相关论文: Random paths with curvature
We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to…
A surface model with skeletons is investigated by using the canonical Monte Carlo simulations. The skeleton is composed of linear chains, which are joined to each other at the rigid junctions. A one-dimensional bending energy is defined on…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force…
We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated…
We investigate the crumpling transition for a dynamically triangulated random surface embedded in two dimensions using an effective model in which the disordering effect of the $X$ variables on the correlations of the normals is replaced by…
A spherical model of skeleton with junctions is investigated by Monte Carlo simulations. The model is governed by one-dimensional bending energy. The results indicate that the model undergoes a first-order transition separating the smooth…
An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
The effect of surface roughness on the structure of liquid crystalline fluids near solid substrates is studied by Monte Carlo simulations. The liquid crystal is modelled as a fluid of soft ellipsoidal molecules and the substrate is modelled…
The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible,…
We measure by Monte Carlo simulations $\g_{string}$ for a model of random surfaces embedded in three dimensional Euclidean space-time. The action of the string is the usual Polyakov action plus an extrinsic curvature term. The system…
The elephant random walk is a history-dependent random walk. We study a class of interacting elephant random walks. Our model includes the exclusion process as a special case. By means of Monte Carlo simulations and mean-field arguments, we…
This article is devoted to methods of construction and study of stochastic models based on Monte Carlo method. A model of Brownian motion, the construction and processing which brings to a world of random numbers and mathematical…
In this paper, we build the foundation for a theory of controlled rough paths on manifolds. A number of natural candidates for the definition of manifold valued controlled rough paths are developed and shown to be equivalent. The theory of…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…