We suggest that the transition that occurs at large Nc in the eigenvalue distribution of a Wilson loop may have a turbulent origin. We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This picture supplem...

The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with small thickness ratio was solved by the linearized theory, which is first approximation at and near surface but fails far fields from body. Such problem W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This field disturbance reexamined this study using asymptotic expansion theory. A syst...

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g. the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from bein...

We consider a discrete bridge from (0, 0) to (2N, 0) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order N with α > 0. We provide a classification of the static and dynamic behaviour of this model according to the value of the parameter α. Our main results concern the hydrodynamic limit and the fluctuations of the bridge. For α < 1,...

In this work, we consider the forced generalized Burgers-Huxley equation and establish existence uniqueness of a global weak solution using Faedo-Galerkin approximation method. Under smoothness assumptions on initial data external forcing, also obtain further regularity results solutions. Taking forcing to be zero, positivity result as well bound classical are estab...

In this paper we enhance the well-known fifth order WENO shock-capturing scheme by using deep learning techniques. This fine-tuning of an existing algorithm is implemented training a rather small neural network to modify smoothness indicators in improve numerical results especially at discontinuities. our approach no further post-processing needed ensure consistency method. Moreover, formal acc...

In this paper, a two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform d...