Related papers: Directed Surfaces in Disordered Media
The dynamics of critical slope self-organized critical models is studied, using a previous mapping into a linear interface depinning model dragged at one end. The model is solved obtaining the complete set of scaling exponents. Some results…
We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point…
We report on some extensive analysis of a recently proposed model [A. Lipowski Phys. Rev. E {\bf 60}, 6255 (1999)] with infinitely many absorbing states. By performing extensive Monte Carlo simulations we have determined critical exponents…
Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
Directed polymers in random media are studied using results of the asymptotic theory of extreme statistics. Despite the strong correlation, one can recover the behavior of independent random variables for high dimensions, using a result…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
In this paper, we define a directed version of the Diffusion-Limited-Aggregation model. We present several equivalent definitions in finite volume and a definition in infinite volume. We obtain bounds on the speed of propagation of…
Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e. transitions in the…
Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not…
Text-guided diffusion models such as DALLE-2, Imagen, eDiff-I, and Stable Diffusion are able to generate an effectively endless variety of images given only a short text prompt describing the desired image content. In many cases the images…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
Spatiotemporal patterns, which are of interest in statistical physics and nonlinear dynamics, form on the tape-peeling trace. Recently, we have proposed a mathematical model to describe these pattern formation in the tape-peeling trace. In…
The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-\alpha n^2)$. We argue that $\alpha$ is a new…
We investigate a novel Marangoni-induced instability that arises exclusively in diffuse fluid interfaces, absent in classical sharp-interface models. Using a validated phase-field Navier-Stokes-Allen-Cahn framework, we linearize the…
In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability…
We study the scaling exponents of a 1+1-dimensional directed polymer in a Brownian random environment introduced by O'Connell and Yor. For a version of the model with boundary conditions that are stationary in a space-time sense we identify…
We present a Monte Carlo study of the bond and site directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \leq 7$. A dimensionless ratio is defined, and an analysis of…
The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…