相关论文: Dynamics of defect formation
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the…
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental…
We study the formation of topological defects in nonequilibrium phase transitions of both classical and quantum field theory. We examine three model systems. 1). The phase transition of a quantum scalar field in a FRW universe is analyzed…
An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities.…
The steady state shock formation in processes like nonconserving asymmetric simple exclusion processes in varied situations is shown to be a nonequilibrium critical phenomenon. The diverging length scales and the quantitative description of…
We study the stochastic motion of a particle subject to spatially varying Lorentz force in the small-mass limit. The limiting procedure yields an additional drift term in the overdamped equation that cannot be obtained by simply setting…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving…
We propose and solve a minimal model of dynamic passage through a second-order phase transition in the presence of symmetry breaking interactions and no dissipation. Our model generalizes the Hamiltonian dynamics of the Painleve'-2 equation…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…
The characteristic size for spatial structure, that emerges when the bifurcation parameter in model partial differential equations is slowly increased through its critical value, depends logarithmically on the size of added noise. Numerics…
We study the behavior of the antiferromagnetic RP$^2$ model in $d=3$. The vacuum structure is analyzed in the critical and low temperature regions, paying special attention to the spontaneous symmetry breaking pattern. Near the critical…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
The formation of an equilibrium quantum state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of non-equilibrium many-body physics. During such crossing, the system breaks its…