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91.
We prove that in some reasonable sense, every possible physical law can be reformulated in terms of symmetries. This result explains the well-known success of the group-theoretic approach in physics. 相似文献
92.
Pierre Degond Stéphane Génieys Ansgar Jüngel 《Journal de Mathématiques Pures et Appliquées》1997,76(10):991-1015
The time-dependent equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear parabolic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are prescribed.The existence of weak solutions is proven. The key of the proof is (i) a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrizes the equations, and (ii) a priori estimates obtained by using the entropy function. Finally, the entropy inequality is employed to show the convergence of the solutions to the thermal equilibrium state as the time tends to infinity. 相似文献
93.
A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ
d
withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections
with statistical mechanics. Of course, polygons on ℤ
d
are defined up to a translation, and the relevant statistic is their perimeter.
A SAP on ℤ
d
is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing
it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher
dimension.
We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's
result, which explains combinatorially the form of the generating function. We then compute the generating function for convex
SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However,
our method suggests that the generating function for convex SAPs on ℤ
d
is always a quotient ofdifferentiably finite power series. 相似文献
94.
95.
Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential Eh and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)2, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D1 and D2 correspond to a ferrous state with isomershift IS of about 1.27 mm s-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s-1, respectively, whereas D3 corresponds to a ferric state with IS and QS of about 0.4 mm s-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, Eh and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed. 相似文献
96.
97.
Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond–1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.Laboratoire associé au Centre National de la Recherche Scientifique-URA D0063. 相似文献
98.
99.
Jean-Marc Hérard 《Comptes Rendus Mathematique》2006,342(10):779-784
We introduce a hyperbolic entropy-consistent model to describe three-phase flows, which ensures that void fractions, mass fractions and pressures remain positive through single waves occurring in the one dimensional solution of the Riemann problem. To cite this article: J.-M. Hérard, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
100.
This Note deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing us to characterize second-order quadratic growth. To cite this article: J.F. Bonnans, A. Hermant, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献