Gaussian random fields

Two results on Gaussian random fields are presented. The first characterizes the unit Gaussian random field by a strong independence property and the second determines Gaussian random fields that are generated by stochastic processes.     

高斯相关随机表面光散射散斑场相位奇异及其特性的理论研究

通过对二维高斯相关随机表面在远场平面上产生的散斑场及其相位的计算模拟, 发现在某一平面上除了实部零值线与虚部零值线有传统相交之外, 还有相切和重合的情况.切点和重合线也可以形成相位奇异, 并且其周围相位分布与传统的实部零值线与虚部零值线相交形成的奇点周围相位的螺旋变化不同, 呈现出对称性和不连续性的特征. 随着光波的传播, 在不同的观察面上散斑场复振幅的实部零值线和虚部零值线的相对位置经历了由相切到重合再到相交的演变过程, 相位奇异现象也随之发生变化. 关键词： 相位奇异 相位跃变 散斑场     

Triangulated random surfaces

A model of discretized random surfaces that contains the extrinsic curvature as well as the usual area term in the action is considered. The renormalization group predicts that at large distances the model is indistinguishable from previous proposals of triangulated surfaces that contained only the area term, but, unlike them, does not grow spikes. The partition function and all its moments are finite and well defined. The model is solved for large d in the vicinity of the IR fixed point. The Hausdorff dimension is ∞ and the entropy exponent agrees with the one obtained by Zamolodchikov and others for the Polyakov action in the continuum.     

Self-affine random surfaces

We consider general d-dimensional random surfaces that are characterized by power-law power spectra defined in both infinite and finite spectral regions. The first type of surfaces belongs to the class of ideal fractals, whereas the second possess both the smallest and the largest scales and physically is more realistic. For both types we calculate the structure functions (SF) exactly; in addition for the second type we obtain the SF's asymptotic expansions. On this basis we show that the surfaces are (in statistical sense) self-affine and approximately self-affine, respectively. Depending on the value of the spectral exponent, we find imbalance between the finite size effects which results in systematic discrepancy in the scaling properties between the two types of surfaces. Explicit expressions for the topothesy, and in the case of second type of surfaces for the large correlation length and cross-over distances are also derived. Received 3 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: oyordanov@aubg.bg     

Diffusion of adsorbates on random alloy surfaces

In this work the diffusion of non-interacting adsorbates on a random AB alloy surface is considered. For this purpose a simple cubic (sc), body-centered cubic (bcc) or face-centered cubic (fcc) auxiliary metal lattice is introduced. The auxiliary lattice is truncated parallel to its (100) plane in such a way that the fourfold hollow positions of the metal surface form a regular net of adsorption sites with square symmetry. The adsorption energy of each adsorption site is determined by its own environment, i.e. by the numbers of direct A or B neighbors. The Monte-Carlo method has been utilized to simulate surface diffusion of adsorbates on such energetically heterogeneous alloy surfaces and to calculate the tracer, jump and chemical diffusion coefficients. The chemical diffusion coefficient was calculated via two different approaches: the fluctuation and the Kubo-Green method. The influence of energetical heterogeneities on the surface diffusion is largely pronounced at low temperatures and low surface coverages, where most of the adatoms are trapped by deep adsorption sites. It was found that at low temperatures the sequential occupation of the different types of adsorption sites can be observed. Received: 24 October 1997 / Accepted: 17 December 1997     

Regions of validity of geometric optics and Kirchhoff approximations for reflection from Gaussian random rough dielectric surfaces

In this paper, the effects of characteristics of incident light and the geometrical parameters to the reflectivity of dielectric Gaussian random rough surfaces are presented. The behaviors of the reflectivity vs. several parameters are quantified using approximate methods: the geometric optics approximation (GOA) and the Kirchhoff approximation (KA) and an exact method called integral method (IM). Finally, we determine the limits of validity of approximate methods by comparisons with IM results. The regions of validity of approximate methods depending of many geometrical and physical parameters: roughness, Brewster and shadowing effects, multiple reflections, surface materials, and nature of polarization. The broader domain of validity (DV) is for KA, at normal TE-polarized incident light, for the higher dielectric permittivity. However, the narrowed DV is for GOA, at normal TM-polarized incident light for lower dielectric permittivity.     

Directed random polymers via nested contour integrals

We study the partition function of two versions of the continuum directed polymer in 1+1$1+1$ dimension. In the full-space version, the polymer starts at the origin and is free to move transversally in R$\mathbb{R}$, and in the half-space version, the polymer starts at the origin but is reflected at the origin and stays in R₋${\mathbb{R}}_{-}$. The partition functions solve the stochastic heat equation in full-space or half-space with mixed boundary condition at the origin; or equivalently the free energy satisfies the Kardar–Parisi–Zhang equation.     

Retention capacity of random surfaces

We introduce a "water retention" model for liquids captured on a random surface with open boundaries and investigate the model for both continuous and discrete surface heights 0,1,…,n-1 on a square lattice with a square boundary. The model is found to have several intriguing features, including a nonmonotonic dependence of the retention on the number of levels: for many n, the retention is counterintuitively greater than that of an (n+1)-level system. The behavior is explained using percolation theory, by mapping it to a 2-level system with variable probability. Results in one dimension are also found.     

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos, an elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors is considered. The correlation functions are derived for the amplitudes and intensities of elastic displacements. A comparison to the numerics in a quarter-Bunimovich stadium demonstrates excellent agreement. The text was submitted by the authors in English.     

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos, an elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors is considered. The correlation functions are derived for the amplitudes and intensities of elastic displacements. A comparison to the numerics in a quarter-Bunimovich stadium demonstrates excellent agreement.