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In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour., Comment: 10 pages, 4 figures, extended version with one new section

The recent observations of surface backscattering enhancement phenomenon from randomly rough Gaussian surfaces with large slopes were reported experimentally and stimulated the critical discussions. In this paper the IEM model with multiple scattering and suitable shadowing function (IEMMS) is developed to be able to predict this phenomenon of backscattering enhancement. The backscattering enhancement may take place when the surface rms slope is of the order of unity and large rms height. Also, the backscattering enhancement can also be predicted from the multiple surface scattering from a very roughly random surface. To the best of the author's acknowledge, this is the first attempt to set up a fully integration equation model for fully theoretical polarized scattering. The derivation of basic surface. Scattering model is provided and a computer simulation is also provided to compare the experimental measurement.

The surface of the ocean, and so such quantities as the significant wave height, can be thought of as a random surface in space which develops over time. In this paper, we explore certain types of random fields (in space and time) as models for the significant wave height and fit these models to data obtained from the TOPEX-Poseidon satellite. The data consist of observations along different one-dimensional tracks over time. It is assumed that, for the region of ocean considered and for a fixed time, the data can be considered stationary. Further-more, the shape of the data suggests that it is reasonable to use a lognormal distribution. As the covariance function may change over time, the model chosen is fitted to the data for each time separately. The data over space exhibit variation at different scales and hence the covariance function needs to reflect this property. Consequently, a mixture of Gaussian functions is assumed for the covariance function. To fit the model to the data, the theoretical variogram is fitted to the empirical variogram using weighted least squares. Stochastic models for the variation of the parameter values were investigated. The results of fitting these models are discussed and interpreted. 1375 1382 Conference code: 62122 Cited By :3

We consider the motion of a discrete d-dimensional random surface interacting by exclusion with a rarefied wall. The dynamics is given by the serial harness process. We prove that the process delocalizes iff the mean number of visits to the set of sites where the wall is present by some random walk is infinite. In case where there is a delocalization, bounds on its speed are obtained.

Post mortem analysis of fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveal self affine graphs with an anomalous scaling exponent $\zeta\approx 0.8$. Attempts to use elasticity theory to explain this result failed, yielding exponent $\zeta\approx 0.5$ up to logarithms. We show that when the cracks propagate via plastic void formations in front of the tip, followed by void coalescence, the voids positions are positively correlated to yield exponents higher than 0.5., Comment: 4 pages, 6 figures

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

The reflection attenuation factor given by Blinn has been widely used as an important factor in the bidirectional reflectance distribution function (BRDF) model based on geometrical optics theory for nearly half a century. However, Blinn's attenuation factor is based on microfacet theory and geometry of equicrural V-grooves caused sharp turning points and obvious error in its function curves. In this paper, a modified geometry attenuation factor based on random surface microfacet theory is presented. We assume that the surface is composed of a large number of microfacets, and the slope of each microfacet is independent of each other and follows Gaussian distribution. The attenuation effect is caused by the masking and shadowing factors in adjacent microfacets. Depending on the slope angles of microfacets, reflection falls in three submodels, i.e., passing model, semi-passing model, and masking/shadowing model when discussing masking/shadowing factor. The modified attenuation factor is given in an integral expression. The modified geometry attenuation factor is simulated and compared with Blinn's geometry attenuation factor. The sharp turning point in Blinn's attenuation factor curve is eliminated and the error of the BRDF curve is reduced. The result shows that the modified geometry attenuation factor reaches better physical rationality and significantly improves the accuracy of BRDF model. Compared with Blinn's geometry attenuation factor, the modification reduces the standard error between BRDF model and existing data from 0.0636 to 0.0084. The cause of the error in Blinn's geometry attenuation factor is analyzed, the equicrural V-grooves assumption of Blinn's geometry attenuation model considers too much reflection attenuation in the condition of small incident angle and large reflect angle. The modification in this paper is based on random surface microfacet theory, in which the angular dependence of adjacent microfacet is eliminated, for this reason the accuracies of geometry attenuation model and BRDF model are improved.

The diffraction of multidirectional random surface waves with one or more rectangular submarine pits is investigated theoretically. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The numerical model involves the superposition of regular-wave diffraction solutions based on linearized shallow water wave theory obtained by a two-dimensional boundary integral approach for water of uniform depth. Numerical results are presented for multi-directional random waves that illustrate the effect of the various wave and pit parameters on the diffraction characteristics of typical single and multiple pit systems.

