The coupling of accurate computational fluid dynamics analysis with optimal control theory has the potential to advance active flow-control for complex fluid systems. In this paper, an optimal control framework for the viscous Burgers equation is constructed based on the Discontinuous Galerkin Method (DGM). A DGM discretization has several potential advantages for optimization studies including...

I previously used Burgers’ equation to introduce a new method of numerical discretisation of pdes. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models all the processes and their subgrid scale interactions. Here I show how boundaries to the physical domain may be naturally incorporated into the numerical modelling of Burgers’ equation. W...

We are concerned with the asymptotic behavior of the solutions of a simplified model describing the evolution of a radiating gas. More precisely, we shall prove the convergence of H solutions toward the classical diffusion wave of the viscous Burgers’ equation by means of entropy methods. The result is also endowed with the same L rate of convergence of that case.

We consider a model for non-static groundwater flow where the saturation-pressure relation is extended by a dynamic term. This approach together with a convective term due to gravity, results in a pseudo-parabolic Burgers type equation. We give a rigorous study of global travelling wave solutions, with emphasis on the role played by the dynamic term and the appearance of fronts.

A microscopic model for a solid-on-solid type of interface under the influence of an external field is introduced. It is proven that in equilibrium the macroscopic profile satisfies a partial differential equation which is (up to a transformation) the stationary Burgers equation. The study is based on the structure of the invariant measures for a related asymmetric simple exclusion process.

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particu...

A quantum algorithm is presented for modeling the time evolution of a continuous field governed by the nonlinear Burgers equation in one spatial dimension. It is a microscopic-scale algorithm for a type-II quantum computer, a large lattice of small quantum computers interconnected in nearest neighbor fashion by classical communication channels. A formula for quantum state preparation is present...

Background: Beef burgers made in Iran contain various compounds such as meat, cereals flour, as well as some spices which can be contaminated to Bacillus cereus, causing gastroenteritis in the consumer. This study is focused onoccurrence of B. cereus in beef burgers marketed in Tehran, capital of Iran. Methods:  In this cross-sectional study, a total of 80 samples of different types of be...