arXiv subjects

Linjie Zhao

Publications and source records attributed to Linjie Zhao.

26 records · Page 2Linked to original sources

arXiv2022

Moderate Deviations for the current and Tagged Particle in Symmetric Simple Exclusion Processes

We prove moderate deviation principles for the tagged particle position and current in one-dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate $1/2$, and the jump is suppressed if there is already one at the target site. We distinguish one particular particle which is called the tagged particle. We first establish a variational formula for the moderate deviation rate functions of the tagged particle positions based on moderate deviation principles from hydrodynamic limit proved by Gao and Quastel \cite{gao2003moderate}. Then we construct a minimizer of the variational formula and obtain explicit expressions for the moderate deviation rate functions.

math.PR↗

arXiv2021

Initial energy deposition and initiation mechanism of nanosecond laser damage caused by KDP surface micro-defects

To enable an exploration of the initiation mechanism of nanosecond laser damage on a potassium dihydrogen phosphate (KDP) surface, a defect-assisted energy deposition model is developed that involves light intensity enhancement and a sub-band gap energy level structure. The simulations provide an explanation on why the laser-induced damage threshold (LIDT) of the KDP crystal is two orders of magnitude lower than the theoretical value. The model is verified by use of the transient images that appear during the laser damage. In addition, the dimensions of the "dangerous" surface defects that are the most sensitive to the laser damage are proposed. This work enables clarification on the initial energy deposition (IED) and initiation mechanism of the nanosecond laser damage caused by the KDP surface defects on micro-nano scale. It is helpful in understanding the laser-matter interactions and to improve the processing technique for high quality optical components.

physics.app-ph↗

arXiv2021

Long-time behavior of SSEP with slow boundary

We consider the symmetric simple exclusion process with slow boundary first introduced in [Baldasso {\it et al.}, Journal of Statistical Physics, 167(5), 2017]. We prove a law of large number for the empirical measure of the process under a longer time scaling instead of the usual diffusive time scaling.

math.PR↗

arXiv2020

Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process

This paper is a further investigation of the problem studied in \cite{xue2020hydrodynamics}, where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on $\mathbb{Z}^d,\, d \geq 3$, and then conjectured that a central limit theorem should hold under a non-equilibrium initial condition. We prove that the aforesaid conjecture is true when the dimension $d$ of the underlying lattice and the infection rate $λ$ of the process are sufficiently large.

math.PR↗

arXiv2020

Application of light diffraction theory to qualify the downstream light field modulation property of mitigated KDP crystals

Micro-milling can effectively remove laser damage sites on a KDP (potassium dihydrogen phosphate) surface and then improve the laser damage resistance of the components. However, the repaired KDP surface could cause light propagating turbulence and downstream light intensification with the potential risk to damage downstream optics. In order to analyze the downstream light field modulation caused by Gaussian mitigation pits on KDP crystals, a computational model of the downstream light diffraction based on the angular spectrum theory and the Gaussian repair contour is established. The results show that the phase offset caused by the repaired surface produces a large light field modulation near the rear KDP surface. The modulation generated in the whole downstream light field is greater than that caused by the amplitude change. Therefore, the phase characteristics of the outgoing light could be suggested as a vital research topic for future research on the downstream light field modulation caused by mitigation contours. Significantly, the experimental results on the downstream light intensity distribution have good agreement with the simulation ones, which proves the validity of the established downstream light diffraction model. The phase characterization of the outgoing light is proposed as an evaluation tool in the repair of KDP crystals. The developed analytical method and numerical discrete algorithm could be also applicable in qualifying the repair quality of other optical components applied in high-power laser systems.

physics.optics↗

arXiv2020

Moderate Deviations for the SSEP with a Slow Bond

We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate $N^2$, except one particular bond, the slow bond, where the rate is $N$. Above, $N$ is the scaling parameter. This model has been considered in the context of hydrodynamic limits, fluctuations and large deviations. We investigate moderate deviations from hydrodynamics and obtain a moderate deviation principle.

math.PR↗

arXiv2019

Hydrodynamics of the Binary Contact Path Process

In this paper we are concerned with the binary contact path process introduced in \cite{Gri1983} on the lattice $\mathbb{Z}^d$ with $d\geq 3$. Our main result gives a hydrodynamic limit of the process, which is the solution to a heat equation. The proof of our result follows the strategy introduced in \cite{kipnis+landim99} to give hydrodynamic limit of the SEP model with some details modified since the states of all vertices are not uniformly bounded for the binary contact path process. In the modifications, the theory of the linear system introduced in \cite{Lig1985} is utilized.

math.PR↗

arXiv2018

The Limiting Behavior of the FTASEP with Product Bernoulli Initial Distribution

We study the facilitated totally asymmetric exclusion process on the one dimensional integer lattice. We investigate the invariant measures and the limiting behavior of the process. We mainly derive the limiting distribution of the process when the initial distribution is the Bernoulli product measure with density $1/2$. We also prove that in the low density regime, the system finally converges to an absorbing state.

math.PR↗