Related papers: Dislocation dynamics in a dodecagonal quasiperiodi…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation…
We numerically examine dynamical irreversible to reversible transitions and random organization for periodically driven gliding dislocation assemblies using the stroboscopic protocol developed to identify random organization in periodically…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
A model system for classical fluids out of equilibrium, referred to as DPD solid (Dissipative Particles Dynamics), is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat…
This paper investigates an elastic dislocation problem within a bounded and multi-layered solid governed by the Lam\'e system. We address the simultaneous reconstruction of the faults, the jumps in displacement and traction fields across…
We study propagation of dissipative structures in inhomogeneous media with a focus on pinning and depinning transitions. We model spatial complexity in the medium as generated by dynamical systems. We are thus able to capture transitions…
Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous…
This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical…
A novel formulation of second-order relativistic viscous fluid dynamics based on the effective Boltzmann equation for quasi-particles with medium-dependent masses is briefly reviewed.~The evolution equations for the shear and bulk…
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove…
We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for…
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy…
We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as…
Reaction-diffusion equation model for a 2-dimensional gas discharge system is introduced in close relationship with the recent experiment by Nasuno. The model shows formation of spots, molecule-like organization of a cluster of spots,…
A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensional crystals described by periodized discrete elasticity models is presented. When the crystal is sheared beyond a critical strain $F=F_{c}$, the strained…
The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of…
We present a molecular dynamics study on atomic self-diffusion in Frank-Kasper type dodecagonal quasicrystals. It is found that the quasicrystal-specific flip mechanism for atomic diffusion as predicted by Kalugin and Katz, indeed occurs in…