Related papers: Steiner Variations on Random Surfaces
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…
We investigate actions for dynamically triangulated random surfaces that consist of a gaussian or area term plus the {\it modulus} of the gaussian curvature and compare their behavior with both gaussian plus extrinsic curvature and…
We consider a subdivision invariant action for dynamically triangulated random surfaces that was recently proposed (R.V. Ambartzumian et. al., Phys. Lett. B 275 (1992) 99) and show that it is unphysical: The grand canonical partition…
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…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
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…
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…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
The critical dynamics of conformal field theories on random surfaces is investigated beyond the previously studied dynamics of the overall area and the genus. It is found that the evolution of the order parameter in physical time performs a…
We consider a numerical approach for a covariant generalised Navier-Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterised by…
In low dimensions, conformal anomaly has profound influence on the critical behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We illustrate this by making a small $D$ expansion of rigid random surfaces, where a…
The Allen-Cahn action functional is related to the probability of rare events in the stochastically perturbed Allen-Cahn equation. Formal calculations suggest a reduced action functional in the sharp interface limit. We prove in two and…
We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients.…
We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
We present the results of a set of Monte Carlo simulations of Dynamically Triangulated Random Surfaces embedded in three dimensions with an extrinsic curvature dependent action. We analyze several observables in the crossover regime and…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this…