Melnikov's criterion for nondifferentiable weak-noise potentials

The stationary probability density of Fokker-Planck models with weak noise is asymptotically of the form exp[–1 /(q)]. If is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, has the properties of a Liapounov function, and can be used, e.g., as a thermodynamic potential in nonequilibrium steady states. We consider systems having several attractors and show, by applying Melnikov's method to the associated Hamiltonian, that in general is not differentiable. A small perturbation of a model with differentiable leads to a nondifferentiable . The method is illustrated on a model used in the treatment of the unstable mode in a laser.     

Differential incoherent scattering of 279.2 keV photons by Zr,Sn, Ta,Pb and U

Differential incoherent scattering cross-section ratios of 279.2 keV photons by zirconium, tin, tantalum, lead and uranium elements are experimentally determined by comparing the peak areas under the degraded photon energy with that of an equivalent aluminium foil employing a high resolution 35 c.c. coaxial Ge(Li) detector. Studies have been made in single configuration in an angular range of 20° to 115°. The results are compared with theoretical values obtained from the non-relativistichfs model of Hubbell and co-workers. The cross-section ratios decrease as the atomic number increases for a given scattering angle.     

Study of electron solvation in polar solvents using path integral calculations

A path-integral Monte Carlo algorithm for the simulation of electrons solvated in polar liquids is briefly outlined, and results are presented for the electron solvated in liquid water.     

等离子体色散函数的数值计算研究

一、引言 文[1]建立了关于等离子体色散函数的四极点近似式Z_(53),但其相对误差较大。本文研究结果表明,根据等离子体色散函数的幂级数展开与渐近展开的直接形式,适当地截取有限项,即可解决大多数关于等离子体色散函数Z(s)的数值计算问题。     

一类新的求全局优化问题的填充函数

填充函数方法是一种寻找全局极小解的有效方法.本文首先对现有的填充函数进行研究分析,然后构造出一类新的填充函数,设计算法,并通过数值试验验证了该函数和算法的有效性.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

Resonant response of a thermalized ensemble of nonlinear oscillators

The analysis is carried out of the response of the center of gravity (dipole moment) of the distribution of noninteracting thermalized nonlinear oscillators to a sinusoidal driving force. Heat bath coupling is modeled by damping and noise. The driving is weak, but the frequency is resonant, so that there is a nonlinear resonance in the phase space. The response has a linear part that can be obtained from the perturbation analysis and a small nonlinear correction that is specific for the resonant structure.     

一类具退化强制的椭圆方程在加权Sobolev空间中重整化解的存在性

运用截断方法研究了一类椭圆方程在加权Sobolev空间中解的存在性.主要采用Marcinkiewicz估计,在得到逼近解序列的截断函数先验估计的基础上,通过选取适当的检验函数,对逼近解序列做合适的估计,以此证明重整化解的存在性.     

单位圆内齐次线性微分方程的有穷级解

研究齐次线性微分方程f(k)+ak-1(z)f(k-1)+…+a1(z)f′+a0(z)f=0,(k∈N)的有穷级解,其中系数是单位圆D={z:|z|<1}内解析函数。推广了D.Benbourenane和L.R.Sons的一个结果,并利用J.Heittokangas,R.Korhonen和J.Rattya的一个估计式得到了方程解的增长估计的上界,部分改进了Chen Z     

激光增益系数ζ(ν)和佛克脱函数的近似积分计算—兼论δ函数在近似计算中的应用

本文分析了激光增益系数ζ(υ)和佛克脱积分函数I(υ,υ_0).指出两函数的积分困难均来源于洛伦兹分布函数和多普勒分布函数的褶积.文中进一步分析了洛伦兹函数φ_N和多普勒函数φ_D,并引出函数的峰宽比α,指出当峰宽比α_N>>α_D时,可以把积分号内的φ_N当作δ函数来处理.反之也然.这样就很容易得到ζ(υ)和I(υ,υ_0)的近似积分.