Related papers: Three waves of chemical dynamics
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical…
The process of technological change can be regarded as a non-deterministic system governed by factors of a cumulative nature that generate cyclical phenomena. In this context, the process of growth and decline of technology can be…
Compression wave analysis started nearly 50 years ago with Fowles.[1] Coperthwaite and Williams [2] gave a method that helps identify simple and steady waves. We have been developing a method that gives describes the non-isentropic…
Simulations of over $10^3$ hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel…
Hyperbolic flows, as formulated by Anosov, are the prototypes of chaotic evolutions in classical dynamical systems. Here we provide a concise updated account of their quantum counterparts originally formulated by Emch, Narnhofer, Thirring…
The nonlinear dynamics of circularly polarized dispersive Alfv{\'e}n wave (AW) envelopes coupled to the driven ion sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
We consider thermal phases of holographic lattices at finite chemical potential in which a continuous internal bulk symmetry can be spontaneously broken. In the normal phase, translational symmetry is explicitly broken by the lattice and…
Quantum mechanical equations of motion are strictly linear in state descriptors, such as wavefunctions and density matrices, but equations describing chemical kinetics and hydrodynamics may be non-linear in concentrations. This…
We present a theory for experimentally observed phenomenon of one dimensional asynchronous waves. The general principle of coexistence of linear and nonlinear solutions of a dynamical system is underlying the present theoretical work. The…
A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…
The study of the phase space of multidimensional systems is one of the central open problems in dynamical systems. Being able to distinguish chaoticity from regularity in nonlinear dynamical systems, as well as to determine the subspace of…
Far from equilibrium, chemical and biological systems can form complex patterns and waves through reaction-diffusion coupling. Fluid motion often interferes with these self-organized concentration patterns. In this study, we investigate the…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…
Multistability of mesoscopic, driven biochemical reaction systems has implications to a wide range of cellular processes. Using several simple models, we show that one class of bistable chemical systems has a deterministic counterpart in…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
Water is one of the most abundant substances on Earth, and ice, i.e., solid water, has more than 18 known phases. Normally ice in nature exists only as Ice Ih, Ice Ic, or a stacking disordered mixture of both. Although many theoretical…