Variational analysis of thermomechanically coupled steady-state rolling problem

A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.

Time Discretized Variational Iteration Method for the Stochastic Volatility Process with Jumps

A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean reversion and volatility clustering between returns and volatility with uphill movements in price asserts. Thus, in this article, we propose to solve the SVPJ model numerically through a discretized variational iteration method (DVIM) to obtain sample paths for the state variable and variance process at various timesteps and replications in order to estimate the expected jump times at various iterates resulting from executing the DVIM as n increases. These jumps help in estimating the degree of randomness in the financial market. It was observed that the average computed expected jump times for the state variable and variance process is moderated by the parameters (variance process through mean reversion), Θ (long-run mean of the variance process), σ (volatility variance process) and λ (constant intensity of the Poisson process) at each iterate. For instance, when = 0.0, Θ = 0.0, σ = 0.0 and λ = 1.0, the state variable cluttered maximally compared to the variance process with less volatility cluttering with an average computed expected jump times of 52.40607869 as n increases in the DVIM scheme. Similarly, when = 3.99, Θ = 0.014, σ = 0.27 and λ = 0.11, the stochastic jumps for the state variable are less cluttered compared to the variance process with maximum volatility cluttering as n increases in the DVIM scheme. In terms of option pricing, the value 52.40607869 suggest a better bargain compared to the value 20.40344029 due to the fact that it yields less volatility rate. MAPLE 18 software was used for all computations in this research.

Variational-integral perturbation corrections of some lower excited states for hydrogen atoms in magnetic fields

A variational-integral perturbation method（VIPM） is established by combining the variational perturbation with the integral perturbation.The first-order corrected wave functions are constructed,and the second-order energy corrections for the ground state and several lower excited states are calculated by applying the VIPM to the hydrogen atom in a strong uniform magnetic field.Our calculations demonstrated that the energy calculated by the VIPM only shows a negative value,which indicates that the VIPM method is more accurate than the other methods.Our study indicated that the VIPM can not only increase the accuracy of the results but also keep the convergence of the wave functions.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.

A GROUND STATE SOLUTION TO THE CHERN-SIMONS-SCHRODINGER SYSTEM

In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over therelative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method.The ground-state(GS)and excited-state energies of the Frhlich bipolaron for the whole range of electron-phonon coupling constantscan be obtained.The energies of the first relaxed excited state(RES)and Franck-Condon(FC)excited state of thebipolaron are also calculated.It is found that the first RES energy is lower than the FC state energy.The comparisonof our GS and RES energies with those in literature is also given.

Ground State, Isoelectronic Ions and Low-Lying Excited States of Lithium Atom in Strong Magnetic Field

In the framework of the variational Monte Carlo method, the ground states of the lithium atom and lithium like ions up to Z = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states , and of the lithium atom in strong magnetic field are also investigated. Simple trial wave functions for lithium are used.

表面电荷密度及介电常数对AlGaN/GaN异质结中二维电子气性质的影响

通过在Al_(x)Ga_(1-x)N层引入离化电荷面密度,结合自发极化和压电极化引起的极化电荷面密度,利用变分法计算二维电子气面密度随Al组分和Al_(x)Ga_(1-x)N厚度的变化关系.研究了相对介电常数对电子气密度的影响,并与实验数据进行了比较.通过在Al_(x)Ga_(1-x)N的相对介电常量中引入高阶项,使得计算结果更好地拟合了高Al组分的电子气密度.计算得到的离化电荷面电荷密度与极化电荷面电荷密度相当,从而证明离化面电荷密度对二维电子气形成的贡献.

一种高斯-重尾切换分布鲁棒卡尔曼滤波器

为降低实际应用中由强未知干扰和仪器故障对观测造成的影响,减轻随机和未建模干扰对系统的侵蚀,从而提升系统在非高斯噪声环境下的状态估计精度,提高滤波器的鲁棒性能,提出了一种基于高斯-重尾切换分布的鲁棒卡尔曼滤波器(Gaussian-heavy-tailed switching distribution based robust Kalman filter,GHTSRKF)。首先,通过自适应学习高斯分布和一种重尾分布之间的切换概率将噪声建模为GHTS(Gaussian-heavy-tailed switching)分布,所设计的GHTS分布可以通过在线调整高斯分布和新的重尾分布之间的切换概率来对非平稳重尾噪声进行建模,具有虚拟协方差的高斯分布用于处理协方差矩阵不准确的高斯噪声。其次,引入两个分别服从Categorical分布与伯努利分布的辅助参数将GHTS分布表示为一个分层高斯形式,进一步利用变分贝叶斯方法推导了GHTSRKF。最后,利用一个仿真场景对几种不同的RKFs(robust Kalman filters)进行了对比验证。结果表明,所提出的GHTSRKF算法的估计精度对初始状态的选取不敏感,精度优于其他RKFs,它的RMSEs最接近噪声信息准确的KFTNC(KF with true noise covariances)的RMSEs(root mean square errors),且当系统与量测噪声是未知时变高斯噪声时,相比于现有的滤波器,GHTSRKF具有更好的估计性能,从而验证了GHTSRKF的有效性。

基于爬坡方向状态划分的MCMC风电功率序列建模方法

由于电网弃风或者灵活性资源不足往往发生在风电大量发电时,故提高风电时间序列模型对大出力状态的建模-抽样精度,有助于后续的电网灵活性资源相关研究。在传统马尔科夫链蒙特卡洛(MCMC)法和持续与波动蒙特卡罗(PV-MC)法基础上,提出一种考虑爬坡方向状态划分的改进方法,以更准确地描述风电出力连续爬坡至大出力状态的过程。该方法以累积分布概率而不是以功率大小均匀划分状态区间,使各个状态区间的样本分布更均匀,提高了风电时间序列模型对大出力状态的建模-抽样精度。通过算例比较所提方法、MCMC法及PV-MC法生成风电功率序列与历史数据的分布特性和统计特性指标,结果表明,所提方法的拟合度较好,且能够有效解决MCMC法和PV-MC法高出力、样本偏少的问题。

Studies on the analytical potential energy function of diatomic molecular ion XY^+ using variational method

A new analytical potential energy function for diatomic molecular ion XY+ is proposed based on the energy consistent method (ECM). The Coulomb potential included in the new ionic potential contains multipole corrections, converges quickly and is variationally, changeable. The new potential and the ECM are applied to variationally studying the potential energies of eight electronic states of several diatomic molecular ions: the A2π state of CO+, the X2∑ g + state of Li 2 + , the X2∑ g + state of He 2 + , the 12∏u state of Na 2 + , the A2∏u state of N 2 + , the X1∑+ state of KrH+, the X2∑+ state of SiO+ and the A2π state of SO+ ion. The present results agree excellently with the experiment-based Rydberg-Klein-Rees (RKR) potentials, and are superior to the commonly used Huxley-Murrell-Sorbie (HMS) analytical potentials, and are better in some cases than some quantum mechanicalab initio potentials in the ionic asymptotic and dissociation regions.

带陡峭位势的分数阶Schrodinger-Poisson系统的基态变号解

本文研究了带陡峭位势的分数阶Schrodinger-Poisson系统的基态变号解的存在性,由于系统中的位势是陡峭位势,这使得系统的能量泛函紧性缺失。运用约束变分法将能量泛函限制在约束集M_(λ)中,证明能量泛函的下确界可以达到,采用形变引理,得到了系统有1个基态变号解,基态变号解有2个结点域,并且基态变号解的能量严格大于基态解能量的2倍。

一类具有陡峭位势临界的分数阶Schrödinger-Poisson系统的基态解

研究了一类具有陡峭位势的临界分数阶Schrödinger-Poisson系统。由于能量泛函的最小值大于零,这使得变分法难以运用和实现,为克服这个困难,构造了Pohozaev型等式和Nehari-Pohozaev-Palais-Smale序列。对非线性项f和参数作适当的假设,通过变分方法,得到了基态解的存在性。

铍原子基态能量和波函数的变分计算

利用变分原理,计算铍原子(含类铍离子)基态非相对论性能量和波函数,计算中考虑了电子间的交换作用以及内外壳层电子的不同屏蔽效应,计算结果与实验值很相符,能量误差小于0.2%.

