Related papers: Chaotic Dynamics in Multidimensional Transition St…
Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
This is the third paper of the series of our studies of the one-dimensional self-gravitating many-body systems. In this paper, we thus study the transition phenomena after the first transition from a quasiequilibrium. We found that…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. This work finds a continuous phase transition when disorder breaks permutation symmetry,…
The transformation of a system from one state to another is often mediated by a bottleneck in the system's phase space. In chemistry these bottlenecks are known as \emph{transition states} through which the system has to pass in order to…
In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (i) the transition of a two-dimensional flow to…
Many fluid-dynamical systems met in nature are quasi-two-dimensional: they are constrained to evolve in approximately two dimensions with little or no variation along the third direction. This has a drastic effect in the flow evolution…
Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and…
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…
We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…
We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori it is possible to define phase space dividing…
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the…
Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid-fluid phase transition in…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
We investigate the existence of multiple turbulent states in highly turbulent Taylor-Couette flow in the range of $\mathrm{Ta}=10^{11}$ to $9\cdot10^{12}$, by measuring the global torques and the local velocities while probing the phase…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…