In single phase flow of a passive tracer through heterogeneous porous media, a mixing layer develops between the tagged and untagged regions of the fluid. The mixing region expands as the time evolves. We have developed a multilength scale theory for the growth of the mixing region induced by a general random velocity field (multi-fractal field). The theory relates the statistics of the mixing ...

The partition function of the discretized superstring in a target superspace of three (Euclidean) bosonic dimensions, is shown, for a fixed triangulation of the random world sheet, to be derived from the partition function of a discretized bosonic string with an external field present in the action in the form of a specific constant matrix, using first order forms of the actions. This latter pa...

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale e...

We propose a parallel and distributed algorithm for solving discrete labeling problems in large scale random fields. Our approach is motivated by the following observations: i) very large scale image and video processing problems, such as labeling dozens of million pixels with thousands of labels, are routinely faced in many application domains; ii) the computational complexity of the current s...

The ground-state structure of the two-dimensional random field Ising magnet is studied using exact numerical calculations. First we show that the ferromagnetism, which exists for small system sizes, vanishes with a large excitation at a random field strength-dependent length scale. This breakup length scale L(b) scales exponentially with the squared random field, exp(A/delta(2)). By adding an e...

• Present modeling abstraction that we call random field optimization. Abstraction captures uncertainty lives on continuous space-time domains. Demonstrate the applicability using case studies. We present a new paradigm for optimization Random fields are powerful aims to capture behavior of variables live infinite-dimensional spaces (e.g., space and time) such as stochastic processes time serie...

In this paper, we face a generalization of the problem of finding the distribution of how long it takes to reach a “target” set T of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the n-length path connections are shown to belong to this generalization. This paper explores how the state space of the Markov chain can ...

This paper describes a new algorithm which discovers the hierarchical organization of a document or media presentation. We use latent semantic indexing to describe the semantic content of the signal, and scale-space segmentation to describe its features at many different scales. We present results from a text document and a video transcript.