沿空留巷充填区域直接顶受力状态探讨与应用

针对综采放顶煤、复合顶板等松软破碎顶板沿空留巷直接顶稳定控制难题,根据沿空留巷顶板活动的时空特征,建立了沿空留巷充填区域直接顶弹性损伤力学模型,推导了充填区域直接顶应力分布表达式,研究了充填区域直接顶应力分布演化规律,进而得到了充填区域直接顶拉应力范围和水平错动范围计算式及相应的演化规律。结果表明:充填区域直接顶受力状态受基本顶回转下沉角和直接顶损伤变量的影响,随着基本顶回转下沉角的增加,拉应力作用范围逐渐减小,水平错动范围逐渐增大。结合新元煤矿3107工作面沿空留巷的工程地质条件,提出了分区域动态加固沿空留巷充填区域直接顶的控制对策,工程应用表明,沿空留巷充填区域顶板下沉量得到了有效地控制,沿空留巷围岩稳定性较好。

锂原子第一激发态能量的变分计算

利用变分原理，计算了锂原子（含类锂离子）第一激发态非相对论性能量，计算中考虑了电子之间的交换相互作用以及内外壳层电子的不同屏蔽效应．将计算结果与实验值进行了比较，误差小于１％ ．

氮原子和类氮离子基态能量的变分计算

利用对角和法则,导出了氮原子和类氮离子(Z=7-12)基态(电子组态为1s22s2p3)非相对论能量的解析表达式.在考虑了电子间交换相互作用以及内外壳层电子的不同屏蔽效应的基础上,利用变分原理计算了能量值,计算结果与实验数据符合得较好,误差均小于0.3%.

黄河天然年径流长期丰枯状态变化特性研究

基于Markov过程分析方法,对黄河陕县528年(1470～1997年)的天然年径流序列进行了分析,结果表明:①黄河年径流在长期的丰枯状态转移中,平水年和偏枯水年的自转移概率均较大,并且无论年径流处于何种初始状态,向偏枯水年转移的概率均大于向偏丰水年转移的概率;②黄河年径流在长期的丰枯状态转移中,出现平水年的状态占优势,而出现丰水年和枯水年的再现时间均较长,并且出现偏枯水年的概率大于出现偏丰水年的概率;③在黄河年径流长期丰枯变化的各态互转移过程中,存在以平水年为状态转移中心的邻态互转移模式,它的存在影响着年径流各态互转移的特性。

山西乡宁—吉县地区黄土高边坡可靠度研究

在山西乡宁—吉县地区实测了7个具有代表性的自然极限状态黄土高边坡断面,建立边坡地层结构模型;选取研究区合理的黄土物理力学参数,并分地层年代对10个典型工点的黄土强度参数内聚力和内摩擦角的变异性进行分析;选取6组典型的强度参数变异系数组合,基于Monte-Carlo法进行可靠度模拟,评价该区边坡稳定性;采用自然类比法进行边坡设计。结果表明:边坡失效概率随坡高的变化趋势一致,均是中等坡高(49.8m)的边坡失效概率较大,低坡和高坡的失效概率较低;当变异系数较小时,边坡失效概率对坡高和坡度的变化敏感,而当变异系数较大时,边坡失效概率对坡高和坡度的变化不敏感;当坡型一定、强度参数变异系数较小时,边坡的稳定系数基本不变,而当参数变异系数超过某一界限时,稳定系数随变异系数的增大而增大,二者存在非线性相关关系;研究区黄土边坡处于基本稳定状态,但其失效概率最大达69.3%,平均21.1%,介于20%～30%的比例为33.3%,大于30%的比例为14.3%,可靠度指标介于-0.5～8.5,其中小于2.7的比例为88.1%;对于坡高约为50m的黄土高边坡,若取30%作为可接受失效概率,边坡坡度需降至45°以下,如果期望可接受失效概率在10%以内,则坡度不宜超过34°。