Kink Interaction Research Articles

Interactions and Dynamics of One-Dimensional Droplets, Bubbles and Kinks

We explore the dynamics and interactions of multiple bright droplets and bubbles, as well as the interactions of kinks with droplets and with antikinks, in the extended one-dimensional Gross–Pitaevskii model including the Lee–Huang–Yang correction. Existence regions are identified for the one-dimensional droplets and bubbles in terms of their chemical potential, verifying the stability of the droplets and exposing the instability of the bubbles. The limiting case of the droplet family is a stable kink. The interactions between droplets demonstrate in-phase (out-of-phase) attraction (repulsion), with the so-called Manton’s method explicating the observed dynamical response, and mixed behavior for intermediate values of the phase shift. Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink–antikink interactions are repulsive, generating counter-propagating shock waves. Our findings reveal dynamical features of droplets and kinks that can be detected in current experiments.

Kink Dynamics in the $\varphi^{4}$ Model with Extended Impurity

The $\varphi^{4}$ theory is widely used in many areas of physics, from cosmology and elementary particle physics to biophysics and condensed matter theory. Topological defects, or kinks, in this theory describe stable, solitary wave excitations. In practice, these excitations, as they propagate, necessarily interact with impurities or imperfections in the on-site potential. In this work, we focus on the effect of the length and strength of a rectangular impurity on the kink dynamics. It is found that the interaction of a kink with an extended impurity is qualitatively similar to the interaction with a well-studied point impurity described by the delta function, but significant quantitative differences are observed. The interaction of kinks with an extended impurity described by a rectangular function is studied numerically. All possible scenarios of kink dynamics are determined and described, taking into account resonance effects. The inelastic interaction of the kink with the repulsive impurity arises only at high initial kink velocities. The

Weak and Strong Interaction of Excitation Kinks in Scalar Parabolic Equations

Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest PDE model of excitable media given by the scalar reaction diffusion-type theta -equations for excitable angular phase dynamics. On the one hand, we qualitatively study geometric kink positions using the comparison principle and the theory of terraces. This yields the minimal initial distance as a global lower bound, a well-defined sequence of collision data for kinks- and antikinks, and implies that periodic pure kink sequences are asymptotically equidistant. On the other hand, we study metastable dynamics of finitely many kinks using weak interaction theory for certain analytic kink positions, which admits a rigorous reduction to ODE. By blow-up type singular rescaling we show that distances become ordered in finite time, and eventually diverge. We conclude that diffusion implies a loss of information on kink distances so that the entropic complexity based on positions and collisions in the GHCA does not simply carry over to the PDE model.

Wide class of logarithmic potentials with power-tower kink tails

We present a wide class of potentials which admit kinks and corresponding mirror kinks with either a power law or an exponential tail at the two extreme ends and a power-tower form of tails at the two neighbouring ends. We analyse kink stability equation in all these cases and show that there is no gap between the zero mode and the beginning of the continuum. Finally, we provide a recipe for obtaining logarithmic potentials with power-tower kink tails and estimate kink–kink interaction strength.

New types of interaction solutions to the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

In this paper, with the aid of symbolic computation system Maple, and based on the simplified Hirota method and ansatz technique, we discussed the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation with [Formula: see text] to obtain lump solutions, lump–kink solutions and three classes of interaction solutions. Comparing our new results with other researchers’ results shows that using this method gives the more opportunity to solve the nonlinear partial differential equations that appear in mathematics, physics, biological engineering and other fields. We also presented profiles of new lump solution, lump–kink solutions and interaction solutions as illustrative examples.

Lump-type solution and breather lump–kink interaction phenomena to a ($$\mathbf{{3{\varvec{+}}1}}$$)-dimensional GBK equation based on trilinear form

In this paper, the multivariate trilinear operators in the ($$3+1$$)-dimensional space are applied to a ($$3+1$$)-dimensional GBK equation. The resulting trilinear form is used to study its wave dynamics. Particularly, we generate a type of new interaction solutions between breather lump-type solitons and other multi-kink solitons, thereby formulating a kind of breather lump–kink solitons. By setting time constants, we change the coordinates of kink solitons to make them collide with the breather lump-type soliton, during which breather lump-type soliton is swallowed eventually by those kink solitons. The evolution behaviours of the breather lump–kink solitons are depicted by plotting 3-D and density graphs from the perspective of wave characteristics.

Critical velocity in kink-defect interaction models: Rigorous results

In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More specifically, we prove that a heteroclinic orbit in the energy level 0 of a 2-dof Hamiltonian Hε is destroyed giving rise to heteroclinic connections between certain elements (at infinity) for exponentially small (in ε) energy levels. In this setting Melnikov theory does not apply because there are exponentially small phenomena.

Long-range interactions of kinks

We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the $\varphi^8$ field theory, although we explore similar issues in example $\varphi^{10}$ and $\varphi^{12}$ models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard $\varphi^4$ model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady states, we make the case that such asymptotics require particular care in setting up multi-soliton initial conditions. A naive implementation of additive or multiplicative ans\"atze gives rise to highly pronounced radiation effects and eventually leads to the illusion of a repulsive interaction between a kink and an antikink in such higher-order field theories. We propose and compare several methods for how to "distill" the initial data into suitable ans\"atze, and we show how these approaches capture the attractive nature of interactions between the topological solitons in the presence of power-law tails (long-range interactions). This development paves the way for a systematic examination of solitary wave interactions in higher-order field theories and raises some intriguing questions regarding potential experimental observations of such interactions. As an Appendix, we present an analysis of kink-antikink interactions in the example models via the method of collective coordinates.

Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon Equation with Attracting Impurity

Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon Equation with Attracting Impurity

Interacting kinks and meson mixing

A Rayleigh–Schrödinger type of perturbation scheme is employed to study weakly interacting kinks and domain walls formed from two different real scalar fields χ and φ. An interaction potential V1(χ,φ) is chosen which vanishes in a vacuum state of either field. Approximate first order corrections for the fields are found, which are associated with scalar field condensates inhabiting the zeroth order topological solitons. The model considered here presents several new and interesting features. These include (1) a condensate of each kink field inhabits the other kink, (2) the condensates contribute an associated mass to the system which vanishes when the kinks overlap, (3) a resulting mass defect of the system for small interkink distances allows the existence of a loosely bound state when the interkink force is repulsive. An identification of the interaction potential energy and forces allows a qualitative description of the classical motion of the system, with bound states, along with scattering states, possible when the interkink force is attractive. (4) Finally, the interaction potential introduces a mixing and oscillation of the perturbative χ and φ meson flavor states, which has effects upon meson–kink interactions.

Multisoliton Dynamics in the Sine-Gordon Model with Two Point Impurities

Collective variables method is used to derive a set of differential equations to describe the dynamics of a kink in the sine-Gordon model with two identical point impurities taking damping into account. It is shown that the scenarios of kink interaction with the waves localized on the impurities, found from the reduced model, are similar to those obtained earlier by numerical integration of the continuous sine-Gordon equation. For the case of the kink passage through the region with the impurities, the structure and properties of the arising on impurities long-lived four-kink multisolitons are analyzed. For the approximate analytical description of the two bound impurity-localized nonlinear waves, the system of differential equations for harmonic oscillators with elastic link is obtained. The analytical model qualitatively reproduces the results of the sine-Gordon equation numerical simulation. The cases of large and small distances between impurities are analyzed. The results of our study uncover new features of the kink-impurity interaction which is important for a number of applications where the sine-Gordon model is used.

Topological defects with power-law tails

We study interactions of kinks and antikinks of the (1 + 1)-dimensional ϕ8 model. In this model, there are kinks with mixed tail asymptotics: power-law behavior at one infinity versus exponential decay towards the other. We show that if a kink and an antikink face each other in way such that their power-law tails determine the kink-antikink interaction, then the force of their interaction decays slowly, as some negative power of distance between them. We estimate the force numerically using the collective coordinate approximation, and analytically via Manton’s method (making use of formulas derived for the kink and antikink tail asymptotics).

Flaming 2π kinks in parametrically driven systems.

Macroscopic extended systems with dissipation and injection of energy can exhibit particlelike solutions. Dissipative kinks with an oscillatory cloak and a family of localized states that connect uniform symmetric states in a magnetic wire forced with a transversal oscillatory magnetic field and in a parametrically driven damped pendula chain are studied. The oscillatory cloak is composed of evanescent waves emitted at the kink position and generated by a resonant mechanism. These waves mediate the kink interaction and generate a family of localized states.

Exact soliton solutions for the interaction of few-cycle-pulse with nonlinear medium

We study the Panilevé property of the coupled equations describing the interaction of few-cycle-pulse with nonlinear medium. And we use the consistent tanh expansion (CTE) method to search for exact interaction soliton solutions of the coupled equations. Many interaction solutions are obtained, such as the one kink-one periodic wave interaction solution, one kink-two periodic waves interaction solution, one kink-one dipole soliton interaction solution, one kink-two dipole solitons interaction solution, and one kink-soliton-one periodic wave interaction solution. We also obtain the kink–kink interaction by using Painlevé truncated expansion method.

