19,572 research outputs found
Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates
We analyze the open boundary partially asymmetric exclusion process with
smoothly varying internal hopping rates in the infinite-size, mean field limit.
The mean field equations for particle densities are written in terms of Ricatti
equations with the steady-state current as a parameter. These equations are
solved both analytically and numerically. Upon imposing the boundary conditions
set by the injection and extraction rates, the currents are found
self-consistently. We find a number of cases where analytic solutions can be
found exactly or approximated. Results for from asymptotic analyses for
slowly varying hopping rates agree extremely well with those from extensive
Monte Carlo simulations, suggesting that mean field currents asymptotically
approach the exact currents in the hydrodynamic limit, as the hopping rates
vary slowly over the lattice. If the forward hopping rate is greater than or
less than the backward hopping rate throughout the entire chain, the three
standard steady-state phases are preserved. Our analysis reveals the
sensitivity of the current to the relative phase between the forward and
backward hopping rate functions.Comment: 12 pages, 4 figure
Bulk-driven non-equilibrium phase transitions in a mesoscopic ring
We study a periodic one-dimensional exclusion process composed of a driven
and a diffusive part. In a mesoscopic limit where both dynamics compete we
identify bulk-driven phase transitions. We employ mean-field theory
complemented by Monte-Carlo simulations to characterize the emerging
non-equilibrium steady states. Monte-Carlo simulations reveal interesting
correlation effects that we explain phenomenologically.Comment: 4 pages, 3 figure
Preparation of Dicke States in an Ion Chain
We have investigated theoretically and experimentally a method for preparing
Dicke states in trapped atomic ions. We consider a linear chain of ion
qubits that is prepared in a particular Fock state of motion, . The
phonons are removed by applying a laser pulse globally to the qubits, and
converting the motional excitation to flipped spins. The global nature of
this pulse ensures that the flipped spins are shared by all the target ions
in a state that is a close approximation to the Dicke state \D{N}{m}. We
calculate numerically the fidelity limits of the protocol and find small
deviations from the ideal state for and . We have demonstrated
the basic features of this protocol by preparing the state \D{2}{1} in two
Mg target ions trapped simultaneously with an Al
ancillary ion.Comment: 5 pages, 2 figure
First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap
We have calculated the first and second sound modes of a dilute interacting
Bose gas in a spherical trap for temperatures () and for
systems with to particles. The second sound modes (which exist
only below ) generally have a stronger temperature dependence than the
first sound modes. The puzzling temperature variations of the sound modes near
recently observed at JILA in systems with particles match
surprisingly well with those of the first and second sound modes of much larger
systems.Comment: a shorten version, more discussions are given on the nature of the
second sound. A long footnote on the recent work of Zaremba, Griffin, and
Nikuni (cond-mat/9705134) is added, the spectrum of the (\ell=1, n_2=0) mode
is included in fig.
Adhesion of surfaces via particle adsorption: Exact results for a lattice of fluid columns
We present here exact results for a one-dimensional gas, or fluid, of
hard-sphere particles with attractive boundaries. The particles, which can
exchange with a bulk reservoir, mediate an interaction between the boundaries.
A two-dimensional lattice of such one-dimensional gas `columns' represents a
discrete approximation of a three-dimensional gas of particles between two
surfaces. The effective particle-mediated interaction potential of the
boundaries, or surfaces, is calculated from the grand-canonical partition
function of the one-dimensional gas of particles, which is an extension of the
well-studied Tonks gas. The effective interaction potential exhibits two
minima. The first minimum at boundary contact reflects depletion interactions,
while the second minimum at separations close to the particle diameter results
from a single adsorbed particle that crosslinks the two boundaries. The second
minimum is the global minimum for sufficiently large binding energies of the
particles. Interestingly, the effective adhesion energy corresponding to this
minimum is maximal at intermediate concentrations of the particles.Comment: to appear in Journal of Statistical Mechanics: Theory and Experimen
Direct strain and elastic energy evaluation in rolled-up semiconductor tubes by x-ray micro-diffraction
We depict the use of x-ray diffraction as a tool to directly probe the strain
status in rolled-up semiconductor tubes. By employing continuum elasticity
theory and a simple model we are able to simulate quantitatively the strain
relaxation in perfect crystalline III-V semiconductor bi- and multilayers as
well as in rolled-up layers with dislocations. The reduction in the local
elastic energy is evaluated for each case. Limitations of the technique and
theoretical model are discussed in detail.Comment: 32 pages (single column), 9 figures, 39 reference
Competency Corner, Part Three: Practice-based Weightings of the CBPS
The first two articles in this series outlined the task, research, terminology and processes the Competence Committee used to develop the Competency-based Performance Standards (CBPS). These standards were designed as a framework for revision of the Canadian Standard Assessment in Optometry (CSAO) to directly link the exam and practice requirements of Canadian Optometrists. This linkage required determination of the relative weight to be assigned to each of the various competencies. Working groups of practising optometrists rated the frequency and criticality of performance of each of the competencies using a standardized rating system. Results indicated that the majority of a revised CSAO would focus on providing comprehensive eye and vision care (78%), followed by management (11%) and collaboration (10%). The ratings also allowed calculation of the appropriate weighting of the underlying general attributes. The heaviest weighting was assigned to candidates’ professional optometric knowledge and the ability to apply this knowledge (41%), followed by communication (27%), planning (13%), ethics (11%) and self-directed learning (8%). The last article in this series will describe work to evaluate the competence-based weightings of the current CSAO and to describe plans for future versions of the CSAO
Dynamic Boundaries in Asymmetric Exclusion Processes
We investigate the dynamics of a one-dimensional asymmetric exclusion process
with Langmuir kinetics and a fluctuating wall. At the left boundary, particles
are injected onto the lattice; from there, the particles hop to the right.
Along the lattice, particles can adsorb or desorb, and the right boundary is
defined by a wall particle. The confining wall particle has intrinsic forward
and backward hopping, a net leftward drift, and cannot desorb. Performing Monte
Carlo simulations and using a moving-frame finite segment approach coupled to
mean field theory, we find the parameter regimes in which the wall acquires a
steady state position. In other regimes, the wall will either drift to the left
and fall off the lattice at the injection site, or drift indefinitely to the
right. Our results are discussed in the context of non-equilibrium phases of
the system, fluctuating boundary layers, and particle densities in the lab
frame versus the frame of the fluctuating wall.Comment: 13 page
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