Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy

In this paper we develop high-order asymptotic-preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi, where asymptotic preserving exponential Runge-Kutta methods for the classical inhomogeneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian steady states characterizing the quantum kinetic behavior. We show that the proposed schemes work with high-order accuracy uniformly in time for all Planck constants ranging from classical regime to quantum regime, and all Knudsen numbers ranging from kinetic regime to fluid regime. Computational results are presented for both Bose gas and Fermi gas

A particle method for the homogeneous Landau equation

We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of the Landau equation, we regularize the collision operator to make sense of the particle solutions. These particle solutions solve a large coupled ODE system that retains all the important properties of the Landau operator, namely the conservation of mass, momentum and energy, and the decay of entropy. We illustrate our new method by showing its performance in several test cases including the physically relevant case of the Coulomb interaction. The comparison to the exact solution and the spectral method is strikingly good maintaining 2nd order accuracy. Moreover, an efficient implementation of the method via the treecode is explored. This gives a proof of concept for the practical use of our method when coupled with the classical PIC method for the Vlasov equation.Comment: 27 pages, 14 figures, debloated some figures, improved explanations in sections 2, 3, and

A New Approximation Method for Constant Weight Coding and Its Hardware Implementation

In this chapter, a more memory-efficient method for encoding binary information into words of prescribed length and weight is presented. The solutions in existing work include complex float point arithmetic or extra memory overhead which make it demanding for resource-constrained computing platform. The solution we propose here solves the problems above yet achieves better coding efficiency. We also correct a crucial error in previous implementations of code-based cryptography by exploiting and tweaking the proposed encoder. For the time being, the design presented in this work is the most compact one for any code-based encryption schemes. We show, for instance, that our lightweight implementation of Niederreiter encrypting unit can encrypt approximately 1 million plaintexts per second on a Xilinx Virtex-6 FPGA, requiring 183 slices and 18 memory blocks