不同层显式格式及在微尺度热传导中的应用

基于指数拟合和牛顿插值多项式构造了用于数值计算偏微分方程的不同层显式格式,应用不同层显式格式可获得不同精度的数值计算结果,并将该算法应用于微结构热传导方程和薄膜强瞬态热传导方程中．     

Development of an optical trap for microparticle clouds in dilute gases

Long-duration experiments with clouds of microparticles are planned for the ICAPS facility on board the International Space Station ISS. The scientific objectives of such experiments are widespread and are ranging from the simulation of aerosol behaviour in Earths atmosphere to the formation of planets in the early solar system. It is, however, even under microgravity conditions, impossible to sustain a cloud of free-floating, microscopic particles for an extended period of time, due to thermal diffusion and due to unavoidable external accelerations. Therefore, a trap for dust clouds is required which prevents the diffusion of the particles, which provides a source of relative velocities between the dust grains and which can also concentrate the dust to higher number densities that are otherwise not achievable. We are planning to use the photophoretic effect for such a particle trap. First short-duration microgravity experiments on the photophoretic motion of microscopic particles show that such an optical particle-cloud trap is feasible. First tests of a two-dimensional trap were performed in the Bremen drop tower.     

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Chromatographic Detection of Trimetoquinol (Inolin®) and its Major Urinary Metabolites in the Horse: A Preliminary Report

Trimetoquinol (TMQ) (1-(3,4,5-trimethoxybenzyl)-6,7-dihydroxy-1,2,3,4-tetrahydroisoquinoline, m.w. 345) is the prototype tetrahydroisoquinoline pharmaceutical. TMQ is marketed as a bronchodilator in human medicine; in horse racing, TMQ is listed as an Association of Racing Commissioners International (ARCI) class 3 foreign substance. As such, TMQ is considered to have the potential to affect racing performance in horses, and a validated qualitative confirmatory method is required to regulate its use in racing. We selected 8 g kg^–1 of TMQ IV as a safe and effective dose for studies on its metabolism and analytical detection in horses. We developed a solid phase extraction method for recovery of TMQ and its metabolites from equine urine, identified suitable high performance liquid chromatographic conditions for these substances and our internal standard, papaverine, and developed a highly sensitive ESI(+)-LC-MS-MS method (estimated LOD, 100 pg mL^–1) for TMQ and its major metabolites in equine urine. Multiple Reaction Monitoring (MRM) analysis of unhydrolyzed post-administration urine showed small amounts of unchanged TMQ, along with glucuronide, methylated, and sulfated metabolites, with glucuronide metabolites predominating. Following glucuronidase hydrolysis, recovered parent TMQ peaked at relatively high concentrations (>300 ng mL^–1) within 1 h of administration and thereafter declined. The methylated metabolites of TMQ peaked later and at comparable total concentrations, and thereafter declined more slowly. These data suggest that glucuronide hydrolysis of post-administration urine samples will allow recovery of readily identifiable quantities of parent TMQ. These findings, combined with the highly sensitive LC-MS-MS detection of parent TMQ described herein suggest that glucuronide hydrolysis of post-administration urine, followed by LC-MS-MS or other analysis, will allow effective regulatory control of this agent in racing horses.Published as # 351 from the Equine Pharmacology, Therapeutics and Toxicology Program at the Maxwell H. Gluck Equine Research Center and Department of Veterinary Science, University of Kentucky. Published as Kentucky Agricultural Experiment Station Article # 04-14-048 with the approval of the Dean and Director, College of Agriculture and the Kentucky Agricultural Experimental Station.Revised: 8 June and 12 July 2004     

Changes in the Seam-Filtration Mode with Stress Redistribution in Country Rock

A mathematical model for the mechanism of increasing oil output of productive seams is developed. The model involves a deliberate conversion of segments of the fault zone of the country rock to a supercritical state, which leads to a local redistribution of stresses in the block massif of rocks and an increase in contour and seam pressures. Based on solving the problem of restricted filtration, it is shown that the use of the proposed mechanism can ensure a relative increase in well production of 5–8%.     

A Solution to a Problem of Jacobson,Kézdy and Lehel

We solve a problem proposed by Jacobson, Kézdy, and Lehel [4] concerning the existence of forbidden induced subgraph characterizations of line graphs of linear k-uniform hypergraphs with sufficiently large minimal edge-degree. Actually, we prove that for each k3 there is a finite set Z(k) of graphs such that each graph G with minimum edge-degree at least 2k²–3k+1 is the line graph of a linear k-uniform hypergraph if and only if G is a Z(k)-free graph.Acknowledgments. We thank the anonymous referees, whose suggestions helped to improve the presentation of the paper.Winter 2002/2003 DIMACS Award is gratefully acknowledged2000 Mathematics Subject Classification: 05C65 (05C75, 05C85)     

Sparse <Emphasis Type="Italic">H</Emphasis>-Colourable Graphs of Bounded Maximum Degree

Let F be a graph of order at most k. We prove that for any integer g there is a graph G of girth at least g and of maximum degree at most 5k¹³ such that G admits a surjective homomorphism c to F, and moreover, for any F-pointed graph H with at most k vertices, and for any homomorphism h from G to H there is a unique homomorphism f from F to H such that h=fc. As a consequence, we prove that if H is a projective graph of order k, then for any finite family of prescribed mappings from a set X to V(H) (with ||=t), there is a graph G of arbitrary large girth and of maximum degree at most 5k^26mt (where m=|X|) such that and up to an automorphism of H, there are exactly t homomorphisms from G to H, each of which is an extension of an f.Supported in part by the National Science Council under grant NSC89-2115-M-110-012Final version received: June 9, 2003     

Cycles in 2-connected graphs

Let be a class of graphs on n vertices. For an integer c, let be the smallest integer such that if G is a graph in with more than edges, then G contains a cycle of length more than c. A classical result of Erdös and Gallai is that if is the class of all simple graphs on n vertices, then . The result is best possible when n-1 is divisible by c-1, in view of the graph consisting of copies of K_c all having exactly one vertex in common. Woodall improved the result by giving best possible bounds for the remaining cases when n-1 is not divisible by c-1, and conjectured that if is the class of all 2-connected simple graphs on n vertices, thenwhere , 2tc/2, is the number of edges in the graph obtained from K_c+1-t by adding n-(c+1-t) isolated vertices each joined to the same t vertices of K_c+1-t. By using a result of Woodall together with an edge-switching technique, we confirm Woodall's conjecture in this paper.     

Growth of Self‐Similar Graphs

Locally finite self‐similar graphs with bounded geometry and without bounded geometry as well as non‐locally finite self‐similar graphs are characterized by the structure of their cell graphs. Geometric properties concerning the volume growth and distances in cell graphs are discussed. The length scaling factor ν and the volume scaling factor μ can be defined similarly to the corresponding parameters of continuous self‐similar sets. There are different notions of growth dimensions of graphs. For a rather general class of self‐similar graphs, it is proved that all these dimensions coincide and that they can be calculated in the same way as the Hausdorff dimension of continuous self‐similar fractals: . © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 224–239, 2004