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41.
Alexandre Joel Chorin 《Communications in Mathematical Physics》1990,132(3):519-536
We consider a simplified model of vorticity configurations in the inertial range of turbulent flow, in which vortex filaments are viewed as random walks in thermal equilibrium subjected to the constraints of helicity and energy conservation. The model is simple enough so that its properties can be investigated by a relatively straightforward Monte-Carlo method: a pivot algorithm with Metropolis weighting. Reasonable values are obtained for the intermittency dimensionD, a Kolmogorov-like exponent , and higher moments of the velocity derivatives. Qualitative conclusions are drawn regarding the origin of non-gaussian velocity statistics and regarding analogies with polymers and with systems near a critical point.This work was supported in part by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, under Contract Number DE-AC03-76SF000098 相似文献
42.
Joel L. Lebowitz Christian Maes Eugene R. Speer 《Journal of statistical physics》1990,59(1-2):117-170
We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on
d
and translation-invariant Gibbs states for a related Hamiltonian on (
d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs. 相似文献
43.
Joel L. Lebowitz Harvey A. Rose Eugene R. Speer 《Journal of statistical physics》1988,50(3-4):657-687
We investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian $$H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}$$ is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL 2 norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied. 相似文献
44.
We investigate the existence of nontranslation invariant (periodic) density profiles, for systems interacting via translation invariant long-range potentials, as minimizers of local mean field free energy functionals. The existence of a second-order transition from a uniform to a nonuniform density at a specified temperature is proven for a class of model systems. 相似文献
45.
Detlef Dürr Sheldon Goldstein Joel L. Lebowitz 《Probability Theory and Related Fields》1987,75(2):279-290
Summary We generalize the results of Spitzer, Jepsen and others [1–4] on the motion of a tagged particle in a uniform one dimensional system of point particles undergoing elastic collisions to the case where there is also an external potential U(x). When U(x) is periodic or random (bounded and statistically translation invariant) then the scaled trajectory of a tagged particle
converges, as A , to a Brownian motion W
D
(t) with diffusion constant
, where
is the average density,
is the mean absolute velocity and –1 the temperature of the system. When U(x) is itself changing on a macroscopic scale, i.e.
, then the limiting process is a spatially dependent diffusion. The stochastic differential equation describing this process is now non-linear, and is particularly simple in Stratonovich form. This lends weight to the belief that heuristics are best done in that form.Dedicated to Frank Spitzer on the occasion of his 60th birthdayWork supported in part by NSF Grants No. PHY 8201708 and No. DMR 81-14726Heisenberg-fellowAlso Department of Physics 相似文献
46.
Jean Bricmont Joel L. Lebowitz Christian Maes 《Journal of statistical physics》1987,48(5-6):1249-1268
We derive a number of new results for correlated nearest neighbor site percolation onZ
d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS
x
h percolate if and only ifh
c
. with0
c
< . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility. 相似文献
47.
2-iodobenzonitrile, its derivatives, and various heterocyclic analogues undergo palladium(0)-catalyzed annulation onto diarylacetylenes or bicyclic alkenes to afford 2,3-diarylindenones and polycyclic aromatic ketones in very good to excellent yields. This reaction represents one of the first examples of the addition of an organopalladium moiety to the carbon-nitrogen triple bond of a nitrile. The reaction is compatible with a number of functional groups. A reaction mechanism, as well as a model accounting for the electronic effects of substituents on the aromatic ring of the nitrile, is proposed. 相似文献
48.
Fonseca GS Umpierre AP Fichtner PF Teixeira SR Dupont J 《Chemistry (Weinheim an der Bergstrasse, Germany)》2003,9(14):3263-3269
Stable transition-metal nanoparticles of the type [M(0)](n) are easily accessible through the reduction of Ir(I) or Rh(III) compounds dissolved in "dry" 1-n-butyl-3-methylimidazolium hexafluorophosphate ionic liquid by molecular hydrogen. The formation of these [M(0)](n) nanoparticles is straightforward; they are prepared in dry ionic liquid whereas the presence of the water causes the partial decomposition of ionic liquid with the formation of phosphates, HF and transition-metal fluorides. Transmission electron microscopy (TEM) observations and X-ray diffraction analysis (XRD) show the formation of [Ir(0)](n) and [Rh(0)](n) nanoparticles with 2.0-2.5 nm in diameter. The isolated [M(0)](n) nanoparticles can be redispersed in the ionic liquid, in acetone or used in solventless conditions for the liquid-liquid biphasic, homogeneous or heterogeneous hydrogenation of arenes under mild reaction conditions (75 degrees C and 4 atm). The recovered iridium nanoparticles can be reused several times without any significant loss in catalytic activity. Unprecedented total turnover numbers (TTO) of 3509 in 32 h, for arene hydrogenation by nanoparticles catalysts, have been achieved in the reduction of benzene by the [Ir(0)](n) in solventless conditions. Contrarily, the recovered Rh(0) nanoparticles show significant agglomeration into large particles with a loss of catalytic activity. The hydrogenation of arenes containing functional groups, such as anisole, by the [Ir(0)](n) nanoparticles occurs with concomitant hydrogenolysis of the C-O bond, suggesting that these nanoparticles behave as "heterogeneous catalysts" rather than "homogeneous catalysts". 相似文献
49.
Abstract— Understanding of reaction mechanisms in photochemistry is advanced both by kinetic measurements to determine rates of reaction and by spectroscopic studies of the structures of precursors and photoproducts. When kinetics and spectroscopy are combined in a time-resolved, multiwavelength spectroscopic measurement on a reacting system, spectra and structures of intermediates can also be determined. In this paper, the application of multidimensional least-squares and factor analysis techniques for resolving overlapped spectra from intermediates in photochemical kinetics are discussed. The methods are employed specifically to resolve Raman spectra of intermediates in triplet-state photoreactions. By varying excitation intensity, spectra of excited-triplet states are resolved from ground states and solvent. By varying the concentration of a triplet quencher in the sample, the Raman spectrum of a sensitizer excited state (benzophe-none) can be resolved from those of acceptor-triplet states or radical photoproducts. Applications of these concepts in other areas of photochemical kinetics are addressed. 相似文献
50.
The measurement of independent sets of NMR residual dipolar couplings (RDCs) in multiple alignment media can provide a detailed view of biomolecular structure and dynamics, yet remains experimentally challenging. It is demonstrated here that independent sets of RDCs can be measured for ubiquitin using just a single alignment medium composed of aligned bacteriophage Pf1 particles embedded in a strained polyacrylamide gel matrix. Using this composite medium, molecular alignment can be modulated by varying the angle between the directors of ordering for the Pf1 and strained gel matrix, or by varying the ionic strength or concentration of the Pf1 particles. This approach offers significant advantages in that greater experimental control can be exercised over the acquisition of multi-alignment RDC data while a homogeneous chemical environment is maintained across all of the measured RDC data. 相似文献