We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed...

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function. The performance of the method is investigated by computing f...

In this paper we present a cross-cutting design principle for binary decision control (BDC) based congestion control systems, such as AIMD. Due to its discontinuity, constructing the switching function, or the onset condition of the congestion bit, must consider the relative degree and zero dynamics of the system based on sliding mode control (SMC) theory. We showed that the relative degree of ...

This paper presents a new Phase Measuring Deflectometry (PMD) method to measure specular object having discontinuous surfaces. A mathematical model is established to directly relate absolute phase and depth, instead of phase and gradient. Based on the model, a hardware measuring system has been set up, which consists of a beam splitter to change the optical path, and two LCD screens to display ...

Many interesting and important control systems evolve on strati ed con guration spaces. Robotic systems, in particular, are of this nature. A legged robot has discontinuous equations of motion near points in the con guration space where each of its \feet" come into contact with the ground, and it is precisely the ability of the robot to lift its feet o of the ground that enables it to move abou...

In this paper, we generalize the idea in our previous work for the Vlasov-Ampère (VA) system [8] and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a fundamental model in the simulation of collisionless magnetized plasmas. Compared to [8], additional care needs to be taken for both the temporal and spatial discretizations to ac...

In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell’s system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theo...

In this paper, we propose energy-conserving numerical schemes for the VlasovAmpère (VA) systems. The VA system is a model used to describe the evolution of probability density function of charged particles under self consistent electric field in plasmas. It conserves many physical quantities, including the total energy which is comprised of the kinetic and electric energy. Unlike the total part...

We describe a modified polyacrylamide gel electrophoresis method with which plasma proteins are excellently resolved in 4 h. We made a three-layer discontinuous gradient gel with concentrations of 80,60, and 45 g of polyacrylamide per liter of tris(hydroxymethyl)aminomethane/ethylenediaminetetraacetic acid/borate buffer, pH 9.2. Time and material needed in the preparation of the gel was greatly...