5,318 research outputs found
On a question of Babadi and Tarokh
In a recent remarkable paper, Babadi and Tarokh proved the "randomness" of
sequences arising from binary linear block codes in the sense of spectral
distribution, provided that their dual distances are sufficiently large.
However, numerical experiments conducted by the authors revealed that Gold
sequences which have dual distance 5 also satisfy such randomness property.
Hence the interesting question was raised as to whether or not the stringent
requirement of large dual distances can be relaxed in the theorem in order to
explain the randomness of Gold sequences. This paper improves their result on
several fronts and provides an affirmative answer to this question
High Order Asymptotic Preserving DG-IMEX Schemes for Discrete-Velocity Kinetic Equations in a Diffusive Scaling
In this paper, we develop a family of high order asymptotic preserving
schemes for some discrete-velocity kinetic equations under a diffusive scaling,
that in the asymptotic limit lead to macroscopic models such as the heat
equation, the porous media equation, the advection-diffusion equation, and the
viscous Burgers equation. Our approach is based on the micro-macro
reformulation of the kinetic equation which involves a natural decomposition of
the equation to the equilibrium and non-equilibrium parts. To achieve high
order accuracy and uniform stability as well as to capture the correct
asymptotic limit, two new ingredients are employed in the proposed methods:
discontinuous Galerkin spatial discretization of arbitrary order of accuracy
with suitable numerical fluxes; high order globally stiffly accurate
implicit-explicit Runge-Kutta scheme in time equipped with a properly chosen
implicit-explicit strategy. Formal asymptotic analysis shows that the proposed
scheme in the limit of epsilon -> 0 is an explicit, consistent and high order
discretization for the limiting equation. Numerical results are presented to
demonstrate the stability and high order accuracy of the proposed schemes
together with their performance in the limit
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