A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, hybrid Monte Carlo on Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures π, which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method that is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous work, the authors explored a method where the phase space π was augmented with Brownian bridges. With this new choice, π is augmented by Ornstein–Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the acceptance rate in the MCMC method. This contrasts with the covariance of OU bridges, which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis–Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.     

Adsorption and Desorption of Triton X-100 in Polystyrene Particles with Different Functionality

An experimental desorption study of Triton X-100 from latices with different functionality is presented. Two different strategies to follow the desorption experiment have been used: first, a discontinuous method based on the wash step (centrifugation-removal-redispersion); and second, a continuous method based on the replacement of the disperse media. The desorption results show that in all cases a residual amount of Triton X-100 remains adsorbed, indicating irreversibility of the surfactant adsorption. Finally, the effect of desorption on the colloidal stability of one type of latex-surfactant complex has been analyzed. Copyright 2000 Academic Press.     

Depolarization of light and pair—pair correlations of argon gas

A simple integral equation for the pair—pair correlation function of a fluid is solved for room temperature argon in the density range 1 to 600 amagat. It is used to calculate the depolarized intensity as a function of density and its sensitivity to the anisotropic pair polarizability. Good agreement with experiment is found at low density. Semi-quantitative agreement is obtained up to 600 amagat.