We derive the loop equations for the d-dimensional n-Hermitian matrix model. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large N the loop equations form a closed set. In particular we derive the loop equations for the n = 2 matrix model recently proposed to describe the coupling of Two-dimensional quantum gravity to conformal ...

The ability to form a fractal colony was shown to be common among several species of the family Enterobacteriaceae. Bacterial spreading growth in a two-dimensional field of nutrient concentration was indicated to be important for this experimental self-similar morphogenesis. As a basic analogy, the diffusion-limited aggregation model was suggested. Fractal dimensions of colonies were mostly in ...

The purpose of mineral exploration is to find ore deposits. The main aim of this work is to use the fuzzy inference system to integrate the exploration layers including the geological, remote sensing, geochemical, and magnetic data. The studied area was the porphyry copper deposit of the Kahang area in the preliminary stage of exploration. Overlaying of rock units and tectonic layers were used ...

Aerial photography was conducted in the high Arctic Ocean during a Chinese research expedition in summer 2010. By partitioning the images into three distinct surface categories (sea ice/ snow, water and melt ponds), the areal fraction of each category, ice concentration and the size and geometry of individual melt ponds, are determined with high-spatial resolution. The ice concentration and mel...

In this paper we describe a new multiscale model for char acterizing positive valued and long range dependent data The model uses the Haar wavelet transform and puts a con straint on the wavelet coe cients to guarantee positivity which results in a swift O N algorithm to synthesize N point data sets We elucidate our model s ability to capture the covariance structure of real data study its mult...

The structure of the clusters of primary carbon black aggregates dispersed in a polymer matrix is studied by small angle neutron and X-ray scattering. The fractal dimension is found to decrease continuously for increasing concentration ~ of carbon black from D = 1.75 at ~ = 0, corresponding to the value for the isolated primary aggregates, to 1.5 in the considered

D = lim log(.iV(A,c)) (1) E-o log1 where .Af(A, e) denotes the smallest number of closed balls of radius > 0 needed to cover the set A. The aim of this paper is to introduce a new fast algorithm for computing the fractal dimension of binary images according to (1). Consider a binary image that is represented as a matrix of binary pixels stored in a rectangular array I(x, y). Let this image deno...

Nienhuis’ truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop having a fugacity of n. We study such loops subjected to a particular kind of staggered field w, which for n → ∞ has the geometrical effect of breaking the three-phase coexistence, linked to the three-colourability of the lattice faces. We show that at T = 0, for w > 1 the model flows...