时间相关单光子计数型激光雷达距离判别法

为了解决光子计数型激光雷达测量系统,收集到的信号存在不确定性的问题,提出一种贝叶斯推论下的马尔可夫信号法,可实现回波峰值位置、峰值幅度等参量的提取,达到信号重建的目的.依据贝叶斯理论,利用后验预设分布模型近似描述参量的先验分布,有效提高对参量存在空间的探测速度.在求解过程中,将这些参量构成一个全局近似解,利用贝叶斯推论对所有全局近似解进行评估,挑选出最合适的全局近似解作为问题的全局最优解.实验表明,该方法具有较高的准确性和良好的鲁棒性.     

高功率巨脉冲输出可调谐金绿宝石激光器及其倍频研究

阐述了可调谐金绿宝石激光器中各参量的最佳化,获得了高达10MW的巨脉冲输出和近600(?)的调谐范围.用LiIO_3晶体倍频,获得的最大功率转换效率为9%.     

低温装置中温度测量的热沉问题

文中讨论了低温装置中的热沉问题。为减少因电引线导热对温度计的热负荷 ,提高温度测量的精度 ,在温度计的引线中加入热沉将是非常必要而且有效的手段。文中解决了不同边界条件下所需的热沉长度的求解问题 ,并讨论了其实际应用     

大振幅简正波

本文将简正波理论推广到大振幅声场,计及声场内的非线性效应。这涉及非线性偏微分方程的固有振动解的问题。简正波具有驻波性质,基本已反映在一阶近似解中。高阶近似解只是非线性引致参量的局部变化或修正,并不影响分布。根据这个概念解决了过去的数学困难,求得了大振幅简正函数,为线性商正函数及其谐频项,此外还有常数项,代表辐射压,与经典辐射压值作了比较。     

给探测线圈安装一个保护套

磁场描绘实验中使用的探测线圈常常因为使用频繁,而探测线圈的线径又太细,手又常常触摸它,很容易将线圈的引线弄断,该线圈的引线一断,焊接很困难。为了解决上述困难,可利用医院打滴流用过的废旧滴流管。经过清洗处理后,将滴流管中最粗的一段管子剪下来,剪去一端管     

3cm相对论返波荡器的粒子模拟研究

运用全电磁的相对论的25维粒子模拟程序MAGIC模拟分析了3cm相对论返波管中注波互作用的非线性过程,得到了器件微波输出功率,效率,工作频率等参量,模拟结果与实验数据较好地一致。对电子注特性参数,慢波结构尺寸,引导磁场进行了优化,获得了器件最佳化运行的工作参数。     

基于非线性薛定谔方程的一种孤子特性的分析

光孤子通信是解决光信息在光纤中长距离传输时衰减和色散问题的一种较为有效的方法.本文在现有带有群速度色散、非线性项、三阶非线性系数以及增益/损耗项的非线性薛定谔方程孤子解的基础上,给出了灵活性的孤子解.采用具有复振幅的行波解作为试探解,将试探解代入原方程,在实部和虚部分离的基础上,引入三个变量函数,最后表征出孤子解波函数的平方,并应用Matlab选择不同的变量函数进行数值模拟,得到图示结果.结果表明孤子解对于参变量变化是敏感的.选择适当的参量,得到合适的孤子,这一结论对光纤中孤子通信具有重要意义.     

光纤布拉格光栅中的隙孤子存在条件

提出光纤布拉格光栅中产生隙孤子的条件和参量制约关系。利用非线性耦合模式方程建立光纤布拉格光栅中孤子的传播方程,通过扰动方法建立了参量的微分方程,计算得到参量近似解。以周期非线性光学介质中隙孤子存在的条件为依据,数学计算分析得到两组参量关系不等式。最终通过数值计算说明了这些参量之间存在制约关系和物理意义。从而理论上说明了在光纤布拉格光栅中隙孤子存在需要选择适当参量。为光纤布拉格光栅中产生隙孤子的实验和进一步的工程应用提供了理论基础。     

