Related papers: Stretched Exponential Relaxation in the Biased Ran…
We revisit the issue of relaxation to thermal equilibrium in the so-called "sheet model", i.e., particles in one dimension interacting by attractive forces independent of their separation. We show that this relaxation may be very clearly…
We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred location (say, the origin), here we consider…
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…
We give a comprehensive mean-field analysis of the Partisan Voter Model (PVM) and report analytical results for exit probabilities, fixation times, and the quasi-stationary distribution. In addition, and similarly to the noisy voter model,…
This paper studies the dynamics of relaxation phenomena in the standard dissipative particle dynamics (DPD) model [Groot and Warren, JCP, 107:4423 (1997)]. Using fluctuating hydrodynamics as the framework of the investigation, we focus on…
We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling…
We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows…
We have investigated the relaxational dynamics for a protein model at various temperatures. Theoretical analysis of this model in conjunction with numerical simulations suggests several relaxation regimes, including a single exponential, a…
We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending…
The stretched exponential relaxation function is used to analyze the relaxation of the glassy state data. Due to the singularity of this function at the origin, this function is inconvenient for data analysis. Concerning this, a Prony…
We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form $D(x)\sim D_0|x|^\alpha$ in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the…
The non-Debye, \textit{i.e.,} non-exponential, behavior characterizes a large plethora of dielectric relaxation phenomena. Attempts to find their theoretical explanation are dominated either by considerations rooted in the stochastic…
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…
This paper introduces a definition of ideological polarization of an electorate around a particular central point. By being flexible about the location or width of the center, this measure enables the researcher to analyze polarization…
Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar…
Averaging, or smoothing, is a fundamental approach to obtain stable, de-noised estimates from noisy observations. In certain scenarios, observations made along trajectories of random dynamical systems are of particular interest. One popular…
The voter model has been extensive studied as an opinion dynamic model, and the role of the zealots has only been discussed recently. We introduce the adaptive voter model with zealots and show that the final distribution of the magnetism…
We introduce a variational method for analyzing limit cycle oscillators in $\mathbb{R}^d$ driven by Gaussian noise. This allows us to derive exact stochastic differential equations (SDEs) for the amplitude and phase of the solution, which…
Two-dimensional (2D) spectroscopy provides information about dissipative processes subsequent to electronic excitation, which play a functional role in energy harvesting materials and devices. This technique is particularly sensitive to…
The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees…