Higher-order Continuum Approximation for Rarefied Gases

The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman-Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman-Enskog approach. The new equations contain higher order terms that are discarded in the Chapman-Enskog method. These make a significant impact on the results for such problems as ultrasound propagation. In this paper, it is shown that these results turn out well with relatively little complication when the expansions are carried to second order in the mean free time, for the example of the relaxation or BGK model of kinetic theory.Comment: 20 pages, 2 figures, RevTeX 4 macro

Chapman-Enskog method and synchronization of globally coupled oscillators

The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes ``inertial'' effects. Second, a modified Chapman-Enskog method is used to derive the amplitude equation for an O(2) Takens-Bogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the Chapman-Enskog method is a convenient alternative to normal form calculations.Comment: 7 pages, 2-column Revtex, no figures, minor change

Notes Procedural Fencing in Retiree Benefits Disputes: Applications of the First-Filed Rule in Federal Courts

Basil Chapman retired from ACF Industries, a railroad-car maker, after thirty-eight years of service. In December 2003, he received an unexpected phone call at his West Virginia home from a union representative, who informed him that an ACF executive wanted to speak with him. When they spoke, the executive informed Mr. Chapman that ACF was planning on changing its retirees’ health coverage plan. The ACF plan would now have a lifetime maximum benefit cap on hospital and surgical expenses for each participant and would require retirees to make monthly contributions. According to court papers filed later, Mr. Chapman responded, “We have a contract. You can’t do that.” Then, he said that he would “file in federal court” against ACF. The next business day, ACF filed a declaratory judgment action in the United States District Court for the Eastern District of Missouri asking the court to rule that retiree benefits were not vested and that ACF accordingly could alter benefits unilaterally. On January 26, 2004, Mr. Chapman, other named plaintiffs, and their union sued ACF in the United States District Court for the Southern District of West Virginia

The Henry Chapman Site (41SM56)

In the mid-1950s, Sam Whiteside conducted excavations at the Henry Chapman site, his site P-5 (41SM56), on Prairie Creek in eastern Smith County, Texas, some 18 miles east of Tyler, Texas. Mr. Whiteside was an amateur archaeologist who discovered and explored numerous sites up and down Prairie Creek as well as other important sites in Smith and adjoining counties. The Chapman site was one of the first sites to be investigated by Mr. Whiteside, and the major part of the work took place there in 1957 and 1958. In August 1957, the site was visited by Edward B. Jelks and Leroy Johnson, who viewed the excavations and examined artifacts collected from there. Mr. Jelks, in notes on record at the Texas Archeological Research Laboratory (TARL) at The University of Texas in Austin, Texas, on August 21, 1958, indicated after observing the artifacts from the Henry Chapman site that the ceramics indicated an Alto focus occupation. He recognized Hickory Engraved and Holly Fine Engraved wares as well as Dunkin Incised and possible Pennington Punctated-Incised sherds. He mentioned that no Crockett Curvilinear Incised or Weches Fingernail Impressed sherds were present (two common types present at the Alto focus type site, the George C. Davis site [41CE19]). E. Mott Davis also visited the site in late 1957, and in February 1959, Davis, Lathel F. Duffield, and William A. Davis collected skeletal material from the site. In a June 15, 1958, newsletter from the East Texas Archeological Society (ETAS), Mr. Whiteside described excavations at the Henry Chapman site that had revealed refuse pits, post holes, and an abundance of pottery sherds indicative of an Alto focus occupation. In the summer of 1983, Mr. Whiteside visited the University of Texas Field School at the George C. Davis site, where he loaned some of his notes and collections from the Chapman site for recording purposes (these are on file at TARL). After Mr. Whiteside’s death, his family graciously allowed me access to his notes and artifacts. Not all of the artifacts have survived, having been stored in paper bags and subjected to several moves, but thanks to Mr. Whiteside’s writing lot numbers on artifacts and listing them in a journal, a majority of them have survived, and thus are suitable for study. Although 50 years have passed since Mr. Whiteside’s work at the Henry Chapman site, it is my intent to now make that work public

Distribution of ions around a charged sphere

Using a new method of calculating the effects of excluded volume, the authors evaluate the distribution of counterions around a charged sphere in thermal equilibrium. In regions of high concentration a saturation of the ion density is found, which is absent in the more conventional Gouy-Chapman model. At the same time the saturation effect of the potential (a property of the Gouy-Chapman model) is removed, giving significant corrections to the values of the potential and concentration at the surface of the sphere