On the Theory of the Virial Development of the Equation of State of Monoatomic Gases

The problem of the condensation of a gas is intimately related to the asymptotic behavior of the virial coefficients, Bm, as m→∞. The problem of the evaluation of the virial coefficients may be divided into two distinctly different ones. The first of these, which is purely combinatorial in nature and is independent of the intermolecular force law, is that of determining the number of a certain type of connected graphs of l points and k lines which are called ``stars.'' This problem is solved by means of generating functions, with the result that the total number of such stars is asymptotically equal to(12l(l−1)k),for almost all k. Arguments are also presented which indicate that the total number of topologically different stars is1l!(12l(l−1)k).With these results the combinatorial problem is essentially solved.The second problem is that of evaluating certain integrals of functions which depend on the intermolecular potential. This problem is not so near to a solution. For a purely repulsive force, asymptotic expressions are obtained for k=l, and k=l+1. The partial contributions to the virial coefficient in these two cases are:(−1)l⋅53(52π)12(2b)l−1(l−1)l5∕2,and(−1)l2⋅5324π3(2b)l−1,respectively. Results for some simple one‐dimensional rigid lines are also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69794/2/JCPSA6-21-11-2056-1.pd

On the Notion of Pressure in a Canonical Ensemble

Recently a controversy has arisen between J. De Boer and H. S. Green concerning the notion of pressure in a canonical ensemble. According to Green, only classically is the pressure as derived from the partition function equal to that obtained from the virial theorem, while at low temperatures, at which quantum effects become important, there will be considerable deviations between the two. De Boer attempts to prove that the two pressures are actually identical. We have come to the same conclusion, and shall show this in several ways; first, by considering a simple example (Section 2), and then in general using the energy representation (Section 3). We believe that the discrepancy between the two pressures which Green has found is in fact due to improper handling of the effect of the wall of the vessel in which the particles are contained. Finally, we are of the opinion that Green's criticism of De Boer's calculation is not justified, and in the last section arguments are given to show that the traces of all commutators of interest in quantum statistical mechanics are zero.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69356/2/JCPSA6-18-8-1066-1.pd

Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line

In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical approximation for diffractive orbits that are scattered once on a flux line. This approximation is uniformly valid for all scattering angles. The diffractive contributions are necessary in order that semiclassical approximations are continuous if the position of the flux line is changed.Comment: LaTeX, 17 pages, 4 figure

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Fracture mechanics life analytical methods verification testing

The objective was to evaluate NASCRAC (trademark) version 2.0, a second generation fracture analysis code, for verification and validity. NASCRAC was evaluated using a combination of comparisons to the literature, closed-form solutions, numerical analyses, and tests. Several limitations and minor errors were detected. Additionally, a number of major flaws were discovered. These major flaws were generally due to application of a specific method or theory, not due to programming logic. Results are presented for the following program capabilities: K versus a, J versus a, crack opening area, life calculation due to fatigue crack growth, tolerable crack size, proof test logic, tearing instability, creep crack growth, crack transitioning, crack retardation due to overloads, and elastic-plastic stress redistribution. It is concluded that the code is an acceptable fracture tool for K solutions of simplified geometries, for a limited number of J and crack opening area solutions, and for fatigue crack propagation with the Paris equation and constant amplitude loads when the Paris equation is applicable

Overt social interaction and resting state in young adult males with autism: core and contextual neural features

Conversation is an important and ubiquitous social behavior. Individuals with Autism Spectrum Disorder (autism) without intellectual disability often have normal structural language abilities but deficits in social aspects of communication like pragmatics, prosody, and eye contact. Previous studies of resting state activity suggest that intrinsic connections among neural circuits involved with social processing are disrupted in autism, but to date no neuroimaging study has examined neural activity during the most commonplace yet challenging social task: spontaneous conversation. Here we used functional MRI to scan autistic males (N=19) without intellectual disability and age- and IQ-matched typically developing controls (N=20) while they engaged in a total of 193 face-to-face interactions. Participants completed two kinds of tasks: Conversation, which had high social demand, and Repetition, which had low social demand. Autistic individuals showed abnormally increased task-driven inter-regional temporal correlation relative to controls, especially among social processing regions and during high social demand. Furthermore, these increased correlations were associated with parent ratings of participants’ social impairments. These results were then compared with previously-acquired resting-state data (56 Autism, 62 Control participants). While some inter-regional correlation levels varied by task or rest context, others were strikingly similar across both task and rest, namely increased correlation among the thalamus, dorsal and ventral striatum, somatomotor, temporal and prefrontal cortex in the autistic individuals, relative to the control groups. These results suggest a basic distinction. Autistic cortico-cortical interactions vary by context, tending to increase relative to controls during Task and decrease during Rest. In contrast, striato- and thalamocortical relationships with socially engaged brain regions are increased in both Task and Rest, and may be core to the condition of autism