The start and evolution of the formation of laser-induced periodic surface structures (LIPSS, ripples) are investigated. The important role of irradiation dose (fluence×number of pulses) for the properties of the generated structures is demonstrated. It is shown how, with an increasing dose, the structures evolve from random surface modification to regular sub-wavelength ripples, then coalesce to broader LIPSS and finally form more complex shapes when ablation produces deep craters. First experiments are presented following this evolution in one single irradiated spot.

The metric $D_{\alpha}(q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $\mathbb{R}^d$ , defined as the infimum of $(\sum_i |q_i - q_{i+1}|^{\alpha})^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$ (where $|·|$ denotes Euclidean distance) has nontrivial geodesics when $\alpha>1$. The cases $1< \alpha

We consider the influence on the surface critical behaviour of a quantum Ising chain of quenched random surface perturbations decaying as a power of the distance from the surface (random Hilhorst-van Leeuwen models). We study, analytically and numerically, the multiscaling behaviour of the surface magnetization and the surface energy density in the case of marginal perturbations., Comment: 14 pages, 5 figures, LaTeX2e, epsf, elsart

A self consistent field theory that describes a part of a contour loop of a random Gaussian surface as a trajectory interacting with itself is constructed. The exponent \nu characterizing the end to end distance is obtained by a Flory argument. The result is compared with different previuos derivations and is found to agree with that of Kondev and Henley over most of the range of the roughening exponent of the random surface., Comment: 7 pages

We describe a method for designing a one-dimensional random surface that acts as a Lambertian diffuser. The method is tested by means of rigorous computer simulations and is shown to yield the desired scattering pattern., Comment: 6 pages, 2 figures

It has recently been suggested by Ambartzumian {ital et} {ital al}. that the modified Steiner functional has desirable properties as an action for random surfaces and hence string world sheets. We perform a simulation of this action on a dynamically triangulated random surface to investigate this claim and find that the surfaces are in a flat phase.

We investigate numerically a dynamically triangulated random surface with extrinsic curvature embedded in a three-dimensional space. Toroidal topology is used, to allow for string tension measurements by a new method. A high statistics test of the finite-size scaling of the specific heat is performed.

Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface and the scaling properties of its contour loops are analyzed. Various exponents that describe the loop ensemble are measured and compared to a scaling theory. This leads to a geometrical criterion of intermittency of scalar fluctuations., 4 pages, 1 figure; comments to kondev@brandeis.edu

Weaddressthemeanderproblem\enumeratealltopologicallyinequivalentcongurations ofa closednonselntersectingplane curveintersecting a givenline throughaxed number ofpoints". We showthatmeandersmaybe viewedasthe congurationsofasuitablefully-packedloopstatistical model dened on a random surface. Using standard results relating critical singularities of a lattice modeltoits gravitationalversiononrandomsurfaces,we predictthe meandercongurationexponent =(29+ p 145)=12 and many other meandric exponents.

We consider a random surface $\Phi$ in $\mathbb{R}^d$ tessellating the space into cells and a random vector field $u$ which is smooth on each cell but may jump on $\Phi$. Assuming the pair $(\Phi, u)$ stationary we prove a relationship between the stationary probability measure $P$ and the Palm probability measure $P_{\Phi}$ of $P$ with respect to the random surface measure associated with $\Phi$. This result involves the flow of $u$ induced on the individual cells and generalizes a well-known inversion formula for stationary point processes on the line. An immediate consequence of this result is a formula for certain generalized contact distribution functions of $\Phi$, and as first application we prove a result on the spherical contact distribution in stochastic geometry. As another application we prove an invariance property for $P_{\Phi}$ which again generalizes a corresponding property in dimension $d = 1$. Under the assumption that the flow can be defined for all time points, we consider the point process $N$ of sucessive crossing times starting in the origin 0. If the flow is volume preserving, then $N$ is stationary and we express its Palm probability in terms of $P_{\Phi}$.

An approximate formula is derived for the on‐axis cross‐polarization discrimination (XPD) of a symmetrical reflector antenna with random surface errors. This XPD depends on only two parameters, namely, the normalized r.m.s. surface error (ϵ/λ) and the polarization‐loss efficiency (n).

