相关论文: Random Surfaces
Fluid properties near rough surfaces are crucial in describing fundamental surface phenomena and modern industrial material design implementations. One of the most powerful approaches to model real rough materials is based on the surface…
In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean field formalism introduced by Saito for…
We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…
We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
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…
The motivation for this article is to derive strict convexity of the surface tension for Lipschitz random surfaces, that is, for models of random Lipschitz functions from $\mathbb Z^d$ to $\mathbb Z$ or $\mathbb R$. An essential innovation…
In this note we give a simple proof for the convergence of stochastic gradient (SGD) methods on $\mu$-convex functions under a (milder than standard) $L$-smoothness assumption. We show that for carefully chosen stepsizes SGD converges after…
The nature of its intrinsic ripples is the key factor for understanding the stability of suspended graphene, and for unraveling the long-standing theoretical debate of the existence of low-dimensional crystalline state. The rippling…
This study presents an experimental dataset documenting the evolution of a turbulent boundary layer downstream of a rough-to-smooth surface transition. To investigate the effect of upstream flow conditions, two groups of experiments are…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
We consider gradient models on the lattice $Z^d$. These models serve as effective models for interfaces and are also known as continuous Ising models. The height of the interface is modelled by a random field with an energy which is a…
We study a system of hard-core particles sliding downwards on a fluctuating one-dimensional surface which is characterized by a dynamical exponent $z$. In numerical simulations, an initially random particle density is found to coarsen and…
A new method has been proposed to evaluate the frictional force in the stationary state. This method is applied to the 1-dimensional model of clean surfaces. The kinetic frictional force is seen to depend on velocity in general, but the…
In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points…
We prove the existence of an ordered low temperature phase in a model of soft-self-avoiding closed random surfaces on a cubic lattice by a suitable extension of Peierls contour method. The statistical weight of each surface configuration…
We study the surface tension and the phenomenon of phase coexistence for the Ising model on $\mathbbm{Z}^d$ ($d \geqslant 2$) with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random…