Multiplication Operators on Weighted Banach Spaces of a Tree

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determine estimates on the operator norm, and show there are no isometries

Non-equilibrium dynamics of an active colloidal "chucker"

We report Monte Carlo simulations of the dynamics of a "chucker": a colloidal particle which emits smaller solute particles from its surface, isotropically and at a constant rate k_c. We find that the diffusion constant of the chucker increases for small k_c, as recently predicted theoretically. At large k_c the chucker diffuses more slowly due to crowding effects. We compare our simulation results to those of a "point particle" Langevin dynamics scheme in which the solute concentration field is calculated analytically, and in which hydrodynamic effects can be included albeit in an approximate way. By simulating the dragging of a chucker, we obtain an estimate of its apparent mobility coefficient which violates the fluctuation-dissipation theorem. We also characterise the probability density profile for a chucker which sediments onto a surface which either repels or absorbs the solute particles, and find that the steady state distributions are very different in the two cases. Our simulations are inspired by the biological example of exopolysaccharide-producing bacteria, as well as by recent experimental, simulation and theoretical work on phoretic colloidal "swimmers".Comment: re-submission after referee's comment

Sampling along reaction coordinates with the Wang-Landau method

The multiple range random walk algorithm recently proposed by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)] is adapted to the computation of free energy profiles for molecular systems along reaction coordinates. More generally, we show how to extract partial averages in various statistical ensembles without invoking simulations with constraints, biasing potentials or unknown parameters. The method is illustrated on a model 10-dimensional potential energy surface, for which analytical results are obtained. It is then applied to the potential of mean force associated with the dihedral angle of the butane molecule in gas phase and in carbon tetrachloride solvent. Finally, isomerization in a small rocksalt cluster, Na4F4, is investigated in the microcanonical ensemble, and the results are compared to those of parallel tempering Monte Carlo.Comment: 6 pages, 5 figure

Absolute FKBP binding affinities obtained via non-equilibrium unbinding simulations

We compute absolute binding affinities for two ligands bound to the FKBP protein using non-equilibrium unbinding simulations. The methodology is straight-forward, requiring little or no modification to many modern molecular simulation packages. The approach makes use of a physical pathway, eliminating the need for complicated alchemical decoupling schemes. Results of this study are promising. For the ligands studied here the binding affinities are typically estimated within less than 4.0 kJ/mol of the target values; and the target values are within less than 1.0 kJ/mol of experiment. These results suggest that non-equilibrium simulation could provide a simple and robust means to estimate protein-ligand binding affinities.Comment: 9 pages, 3 figures (no necessary color). Changes made to methodology and results between revision

Evaluation and study of advanced optical contamination, deposition, measurement, and removal techniques

A program is described to design, fabricate and install an experimental work chamber assembly (WCA) to provide a wide range of experimental capability. The WCA incorporates several techniques for studying the kinetics of contaminant films and their effect on optical surfaces. It incorporates the capability for depositing both optical and contaminant films on temperature-controlled samples, and for in-situ measurements of the vacuum ultraviolet reflectance. Ellipsometer optics are mounted on the chamber for film thickness determinations, and other features include access ports for radiation sources and instrumentation. Several supporting studies were conducted to define specific chamber requirements, to determine the sensitivity of the measurement techniques to be incorporated in the chamber, and to establish procedures for handling samples prior to their installation in the chamber. A bibliography and literature survey of contamination-related articles is included

Understanding fragility in supercooled Lennard-Jones mixtures. I. Locally preferred structures

We reveal the existence of systematic variations of isobaric fragility in different supercooled Lennard-Jones binary mixtures by performing molecular dynamics simulations. The connection between fragility and local structures in the bulk is analyzed by means of a Voronoi construction. We find that clusters of particles belonging to locally preferred structures form slow, long-lived domains, whose spatial extension increases by decreasing temperature. As a general rule, a more rapid growth, upon supercooling, of such domains is associated to a more pronounced super-Arrhenius behavior, hence to a larger fragility.Comment: 14 pages, 14 figures, minor revisions, one figure adde

Cation Transport in Polymer Electrolytes: A Microscopic Approach

A microscopic theory for cation diffusion in polymer electrolytes is presented. Based on a thorough analysis of molecular dynamics simulations on PEO with LiBF$_4$ the mechanisms of cation dynamics are characterised. Cation jumps between polymer chains can be identified as renewal processes. This allows us to obtain an explicit expression for the lithium ion diffusion constant D_{Li} by invoking polymer specific properties such as the Rouse dynamics. This extends previous phenomenological and numerical approaches. In particular, the chain length dependence of D_{Li} can be predicted and compared with experimental data. This dependence can be fully understood without referring to entanglement effects.Comment: 4 pages, 4 figures, Physical Review Letters in pres

Dynamical clustering of counterions on flexible polyelectrolytes

Molecular dynamics simulations are used to study the local dynamics of counterion-charged polymer association at charge densities above and below the counterion condensation threshold. Surprisingly, the counterions form weakly-interacting clusters which exhibit short range orientational order, and which decay slowly due to migration of ions across the diffuse double layer. The cluster dynamics are insensitive to an applied electric field, and qualitatively agree with the available experimental data. The results are consistent with predictions of the classical theory only over much longer time scales

Heat Conduction in two-dimensional harmonic crystal with disorder

We study the problem of heat conduction in a mass-disordered two-dimensional harmonic crystal. Using two different stochastic heat baths, we perform simulations to determine the system size (L) dependence of the heat current (J). For white noise heat baths we find that J ~ 1/L^a with $a \approx 0.59$ while correlated noise heat baths gives $a \approx 0.51$. A special case with correlated disorder is studied analytically and gives a=3/2 which agrees also with results from exact numerics.Comment: Revised version. 4 pages, 3 figure

Competition of the connectivity with the local and the global order in polymer melts and crystals

The competition between the connectivity and the local or global order in model fully-flexible chain molecules is investigated by molecular-dynamics simulations. States with both missing (melts) and high (crystal) global order are considered. Local order is characterized within the first coordination shell (FCS) of a tagged monomer and found to be lower than in atomic systems in both melt and crystal. The role played by the bonds linking the tagged monomer to FCS monomers (radial bonds), and the bonds linking two FCS monomers (shell bonds) is investigated. The detailed analysis in terms of Steinhardt's orientation order parameters Q_l (l = 2 - 10) reveals that increasing the number of shell bonds decreases the FCS order in both melt and crystal. Differently, the FCS arrangements organize the radial bonds. Even if the molecular chains are fully flexible, the distribution of the angle formed by adjacent radial bonds exhibits sharp contributions at the characteristic angles {\theta} = 70{\deg}, 122{\deg}, 180{\deg}. The fractions of adjacent radial bonds with {\theta} = 122{\deg}, 180{\deg} are enhanced by the global order of the crystal, whereas the fraction with 70{\deg} < {\theta} < 110{\deg} is nearly unaffected by the crystallization. Kink defects, i.e. large lateral displacements of the chains, are evidenced in the crystalline state.Comment: J. Chem. Phys. in pres