Chromium (VI) (Cr(VI)) contamination of soil and groundwater is considered a major environmental concern. Bioreduction of Cr(VI) to chromium (III) (Cr(III)) can be considered an effective technology in remediating Cr(VI) contaminated sites. Among the Cr(VI) reducing bacteria, Shewanella oneidensis MR-1 (MR-1) is relatively effective. Reduction of Cr(VI) by MR-1 is defined by the dual-enzyme kin...

We analyze arbitrary order linear finite volume transport schemes and show asymptotic stability in L and L∞ for odd order schemes in dimension one. It gives sharp fractional order estimates of convergence for BV solutions. It shows odd order finite volume advection schemes are better than even order finite volume schemes. Therefore the Gibbs phenomena is controled for odd order finite volume sc...

We present a numerical method for the «-dimensional initial value problem for the scalar conservation law u{xx , ... , x„ , t)¡ + Y!¡=\ fi(u)x¡ = 0 , u(xx.Xn , 0) = «o(*i > • • • , xn). Our method is based on the use of dimensional splitting and Dafermos's method to solve the one-dimensional equations. This method is unconditionally stable in the sense that the time step is not limited by the s...

We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. We consider the Neumann or oblique boundary condition, the state constraint boundary condition and Dirichlet boundary condition. We establish general convergence results for viscosity solutions to asymptotic solutions as time goes to infinity via an...

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the doubled space and transform as vectors under Tduality. The gauge algebra defines a T-duality covariant bracket. For the case in which the parameters and fields are T-dual to o...

This paper will give the numerical difference scheme with Dirichlet boundary condition, and prove stability and convergence of the difference scheme, final numerical experiment results also confirm effectiveness of the algorithm. KeywordsFractional derivative; Numerical difference scheme; The gradient regularization method.

We consider Courant and Courant-Jacobi brackets on the stable tangent bundle TM ×R of a differentiable manifold and corresponding Dirac, Dirac-Jacobi and generalized complex structures. We prove that Dirac and Dirac-Jacobi structures on TM × R can be prolonged to TM × R, k > h, by means of commuting infinitesimal automorphisms. Some of the stable, generalized, complex structures are a natural g...

In this paper, we consider an explicit exponential method of classical order two for the time discretisation of quasi-linear parabolic problems. The numerical scheme is based on a Magnus integrator and requires the evaluation of two exponentials per step. Our convergence analysis includes parabolic partial differential equations under a Dirichlet boundary condition and provides error estimates ...

Newest vertex bisection (NVB) is a popular local mesh-refinement strategy for regular triangulations which consist of simplices. For the 2D case, we prove that the meshclosure step of NVB, which preserves regularity of the triangulation, is quasi-optimal and that the corresponding L-projection onto lowest-order Courant finite elements (P1-FEM) is always H-stable. Throughout, no additional assum...

In general we will be searching for methods of solving problems containing terms where the courant condition is too restrictive for practical computation; typical in this regard is the inclusion of diffusion or thermal conduction which contain second derivatives in space implying that time steps must scale as ∆t ∝ 1/(∆x). In this case we can not solve the problems explicitly but rather solve (a...