60,728 research outputs found
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 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
while correlated noise heat baths gives . 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
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