Kink Interaction Research Articles

The kink chain revisited

The equilibrium configuration of a kink chain consisting of kink pairs, formed in a dislocation segment bowing out under the action of an applied stress σ, is determined by deriving an expression for the enthalpy H(σ), taking account of all kink–kink interactions. For a realistic description, instead of the usual 1/r asymptotic potential, the Püschl potential must be used, which does not diverge when two kinks of the same sign approach each other. For a given applied stress σ, above a critical stress there exist, due to geometrical restraints, a number of different bow-out configurations with different numbers of kink pairs and the problem is to find the ‘ground state’, which is the state with the lowest enthalpy. This can only be done by numerical or semi-graphical methods. Since the ground state can only be reached by thermal activation, there is an asymmetry in the forward and backward movement. It is found that in the equilibrium configuration the kinks of the same sign generally accumulate at the two opposite side arms, leaving a longer straight segment in between. When the bow-out height of the kink chain approaches the height resulting from the line tension model, the influence of the long-range back-stress caused by the overall curvature cannot be neglected and it limits the accessible height.

Interaction of kinks for semilinear wave equations with a small parameter

We consider a class of semilinear wave equations with a small parameter and nonlinearities such that the equations have exact kink-type solutions. The main result consists in obtaining sufficient conditions for the nonlinearities under which the interaction of kinks preserves the sine-Gordon scenario. This means that the interaction occurs without changing the waves shape and with shifts of trajectories.

Interactions among periodic waves and solitary waves for a higher dimensional system

The general variable separated approach is successfully extended to the (2+1)-dimensional physical model and we obtain a universal formula involving arbitrary number of variable separated functions. Because of the existence of the arbitrary functions in the universal formula, many new types of structures of periodic waves, for example, the periodic–periodic interaction waves, periodic–kink interaction waves, periodic–peakon interaction waves, periodic–compacton interaction waves, periodic–foldon interaction waves, etc, are investigated both analytically and graphically. Some novel features or interesting behaviours are revealed.

Coarsening dynamics of the one-dimensional Cahn-Hilliard model

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We characterize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system. A set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations. We also compare these dynamics with the bubble dynamics deduced from the classical kink interaction computation where our model seems to be more appropriated. In the case of two bubbles, we deduce analytical expressions for the bubble's position and the bubble's width. Besides, a simple description of the ulterior dynamics is presented.

Interaction of sine-Gordon kinks with defects: the two-bounce resonance

A model of soliton–defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for weak defects. Matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem, which are then used to derive analytical formulas for the locations of the well known two- and three-bounce resonance windows, as well as several other phenomena seen in numerical simulations.

Step dynamics and step–step interactions on the chiral Cu(5 8 90) surface

Abstract In this paper we discuss particular aspects of the high-Miller-index Cu(5 8 90) surface. We focus on the mobility of steps and energetic step–step interactions and the possible influence of kink–kink interactions on the step structure. One important goal of this paper is to give a detailed insight into the characteristics of a typical real high-Miller-index surface, such surfaces are frequently used as substrates in enantioselective reactions because of their chiral surface properties.

Asymptotics of Kink--Kink Interaction for Sine-Gordon Type Equations

We consider a class of semilinear wave equations with a small parameter e. The nonlinearity of F(u) is assumed to be such that the corresponding equation has an exact self-similar solution of kink type. For F(u), we obtain sufficient conditions for two kinks to interact (in the sense of the leading term of the asymptotics with respect to e) in the same way as the kinks of the sine-Gordon equation.

Quantum necking in stressed metallic nanowires.

When a macroscopic metallic wire is subject to tensile stress, it necks down smoothly as it elongates. We show that nanowires with radii comparable to the Fermi wavelength display remarkably different behavior. Using concepts from fluid dynamics, a partial differential equation for nanowire shape evolution is derived from a semiclassical energy functional that includes electron-shell effects. A rich dynamics involving movement and interaction of kinks connecting locally stable radii is found, and a new class of universal equilibrium shapes is predicted.

Kink-pair mechanisms for a/2 〈111〉 screw dislocation motion in bcc tantalum

The structure, energetics, and multiplicity of kinks on an a/2 〈111〉 screw dislocation in bcc Ta have been studied in detail via atomistic computer simulation, using quantum-based multi-ion interatomic potentials derived from model generalized pseudopotential theory (MGPT) together with a robust Green's function simulation technique. The stable core structure of the rigid screw dislocation is predicted to be weakly polarized and spread out on three {110} planes in 〈112〉 directions, with two energetically equivalent configurations. This double degeneracy leads to the possibility of anti-phase defects forming on the dislocation line as well multiple kinks and kink pairs. The zero-stress formation energies of 16 possible kink-pair configurations for bcc Ta have been calculated and are in the range 0.67–1.84 eV. The lowest kink-pair energy of the perfect screw is in good agreement with the best current empirical estimate. Under an applied stress, the corresponding kink–kink interaction energy displays a λ −1 elastic attraction when the separation λ is larger than 7 b=20 Å, while the stress needed to maintain the kink pair varies as λ −1.5.

Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model

We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.

Determining Static Stresses of Deformed Solitons

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the static stresses of the deformed $\Phi ^4$-kink that are produced by the excitation of the internal soliton mode are exactly determined. The kink interaction potential at large distances is considered for the example of the nonlinear Klein-Gordon system. A general approach to the problem of exactly determining the intersoliton potential for the entire set of physically admissible two-soliton configurations is discussed.

Deformation by a kink mechanism in high temperature materials

A new double kink dislocation model has been developed to explain the temperature dependence of the yield stress in materials such as oxides and intermetallics that require high temperatures for plastic flow. The major variation in the free energy for the formation of a double kink nucleus with stress is the kink–kink interaction energy. However, there is also a stress dependence of the pre-exponential factor in the strain rate constitutive equation arising from kink diffusion. Numerical solution of the resulting equations shows that there are temperature regimes where the stress varies logarithmically with temperature. The model explains quantitatively the temperature dependence of the critical resolved shear stress on different slip systems for sapphire and spinel in terms of different activation energies for kink diffusion. The model can be modified to explain compositional softening in spinel by incorporating enhanced kink nucleation at cation vacancies. This changes both the pre-exponential term and the activation energy and explains why the critical resolved shear stress (CRSS) decreases as the inverse of the square of the vacancy concentration, as is observed.

Half-kink lattice solution of the phi6model

Investigation of a great number of physical systems shows that a scaled Landau free energy density of the form describes a first-order phase transition. To study the formation of static domain walls in these systems we include a spatial gradient (Ginzburg) term of the scalar order parameter . At the transition temperature (Tc) the potential has three degenerate minima corresponding to an asymmetric domain wall (i.e. a half-kink solution). We have obtained the associated kink lattice solution, its energy of formation and asymptotic kink--kink interaction. In addition, we report a `pulse' lattice solution below Tc.

Classical and non-classical interaction of kinks in some bubbly mediums

Properties of nonlinear waves in one of the nonlinear partial differential equations are investigated. The kinks with the solitonic, but unusual from the classic viewpoint, behaviour are found. The equation itself does not possess the Painlevé property.

Interactions of topological kinks in two coupled rings of nonlinear oscillators

Two discrete rings of nonlinear oscillators with topologically trapped kinks exhibit features due to coupling interactions between the rings. These interaction effects include phase locking between kinks in different rings, precession of the kink/antikink collision region, excitation of kink/antikink pairs, and time-dependent switching. We study these phenomena in simulations of two coupled discrete sine-Gordon equations, and in experiments on two inductively coupled rings of niobium Josephson junctions. @S0163-1829~98!06237-7#

Nonlocal Josephson electrodynamics of plates of finite thickness

A nonlocal integrodifferentical equation describing the electrodynamics of a Josephson junction between superconductors of finite thickness in the direction of the magnetic field is derived. It is shown that the interaction of kinks always exhibits long-range power-law asymptotic behavior, which can strongly influence the motion of vortices in and the current-voltage characteristic of even a thick contact. The spectrum of low-amplitude excitations is studied.

The power spectrum associated with a kink chain oscillating in a non-stokesian atmosphere of paraelastic interstitials

The power spectrum of a built-in kink chain oscillating in an atmosphere of paraelastic interstitials was investigated numerically using a fast Fourier transform technique. Above a sharply defined value of the strain amplitude, odd-harmonic generation is observed only at the low-temperature side of the dislocation relaxation peak associated with interstitial—kink interaction. At moderately high strain amplitudes, a strong enhancement of the harmonics situated in the immediate vicinity of the natural resonance frequency of the chain and complete depression of the rest are clearly seen. Finally, the onset of quasi-chaotic kink oscillations is detected when the system is driven into the super-Snœk regime where atmospheric tearing takes place.

Particle aspects of kink interactions

A simple method to compute the interaction between moving solitons in 1+1 dimensions is presented. Particle aspects of these field configurations are discussed and the interactions of sine-Gordon andφ 4 kinks are worked out as examples. The ground-state energy of a kink in a large box is also derived.

Interactions of kinks with defect modes

We derive and analyzed a two degree-of-freedom collective coordinate (CC) model to describe interactions of a kink soliton with a localized defect mode. Numerical simulations, supported by approximate analytic calculations, reveal a sequence of transmitted and reflected states but no permanent capture within the CC model.

On the dynamics of kink-type solitons in an elastic medium

The question of kink-type (domain-wall-type) topological soliton motion with a kink interaction with the elastic deformation field was considered. The viscosity of the deformation field was taken into account. It is shown that kink motion with a velocity in some interval around the sound velocity is impossible for some relations between the system parameters (elastic gap effect). For small coupling constants or a large viscosity the elastic gap does not exist. The results can describe the domain wall dynamics in magnetics or the proton kink dynamics in systems with hydrogen bounds.