In an attempt to confirm the presence or absence of central nervous tissue in commercially prepared beefburgers, four burgers were processed and stained using routine histological laboratory techniques. Constituent parts of the burgers could be identified readily. In this small sample no central nervous tissue was found. There is currently considerable general interest in the contents of foodst...

We discuss the structure of shock singularities of the Burgers-Hopf hierarchy. It is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy. The stratification is associated with the Birkhoff decomposition of the Grassmannian given by the set of linear spaces spanned by the hierarchy. We then construct integrable hierarchy o...

We study the kinetics of two-species annihilation, A + B → 0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t −1/3 , compared to t −1/4 density decay in A+B → 0 with isotropic diffusion and either with or without the hard-core repulsion....

For Burgers equations with real data and complex forcing terms, Lerner, Morimoto and Xu [Instability of the Cauchy-Kovalevskaya solution for a class of non-linear systems, Amer. J. Math. 2010] proved that only analytical data generate local C solutions. The corresponding instabilities are however not observed numerically; rather, numerical simulations show an exponential growth only after a del...

In this study, the Lie group method for constructing exact and numerical solutions of the generalized time-dependent variable coefficients Burgers’, Burgers’–KdV, and KdV equations with initial and boundary conditions is presented. Lie group theory is applied to determine symmetry reductions which reduce the nonlinear partial differential equations to ordinary differential equations. The obtain...

Spontaneous formation of a cylindrical density cavity, or "plasma hole," has been observed in a rotating magnetized plasma. Density of the plasma hole is one-tenth of that of ambient plasma and is bounded by a steep transition layer of the order of several ion Larmor radii. The flow velocity field associated with the plasma hole is experimentally determined, exhibiting a monopole vortical struc...

Spatially coarse-grained (or effective) versions of nonlinear partial differential equations must be closed with a model for the unresolved small scales. For systems that are known to display fractal scaling, we propose a model based on synthetically generating a scale-invariant field at small scales using fractal interpolation, and then analytically evaluating its effects on the large, resolve...

We discuss the structure of shock singularities of the Burgers-Hopf hierarchy. It is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy. The stratification is associated with the Birkhoff decomposition of the Grassmannian given by the set of linear spaces spanned by the hierarchy. We then construct integrable hierarchy o...

Abstract In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|e 2/2, β ≥ 0, x ∈ R. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted ge...