3cm相对论返波荡器的粒子模拟研究

 运用全电磁的相对论的25维粒子模拟程序MAGIC模拟分析了3cm相对论返波管中注波互作用的非线性过程，得到了器件微波输出功率，效率，工作频率等参量，模拟结果与实验数据较好地一致。对电子注特性参数，慢波结构尺寸，引导磁场进行了优化，获得了器件最佳化运行的工作参数。     

基于梯度阈值自适应处理的红外图像超分辨率重建

超分辨率图像重建中,Huber马尔可夫随机场模型是一种常用的正则化算子.针对Huber函数中固定梯度阈值引起图像重建效果不佳的问题,本文提出一种梯度阈值自适应处理的红外图像超分辨率重建算法.在最大后验概率理论框架下,构造了基于数据项和正则项的正则化模型;通过迭代的方式,利用中间重建结果不断更新正则化参量,解决了Huber马尔可夫随机场模型中梯度阈值不易选择的难题.实验结果表明,改进算法能够根据局部梯度特征自适应选择相应的正则化参量并找到最优解,较好恢复目标细节的同时有效抑制了图像噪音.     

Nonlinear,nondispersive wave equations: Lagrangian and Hamiltonian functions in the hodograph transformation

The hodograph transformation is generally used in order to associate a system of linear partial differential equations to a system of nonlinear (quasilinear) differential equations by interchanging dependent and independent variables. Here we consider the case when the nonlinear differential system can be derived from a Lagrangian density and revisit the hodograph transformation within the formalism of the Lagrangian-Hamiltonian continuous dynamical systems.Restricting to the case of nondissipative, nondispersive one-dimensional waves, we show that the hodograph transformation leads to a linear partial differential equation for an unknown function that plays the role of the Lagrangian in the hodograph variables. We then define the corresponding hodograph Hamiltonian and show that it turns out to coincide with the wave amplitude. i.e., with the unknown function of the independent variables to be solved for in the initial nonlinear wave equation.     

Entropy production by block variable summation and central limit theorems

We prove a strict lower bound on the entropy produced when independent random variables are summed and rescaled. Using this, we develop an approach to central limit theorems from a dynamical point of view in which the entropy is a Lyapunov functional governing approach to the Gaussian limit. This dynamical approach naturally extends to cover dependent variables, and leads to new results in pure probability theory as well as in statistical mechanics. It also provides a unified framework within which many previous results are easily derived.Partially supported by an NSF postdoctoral fellowshipPartially supported by NSF grant DMS-8905772; A. P. Sloan Fellow in Mathematics     

Quasi-equilibrium closure hierarchies for the Boltzmann equation

In this paper, explicit method of constructing approximations (the triangle entropy method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a problem (such as, for example, rates of processes) as new independent variables.

The work of the method is demonstrated on the Boltzmann's-type kinetics. New macroscopic variables are introduced (moments of the Boltzmann collision integral, or scattering rates). They are treated as independent variables rather than as infinite moment series. This approach gives the complete account of rates of scattering processes. Transport equations for scattering rates are obtained (the second hydrodynamic chain), similar to the usual moment chain (the first hydrodynamic chain). Various examples of the closure of the first, of the second, and of the mixed hydrodynamic chains are considered for the hard sphere model. It is shown, in particular, that the complete account of scattering processes leads to a renormalization of transport coefficients.

The method gives the explicit solution for the closure problem, provides thermodynamic properties of reduced models, and can be applied to any kinetic equation with a thermodynamic Lyapunov function.     

A joint characterization of directed divergence,inaccuracy, and their generalizations

Starting with an additive property for distributions of two statistically independent random variates in terms of different sum functions, we have characterized two general measures associated with two distributions of a discrete random variate. One of these measures is logarithmic, while the other contains powers of variables. An interesting aspect is that under suitable additional boundary conditions the logarithmic measure leads to measure of information (directed divergence) studied by Kullback and measure of inaccuracy studied by Kerridge, while the other solution leads to their parametric generalizations.     

Reductions and conserved quantities for discrete compound KdV–Burgers equations

We present two methods to reduce the discrete compound KdV–Burgers equation, which are reductions of the independent and dependent variables: the translational invariant method has been applied in order to reduce the independent variables; and a discrete spectral matrix has been introduced to reduce the number of dependent variables. Based on the invariance of a discrete compound KdV--Burgers equation under infinitesimal transformation with respect to its dependent and independent variables, we present the determining equations of transformation Lie groups for the KdV--Burgers equation and use the characteristic equations to obtain new forms of invariants.     

Solutions for Two-Dimensional Dilaton Gravity

In a recent paper Frolov, Hendy, and Larsen(1996) obtained a set of two nonlinear second-ordercoupled partial differential equations of 2D dilatongravity. They obtained a special solution assuming all the dependent variables were independent oftime. In the present work we reduce the above set ofequations to a simple form, from which we obtain a classof solutions that includes the solution of Frolov, Hendy, and Larsen as a special case.     

Transport in two dimensions. II the thermal conductivity coefficient

The study of generalized transport coefficients in two dimensions is continued. In this article, the thermal conductivity coefficient is examined. The Mori formalism is used and the set of variables consists of all finite multilinear products of two collective conserved variables, the energy density and the momentum density. The tensorial symmetry of Euler and dissipative matrix elements is taken into account explicitly. Two simultaneous non-linear integral equations are obtained, the asymptotic solution for which behave in the same manner as the self-diffusion coefficient studied in an earlier paper. However, the coefficient is dependent upon the intermolecular potential. The heat current auto-correlation function decays asymptotically as $\text{[t}\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{t]}{}^{\mathrm{?1}}$. The asymptotic form for the shear viscosity coefficient is examined briefly and found to be independent of the intermolecular potential. A better approximation for the coefficient of the asymptotic form of the self-diffusion coefficient is presented.     

二维均匀流与重力短峰波相互作用解析

短峰波和海流广泛分布于海洋之中,但二者的相互作用直到近些年才逐渐受到关注,根据速度势函数理论,推导二维均匀流与重力短峰波的相互作用,区别于之前的研究,推导时不考虑波面的毛细影响,避免了将位置变量(x)与时间变量(t)绑定的假设,使得二阶速度势函数包含了的时间(t)一阶项,从而给出了完整的二维流与短峰波交互作用的二阶解析解,对比结果说明上述考虑对于波流共同作用结果有影响,尤其是在波高较大时,影响更加明显,所得结果,可用于高波浪条件下海洋波浪与流相互作用的计算.     

Classification of exactly solvable potential problems

A differential equation with a known solution is transformed by changing both its dependent and independent variables, and the resulting nonlinear differential equation is then compared with the Schrödinger equation. The method is demonstrated using the confluent hypergeometric differential equation and the solutions to hydrogen, SHO and l=0 Morse potential problems are obtained.     

线状铜电极在磷酸溶液中电流混沌振荡的同步行为

研究了恒电位下两个铜线电极在磷酸溶液中的电流混沌振荡行为 ,通过恒定不同的电位数值 ,改变单个电极的电流振荡混沌行为 ,研究了不同混沌间的相互作用 .调整线电极间的距离 ,研究了电极间距对电流振荡行为的影响 .实验中两电极的振荡间呈现了复杂的耦合作用 ,耦合后的频率与耦合前电极原有的频率不同 .两电极的混沌电流振荡中呈现出同步、准周期同步和反相同步等现象 .电极距离一定时 ,振荡波形差别很大的两电极的电流容易呈现反相同步和准周期同步 ,波形差别不大时容易产生同步 .强的耦合导致电极间电流振荡的同步 ,电极距离的加大 ,电极间电流振荡难以产生同步 .对耦合作用机制也进行了探讨