Based on the capability of confocal microscopy to profile rough surfaces, Quartel and Sheppard have proposed an algorithm to reconstruct surface profiles from scattering data. We determine the range of applicability of the algorithm by investigating the effects of the roughness and correlation length of a random surface on the reconstruction.

European manufacturers have proposed a set of surface roughness parameters based on an examination of the variation in slope of the bearing ratio curve of a surface profile. It is shown, that the proposed procedure provides no useful information, and indeed is misleading, since the bearing ratio curve of even a normally-distributed random surface profile exhibits the expected variation in slope when plotted on rectangular coordinates. On the other hand, the desired information is readily obtained by a similar examination of the cumulative height distribution of a surface profile (the unity complement of the bearing ratio) when it is plotted on normal probability coordinates.

We present a method for generating numerically a one-dimensional random surface, defined by the equation $x_3 = \zx$, that suppresses single-scattering processes in the scattering of light from it within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles., Comment: 3 pagers (Latex), 3 figures

1. Entanglement Complexity of Polymers.- Entanglements of polymers.- Entropic exponents of knotted lattice polygons.- The torsion of three-dimensional random walk.- 2. Knot Energies.- Self-repelling knots and local energy minima.- Properties of knot energies.- Energy and thickness of knots.- On distortion and thickness of knots.- 3. Random Linking.- Percolation of linked circles.- Minimal links in the cubic lattice.- 4. Effect of Geometrical Constraints.- Knots in graphs in subsets of Z3.- Topological entanglement complexity of polymer chains in confined geometries.- 5. Surfaces and Vesicles.- Survey of self-avoiding random surfaces on cubic lattices: Issues, controversies, and results.- Computational methods in random surface simulation.- A model of lattice vesicles.

We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of the large-N character expansion approach as well as potential physical applications of our results., 37 pages LaTeX; Some clarifying comments added, last Section rewritten

We study an anomalous behavior of the height fluctuation width in the crossover from random to coherent growths of surface for a stochastic model. In the model, random numbers are assigned on perimeter sites of surface, representing pinning strengths of disordered media. At each time, surface is advanced at the site having minimum pinning strength in a random subset of system rather than having global minimum. The subset is composed of a randomly selected site and its $(\ell-1)$ neighbors. The height fluctuation width $W^2(L;\ell)$ exhibits the non-monotonic behavior with $\ell$ and it has a minimum at $\ell^*$. It is found numerically that $\ell^*$ scales as $\ell^*\sim L^{0.59}$, and the height fluctuation width at that minimum, $W^2(L;\ell^*)$, scales as $\sim L^{0.85}$ in 1+1 dimensions. It is found that the subset-size $\ell^*(L)$ is the characteristic size of the crossover from the random surface growth in the KPZ universality, to the coherent surface growth in the directed percolation universality., Comment: 13 postscript files

We have investigated the characteristics of gas flow in microchannels under the coupled effects of random surface roughness and velocity slip by the method of computational fluid dynamics. The random surface roughness is modeled by fractal geometry, and the velocity slip on boundary is described by second-order slip law. Results show that the simulated curves obtained by considering both second-order slip law and random surface roughness are in good agreement with experimental data in a range of averaged Knudsen number from 0.025 to 0.59, while the one gained by using Maxwell slip law are in agreement with experimental data in a range of averaged Knudsen number extending up to 0.1. Random surface roughness has an obvious effect on velocity slip: as relative surface roughness increases, velocity slip coefficients decrease. An approximate relation between relative surface roughness and velocity slip coefficients is given according to the results. Last but not least, random surface roughness has a significant effect on the pressure, velocity and Poiseuille number.

We have studied the dynamics of contact lines formed by water-alkane interfaces in capillaries with random surface disorder. We find that the contact-line velocity V scales with the applied capillary pressure P as V∼ (P – Pt)ζ over two decades in V. This is consistent with a critical depinning transition. We obtain this result by using a sensitive ac differential-pressure measurement technique to measure dP/dV. We find that dP/dV αV−0 8 (5) implying that 1/ζ = 0. 20 (5).

