Many second order accurate non-oscillatory schemes are based on the Minmod limiter, for example the Nessyahu-Tadmor scheme. It is well known that the Lperror of monotone finite difference methods for the linear advection equation is of order 1/2 for initial data in W (Lp), 1 ≤ p ≤ ∞, see [2]. For a second or higher order non-oscillatory schemes very little is known because they are nonlinear ev...

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization...

We present a characterization of molybdenum sources, ΓMo , core Mo density, nMo, and their dependencies on Alcator C-Mod operational regimes. This includes sources from the divertor, the inner wall and the ICRF antenna limiters. We also present information characterizing the penetration of these impurities into the core plasma under different conditions based on penetration factors, PF=nMo/ΓMo ...

In this letter, we study the modulo-limit modulator whose input signal is a causal stable ARMA process. We prove that for all the cases, the normalized quantization error can be taken as a uniformly distributed white noise.

New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux conservative hyperbolic) system, advanced numerical methods from CFD (computational fluid dynamics) have been successfully applied. A flux limiter mechanism has b...

Exciton–polaritons in optical cavities exhibit strong nonlinearities predominantly because of the third-order Kerr-like interactions mediated by excitonic component. Under quasi-resonant excitation, depending on energy incident laser, it results limiting or bistable behavior. The latter phenomenon is manifested hysteresis loop observed input–output power characteristics, when a cavity quasi-res...

For the initial value problem of scalar conservation laws, a bound-preserving property is desired for numerical schemes in many applications. Traditional methods to enforce a discrete maximum principle by defining the extrema as those of grid point values in finite difference schemes or cell averages in finite volume schemes usually result in an accuracy degeneracy to second order around smooth...