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61.
Kinetic selection principles have been shown to be useful and physically reasonable in nonlinear hyperbolic problems with
large amplitude phase transitions. We refer to Abeyaratne and Knowles, [A-K], for discussion on the subject. They also have
been used for degenerate nonlinear problems, where the genuine nonlinearity property of Lax is violated. This is the framework
of Liu, [Li], in the kinetic situation of Hayes and Le Floch, [H-L], where their so-called non classical shocks may be seen
as small amplitude phase transitions. Here, we describe the local geometry generated by the generic non genuinely nonlinear
assumption. A geometric kinetic criterion can be used to select indeterminate simple waves and obtain the well-posedness of
the local Riemann problem. A particular case is the entropic kinetic criterion of Hayes and Le Floch.
Sunto Principi di selezione cinetica sono stati mostrati utili e fisicamente ragionevoli in problemi iperbolici con transizioni di fase di grande ampiezza. Ci riferiamo ad Abeyaratne e Knowles, [A-K], per discussioni sull'argomento. Detti principi sono stati usati per problemi nonlineari degeneri, dove la proprietà di genuina nonlinearità di Lax è violata. Questo è la prospettiva di Liu, [Li], nella situazione cinetica di Hayes e Le Floch, [H-L], dove i loro così detti urti non classici possono essere considerati come transizioni di fase di piccola ampiezza. Qui, descriviamo la geometria locale generata dall'ipotesi generica genuinamente nonlineare. Un criterio di geometria cinetica può essere usato per selezionare onde semplici indeterminate ed ottenere la buona posizione per il problema locale di Riemann. Un caso particolare è il criterio di entropia cinetico di Hayes e Le Floc.相似文献
62.
Jayanth R. Banavar Oscar Gonzalez John H. Maddocks Amos Maritan 《Journal of statistical physics》2003,110(1-2):35-50
Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness. 相似文献
63.
The authors study the bifurcation problems of rough heteroclinic loop connecting three saddle points for the case β1 > 1, β2 > 1, β3 < 1 and β1β2β3 < 1. The existence, number, coexistence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied. Meanwhile, the bifurcation surfaces and existence regions are given. 相似文献
64.
K. S. Birdi 《Colloid and polymer science》1997,275(6):561-566
The surface tension versus temperature data of homologous series of n-alkanes and n-alkenes is analyzed. Critical temperatures are shown to be predicted from these data, with a very high precision, after some
corrections are made. The corrections are shown to arise from the effect of the critical pressure on the extrapolated data
to surface tension approaching zero.
Received: 29 October 1996 Accepted: 13 December 1996 相似文献
65.
Ph. Batchelor 《Commentarii Mathematici Helvetici》1998,73(3):337-352
On estime la dérivée des petites valeurs propres du Laplacien sur une famille de surfaces de Riemann. Ces valeurs propres
sont considérées comme des fonctions sur l'espace de Teichmüller, et l'estimation des dérivées peut s'exprimer dans ce contexte.
Received: December 21, 1995 相似文献
66.
We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities
of the embedded Markov chain are found in terms of Riemann boundary value problems, a necessary and sufficient condition of
ergodicity is proved. Explicit formulas are obtained for the case where the generating function of the arrival group size
is rational. Resonance between the vacation rate and the system is studied. Complete formulas are given for the cases of single
and geometric arrivals.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
67.
YangKeren LuShipan 《数学研究》1994,27(1):191-193
We introduce strong derivative, the corresponding Z-integrable and other related concepts. Also, we give an improved version of the fundamental theorem of calculus. 相似文献
68.
The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational
field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that
they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as
the key observable parameter. This solution provides a formal demonstration of the identity between the special and general
relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By
solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for
realistic journeys to the stars.
1 Both authors contributed equally to this paper. 相似文献
69.
A novel type of corner reflector for the reflection of surface plasmon polariton (SPP) is proposed. The reflector consists
of two layers of compensatory media whose permittivity and permeability take opposite signs to that of the corresponding layer
of the SP waveguide. By rigorously solving Maxwell's equations, the reflected SPP is proved to exist. The transverse wave
vector of the reflected SPP is always antiparallel to that of the incident SPP and no phase retardation is introduced. 相似文献
70.
A. S. Kholodov Ya. A. Kholodov 《Computational Mathematics and Mathematical Physics》2006,46(9):1560-1588
Previously formulated monotonicity criteria for explicit two-level difference schemes designed for hyperbolic equations (S.K. Godunov’s, A. Harten’s (TVD schemes), characteristic criteria) are extended to multileveled, including implicit, stencils. The characteristic monotonicity criterion is used to develop a universal algorithm for constructing high-order accurate nonlinear monotone schemes (for an arbitrary form of the desired solution) based on their analysis in the space of grid functions. Several new fourth-to-third-order accurate monotone difference schemes on a compact three-level stencil and nonexpanding (three-point) stencils are proposed for an extended system, which ensures their monotonicity for both the desired function and its derivatives. The difference schemes are tested using the characteristic monotonicity criterion and are extended to systems of hyperbolic equations. 相似文献