Related papers: Nonlinear analog of the complexity-stability trans…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field,…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Highlights: \begin{itemize} \item Relativistic effect of crystal dynamics "freezing". \item Non-statistical model of thermodynamic equilibration. \end{itemize} The dynamics of oscillations of a one-dimensional atomic chain is investigated…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior.…
A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the…
Starting from a linear fractional representation of a linear system affected by constant parametric uncertainties, we demonstrate how to enhance standard robust analysis tests by taking available (noisy) input-output data of the uncertain…
In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
We consider transition to strong turbulence in an infinite fluid stirred by a gaussian random force. The transition is {\bf defined} as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation…
Software systems are widely observed to grow in size, complexity, and interdependence over time, yet many large-scale systems remain stable despite persistent structural burden. This apparent tension suggests a limitation in one-dimensional…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
A procedure is introduced which allows to represent the dynamics of a non-equilibrium system violating detailed balance by its steady state loop fluxes. It is shown that detailed balance is restored in this representation, such that the…
A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input…
A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise.…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…