Kink propagation and trapping in a two-dimensional curved Josephson junction

Abstract

Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type. A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations. The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.

A modified predictor–corrector scheme for the two-dimensional sine-Gordon equation

“…Numerical approaches to the damped SG equation can be found in [31] who considers dimensionless loss factors and unit less normalized bias. Also in [17] who studied the nonlinear wave propagation in a planar wave guide consisting of two rectangular regions joined by a bent of constant curvature using as a model the kink solutions of the SG equation, where this can be considered as a part of analogous works examining the effect of the curvature to analogous nonlinear physical phenomena -see [3,13,20,24,30,33] etc. Finally, by [12] where the method arises from a two-step one-parameter leapfrog scheme, which is a generalization to that used by [11] and [6].…”

Spin-glass-like behaviour in ball milled Fe30Cr70 alloy studied by ac magnetic susceptibility

“…Among them, the most recent striking features are the observation of an Invar behaviour in Fe-Cu [7], and the enhancement (∼150 K) of an intrinsic physical property such as the Curie temperature of mechanically stressed and thermally treated Fe 64 Ni 36 Invar alloy [8,9], leading to an extension of the temperature range for having low-or near-zero thermal expansion coefficient in this material below the magnetic ordering temperature. In the case of ball milled Fe x Cr 100−x , the magnetic behaviour could be significantly modified by the disordered intergranular region [10,11].…”

A numerical meshless method of soliton-like structures model via an optimal sampling density based kernel interpolation

“…Because of its wide applications [58][59][60][61], SGE is studied with exact solutions and different numerical solutions, and we refer the interested reader to Refs. [10][11][12][13][14][15][16][17][18][19]40,[62][63][64][65][66][67][68][69] for more details.…”

“…Soliton solutions in different analytical methods and numerical techniques for some well-known PDE, such as the Korteweg-de Vries equation, the nonlinear Schrödinger equation and the sine-Gordon equation (SGE) [4] etc., can be found in [5]. According to the representation of approximate solutions, the numerical methods for nonlinear PDEs include four main classes: the finite difference methods (FDMs), the finite element methods (FEMs), the finite volume methods (FVMs) and the spectral methods [4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”