Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.Comment: 26 page

Measurement of statistical evidence on an absolute scale following thermodynamic principles

Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p-values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically-based framework in which measurement of E on an absolute scale, for which "one degree" always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.Comment: Final version of manuscript as published in Theory in Biosciences (2013

Statistical Evidence Measured on a Properly Calibrated Scale Across Nested and Non-nested Hypothesis Comparisons

Statistical modeling is often used to measure the strength of evidence for or against hypotheses on given data. We have previously proposed an information-dynamic framework in support of a properly calibrated measurement scale for statistical evidence, borrowing some mathematics from thermodynamics, and showing how an evidential analogue of the ideal gas equation of state could be used to measure evidence for a one-sided binomial hypothesis comparison (coin is fair versus coin is biased towards heads). Here we take three important steps forward in generalizing the framework beyond this simple example. We (1) extend the scope of application to other forms of hypothesis comparison in the binomial setting; (2) show that doing so requires only the original ideal gas equation plus one simple extension, which has the form of the Van der Waals equation; (3) begin to develop the principles required to resolve a key constant, which enables us to calibrate the measurement scale across applications, and which we find to be related to the familiar statistical concept of degrees of freedom. This paper thus moves our information-dynamic theory substantially closer to the goal of producing a practical, properly calibrated measure of statistical evidence for use in general applications

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Nanopillar Arrays on Semiconductor Membranes as Electron Emission Amplifiers

A new transmission-type electron multiplier was fabricated from silicon-on-insulator (SOI) material by integrating an array of one dimensional (1D) silicon nanopillars onto a two dimensional (2D) silicon membrane. Primary electrons are injected into the nanopillar-membrane system from the flat surface of the membrane, while electron emission from the other side is probed by an anode. The secondary electron yield (SEY) from nanopillars is found to be about 1.8 times that of plane silicon membrane. This gain in electron number is slightly enhanced by the electric field applied from the anode. Further optimization of the dimensions of nanopillars and membrane and application of field emission promise an even higher gain for detector applications and allow for probing of electronic/mechanical excitations in nanopillar-membrane system excited by incident particles or radiation.Comment: 4 figure

Effect of sintering temperature under high pressure in the uperconductivity for MgB2

We report the effect of the sintering temperature on the superconductivity of MgB2 pellets prepared under a high pressure of 3 GPa. The superconducting properties of the non-heated MgB2 in this high pressure were poor. However, as the sintering temperature increased, the superconducting properties were vastly enhanced, which was shown by the narrow transition width for the resistivity and the low-field magnetizations. This shows that heat treatment under high pressure is essential to improve superconducting properties. These changes were found to be closely related to changes in the surface morphology observed using scanning electron microscopy.Comment: 3 Pages including 3 figure

Lanczos exact diagonalization study of field-induced phase transition for Ising and Heisenberg antiferromagnets

Using an exact diagonalization treatment of Ising and Heisenberg model Hamiltonians, we study field-induced phase transition for two-dimensional antiferromagnets. For the system of Ising antiferromagnet the predicted field-induced phase transition is of first order, while for the system of Heisenberg antiferromagnet it is the second-order transition. We find from the exact diagonalization calculations that the second-order phase transition (metamagnetism) occurs through a spin-flop process as an intermediate step.Comment: 4 pages, 4 figure