I review the state of knowledge about random surface ensembles in continuous embedding spaces and their possible role in defining strings in arbitrary dimensions. The application of rigorous statistical mechanics, approximate calculation and numerical simulation is described.

Large $N$ matrix models modified by terms of the form $ g(\Tr\Phi^n)^2$ generate random surfaces which touch at isolated points. Matrix model results indicate that, as $g$ is increased to a special value $g_t$, the string susceptibility exponent suddenly jumps from its conventional value $\gamma$ to ${\gamma\over\gamma-1}$. We study this effect in \L\ gravity and attribute it to a change of the interaction term from $O e^{\alpha_+ \phi}$ for $g, Comment: 15 pages, PUPT-1486 (last paragraph of sec. 2 revised)

We study the scaling limit of a model of a tethered crumpled D-dimensional random surface interacting through an exclusion condition with a fixed impurity in d-dimensional Euclidean space by the methods of Wilson's renormalization group. In this paper we consider a hierarchical version of the model and we prove rigorously the existence of the scaling limit and convergence to a non-Gaussian fixed point for $1 \leq D< 2$ and $\epsilon >0$ sufficiently small, where $\epsilon = D - (2-D) {d\over 2}$., Comment: 47 pages in simple Latex, PAR-LPTHE 9346

For a random surface with extrinsic curvature the performance of a Metropolis simulation near the critical point can be improved by modifying the algorithm. The errors for various quantities can be reduced slightly whilst at the same time achieving a reduction in CPU time of order 30%.

We consider self-avoiding Nambu-Goto open strings on a random surface. We have shown that the partition function of such a string theory can be calculated exactly. The string susceptibility for the disk is evaluated to be $-\frac{1}{2}$. We also consider modifications of the Nambu-Goto action which are exactly soluble on a random surface., Comment: 12 pages, LaTex, KEK-TH-361

Ambartzumian et.al. suggested that the modified Steiner action functional had desirable properties for a random surface action. However, Durhuus and Jonsson pointed out that such an action led to an ill-defined grand-canonical partition function and suggested that the addition of an area term might improve matters. In this paper we investigate this and other related actions numerically for dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously., Comment: 8 pages

The saddle point equation described by the eigenvalues of N by N Hermitian matrices is analized for a finite N case and the scaling relation for the large N is considered. The critical point and the critical exponents of matrix model are obtained by the finite N scaling. One matrix model and two matrix model are studied in detail. Small N behavior for n-Ising model on a random surface is investigated., Comment: 16page(latex)

It has been suggested that the modified Steiner action functional has desirable properties for a random surface action. In this paper we investigate the scaling of the string tension and massgap in a variant of this action on dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously., Comment: 7 pages, COLO-HEP-328

We investigate a dynamically triangulated random surface action that consists of a gaussian term plus the modulus of the intrinsic scalar curvature. We find that the flips are frozen out and the internal geometry is regularized as the coefficient of the latter term is increased. Such a term thus provides a way of interpolating between dynamically triangulated (ie fluid) and crystalline random surfaces., Comment: 7 pages, COLO-HEP-316

We consider methods of interpolating between the crystalline and dynamically triangulated random surface models. We argue that actions based on the deviation from six of the coordination number at a site are inadequate and propose an alternative based on Alexander moves. Two simplified models, one of which has a phase transition and the other of which does not, are discussed., Comment: 6 pages plain TeX and 5 encapsulated postscript figures, OUTP-93/17P

We analyze numerically the critical properties of a two-dimensional discretized random surface with extrinsic curvature embedded in a three-dimensional space. The use of the toroidal topology enables us to enforce the non-zero external extension without the necessity of defining a boundary and allows us to measure directly the string tension. We show that a phase transition from the crumpled phase to the smooth phase observed earlier for a spherical topology appears also for a toroidal surface for the same finite value of the coupling constant of the extrinsic curvature term. The phase transition is characterized by the vanishing of the string tension. We discuss the possible non-trivial continuum limit of the theory, when approaching the critical point. Numerically we find a value of the critical exponent $\n$ to be between .38 and .42. The specific heat, related to the extrinsic curvature term seems not to diverge (or diverge slower than logarithmically) at the critical point., Comment: figures available as postscript files on request. 28 pages plus figures

Based on the Kirchhoff approximation and the theoretical analysis of the random light fields, the speckle intensity distributions in the extremely deep Fresnel diffraction region are simulated. The fractal property of the speckles as well as the relation between the speckle intensity distribution and the corresponding random surface is investigated. We design a microscope system to detect experimentally the speckles in the extremely deep Fresnel diffraction region, and the experimental results prove the conclusions drawn from our simulations.

