The engineering properties of collapsible loess have significant uncertainty. Accurate prediction deformation is crucial for the safety construction in areas. Taking typical stratum as research object Xi’an, based on random field theory, combined with Monte Carlo strategy and modulus reduction method, stochastic finite element analysis self-weight collapsibility carried out to study influence s...

In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using...

We study a two-dimensional bosonic field theory with a random defect line. The theory has a background field coupled to the field variables at the defect line, which renders the model non-integrable. However, as the background field is random, and the disorder is implemented through the replica trick, the model becomes inte-grable, allowing us to use the form-factor method to compute the exact ...

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion in ε = 4− d. Up to two loop, the FRG agrees with rigorous bounds, correctly reproduces the leading logarithmic corrections at the upper critic...

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed ...

A number of recent papers have provided evidence that practical design questions about neural networks may be tackled theoretically by studying the behavior of random networks. However, until now the tools available for analyzing random neural networks have been relatively ad hoc. In this work, we show that the distribution of pre-activations in random neural networks can be exactly mapped onto...

Recurrent spiking neural networks can provide biologically inspired model of robot controller. We study here the dynamics of large size randomly connected networks thanks to ”mean field theory”. Mean field theory allows to compute their dynamics under the assumption that the dynamics of individual neuronsare stochastically independent. We restrict ourselves to the simple case of homogeneous cen...

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 ...

In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an explicit operator construction of the corresponding collective field theory in terms of a bosonic field on a hyperelliptic Riemann surface, with special ope...