arXiv subjects
Publications and source records attributed to Zhipeng Liu.
When the value $L$ of the directed landscape at a point $(\mathbf{p};\mathbf{q})$ is sufficiently large, the geodesic from $\mathbf{p}$ to $\mathbf{q}$ 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 Gaussians.
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.
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a 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 at the same speed 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.
This paper investigates the system outage performance of a simultaneous wireless information and power transfer (SWIPT) based two-way decode-and-forward (DF) relay network, where potential hardware impairments (HIs) in all transceivers are considered. After harvesting energy and decoding messages simultaneously via a power splitting scheme, the energy-limited relay node forwards the decoded information to both terminals. Each terminal combines the signals from the direct and relaying links via selection combining. We derive the system outage probability under independent but non-identically distributed Nakagami-m fading channels. It reveals an overall system ceiling (OSC) effect, i.e., the system falls in outage if the target rate exceeds an OSC threshold that is determined by the levels of HIs. Furthermore, we derive the diversity gain of the considered network. The result reveals that when the transmission rate is below the OSC threshold, the achieved diversity gain equals the sum of the shape parameter of the direct link and the smaller shape parameter of the terminal-to-relay links; otherwise, the diversity gain is zero. This is different from the amplify-and-forward (AF) strategy, under which the relaying links have no contribution to the diversity gain. Simulation results validate the analytical results and reveal that compared with the AF strategy, the SWIPT based two-way relaying links under the DF strategy are more robust to HIs and achieve a lower system outage probability.
We report the experimental results of simultaneous measurements on the electron and X-ray spectra from near-critical-density (NCD) double-layer targets irradiated by relativistic femtosecond pulses at the intensity of 5E19 W/cm^2. The dependence of the electron and X-ray spectra on the density and thickness of the NCD layer was studied. For the optimal targets, electrons with temperature of 5.5 MeV and X-rays with critical energy of 5 keV were obtained. 2D particle-in-cell simulations based on the experimental parameters confirm the electrons are accelerated in the plasma channel through direct laser acceleration, resulting in temperature significantly higher than the pondermotive temperature. Bright X-rays are generated from betatron emission and Thomson backscattering before the electrons leave the double-layer targets.
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.
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.
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.
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.
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.
We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model. Technically, two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes. One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures; the other is to evaluate the growth rate of KHI from the slopes of morphological functionals. Physically, it is found that the time histories of width of mixing layer, TNE intensity, and boundary length show high correlation and attain their maxima simultaneously. The viscosity effects are twofold, stabilize the KHI, and enhance both the local and global TNE intensities. Contrary to the monotonically inhibiting effects of viscosity, the heat conduction effects firstly refrain then enhance the evolution afterwards. The physical reasons are analyzed and presented.
We study the slowing down of particle beams passing through the dusty plasma with power-law kappa-distributions. Three plasma components, electrons, ions and dust particles, can have different kappa-parameter. We derive the deceleration factor (the velocity moment equation) and the slowing down time of a test particle, and numerically study the slowing down properties of an electron beam, a proton beam and a dust particle beam, respectively, in the kappa-distributed dusty plasma. We show that the slowing down properties of particle beams depend strongly on the kappa-parameters of the plasma components, and the dust component plays a dominant role in the slowing down. And the slowing down also depends on mass and charge of the dust particles in the dusty plasma. More detailed results are shown in 17 numerical graphs.
The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at equal time is known to converge to the Airy process or its variations. However, the temporal process, or more generally the two-dimensional space-time fluctuation field, is less well understood. We consider this question for the periodic TASEP (totally asymmetric simple exclusion process). For a particular initial condition, we evaluate the multi-time and multi-location distribution explicitly in terms of a multiple integral involving a Fredholm determinant. We then evaluate the large time limit in the so-called relaxation time scale.
We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0 0$, samples $M(t_{1}),\ldots ,M(t_{d})$ with complexity $o(c(d)\,d^{ε})$. Moreover, if $X_{n}$ has an a.s. converging series representation, then $M$ can be a.s. approximated with error $δ$ uniformly over $T$ and with complexity $O(1/(δ\log (1/δ))^{1/α})$, where $α$ relates to the Hölder continuity exponent of the process $X_{n}$ (so, if $X_{n}$ is Brownian motion, $α=1/2$).
Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. In this paper, we propose a novel approach to controlled islanding based on weak submodularity. Our formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. We relax the problem to a formulation with bounded submodularity ratio and a matroid constraint, and propose an approximation algorithm which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems.
This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a discrete optimization problem with bounded submodularity ratio, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system.
We consider the totally asymmetric simple exclusion process on a ring with flat and step initial conditions. We assume that the size of the ring and the number of particles tend to infinity proportionally and evaluate the fluctuations of tagged particles and currents. The crossover from the KPZ dynamics to the equilibrium dynamics occurs when the time is proportional to the 3/2 power of the ring size. We compute the limiting distributions in this relaxation time scale. The analysis is based on an explicit formula of the finite-time one-point distribution obtained from the coordinate Bethe ansatz method.
We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when time is proportional to the $3/2$ power of the ring size. We obtain the limit of the height function along the direction of the characteristic line in this time scale. The two-point covariance function in this scale is also discussed.