We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation. 相似文献
The present work deals with the spatially extended oscillatory Belousov Zhabotinsky reaction-diffusion system carried out in an anisotropic environment of phosphatidylcholines/water binary system, which presents layered aqueous domains separated by lipid bilayers. We report the occurrence of stable Turing patterns, spiral waves, and other exotic structures in phospholipids bilayers that are generally used as a models for cell plasma membranes. 相似文献
Derrida's random energy model is considered. Almost sure andLP convergence of the free energy at any inverse temperature are proven. Rigorous upper and lower bounds to the finite size corrections to the free energy are given. 相似文献
Multielement determinations by high-flux absolute n.a.a. require careful methodology to avoid systematic error. The ORNL high-flux facility with a thermal flux of 5 ·1014 cm-2 s-1 and a thermal-to-resonance flux ratio of
Results in p.p.m followed by (per cent counting statistical error).
b
Computer forced result.Also V,Se,Sr,Sb,Cs and au (forced) were not detected.
c
Element possibly present but missed by peak-finding routine.7 35–45, was used in developing an instrumental absolute multielement method. The detector was calibrated for absolute counting with two independent sets of radioactivity standards for four detector- -source distances; the absolute activities of the standards were reproducible within accuracies of 9%. Five sources of systematic error were investigated: (a) correction for counting of cylindrical sources for 26 γ-ray energies reached 14–17% for photon energies below 500 keV; (b) flux variation during bombardment and within the irradiation capsule volume was not significant; (c) samples were sufficiently stable during high-flux bombardment; (d) multi-element impurities in accessory materials (polyethylene and “Nucleopore” filters) were not significant; (e) correction for sample activation during rabbit transfer was necessary for short bombardments, e.g., 8.6 % for 6 s and 19.6 % for 4 s. This methodology resulted in accuracies of 10–15 % for most elements, as determined by analysis of N.B.S. orchard leaves and coal and of Bowen's kale standards. The method was applied to a preliminary chronological study of environmental baselines and contamination levels, based on tree ring samples, covering a period of 100 years.
Some cis,cis,cis-RuX(2)(Me(2)SO)(2)(1,2-Me(2)Im)L complexes [L = 1,2-Me(2)Im (1,2-dimethylimidazole) or Me(3)Bzm (1,5,6-trimethylbenzimidazole), X = Cl or Br, and Me(2)SO = S-bonded DMSO] have been synthesized and their rotamers studied in CDCl(3). From 2D NMR data, cis,cis,cis-RuCl(2)(Me(2)SO)(2)(1,2-Me(2)Im)(Me(3)Bzm) has 1,2-Me(2)Im in position "a" (cis to both Me(2)SO's and cis to "b") and Me(3)Bzm in position "b" (trans to one Me(2)SO and cis to the other). There are two stable atropisomers [head-to-tail (HT, 84%) and head-to-head (HH, 16%), defining the aromatic H of Ru-N-C-H as head for both ligands]. Me(3)Bzm has the same orientation in both atropisomers. In this orientation, the unfavorable interligand steric interactions of Me(3)Bzm with the Me(2)SO and 1,2-Me(2)Im ligands appear to be countered by favorable electrostatic attraction between the delta+ N(2)CH moiety of Me(3)Bzm and the delta- cis Cl ligands. The 1,2-Me(2)Im lacks a delta+ N(2)CH group, and its orientation is dominated by steric effects of the 2-Me group. The NMR spectrum of cis,cis,cis-RuCl(2)(Me(2)SO)(2)(1,2-Me(2)Im)(2) is consistent with four rotamers in restricted rotation about both Ru-N bonds: two HH and two HT. 2D NMR techniques (NOESY and ROESY) afforded complete proton signal assignments. The ligand disposition could be assessed from the large chemical shift dispersion of some 1,2-Me(2)Im ligand signals (Delta 0.86-1.52 ppm) arising from cis-1,2-Me(2)Im shielding modulated by deshielding influences of the cis halides. The relative stability of the four rotamers correlates best with steric interactions between the 2-Me groups and the Me(2)SO ligands. The most favorable conformer (46%) is the HH rotamer with both 2-Me groups pointing away from the Me(2)SO ligands. The least favorable conformer (14%) was also HH, but the methyl groups in this case point toward the Me(2)SO ligands. In the HT conformers of intermediate stability ( approximately 20%), one 2-Me group is toward and the other is away from the Me(2)SO ligands. The exchange cross-peaks in the 2D spectra are unusually informative about the dynamic processes in solution; the spectra provide evidence that the rotamers interchange in a definite pattern of succession. Thus, all conceivable exchange pathways are not available. 1,2-Me(2)Im "b" can rotate regardless of the orientation of 1,2-Me(2)Im "a". 1,2-Me(2)Im "a" can rotate only when "b" has the orientation with its 2-Me group directed away from "a". Thus, 1,2-Me(2)Im "b" can switch 1,2-Me(2)Im "a" rotation on or off. 相似文献
Electron spin resonance (ESR) and quasielastic laser scattering (QELS) measurements have been carried out on sodium taurodeoxycholate (NaTDC) micellar aqueous solutions. Computer simulation of the ESR line shape has been used to quantitatively analyze the rotational dynamics of the cholestan-spin label (CSL) dissolved by the NaTDC micellar aggregates as a function of temperature and NaCl concentration. The local reorientation of CSL has been accounted for motionally-averaged g- and A-tensors assuming fast oscillation around the spin-probe long molecular axis. The overall Brownian tumbling of CSL-micelle complexes has been modeled by an axially symmetric rotational tensor. Good agreement with experimental spectra is obtained. Best-fit rotational parameters and QELS data suggest that, in the circumstance of large aggregation, NaTDC micelles have cylindrical shape and micellar growth occurs along the cylinder axis. 相似文献
We have studied domain growth in nematic liquid crystals using a lattice Boltzmann algorithm to solve the full, three-dimensional equations of hydrodynamics. An initially cylindrical V (bend) domain in an H (splay) state grows or shrinks anisotropically in agreement with experiment. A disclination loop forms at the mid-point of the wall surrounding the domain. We argue that different director configurations at different points on the loop lead to velocity anisotropy and show that both elastic effects and backflow are relevant. We discuss the dependence of the domain wall velocity on surface tilt and on the magnitude of an applied electric field. 相似文献
Recently, polyethylene glycols (PEGS) of various molecular weights have been proposed as solvent promoters for various reactions 1, 2. We wish to report on the use of PEG 400 as solvent for the anionic activation of potassium thioacetate, which could be used for the preparation of alkyl and benzyl thioacetates from the corresponding halides or alcohol derivatives. The method can be synthetically significant, since from thioacetates the corresponding thiols can be easily prepared under a variety of mild conditions 3. 相似文献
