this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

The pair-correlation function g(r, t) and its Fourier transform, the structure factor S(q, t), are computed during the gelation process of identical spherical particles using the diffusion-limited cluster-cluster aggregation model in a box. This numerical analysis shows that the time evolution of the characteristic cluster size ξ exhibits a crossover close to the gel time tg which depends on th...

We consider a recently suggested "equation of state" for natively folded proteins, and verify its validity for a set of about 5800 proteins. The equation is based on a fractal viewpoint of proteins, on a generalization of the Landau-Peierls instability, and on a marginal stability criterion. The latter allows for coexistence of stability and flexibility of proteins, which is required for their ...

We study the critical properties of the Bak-Sneppen coevolution model on scalefree networks by Monte Carlo method. We report the distribution of the avalanche size and fractal activity through the branching process. We observe that the critical fitness fc(N) depends on the number of the node such as fc(N) ∼ 1/ log(N) for both the scale-free network and the directed scale-free network. Near the ...

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

2014 In a recent article we have shown that, by applying sophisticated summation methods to Wilson-Fisher’s 03B5-expansion, it is possible from the presently known terms of the series to obtain accurate values of critical exponents for the 0 ( n ) symmetric n-vector model : these values are consistent with the best estimates obtained from threedimensional Renormalization Group calculations and,...

Fractures play an important role in steam production from geothermal reservoirs. It has been a challenge for a long time to characterize materials with a high density of fractures such as The Geysers rock. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of Berea sandstone. Methods to characterize the difference between the two have be...

It is well known that the permeability and density of an aggregate decreases with its size, affecting its settling velocity and coagulation rate (rate of particle capture) with other particles. This change in aggregate density with size can be described by fractal scaling relationships. Two distinctly different fractal scaling approaches, however, have been used to describe aggregate permeabili...

This paper introduces evolutionary computing to frac-tal image compression. In fractal image compression 1] a partitioning of the image into ranges is required. We propose to use evolutionary computing to nd good partitionings. Here ranges are connected sets of small square image blocks. Populations consist of N p conng-urations, each of which is a partitioning with a fractal code. In the evolu...

A global optimization algorithm i s introduced which generalizes Kushner’s univariate search [1]. It aims to minimize the number o f probes (function evaluations) required for a g i v e n confidence in the results. All known p r o b e s contribute to a stochastic model of the underly ing “score surface”; this model is interrogated for the location most likely to exceed the current result goal. ...