Analogues of Non-Gibbsianness in Joint Measures of Disordered Mean Field Models

It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity properties of the conditional probabilities in finite volume of the following mean field models: (a) joint measures of random field Ising, (b) joint measures of dilute Ising, (c) decimation of ferromagnetic Ising. The conditional probabilities are functions of the empirical mean of the conditionings; so we look at the large volume behavior of these functions to discover non-trivial limiting objects. For (a) we find (1) discontinuous dependence for almost any realization and (2) dependence of the conditional probabilities on the phase. In contrast to that we see continuous behavior for (b) and (c), for almost any realization. This is in complete analogy to the behavior of the corresponding lattice models in high dimensions. It shows that non-Gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean-field models.     

Asymptotic normality of discounted random series with applications in reliability and queueing

It is proved that a certain kind of randomly discounted random sums is asymptotically normal as the discount constant tends to zero. For replaceable systems with random lifetime, these sums represent the total discounted cost of policies of the age-replacement type; other applications to queueing and related areas are also indicated.     

纳米随机激光

介绍了以纳米ZnO粉末作为增益介质产生的随机激光。讲述了随机激光的特点、发展历史和它的应用前景。文章以随机激光的理论为基础，描述了四种主要的用于随机激光研究的方法。     

克尔型非线性薄膜波导的TE模

对于芯区为克尔型非线性介质，覆盖层和衬底为线性介质的平板波导，用Ｋｒｙｌｏｖ－Ｂｏｇｏｌｉｕｂｏｖ－Ｍｉｔｒｏｐｏｌｓｋｙ的渐近法导出了色散方程及场分布的二阶近似数学表达式，计算量大为减少且结果精确。给出了对称和非对称情况的典型实例。     

Numerical study of local and global persistence in directed percolation

The local persistence probability P _l (t) that a site never becomes active up to time t, and the global persistence probability P _g (t) that the deviation of the global density from its mean value does not change its sign up to time t are studied in a (1+1)-dimensional directed percolation process by Monte-Carlo simulations. At criticality, starting from random initial conditions, P _l (t) decays algebraically with the exponent . The value is found to be independent of the initial density and the microscopic details of the dynamics, suggesting is an universal exponent. The global persistence exponent is found to be equal or larger than . This contrasts with previously known cases where . It is shown that in the special case of directed-bond percolation, P _l (t) can be related to a certain return probability of a directed percolation process with an active source (wet wall). Received: 15 December 1997 / Revised: 6 April 1998 / Accepted: 29 May 1998     

Natural convection in a vertical strip immersed in a porous medium

In this work, the conjugated heat transfer characteristics of a thin vertical strip of finite length, placed in a porous medium has been studied using numerical and asymptotic techniques. The nondimensional temperature distribution in the strip and the reduced Nusselt number at the top of the strip are obtained as a function of the thermal penetration parameter s, which measures the thermal region where the temperature of the strip decays to the ambient temperature of the surrounding fluid. The numerical values of this nondimensional parameter permits to classify the different physical regimes, showing different solutions: a thermally long behaviour, an intermediate transition and a short strip limit.     

Path Collapse for an Inhomogeneous Random Walk

On an open interval we follow the paths of a Brownian motion which returns to a fixed point as soon as it reaches the boundary and restarts afresh indefinitely. We determine that two paths starting at different points either cannot collapse or they do so almost surely. The problem can be modelled as a spatially inhomogeneous random walk on a group and contrasts sharply with the higher dimensional case in that if two paths may collapse they do so almost surely.     

Random sampling within the framework of a multivariate principal-agent approach

In this paper, we analyze a specific class of principal-agent models which seems to be sufficiently general to cover applications in environmental economics with upstream-downstream problems as an example. In our basic model, the observation outcome is ann-dimensional random vectorx and only the first and second moments ofx are common knowledge. We study the effects of random sampling in the presence of costly signals. For this purpose, we assume that the principal and the agent use a simple statistical procedure, i.e. their contract will be based on the mean of a random sample with sampling costs dependent on the sample size. It is shown that there exists an optimal sample size. We investigate the relationship between the optimal sample size, the marginal sampling costs, and the agent's risk aversion.     

Field analysis of a general chiral planar waveguide

The propagation characteristics of general chiral planar waveguides are presented. This is the first time the eigen equation is given in a simple formulation. The results indicate that there are two types of field distribution which is related to the working wavelength and chiral admittance. When the chiral admittance is larger than a certain value, the fields of one kind of circularly polarized wave in the core become exponentially damping in the transverse direction. This work was supported by the “Foundations for the Ph.D Programs of China”     

Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media (Ⅱ)

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.