Related papers: Dynamics below the depinning threshold
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
This paper studies the stability of an abstract thermoelastic system with Cattaneo's law, which describes finite heat propagation speed in a medium. We introduce a region of parameters containing coupling, thermal dissipation, and possible…
We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves,…
We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the…
A molecular-dynamics type simulation method, which is suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinning-like…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Using one loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…
This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and…
We study the dynamics of an elastic chain driven on a disordered substrate and analyze numerically the statistics of force fluctuations at the depinning transition. The probability distribution function of the amplitude of the slip events…
A variety of soft and hard condensed matter systems are known to form stripe patterns. Here we use numerical simulations to analyze how such stripe states depin and slide when interacting with a random substrate and with driving in…
We perform via $\Gamma$-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can…
The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration…
Size-dependence of plastic flow is studied by discrete dislocation dynamical simulation of systems with various numbers of interacting linear edge dislocations while the stress is slowly increased. Regions between avalanches in the…
We investigate the Kondo model with time-dependent couplings that are periodically switched on and off. On the Toulouse line we derive exact analytical results for the spin dynamics in the steady state that builds up after an infinite…
The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
The dynamics of a one-dimensional crystalline interface model with long-range interactions is investigated. In the absence of randomness, the linear response mobility decreases to zero when the temperature approaches the roughening…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…