相关论文: Universality and conformal non-invariance in self-…

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height…

In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we consider the distribution of the ratio of persistence…

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…

Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review…

An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a…

The scaling properties of one-dimensional deconstructed surfaces are studied by numerical simulations of a disaggregation model. The model presented here for the disaggregation process takes into account the possibility of having quenched…

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially…

A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…

In a recent paper, Zhou, Ponnusamy, and Rasila [Math. Nachr. (2025)] have established that the conformal deformations, with parameter $\epsilon>0$, of a Gromov hyperbolic space via Busemann functions are uniform spaces for sufficiently…

We study the influence of surface roughness on the adhesion of elastic solids. Most real surfaces have roughness on many different length scales, and this fact is taken into account in our analysis. We consider in detail the case when the…

We show, using standard results in length spectrum rigidity and symplectic homology, that if the unit tangent bundles of two compact surfaces of negative curvature are exact symplectomorphic, then the underlying surfaces are isometric, and…

The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a linear differential equation of the first order, which previously did not appear in the literature and which is satisfied…

We show that universal rigidity of a generic bar and joint framework (G,p) in the line depends on more than the ordering of the vertices. In particular, we construct examples of one-dimensional generic frameworks with the same graph and…

We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites…

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are…

We prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains. The result applies to uniformly random lozenge tilings of large…

The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…

We prove that Alexandrov's conjecture relating the area and diameter of a convex surface holds for the surface of a general ellipsoid. This is a direct consequence of a more general result which estimates the deviation from the optimal…