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We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…
The kinetics of irreversible annihilation of charged particles performing overdamped motion induced by long-range interaction force, $F(r)\sim r^{-\lambda}$, is investigated. The system exhibits rich kinetic behaviors depending on the force…
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and…
One well-known argument about one dimensional(1D) system is that 1D phase transition at finite temperature cannot exist, despite this concept depends on conditions such as range of interaction, external fields and periodicity. Therefore 1D…
In this paper, we consider a structurally damped elastic equation under hinged boundary conditions. Fully-discrete numerical approximation schemes are generated for the null controllability of these parabolic-like PDEs. We mainly use finite…
Nonequilibrium transport measurements in mesoscopic quasi-ballistic 2D electron systems show an enhancement in the differential conductance around the Fermi energy. At very low temperatures, such a zero-bias anomaly splits, leading to a…
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a non-zero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set…
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into…
In this paper, we explore the localization transition and the scaling properties of both quasi-one-dimensional and two-dimensional quasiperiodic systems, which are constituted from coupling several Aubry-Andr\'{e} (AA) chains along the…
In this work, we study the slow entropy type invariant of a dynamical system proposed by A. M. Vershik. We provide an explicit construction of a system whose class of scaling entropy sequences is empty. For this unstable case, we introduce…
Several three-dimensional Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the passing generic vehicles (Ahmed bodies) are presented. The relative motion of vehicles was obtained using a combination of deforming and sliding…
Unsupervised anomaly detection (AD) is a challenging task in realistic applications. Recently, there is an increasing trend to detect anomalies with deep neural networks (DNN). However, most popular deep AD detectors cannot protect the…
In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the…
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of…
We demonstrate that 3+1-dimensional quantum electrodynamics with fermionic charges, fermionic monopoles, and fermionic dyons arises at the edge of a 4+1-dimensional gapped state with short-range entanglement. This state cannot be…
We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the…
Phase change energy storage is getting increasing attention as a representative technology to achieve carbon neutrality. The phase change process exists typical phenomenon of asymmetry that affects the energy storage performance. However,…
Here I provide additional experimental information and criticise the analysis, modelling, interpretation and claims presented in the recent paper [Nature Communications 11, 4942 (2020)]. I argue that the authors have no clear experimental…