Fifty Shades of Stigma: Exploring the Health Care Experiences of Kink-Oriented Patients

IntroductionThe term kink describes sexual behaviors and identities encompassing bondage, discipline, domination and submission, and sadism and masochism (collectively known as BDSM) and sexual fetishism. Individuals who engage in kink could be at risk for health complications because of their sexual behaviors, and they could be vulnerable to stigma in the health care setting. However, although previous research has addressed experiences in mental health care, very little research has detailed the medical care experiences of kink-oriented patients. AimTo broadly explore the health care experiences of kink-oriented patients using a community-engaged research approach. MethodsAs part of the Kink Health Project, we gathered qualitative data from 115 kink-oriented San Francisco area residents using focus groups and interviews. Interview questions were generated in collaboration with a community advisory board. Data were analyzed using a thematic analysis approach. Main Outcome MeasuresThemes relating to kink-oriented patients' experience with health and healthcare. ResultsMajor themes included (i) kink and physical health, (ii) sociocultural aspects of kink orientation, (iii) the role of stigma in shaping health care interactions, (iv) coming out to health care providers, and (v) working toward a vision of kink-aware medical care. The study found that kink-oriented patients have genuine health care needs relating to their kink behaviors and social context. Most patients would prefer to be out to their health care providers so they can receive individualized care. However, fewer than half were out to their current provider, with anticipated stigma being the most common reason for avoiding disclosure. Patients are often concerned that clinicians will confuse their behaviors with intimate partner violence and they emphasized the consensual nature of their kink interactions. ConclusionLike other sexual minorities, kink-oriented patients have a desire to engage with their health care providers in meaningful discussions about their health risks, their identities, and their communities without fear of being judged. Additional research is needed to explore the experiences of kink-oriented patients in other areas of the country and internationally.

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect.

The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.

О возбуждении солитонов при взаимодействии кинков уравнения синус-Гордона с притягивающей примесью

Исследованы аналитически и численно структура и свойства локализованных двух- и трех-кинковых решений уравнения синус-Гордона, возбуждаемых в области притягивающей примеси. Рассмотрены случаи одиночной и двойной пространственно протяженной примеси.

Effect of ionic strength on the Mg content of calcite: Toward a physical basis for minor element uptake during step growth

This experimental study determined the effect of ionic strength (IS) on the uptake of Mg into calcites that grew by the classical step propagation process. Using flow-through AFM and defined solution chemistry, calcite was grown in NaCl and KCl solutions of known supersaturation state while measuring the corresponding growth kinetics. Analysis of the resulting calcite compositions by SIMS shows that Mg content is inversely correlated with IS for both electrolytes. A sixfold increase in IS decreases the Mg-content by up to 40%. Overgrowths that developed in NaCl solutions contain more Mg than samples that grew in KCl solutions. The corresponding kinetic measurements reveal that step propagation rates are independent of IS within experimental error but are electrolyte-specific. In NaCl solutions, steps with the obtuse geometry move significantly faster than acute steps, but in KCl solutions, the acute and obtuse steps move at similar rates. Analysis of the data suggests that the decrease in Mg content with increasing IS arises from the interplay of ion–kink interactions between the background cations (Na + or K +), the primary solute cation (Ca 2+), and the impurity (Mg 2+). A simple physical model proposes that increasing levels of electrolytes block the attachment of the strongly hydrated Mg 2+ ion relative to Ca 2+ but the effects are step-specific for each type of electrolyte. Whereas K + interacts weakly with kink sites along both step directions, Na + interacts preferentially with acute steps and, consequently, slows their rate of step propagation relative to obtuse steps. Because Na + increases the fraction of the surface that develops from acute steps and because Mg is preferentially incorporated into the kink sites of acute steps, calcite overgrowths developed in NaCl solutions contain more Mg than those in grown in KCl. Thus, the salt-specific Mg contents measured in this study can be explained by shifts in the distribution of step types and the ability of each step type to incorporate Mg. The findings reconcile apparent discrepancies regarding the effect of IS on calcite kinetics and Mg incorporation observed in laboratory-based studies.

Dynamics of Strongly Nonlinear Kinks and Solitons in a Two-Layer Fluid

Perturbation theory is developed for interaction of strongly nonlinear solitary waves close to the limiting, tabletop solitons (Π-solitons). The method is based on representing each soliton as a compound of two kinks so that the interaction of N solitons is treated as the interaction of 2N kinks. As an example the Miyata–Choi–Camassa equations for a two-layer fluid is considered. Equations for kink coordinates are obtained and analyzed. Some nontrivial features of two-soliton interaction characteristic of the strongly nonlinear case are established.

Dynamics of Domain Walls in Pattern Formation with Traveling-Wave Forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.