Related papers: Topological defects with power-law tails
We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between…
We look for long-living topological solutions of classical nonlinear $(1+1)-$ dimensional $\varphi^4$ field theory. To that effect we use the well-known cut-and-match method. In this framework, new long-living states are obtained in both…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a P\"oschl-Teller potential at integer level $\sigma$. The cases $\sigma=1$ and $2$ are the well-known Sine-Gordon and $\phi^4$…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…
In this work, we study kink collisions in a scalar field model with scalar-kinetic coupling. This model supports kink/antikink solutions with inner structure in the energy density. The collision of two such kinks is simulated by using the…
The frictional dynamics of interacting surfaces under forced translation are critically dependent on lattice commensurability. Performing experiments in a trapped-ion friction emulator, we observe two distinct structural and frictional…
We study the kink motion for the one-dimensional stochastic Allen-Cahn equation and its mass conserving counterpart. Using a deterministic slow manifold, in the sharp interface limit for sufficiently small noise strength we derive an…
We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero modes should be handled in…
Quantal systems are predicted to show a change-over from exponential decay to power law decay at very long times. Although most theoretical studies predict integer power-law exponents, recent measurements by Rothe et al. of decay…
We present a model of two-kinks resulting from an explicit composition of two standards kinks of the $\phi^4$ model based on the procedure of Ref. \cite{uchiyama}. The two-kinks have an additional parameter accounting for the separation of…
The force exerted by a semi-infinite inhomogeneous superconductor with a planar interface to vacuum on a magnetic tip is studied theoretically in the absence of external magnetic fields. It is shown that the force has a contribution from…
In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a $(1+1)$-dimensional space-time the defects are classically degenerate in mass kinks, but in…
We consider the evolution of two contact-interacting harmonically-trapped particles following an arbitrary quench in interaction strength. We calculate the post-quench particle separation as a function of time and the total post-quench…
The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can…
We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called K\"ucken-Champod model…
High-resolution imaging provides dense trajectories of migrating cells, flocking animals, and synthetic active particles, from which interaction laws can be determined with a wide variety of methods. Yet, distinguishing whether front-back…
We investigate kink-antikink scattering in the $\lambda \phi^4$ model in the presence of an additional scalar field, $\psi$, that is in its quantum vacuum and interacts with $\phi$ via a $\xi \phi^2\psi^2$ term where $\xi$ is the coupling.…
In this paper we present a detailed and exact study of the probability density function $P(F)$ of the total force $F$ acting on a point particle belonging to a perturbed lattice of identical point sources of a power law pair interaction.…
We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study…