Related papers: Dynamical Transition Theory of Hexagonal Pattern F…
Mean square displacements of hydrogen atoms in glass-forming materials and proteins, as reported by incoherent elastic neutron scattering, show kinks in their temperature dependence. This crossover, known as the dynamical transition,…
A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
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…
In this paper we study homoclinic tangles formed by transversal intersections of the stable and the unstable manifold of a {\it non-resonant, dissipative} homoclinic saddle point in periodically perturbed second order equations. We prove…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition…
We use an analytic criterion for vanishing of exponential damping of correlations developed previously (Piasecki et al, J. Chem. Phys., 133, 164507, 2010) to determine the threshold volume fractions for structural transitions in hard sphere…
Curved-sided hexagrams with multiple equilibrium states have great potential in engineering applications such as foldable architectures, deployable aerospace structures, and shape-morphing soft robots. In Part I, the classical stability…
We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…
We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original…
We review recent developments in structural-dynamical phase transitions in trajectory space. An open question is how the dynamic facilitation theory of the glass transition may be reconciled with thermodynamic theories that posit a…
We study classical two-dimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spin-nematic "order by disorder" transition is developed based on the self-consistent determination of the…
In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes…
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…