Related papers: Pattern Formation in Interface Depinning and Other…
We study roughening interfaces with a constant slope that become self organized critical by a rule that is similar to that of invasion percolation. The transient and critical dynamical exponents show Galilean invariance. The activity along…
This paper addresses the problem of wave scattering at a moving interface formed by a space-time modulation step. Specifically, it derives, using the technique of frame hopping with Lorentz transformation, the formula for the corresponding…
We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain…
We study the steady state structure and dynamics of a 2-d Ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity $v_{e}$. In the strong coupling limit the problem maps onto an…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
We establish a thermodynamic limit and Gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces. The results hold for the standard ballistic deposition model as well as…
We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains.…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
We review in these notes some dynamical properties of interfaces in random media submitted to an external force. We focuss in particular to the response to a very small force (so called creep motion) and discuss various theoretical aspects…
Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…
The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the `En-Passant' family of crack…
We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining…
The cellular basis for the adaptive immune response during antigen recognition relies on a specialized protein interface known as the immunological synapse (IS). Understanding the biophysical basis for protein patterning by deciphering the…
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of…
To comprehend the complexities of the ice-water interface, we perform a study that attempts to correlate the altered dynamics of water to its perturbed structure at, and due to, the interface. The deviation from bulk values of structural…
A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as…
Cooperation and self-organized criticality are two main keywords in current studies of evolution. We propose a generalized Bak-Sneppen model and provide a natural mechanism which accounts for both phenomena simultaneously. We use the…
We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly…