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981.
Goujon C Thomas N Dalloz-Dubrujeaud B 《The European physical journal. E, Soft matter》2003,11(2):147-157
Recent studies have pointed out the importance of the
basal friction on the dynamics of granular flows. We present
experimental results on the influence of the roughness of the
inclined plane on the dynamics of a monodisperse dry granular
flow. We found experimentally that there exists a maximum of the
friction for a given relative roughness. This maximum is shown
to be independent of the slope angle. This behavior is observed
for four planes with different bump sizes (given by the size of
the beads glued on the plane) from 200 m to 2 mm. The relative
roughness corresponding to the maximum of the friction can be
predicted with a geometrical model of stability of one single
bead on the plane. The main parameters are the size of the bumps
and the size of the flowing beads. In order to obtain a higher
precision, the model also takes into account the spacing between
the bumps of the rough plane. Experimental results and model are
in good agreement for all the planes we studied. Other
parameters, like the sphericity of the beads, or irregularities
in the thickness of the layer of glued particles, are shown to
be of influence on the friction. 相似文献
982.
Rein van der Hout 《Journal of Differential Equations》2003,192(1):188-201
Let and be the unit disk and the unit sphere, and let be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time. 相似文献
983.
Suppose r ≥ 2 is a real number. A proper r‐flow of a directed multi‐graph is a mapping such that (i) for every edge , ; (ii) for every vertex , . The circular flow number of a graph G is the least r for which an orientation of G admits a proper r‐flow. The well‐known 5‐flow conjecture is equivalent to the statement that every bridgeless graph has circular flow number at most 5. In this paper, we prove that for any rational number r between 2 and 5, there exists a graph G with circular flow number r. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 304–318, 2003 相似文献
984.
Ramaz Botchorishvili Benoit Perthame Alexis Vasseur. 《Mathematics of Computation》2003,72(241):131-157
We consider a simple model case of stiff source terms in hyperbolic conservation laws, namely, the case of scalar conservation laws with a zeroth order source with low regularity. It is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced CFL condition and refined meshes required because of the lack of accuracy on equilibrium states. The source term should be taken into account in the upwinding and discretized at the nodes of the grid. In order to solve numerically the problem, we introduce a so-called equilibrium schemes with the properties that (i) the maximum principle holds true; (ii) discrete entropy inequalities are satisfied; (iii) steady state solutions of the problem are maintained. One of the difficulties in studying the convergence is that there are no estimates for this problem. We therefore introduce a kinetic interpretation of upwinding taking into account the source terms. Based on the kinetic formulation we give a new convergence proof that only uses property (ii) in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions. The computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that, in comparison with an usual upwind scheme, the corresponding equilibrium version is far more accurate. Furthermore, numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients.
985.
C. A. Morales 《Transactions of the American Mathematical Society》2003,355(2):735-745
Let be an Axiom A flow with a transverse torus exhibiting a unique orbit that does not intersect . Suppose that there is no null-homotopic closed curve in contained in either the stable or unstable set of . Then we show that has either an attracting periodic orbit or a repelling periodic orbit or is transitive. In particular, an Anosov flow with a transverse torus is transitive if it has a unique periodic orbit that does not intersect the torus.
986.
We introduce and analyze a simple probabilistic cellular automaton which emulates the flow of cars along a highway. Our Traffic CA captures the essential features of several more complicated algorithms, studied numerically by K. Nagel and others over the past decade as prototypes for the emergence of traffic jams. By simplifying the dynamics, we are able to identify and precisely formulate the self-organized critical evolution of our system. We focus here on the Cruise Control case, in which well-spaced cars move deterministically at maximal speed, and we obtain rigorous results for several special cases. Then we introduce a symmetry assumption that leads to a two-parameter model, described in terms of acceleration () and braking () probabilities. Based on the results of simulations, we map out the (, ) phase diagram, identifying three qualitatively distinct varieties of traffic which arise, and we derive rigorous bounds to establish the existence of a phase transition from free flow to jams. Many other results and conjectures are presented. From a mathematical perspective, Traffic CA provides local, particle-conserving, one-dimensional dynamics which cluster, and converge to a mixture of two distinct equilibria. 相似文献
987.
We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered to be functions of the flux intensity. The medium is initially dry and we neglect capillarity, so that a sharp wetting front proceeds into the medium. We consider the open problem of the continuation of the solution possibly in the case of onset of singularities, which can be interpreted as a local collapse of the medium. In particular we analyze the case in which the boundary pressure has a piecewise constant derivative. 相似文献
988.
LI Jiayu 《数学年刊B辑(英文版)》2000,21(1):121-130
1.IntroductionLetMandNbetwoRiemannianmanifoldsofdimensionmandn.Supposetheirmetricsaregivenbydski~giid-c'dxianddsX~h.odu"duo.Letu:M~Nbeasmoothmap.Theenergydensityfunctionofuisgivenbye(u)~g'jCZh.,~Ical'.ThetotalenergyisdefinedbyE(u)=[e(u)dx.iMAmappingu:M~NiscalledaharmonicmapifitisaclassicalsolutionoftheEulerLagrangeequationofE(u)whichcanbewrittenasT"(U(X))~AU"(X) r3.(U(X))ZZg.j~0,whereT(u)iscalledthetensionfieldofu.Thecorrespondingparabolicsystemwithinitialdata"o(x)knownastheheatequ… 相似文献
989.
Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph is defined as follows. Its nodes are formed by the set of local minima and the set of local maxima. Two nodes (a local minimum and a local maximum) are connected in by means of an edge if some trajectory of the corresponding gradient flow connects them. Given a natural number k, we construct a function f such that the length of the shortest path in between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric. 相似文献
990.
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n to a value
t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of
t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence. 相似文献