We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous
Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local
(in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedness result is shown for
all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying
to a strong angular singularity, except in the special case of Maxwell molecules.
Our proof relies on the ideas of Tanaka (Z. Wahrscheinlichkeitstheor. Verwandte. Geb. 46(1):67–105, [1978]) we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to
couple two such processes started with two different initial conditions, in such a way that they almost surely remain close
to each other. 相似文献
An anisotropic adaptation process is applied to a three-dimensional incompressible two-phase flow solver. The solver uses a level set/finite element method on unstructured tetrahedral meshes. We show how the level set function can be used to build an anisotropic mesh with good properties. Some computations with a strong transient character and large densities ratios (1/1000) are presented. We show that the efficiency of the computations can be deeply enhanced by mesh adaptations. 相似文献
Photoemission microspectroscopy on the layered misfit compound (PbS)1.13TaS2 provides direct evidence for Ta substitution into PbS layers as well as for Pb substitution into TaS2 layers. This metal cross substitution alters the charge balance between alternating layers and can explain the remarkable stability of (PbS)1.13TaS2 and, possibly, of analogous misfit compounds. It is suggested that even formally stoichiometric misfit compounds can be stabilized by this mechanism. 相似文献
We study the equilibrium properties of a liquid phase condensed at the nanoscale between the surfaces of a sharp crack in fused silica in a moist controlled atmosphere. The extension of the condensed phase along the fracture is measured by in situ atomic force microscopy phase imaging and it is shown to be determined by a critical distance between the opposite crack surfaces, which is an increasing function of humidity. The present technique is very promising for measuring the properties of confined liquids at the nanoscale as well as for modeling the physics and chemistry of slow crack propagation in glasses. 相似文献
The recently discovered coexistence of multifragmentation and residue production for the same total transverse energy of light charged particles, which has been dubbed bimodality like it has been introduced in the framework of equilibrium thermodynamics, can be well reproduced in numerical simulations of heavy ion reactions. A detailed analysis shows that fluctuations (introduced by elementary nucleon-nucleon collisions) determine which of the exit states is realized. Thus, we can identify bifurcation in heavy ion reactions as a critical phenomenon. Also the scaling of the coexistence region with beam energy is well reproduced in these results from the quantum molecular dynamics simulation program. 相似文献
Dual energy X-ray absorptiometry (DXA), histomorphometry and X-ray microtomography (microCT) were used to assess effects of risedronate and testosterone in a combined rat model of orchidectomy (ORX) and local paralysis induced by botulinum neurotoxin (BTX). Four groups of mature rats were studied for 1 month: SHAM operated; ORX and right hindlimb immobilization (BTX); ORX+BTX+risedronate or testosterone. Changes in bone and body composition were measured by DXA (BMC, lean and fat mass), histomorphometry (BV/TV(2D), Tb.Th and microarchitectural parameters) and microCT (BV/TV(3D), SMI and cortical parameters). ORX and BTX had additive effects on bone loss since differences were maximized on the immobilized bone. The decrease in BMC on the tibial metaphysis reached -33.6% vs. -11.3% in the non-immobilized limb. BV/TV and Tb.N decreased and Tb.Sp increased in both hindlimbs whereas Tb.Th was significantly lower only in the immobilized limb. Decrease of tibial cortical area and thickness was greater in the immobilized limb. Risedronate prevented BMC, BV/TV and architecture loss but not reduction in Tb.Th. Cortical bone was preserved only in the non-immobilized limb. Testosterone was unable to prevent trabecular and cortical bone loss, but it prevents loss of whole body lean mass. In conclusion, ORX and BTX resulted in additive effects on bone loss. Risedronate had protective effects on trabecular bone loss but was less effective on cortical bone. 相似文献
Structured hybrid nanoparticles were synthesized via surface‐initiated atom transfer radical polymerization of MMA from ordered mesoporous silica (OMS) nanoparticles with various morphologies. The design of the OMS particles was adjusted to target either spherical core‐shell or cylindrical morphologies with a mean diameter below 400 nm. The polymer growth via ATRP from the silica surface was well‐controlled as demonstrated by the macromolecular characteristics of the grafted chains. Original hybrid multilayered nanoparticles composed of either a dense silica core or hollow core; an inner OMS shell showing radial orientation of the mesopores and an outer PMMA shell with controlled thickness were successfully prepared.
A series of 2,5‐distyrylfuran derivatives bearing pentafluorophenyl‐ and cyanovinyl units have been synthesized for aggregation‐induced emission (AIE). The effect of the type and extent of the supramolecular connections on the AIE of the furan derivatives were examined and correlated with their X‐ray crystal structures. It was found that the simultaneous presence of cyano and perfluorophenyl units strongly enhances the fluorescence upon aggregation. Single‐crystal X‐ray diffraction analysis confirmed that C?H???F, F???F, C?H???nitrile, Ar???ArF (Ar=aryl, ArF=fluoroaryl), and nitrile???ArF intra‐ and intermolecular interactions drive the topology of the molecule and that solid‐state supramolecular contacts favor AIE of the furan derivatives. 相似文献