The Burgers equation with linear damping has been subjected to Lie's group theoretic method of infinitesimal transformation to derive its solutions. To the best of our knowledge, we are the first to obtain a new similarity variable for an equation of the Burgers type and therefore provide new solutions.

In this paper, we discuss a link of Itô’s stochastic differential equations to nonlinear partial differential equations of Burgers type. Under certain conditions, we derive a generalised Burgers equation from a stochastic differential equation. We also give some economic interpretation of our result as well as the relevant conditions. Mathematics Subject Classification (2000): 60H10, 35K58, 91G99.

We calculate (to rst order in the Burgers vector) the energy of introducing dislocations into Stranski-Krastanow islands having equilibrium shape. These results suggest that misst dislocations of diierent Burgers vector tend to segregate spatially within the islands, which may aaect the mosaic structure of lms formed by island coalescence.

Higher-order accurate finite-difference schemes for solving the unsteady Burgers’ equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented. The unsteady Burgers’ equation belongs to a few nonlinear partial differential equations which has an exact solution, and it allows one to compare the numerical solution with the exact one, and the properti...

A photovoltaic thermal hybrid solar cell is being developed for an energy conversion efficiency higher than the Shockley-Queisser limit, consisting of two junctions with different bandgaps operating on top of a thermal collector at 450 C under solar radiation focused by a concentrator. InxGa1-xN thin films are used due to their wide bandgap range and their stability at high temperatures. The ta...

In this study, the D-optimal mixture design methodology was applied to determine the optimised proportions of inulin, β-glucan and breadcrumbs in formulation of low-fat beef burgers containing pre-emulsified canola and olive oil blend. Also, the effect of each of the ingredients individually as well as their interactions on cooking characteristics, texture, colour and sensory properties of low-...

Velocity structure functions (up 82up) m are calculated for vortex models of isotropic turbulence. An integral operator is introduced which defines an isotropic two-point field from a volume-orientation average for a specific solution of the Navier–Stokes equations. Applying this to positive integer powers of the longitudinal velocity difference then gives explicit formulas for (up 82up) m as a...

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standardmodels created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a s...

In this paper we discuss the eeect of the lter shape on large-eddy simulation of turbulent ows and back it up by an analysis of large scale dynamics and kinetic energy budget. For the sake of simplicity, we consider numerical simulation of one-dimensional homogeneous ow, governed by the viscous Burgers equation. Large eddy simulations of the solution of Burgers equation are performed using subg...