Discrete Boltzmann Modeling of Plasma Shock Wave

Plasma shock waves widely exist and play an important role in high-energy-density environment, especially in the inertial confinement fusion. Due to the large gradient of macroscopic physical quantities and the coupled thermal, electrical, magnetic and optical phenomena, there exist not only hydrodynamic non-equilibrium (HNE) effects, but also strong thermodynamic non-equilibrium (TNE) effects around the wavefront. In this work, a two-dimensional single-fluid discrete Boltzmann model is proposed to investigate the physical structure of ion shock. The electron is assumed inertialess and always in thermodynamic equilibrium. The Rankine-Hugoniot relations for single fluid theory of plasma shock wave is derived. It is found that the physical structure of shock wave in plasma is significantly different from that in normal fluid and somewhat similar to that of detonation wave from the sense that a peak appears in the front. The non-equilibrium effects around the shock front become stronger with increasing Mach number. The charge of electricity deviates oppositely from neutrality in upstream and downstream of the shock wave. The large inertia of the ions causes them to lag behind, so the wave front charge is negative and the wave rear charge is positive. The variations of HNE and TNE with Mach number are numerically investigated. The characteristics of TNE can be used to distinguish plasma shock wave from detonation wave.

When the geodesic becomes rigid in the directed landscape

When the value $L$ of the directed landscape at a point is sufficiently large, the geodesic to this point is rigid and its location fluctuates of order $L^{-1/4}$ around its expectation. We further show that at a midpoint of the geodesic, the location of the geodesic and the value of the directed landscape after appropriate scaling converge to two independent Gaussian.

One point distribution of the geodesic in directed last passage percolation

We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one point distribution of the geodesic location joint with the last passage times, and its limit when the size goes to infinity.

Limiting one-point distribution of periodic TASEP

The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in the KPZ universality class in a periodic domain. Unlike the infinite line case, the limiting one point distribution depends non-trivially on the scaled time parameter. We study several properties of this distribution for the case of the periodic step and flat initial conditions. We show that the distribution changes from a Tracy-Widom distribution in the small time limit to the Gaussian distribution in the large time limit, and also obtain right tail estimate for all time. Furthermore, we establish a connection to integrable differential equations such as the KP equation, coupled systems of mKdV and nonlinear heat equations, and the KdV equation.

System Outage Probability of PS-SWIPT Enabled Two-Way AF Relaying with Hardware Impairments

In this paper, we investigate the system outage probability of a simultaneous wireless information and power transfer (SWIPT) based two-way amplify-and-forward (AF) relay network considering transceiver hardware impairments (HIs), where the energy-constrained relay node processes the received signals based on a power splitting protocol and the two terminals employ a selection combining (SC) scheme to exploit the signals from the direct and relaying links. Assuming independent but non-identically distributed Nakagami-m fading channels, we derive the system outage probability in a closed-form, which enables us to identify two crucial ceiling effects on the system outage probability caused by HIs in the high data rate regions, i.e., relay cooperation ceiling (RCC) and overall system ceiling (OSC). Specifically, the RCC prevents the relaying link from participating in cooperative communications, while the OSC leaves the overall system in outage. Furthermore, we derive the achievable diversity gain of the considered network, which shows that the diversity gain equals either the shape parameter of the direct link or zero. Computer simulations are provided to validate the correctness of our analytical results, and study the effects of various system parameters on the system outage performance and the optimal power splitting ratio, as well as the energy efficiency.

Joint Optimization of Spectrum and Energy Efficiency Considering the C-V2X Security: A Deep Reinforcement Learning Approach

Cellular vehicle-to-everything (C-V2X) communication, as a part of 5G wireless communication, has been considered one of the most significant techniques for Smart City. Vehicles platooning is an application of Smart City that improves traffic capacity and safety by C-V2X. However, different from vehicles platooning travelling on highways, C-V2X could be more easily eavesdropped and the spectrum resource could be limited when they converge at an intersection. Satisfying the secrecy rate of C-V2X, how to increase the spectrum efficiency (SE) and energy efficiency (EE) in the platooning network is a big challenge. In this paper, to solve this problem, we propose a Security-Aware Approach to Enhancing SE and EE Based on Deep Reinforcement Learning, named SEED. The SEED formulates an objective optimization function considering both SE and EE, and the secrecy rate of C-V2X is treated as a critical constraint of this function. The optimization problem is transformed into the spectrum and transmission power selections of V2V and V2I links using deep Q network (DQN). The heuristic result of SE and EE is obtained by the DQN policy based on rewards. Finally, we simulate the traffic and communication environments using Python. The evaluation results demonstrate that the SEED outperforms the DQN-wopa algorithm and the baseline algorithm by 31.83 % and 68.40 % in efficiency. Source code for the SEED is available at https://github.com/BandaidZ/OptimizationofSEandEEBasedonDRL.

Periodic TASEP with general initial conditions

We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point distributions in the space-time plane. The formulas are given in terms of an integral involving a Fredholm determinant. We then evaluate the large-time, large-period limit in the relaxation time scale, which is the scale such that the system size starts to affect the height fluctuations. The limit is obtained assuming certain conditions on the initial condition, which we show that the step, flat, and step-flat initial conditions satisfy. Hence, we obtain the limit theorem for these three initial conditions in the periodic model, extending the previous work on the step initial condition. We also consider uniform random and uniform-step random initial conditions.

Multi-point distribution of TASEP

Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to discrete TASEP model with step initial condition. In this paper, we obtain a finite time multi-point distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity proportionally for both step and flat initial conditions. These limiting distributions are expected to be universal for all the models in the Kardar-Parisi-Zhang universality class.

Integral formulas of ASEP and $q$-TAZRP on a ring

In this paper, we obtain the transition probability formulas for the Asymmetric Simple Exclusion Process (ASEP) and the $q$-deformed Totally Asymmetric Zero Range Process ($q$-TAZRP) on the ring by applying the coordinate Bethe ansatz. We also compute the distribution function for a tagged particle with general initial condition.

Nonextensivity and q-distribution of a relativistic gas under an external electromagnetic field

We investigate the nonextensivity and the q-distribution of a relativistic gas under an external electromagnetic field. We derive a formula expression of the nonextensive parameter q based on the relativistic generalized Boltzmann equation, the relativistic q-H theorem and the relativistic version of q-power-law distribution function in the nonextensive q-kinetic theory. We thus provide the connection between the parameter 1-q and the differentiation of the temperature field of the gas as well as the four-potential with respect to time and space coordinates, and therefore present the nonextensivity for the gas a clearly physical meaning.