Related papers: Critical phases in the raise and peel model
We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a $Z_3$ or $Z_4$ symmetry broken density-wave ground state. Our protocol…
It is shown that the critical layer analysis, involved in the linear theory of internal modes, can be extended continuously into the early nonlinear regime. For the m=1 resistive mode, the dynamical analysis involves two small parameters:…
Pressure-gradient-induced separation of swept and unswept turbulent boundary layers, based on the DNS studies of Coleman et al. (J. Fluid Mech. 2018 & 2019), have been analyzed for various nonequilibrium effects. The goal is to isolate…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
Process Reward Models (PRMs) are a powerful mechanism for steering large language model reasoning by providing fine-grained, step-level supervision. However, this effectiveness comes at a significant cost: PRMs require expert annotations…
We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We consider partial exclusion processes~(PEPs) on the one-dimensional square lattice, that is, a system of interacting particles where each particle random walks according to a jump rate satisfying an exclusion rule that allows up to a…
Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we…
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…
A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a non-zero value of the packing fraction. The zero-temperature constraint of force-balance plays a crucial role in…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Reconstructing high-quality images from substantially undersampled k-space data for accelerated MRI presents a challenging ill-posed inverse problem. While supervised deep learning has revolutionized this field, it relies heavily on large…
The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based on a linear time-invariant plant model is studied. Based on the long-time behavior of the solution of the Riccati Differential…
We study the critical droplet for a close-to-equilibrium Widom-Rowlinson model of interacting particles, represented by disks of radius $1$, in the two-dimensional plane at low temperature. The critical droplet is the set of macroscopic…
Crystal plasticity models connect macroscopic deformation with the physics of microscale slip in polycrystalline materials. These models can be calibrated using global stress-strain curves, but the resulting parametrization is often not…