Path integral evaluation of the kinetic isotope effects based on the quantum instanton approximation

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral Monte-Carlo evaluation of relevant thermodynamic quantities. The central ingredients of the method are the Monte-Carlo estimators for the logarithmic derivatives of the partition function and the delta-delta correlation function. Several alternative estimators for these quantities are described here and their merits are compared on the benchmark hydrogen-exchange reaction, H+H_2->H_2+H on the Truhlar-Kuppermann potential energy surface. Finally, a qualitative discussion of issues arising in many-dimensional systems is provided.Comment: 11 pages, 2 figures, proceeding

The Thatcher Experiment: The First Two Years

macroeconomics, Thatcher

Exploiting classical nucleation theory for reverse self-assembly

In this paper we introduce a new method to design interparticle interactions to target arbitrary crystal structures via the process of self-assembly. We show that it is possible to exploit the curvature of the crystal nucleation free-energy barrier to sample and select optimal interparticle interactions for self-assembly into a desired structure. We apply this method to find interactions to target two simple crystal structures: a crystal with simple cubic symmetry and a two-dimensional plane with square symmetry embedded in a three-dimensional space. Finally, we discuss the potential and limits of our method and propose a general model by which a functionally infinite number of different interaction geometries may be constructed and to which our reverse self-assembly method could in principle be applied.Comment: 7 pages, 6 figures. Published in the Journal of Chemical Physic

Path-integral virial estimator for reaction rate calculation based on the quantum instanton approximation

The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial-type estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.Comment: 23 pages, 5 figures, 1 tabl

Method and system for detecting a failure or performance degradation in a dynamic system such as a flight vehicle

A method and system for detecting a failure or performance degradation in a dynamic system having sensors for measuring state variables and providing corresponding output signals in response to one or more system input signals are provided. The method includes calculating estimated gains of a filter and selecting an appropriate linear model for processing the output signals based on the input signals. The step of calculating utilizes one or more models of the dynamic system to obtain estimated signals. The method further includes calculating output error residuals based on the output signals and the estimated signals. The method also includes detecting one or more hypothesized failures or performance degradations of a component or subsystem of the dynamic system based on the error residuals. The step of calculating the estimated values is performed optimally with respect to one or more of: noise, uncertainty of parameters of the models and un-modeled dynamics of the dynamic system which may be a flight vehicle or financial market or modeled financial system

Federal Appellate Court Decision in Environmental Defense Fund et al., Plaintiffs Appellees, v. Tennessee Valley Authority et al., Defendants-Appellants, No. 74-1139

Federal Appellate Court decision in the case of EDF v. TVA, upholding the lower court\u27s decision in favor of TVA, allowing the construction of the Tellico Dam to go forward. This decision was published in West\u27s Federal Reporter at 492 F.2d 466 (1974)

The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior

We introduce a procedure to infer the repeated-game strategies that generate actions in experimental choice data. We apply the technique to set of experiments where human subjects play a repeated Prisoner's Dilemma. The technique suggests that two types of strategies underly the data