-ellipsoids in the spaces in the metrics of the spaces .     

Approximation of the soluticon of the stochastic navier-stokes equation ∗

We consider a stochastic equation of the Navier-Stokes type containing a noise part given by a stochastic Ito integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the solutions of a sequence of linear equations with additive noise. We prove the convergence in mean squares     

Order of Approximation by Hermite-Fejer Interpolating Polynomials in the Complex Plane

Suppose that either the outer mapping function of a domain D has continuous second derivatives or D is a strictly star domain. In this paper we first establish two inequalities concerning polynomials at Fejer's points with multiplicity (3 + 1). Using these two inequalities, we obtain the order of approximation in Lp(dD), 0相似文献   

On the Approximation of Combination of Linear Operators

Let f(x)∈C_(2π).For Valle-Poussin integrals V_n(f,x)=(2n)!! 1(2n-1)!! 2πintegral grom -πto π(f(x 1)cos~(2n)t/2 dt), Z.Ditzian and G.Freud considered the approximation of their combination writingV_(n,1)(f,x)=2V_(2n-1)(f,x)-V_(n-1)(f,x),V_(n,2)(f,x)=8/3V_(4n-1)(f,x)-2V_(2n-1)(f,x) 1/3V_(n-1)(f,x), they proved that V_(n,1)(f,x)-f(x)=O(ω_4(f,1/n~(1/2))), V_(n,2)(f,x)-f(x)=O(ω_6(f,1/n(1/2))) In this paper, using the asymptotic expansions of linear operators with many terms,we generalize the above result to the case of eombination of m terms, where mis an arbtirary positive integer.     

On the Post-Darwin Approximation of the Maxwell–Lorentz Equations of Motion of Point Charges in the Absence of Neutrality

Ukrainian Mathematical Journal - The existence of holomorphic (in time) solutions of the nonrelativistic equations of motion of nonneutral systems of point charges that do not contain inverse...     

A ■_n-Related Family of Homotopy Elements in the Stable Homotopy of Spheres

To determine the stable homotopy groups of spheres π_*(S) is one of the central problems in homotopy theory. Let p be a prime greater than 5. The authors make use of the May spectral sequence and the Adams spectral sequence to prove the existence of a ■_n-related family of homotopy elements, β1ω_nγ_s, in the stable homotopy groups of spheres, where ■_n 3, 3≤s p-2 and the ■_n-element was detected by X. Liu.