Kinetics of thermal rearrangements in the Delta2-Thujene system: a full quadrisection of a perturbed bicyclo[3.1.0]hex-2-ene

Further insight into the behavior of suppositional diradicals in a caldera is sought in the thermal rearrangements among the four "Delta2-thujenes", two 1-isopropyl-4-methylbicyclo[3.1.0]hex-2-enes [(-)-cis-1 and (+)-trans-2] and two isomers, exo- and endo-3-isopropyl-6-methylbicyclo[3.1.0]hex-2-ene [(+)-exo-3 and (-)-endo-4]. Optically pure trans-3-isopropyl-5-vinylcyclopentene (5) is the final, strongly thermochemically favored product, the result of an intramolecular homodienyl shift of a methyl hydrogen atom in (-)-endo-4. The set of twelve specific rate constants, four sets of three each, that define the interrelations among the four isomers has been extracted from data acquired starting from each isomer. An attractive mechanistic hypothesis involving an intermediate diradical of iso conformation, common, for example, to both (-)-cis-1 and (+)-exo-3 (as educts), that proceeds to an anticonformer common to both (+)-trans-2 and (-)-endo-4 does not lead to a satisfactory rationalization of the product distribution. Addition of a second mechanistic conceptual scheme, that of a diradical-in-transit behaving as if there were a measure of continuous bonding (for example, (+)-trans-2 proceeding directly to (-)-cis-1), improves agreement with experiment. Over a 30 degrees C range of temperature, there is no credible change in product distribution.     

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

A comparison between transitions induced by random and periodic fluctuations

It is shown that a certain class of nonlinear systems possesses a unique and stable stationary state when subjected to periodic dichotomous modulations of an external parameter. This result enables us to define a probability density for the system and to characterize its shape and support. We compare this probability density with the one obtained in the case that the external parameter fluctuates randomly like a Markovian dichotomous noise and discuss various fluctuation-induced transition phenomena. The effects of these two types of fluctuations are quite dissimilar: the random fluctuations give rise to a richer behavior. The results are applied to the Freedericksz transition in nematic liquid crystals.Fellow of the University of Texas at Austin.     

Randomly rattled ratchets

Summary Ratchets are anisotropic periodic potentials. Particles subject to ratchet forces and simultaneously to thermal and nonthermal fluctuations can rectify the nonequilibrium noise, thereby extracting energy from incoherent and otherwise symmetric random forces. In this paper I describe some simple models which illustrate this phenomenon, highlighting two particular mechanisms leading to fluctuation-induced current. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994. Address after July 1, 1994: Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.     

Nonlinear parabolic stochastic differential equations with additive colored noise onR d ×R +: A regulated stochastic quantization

We prove the existence of solutions to the nonlinear parabolic stochastic differential equation $$({\partial \mathord{\left/ {\vphantom {\partial {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} - \Delta )\varphi = - V'(\varphi ) + \eta _c $$ for polynomialsV of even degree with positive leading coefficient and ν _c a gaussian colored noise process onR ^d ×R ₊. When ν _c is colored enough that the gaussian solution to the linear problem has Hölder continuous covariance, the nongaussian processes are almost surely realized by continuous functions. Uniqueness, regularity properties, asymptotic perturbation expansions and nonperturbative fluctuation bounds are obtained for the infinite volume processes. These equations are a cutoff version of the Parisi-Wu stochastic quantization procedure forP(?) _d models, and the results of this paper rigorously establish the nonperturbative nature of regularization via modification of the noise process. In the limit ν _c → gaussian white noise we find that the asymptotic expansion and the rigorous bounds agree for processes corresponding to the (regulated) stochastic quantization of super-renormalizable and small coupling, strictly renormalizable scalar field theories and disagree for nonrenormalizable models.