Related papers: Examining the evolution of phase-space elements fo…
We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise…
This paper investigates the dynamics of cosmological models incorporating nonlinear electrodynamics (NLED), focusing on their stability and causality. We explore two specific NLED models: the Power-Law and Rational Lagrangians. We assess…
The motility of the worm nematode \textit{Caenorhabditis elegans} is investigated in shallow, wet granular media as a function of particle size dispersity and area density ($\phi$). Surprisingly, we find that the nematode's propulsion speed…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…
Gastrulation, namely cell internalization, is a significant milestone during the development of metazoans from worm to human, which generates multiple embryonic layers with distinct cell fates and spatial organizations. Although many…
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group $\mathrm{SO}(3)$ by identifying closed form expressions for geometric quantities such as covariant derivative and parallel transport in exponential…
Mini-proteins and peptides manifest dynamic conformational fluctuation and involve mutual interconversion among metastable states. A robust mapping of the conformational landscape underlying mini-proteins and peptides often requires…
We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model…
This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical…
Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest exponent is a measure of the time horizon over which the evolution of the system can be…
We study changes in the chaotic properties of a many-body system undergoing a solid-fluid phase transition. To do this, we compute the temperature dependence of the largest Lyapunov exponents $\lambda_{max}$ for both two- and…
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…
We model the neuronal circuit of the C.elegans soil worm in terms of Hindmarsh-Rose systems of ordinary differential equations, dividing its circuit into six communities pointed out by the walktrap and Louvain methods. Using the numerical…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…
A generalized set of Clifford cellular automata, which includes all Clifford cellular automata, result from the quantization of a lattice system where on each site of the lattice one has a $2k$-dimensional torus phase space. The dynamics is…
We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho(p,q)$. Of particular interest is $\lambda_2$, an exponent which quantifies the rate at which chaotically evolving…
In this paper, we propose an implicit staggered algorithm for crystal plasticity finite element method (CPFEM) which makes use of dynamic relaxation at the constitutive integration level. An uncoupled version of the constitutive system…