In applying an ocean lidar equation, a reflectance and a refractivity of a random surface of the water is the most difficult parameter for an actual ocean lidar observation. A flight test of an airborne ocean lidar and a surface test of a shipboard ocean lidar showed variations of intensity of light scattered from a depth of the water. We built a multiparameteric shipboard ocean lidar to examine a hypothesis that variations of light scattered or fluorescence from the depth could be given as a function of light reflected at the surface of the water. As a result, we have confirmed that light scattered or fluorescence from the depth was independently given from variations of light reflected at the surface of the water on the current lidar system.

Surface melting on clusters is investigated by a combination of analytic modeling and computer simulation. Homogeneous argonlike clusters bound by Lennard-Jones forces and Cu-like clusters bound by ``embedded-atom'' potentials are the systems considered. Molecular-dynamics calculations have been carried out for clusters with 40--147 atoms. Well below the bulk melting temperature, the surfaces become very soft, exhibiting well-defined diffusion constants even while the cores remain nearly rigid and solidlike. The simulations, particularly animations, of atomic motion reveal that the surface melting is associated not with amorphous, random surface structures in constant, irregular motion, but rather with large-amplitude, organized, collective motion of most of the surface atoms accompanied by a few detached atoms (``floaters'') and holes. At any time, a few of the surface atoms are out of the surface layer, leaving vacancies; these promoted particles wander diffusively, the holes also but less so; the floaters occasionally exchange with atoms in the surface layer. This result is the basis for an analytic, statistical model. The caloric curves, particularly the latent heats, together with the results from an analytical model, show that surface melting of clusters is a ``phase change'' different from the homogeneous melting of clusters.

A highly vectorized FORTRAN program for Monte Carlo simulation of dynamical triangulated random surfaces with extrinsic curvature is presented. It is an implementation of a new procedure to measure the string tension. We summarize the method and give a detailed description of the program.

The random sequential adsorption of parallel (aligned) squares is studied by computer simulation. A new precise value of the maximum (jamming) coverage is found: ${\mathrm{\ensuremath{\theta}}}_{\mathit{J}}$=0.562 009\ifmmode\pm\else\textpm\fi{}0.000 004. The dynamics for times t\ensuremath{\gtrsim}6000 agree with Swendsen's prediction ${\mathrm{\ensuremath{\theta}}}_{\mathit{J}}$-\ensuremath{\theta}(t)\ensuremath{\sim}c(lnt)/t. Various two-point correlation functions are measured, and the effects of the finite size and the discretization of the adsorbing surface are also investigated.

Previous simulations of a self-avoiding, closed random surface with restricted topology (without handles) on a three-dimensional lattice have shown that its behavior on long length scales is consistent with that of a branched-polymer. It is shown analytically that such a surface with an unrestricted number of handles has a qualitatively different geometry and therefore is in a different universality class. The effect of a net external pressure is to suppress the handles and collapse the surface into a branched polymer-like configuration. Topology is thus shown to be a key factor in determining the universality class of the system.

equality properties are discussed and some open problems are presented. In this paper we discuss a simple discrete random surface introduced within a statistical mechanics context in [ANI, AN2]. Our purpose here is to survey some stochastic ordering/inequality properties and some easily stated open problems. For the sake of simplicity, we will mainly deal with a limiting case (corresponding to infinite temperature) of the model treated in [ANI, AN2]. We begin by discussing some of the physical motivation behind such random surface models. For more physical background and for other random surface models, see the papers in [DD] and the references in [ANI, AN2].

A technique is presented that uses an expansion in unperturbed modes to calculate acoustic scattering from ocean surface waves in a shallow water waveguide. The basic formalism as well as a useful extension to account for the difference between the water column and the domain in which the modes are calculated. The coupling between the modes due to the waves is local at the ocean surface, unlike the coupling of local modes. Numerical examples of the calculation are given for both a sinusoid surface wave and a random surface wave with a typical wind driven spectrum.