The changing patterns of group politics in Britain

Two interpretations of ways in which group politics in Britain have presented challenges to democracy are reviewed: neo-corporatism or pluralistic stagnation and the rise of single issue interest groups. The disappearance of the first paradigm created a political space for the second to emerge. A three-phase model of group activity is developed: a phase centred around production interests, followed by the development of broadly based 'other regarding' groups, succeeded by fragmented, inner directed groups focusing on particular interests. Explanations of the decay of corporatism are reviewed. Single issue group activity has increased as party membership has declined and is facilitated by changes in traditional media and the development of the internet. Such groups can overload the policy-making process and frustrate depoliticisation. Debates about the constitution and governance have largely ignored these issues and there is need for a debate

Clonal kinetics and single-cell transcriptional profiling of CAR-T cells in patients undergoing CD19 CAR-T immunotherapy

Chimeric antigen receptor (CAR) T-cell therapy has produced remarkable anti-tumor responses in patients with B-cell malignancies. However, clonal kinetics and transcriptional programs that regulate the fate of CAR-T cells after infusion remain poorly understood. Here we perform TCRB sequencing, integration site analysis, and single-cell RNA sequencing (scRNA-seq) to profile CD8+ CAR-T cells from infusion products (IPs) and blood of patients undergoing CD19 CAR-T immunotherapy. TCRB sequencing shows that clonal diversity of CAR-T cells is highest in the IPs and declines following infusion. We observe clones that display distinct patterns of clonal kinetics, making variable contributions to the CAR-T cell pool after infusion. Although integration site does not appear to be a key driver of clonal kinetics, scRNA-seq demonstrates that clones that expand after infusion mainly originate from infused clusters with higher expression of cytotoxicity and proliferation genes. Thus, we uncover transcriptional programs associated with CAR-T cell behavior after infusion.Published versio

Age structure, dispersion and diet of a population of stoats (Mustela erminea) in southern Fiordland during the decline phase of the beechmast cycle

The dispersion, age structure and diet of stoats (Mustela erminea) in beech forest in the Borland and Grebe Valleys, Fiordland National Park, were examined during December and January 2000/01, 20 months after a heavy seed-fall in 1999. Thirty trap stations were set along a 38-km transect through almost continuous beech forest, at least 1 km apart. Mice were very scarce (nights, C/100TN) along two standard index lines placed at either end of the transect, compared with November 1999 (>60/100TN), but mice were detected (from footprints in stoat tunnels) along an 8 km central section of the transect (stations 14-22). Live trapping with one trap per station (total 317.5 trap nights) in December 2000 caught 2 female and 23 male stoats, of which 10 (including both females) were radio collared. The minimum range lengths of the two females along the transect represented by the trap line were 2.2 and 6.0 km; those of eight radio-tracked males averaged 2.9 ± 1.7 km. Stations 14-22 tended to be visited more often, by more marked individual stoats, than the other 21 stations. Fenn trapping at the same 30 sites, but with multiple traps per station (1333.5 trap nights), in late January 2001 collected carcasses of 35 males and 28 females (including 12 of the marked live-trapped ones). Another two marked males were recovered dead. The stoat population showed no sign of chronic nutritional stress (average fat reserve index = 2.8 on a scale of 1-4 where 4 = highest fat content); and only one of 63 guts analysed was empty. Nevertheless, all 76 stoats handled were adults with 1-3 cementum annuli in their teeth, showing that reproduction had failed that season. Prey categories recorded in descending frequency of occurrence were birds, carabid beetle (ground beetle), weta, possum, rat, and mouse. The frequencies of occurrence of mice and birds in the diet of these stoats (10% and 48%, respectively) were quite different from those in stoats collected in Pig Creek, a tributary of the Borland River (87%, 5%), 12 months previously when mice were still abundant. Five of the six stoat guts containing mice were collected within 1 km of stations 14-22