相关论文: Self-avoiding random surfaces with fluctuating top…

In this paper we construct an end of a self-similar shrinking solution of the mean curvature flow asymptotic to an isoparametric cone C and lying outside of C. We call a cone C in $R^{n+1}$ an isoparametric cone if C is the cone over a…

A simple scenario of the formation of geological landscapes is suggested and the respective lattice model is derived. Numerical analysis shows that the arising non-Gaussian surfaces are characterized by the scale-dependent Hurst exponent,…

We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…

Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused…

Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…

We perform Monte Carlo simulations of a four-dimensional gauge invariant spin system which describes random surfaces with gonihedric action. We develop the analogy between the flat-crumpled phase transition of the lattice surface model and…

We solve the problem of prescribing different types of curvatures (principal, mean or Gaussian) on rotational surfaces in terms of arbitrary continuous functions depending on the distance from the surface to the axis of revolution. In this…

We show some generic (robust) properties of smooth surfaces immersed in the real 3-space (Euclidean, affine or projective), in the neighbourhood of a {\em godron} (term due to R.Thom): an isolated parabolic point at which the (unique)…

We construct some positive entropy automorphisms of rational surfaces with no periodic curves. The surfaces in question, which we term tri-Coble surfaces, are blow-ups of the projective plane at 12 points which have contractions down to…

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…

Total five different types of translation surfaces, based upon planarity of translating curves and the absolute figure, arise in a Galilean 3-space. Excepting the type in which both of translating curves are non-planar we obtain these…

This paper gives a detailed derivation of the surface of a tri-axial ellipsoid. The general result is in terms of the elliptic integrals of the first and second kind. It is in checked for all special cases included and the corresponding…

Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…

This paper aims to establish the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties.…

We present a random-interface representation of the three-dimensional (3D) Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model and its 2D cross section. Extensive simulations have been…

The two-dimensional Ising model is studied at the boundary of a half-infinite cylinder. The three regular lattices (square, triangular and hexagonal) and the three regimes (sub-, super- and critical) are discussed. The probability of having…

There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…

Given the ensemble of random Gaussian Laplace eigenfunctions on the three-dimensional torus (`3d arithmetic random waves'), we investigate the $1$-dimensional Hausdorff measure of the nodal intersection curve against a compact regular toral…

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the…

We construct a weakly complete flat surface in hyperbolic 3-space having a pair of hyperbolic Gauss maps both of whose images are contained in an arbitrarily given open disc in the ideal boundary of H^3. This construction is accomplished as…