On the Boltzmann-Grad limit for the Broadwell model of the Boltzmann equation

An example is given of a model dynamics for which the Broadwell model of the Boltzmann equation seems to appear in the formal stage of the Boltzmann-Grad limit, but actually does not.     

Comments on some aspects of boltzmannH theorem using reversible molecular dynamics

We calculate the BoltzmannH function for a repulsive Lennard-Jones fluid using Levesque and Verlet’s reversible molecular dynamics algorithm. We find, as predicted by Jaynes, that for certain initial states,H increases as a function of time. We also discuss the Grad limit within such a simulation     

Fluctuations around the Boltzman equation

For a system of hard spheres we prove the convergence of the second moment of the fluctuation field in the low-density limit. This extends a previous result by van Beijeren, Lanford, Lebowitz and Spohn⁽¹⁾ to nonequilibrium states.     

A Conversation with Robert F. Christy – Part II

Robert F. Christy, Institute Professor of Theoretical Physics Emeritus at Caltech, recalls his wartime work at Los Alamos on the critical assembly for the plutonium bomb (“the Christy bomb”); the Alamogordo test, July 16, 1945; the postwar concerns of ALAS (Association of Los Alamos Scientists); his brief return to the University of Chicago and move to Caltech; friendship with and later alienation from Edward Teller; work with Charles and Tommy Lauritsen and William A. Fowler in Caltech’s Kellogg Radiation Laboratory; Freeman Dyson’s Orion Project; work on the meson and RR Lyrae stars; fellowship at Cambridge University; 1950s Vista Project at Caltech; his opposition to the Strategic Defense Initiative; and his post-retirement work for the National Research Council’s Committee on Dosimetry and on inertial-confinement fusion.     

CCD光谱层析技术重建氩等离子束射流三维温度场

根据谱线相对强度法,提出了利用正交面阵CCD光谱层析技术,实时重建氩等离子束射流三维温度场的方法.通过CCD获得的待测场图像与没有射流射出时在待测场处放置的坐标纸图像进行比对,测最了实际待测场的大小;利用步进电机带动光纤探针对待测场进行扫描,通过光谱仪获得了待测场的光强分布.根据谱线相对强度法中谱线选取的原则,选择了696.5和763.5 nm两条谱线作为研究对象.为防止CCD接收光强过饱和及待测场边缘光谱信息的损失,根据待测场的大小和光强分布设计了梯度衰减片,再通过窄带滤波片获得了待测场的光谱信息.结果表明与光纤光谱扫描法获得的结果吻合较好,不确定度为3.3%.系统满足了实时重建三维温度场的要求,为等离子束射流后续的密度场、压力场和速度场的实时诊断提供了坚实基础.     

Properties and Phenomena: Basic Plasma Physics and Fusion Research in Postwar America

I review the changing conceptions of basic physics that the U.S. plasma-physics community put forward in postwar America. I give special attention to the tense relationship between fusion research and the more general study of plasmas in astrophysics, space science, and industry.Although fusion research often led to results that were regarded as basic plasma physics, its dominating influence tended to weaken other plasma work, as becomes evident when I compare the public statements and professional fortunes of plasma scientists during the 1960s, when fusion research experienced a downturn, with those of the 1970s, when fusion research flourished. I also show that the plasmaphysics community’s conceptions of basic physics were not highly regarded or easily understood by science administrators and the general physics community. To make this point, I contrast two general ideas of basic physics: the Big Questions conception and the Properties and Phenomena conception. Gary J.Weisel; Gary J.Weisel is Associate Professor of Physics at Penn State Altoona in Altoona, Pennsylvania. His historical research focuses on the development of subdisciplines in twentieth-century physics. He also carries out research in nuclear physics and materials science.     

Some Estimates for 2-Dimensional Infinite and Bounded Dilute Random Lorentz Gases

We present a (mostly) rigorous approach to unbounded and bounded (open) dilute random Lorentz gases. Relying on previous rigorous results on the dilute (Boltzmann–Grad) limit we compute the asymptotics of the Lyapunov exponent in the unbounded case. For the bounded open case in a circular region we give here an incomplete rigorous analysis which gives the asymptotics for large radius of the escape rate and of the rescaled quasi-invariant (q.i., or quasi-stationary) measure. We finally give a complete proof on existence and asymptotic properties of the q.i. measure in a one-dimensional caricature.     

Finite element potentials

We present an explicit and efficient way for constructing finite elements with assigned gradient, or curl, or divergence. Some simple notions of homology theory and graph theory applied to the finite element mesh are basic tools for devising the solution algorithms.     

A Conversation with William A. Fowler – Part II

Physicist William A.Fowler initiated an experimental program in nuclear astrophysics after World War II. He recalls here the Steady State versus Big Bang controversy and his celebrated collaboration with Fred Hoyle and Geoffrey and Margaret Burbidge on nucleosynthesis in stars. He also comments on the shift away from nuclear physics in universities to large accelerators and national laboratories.John Greenberg received his Ph.D. degree from the University of Wisconsin and was Caltech research fellow in history from 1980–1984. The Editors were saddened to learn that he died while this interview was in press. Requests for reprints may be directed to Judith R. Goodstein, Institute Archives 015A-74, Caltech, Pasadena, CA 91125 USA; e-mail: jrg@caltech.edu.     

Grad theory and extended thermodynamics

Grad-type approaches introduce an ansatz involving tensor Hermite functions with coefficients expresed in terms of moments of the ansatz. This formalism in usual form yields terms linear in first-order spatial derivatives in kinetic equations for the moments. Such terms disagree with alternative statistical derivations and phenomenological arguments. This disagreement is removed if different ansatzes are used to calculate entropy and moment equations. These are non-unique, and so Grad theory, while providing theoretical expressions for transport coefficients, does not serve uniquely to determine the structure of phenomenological equations.