Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System

We study the Hilbert expansion for small Knudsen number $\varepsilon$ for the Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi \theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\ }\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).$Our main result states that if the Hilbert expansion is valid at$t=0$for well-prepared small initial data with irrotational velocity$u_0$, then it is valid for$0\leq t\leq \varepsilon ^{-{1/2}\frac{2k-3}{2k-2}},$where$\rho_{0}(t,x)$and$ u_{0}(t,x)$satisfy the Euler-Poisson system for monatomic gas$\gamma=5/3$

A sharp stability criterion for the Vlasov-Maxwell system

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria

From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality

By means of Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the de Sitter special relativity and their UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a complete Yang model at both classical and quantum level can be presented and there really exist Snyder's model, the dS special relativity and the duality.Comment: 7 papge

Template Generation - A Graph Profiling Algorithm

The availability of high-level design entry tooling is crucial for the viability of any reconfigurable SoC architecture. This paper presents a template generation algorithm. The objective of template generation step is to extract functional equivalent structures, i.e. templates, from a control data flow graph. By profiling the graph, the algorithm generates all the possible templates and the corresponding matches. Using unique serial numbers and circle numbers, the algorithm can find all distinct templates with multiple outputs. A new type of graph (hydragraph) that can cope with multiple outputs is introduced. The generated templates pepresented by the hydragraph are not limited in shapes, i.e., we can find templates with multiple outputs or multiple sinks

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

Mapping and Scheduling of Directed Acyclic Graphs on An FPFA Tile

An architecture for a hand-held multimedia device requires components that are energy-efficient, flexible, and provide high performance. In the CHAMELEON [4] project we develop a coarse grained reconfigurable device for DSP-like algorithms, the so-called Field Programmable Function Array (FPFA). The FPFA devices are reminiscent to FPGAs, but with a matrix of Processing Parts (PP) instead of CLBs. The design of the FPFA focuses on: (1) Keeping each PP small to maximize the number of PPs that can fit on a chip; (2) providing sufficient flexibility; (3) Low energy consumption; (4) Exploiting the maximum amount of parallelism; (5) A strong support tool for FPFA-based applications. The challenge in providing compiler support for the FPFA-based design stems from the flexibility of the FPFA structure. If we do not use the characteristics of the FPFA structure properly, the advantages of an FPFA may become its disadvantages. The GECKO1project focuses on this problem. In this paper, we present a mapping and scheduling scheme for applications running on one FPFA tile. Applications are written in C and C code is translated to a Directed Acyclic Graphs (DAG) [4]. This scheme can map a DAG directly onto the reconfigurable PPs of an FPFA tile. It tries to achieve low power consumption by exploiting locality of reference and high performance by exploiting maximum parallelism

Systematic {\it ab initio} study of the magnetic and electronic properties of all 3d transition metal linear and zigzag nanowires

It is found that all the zigzag chains except the nonmagnetic (NM) Ni and antiferromagnetic (AF) Fe chains which form a twisted two-legger ladder, look like a corner-sharing triangle ribbon, and have a lower total energy than the corresponding linear chains. All the 3d transition metals in both linear and zigzag structures have a stable or metastable ferromagnetic (FM) state. The electronic spin-polarization at the Fermi level in the FM Sc, V, Mn, Fe, Co and Ni linear chains is close to 90% or above. In the zigzag structure, the AF state is more stable than the FM state only in the Cr chain. It is found that the shape anisotropy energy may be comparable to the electronic one and always prefers the axial magnetization in both the linear and zigzag structures. In the zigzag chains, there is also a pronounced shape anisotropy in the plane perpendicular to the chain axis. Remarkably, the axial magnetic anisotropy in the FM Ni linear chain is gigantic, being ~12 meV/atom. Interestingly, there is a spin-reorientation transition in the FM Fe and Co linear chains when the chains are compressed or elongated. Large orbital magnetic moment is found in the FM Fe, Co and Ni linear chains