TIME ASYMPTOTIC BEHAVIOR OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

The isentropic bipolar compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l（R3） ∩ B˙ s 1,1 （R3） with l ≥ 4 and s ∈ （0, 1], it is shown that the momenta of the charged particles decay at the optimal rate （1＋t） 1 4 s 2 in L2 -norm, which is slower than the rate （1＋t） 3 4 s 2 for the compressible Navier-Stokes （NS） equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both （1 ＋ t） 3 4 due to the cancellation effect from the interplay interaction of the charged particles.

THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

BOUND STATES FOR A STATIONARY NONLINEAR SCHRDINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3

We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0

COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R^3

The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl（R3） （R3） for 1 〉 4 and s E （0, 1], it is shown that the density and temperature for each charged particle （like electron or ion） decay at the same optimal rate （1 ＋ t）-3/4, but the momentum for each particle decays at the optimal rate （1 ＋ t）-1/4-3/2 which is slower than the rate （1 ＋ t）-3/4-3/2 for the compressible Navier-Stokes （NS） equations [19] for same initial data. However, the total momentum tends to the constant state at the rate （1 ＋t）-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.

SYMPLECTIC STRUCTURE OF POISSON SYSTEM

When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.

GLOBAL EXISTENCE OF SMOOTH SOLUTION FOR BOLTZMANN-POISSON SYSTEM WITH SMALL DATA

In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.

ESTIM ATES OF ENERGIESAND MOMENTS FOR SOLUTIONS OF BOLTZM ANN-POISSON SYSTEM

In this paper, the properties ofthe solutions ofBoltzm ann-Poisson system in three di- m ensions are considered. The estim ates ofthe energies (the kinetic and the potentialenergies) and the γ-th m om ents w ith γ∈[2,3) are obtained. The latter answ ers an open problem .

QUASI-NEUTRAL LIMIT OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

This paper is concerned with the quasi-neutral limit of the bipolar NavierStokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible NavierStokes equations as the Debye length goes to zero. Moreover, if we let the viscous coefficients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations.

Ground State Solutions for Schrdinger-Poisson Systems

This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.

Global Weak Solutions of Initial Boundary Value Problem for Boltzmann-Poisson System with Absorbing Boundary

This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.

Ground State Solutions for a Kind of Schrödinger-Poisson System with Upper Critical Exponential Convolution Term

This paper mainly discusses the following equation: where the potential function V : R3 → R, α ∈ (0,3), λ > 0 is a parameter and Iα is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.

The Weak Solutions to Initial Boundary Value Problem for Boltzmann-Poisson System

In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.

Ground States for a Class of Nonlinear Schrodinger-Poisson Systems with Positive Potential

Based on Nehari manifold, Schwarz symmetric methods and critical point theory, we prove the existence of positive radial ground states for a class of Schrodinger-Poisson systems in , which doesn’t require any symmetry assumptions on all potentials. In particular, the positive potential is interesting in physical applications.

二维线性化Navier-Stokes-Poisson方程解的逐点估计

本文研究了二维空间线性化的等熵可压缩Navier-Stokes-Poisson方程柯西问题.通过把方程组转变成关于单个函数的方程,求解出各个函数,得到方程组的格林函数.利用对格林函数的详细分析,获得了方程组解的逐点估计.结果显示方程组中电流密度以热核的速度衰减,动量密度衰减慢得多,且其L2范数不衰减.

通过嵌合管来增强负Poisson比结构的耐撞性能

为了提高结构耐撞性,从而实现车辆轻量化,提出了一种嵌合管(由薄壁方形管嵌入双箭头格子而组成的)具有负Poisson比的增强型结构。通过负Poisson比的收缩效应,来增强负Poisson比结构和嵌合管的耦合作用。建立了增强型结构的有限元模型,并通过压缩试验,来验证其准确性;通过数值方法,在轴向载荷下,比较双箭头点阵结构、结构填充管和嵌合管负Poisson比增强型结构的耐撞性能,并进行了参数分析。结果表明:与双箭头点阵结构和填充管结构相比,增强型结构的总吸收能量为1.12 MJ,提升了约40%;比吸能13.2 kJ/kg,提升了约30%;短梁的夹角70°、长梁的夹角40°、长梁厚度1.4~1.6 mm、短梁厚度1.2 mm的结构填充管结构,具有较大的比吸能和较小的碰撞峰值力;增加嵌管厚度显著提升耐撞性能,但结构质量急剧增加,嵌管厚度达到1.2 mm左右时,兼顾耐撞性和轻量化的需求。

A gated recurrent unit model to predict Poisson’s ratio using deep learning

Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.

基于DP算法的Poisson回归模型的变量选择

利用已有的DP算法,对Poisson回归模型的似然函数进行优化估计出模型的参数,分别写出Lasso、Adaptive Lasso、SCAD、MCP 4种惩罚似然函数,用DP算法进行求解,实现变量选择.为了实现算法的自动变量选择,在对惩罚参数的选择上,使用了AIC、BIC信息准则.为了验证DP算法的可行性,通过随机模拟的方式生成数据进行求解.在各项指标下,将DP算法与已有的相关算法进行对比.

Random vibration of hysteretic systems under Poisson white noise excitations

Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

广义结构Poisson括号与Casimir函数

证明了广义结构Poisson括号恒等于零的相关结果并得到验证,改进了广义Poisson括号的Casimir函数的结果,并得到了一个推论。