70,752 research outputs found
Condensation transitions in a model for a directed network with weighted links
An exactly solvable model for the rewiring dynamics of weighted, directed
networks is introduced. Simulations indicate that the model exhibits two types
of condensation: (i) a phase in which, for each node, a finite fraction of its
total out-strength condenses onto a single link; (ii) a phase in which a finite
fraction of the total weight in the system is directed into a single node. A
virtue of the model is that its dynamics can be mapped onto those of a
zero-range process with many species of interacting particles -- an exactly
solvable model of particles hopping between the sites of a lattice. This
mapping, which is described in detail, guides the analysis of the steady state
of the network model and leads to theoretical predictions for the conditions
under which the different types of condensation may be observed. A further
advantage of the mapping is that, by exploiting what is known about exactly
solvable generalisations of the zero-range process, one can infer a number of
generalisations of the network model and dynamics which remain exactly
solvable.Comment: 23 pages, 8 figure
Criticality and Condensation in a Non-Conserving Zero Range Process
The Zero-Range Process, in which particles hop between sites on a lattice
under conserving dynamics, is a prototypical model for studying real-space
condensation. Within this model the system is critical only at the transition
point. Here we consider a non-conserving Zero-Range Process which is shown to
exhibit generic critical phases which exist in a range of creation and
annihilation parameters. The model also exhibits phases characterised by
mesocondensates each of which contains a subextensive number of particles. A
detailed phase diagram, delineating the various phases, is derived.Comment: 15 pages, 4 figure, published versi
An exactly solvable dissipative transport model
We introduce a class of one-dimensional lattice models in which a quantity,
that may be thought of as an energy, is either transported from one site to a
neighbouring one, or locally dissipated. Transport is controlled by a
continuous bias parameter q, which allows us to study symmetric as well as
asymmetric cases. We derive sufficient conditions for the factorization of the
N-body stationary distribution and give an explicit solution for the latter,
before briefly discussing physically relevant situations.Comment: 7 pages, 1 figure, submitted to J. Phys.
Correlation function algebra for inhomogeneous fluids
We consider variational (density functional) models of fluids confined in
parallel-plate geometries (with walls situated in the planes z=0 and z=L
respectively) and focus on the structure of the pair correlation function
G(r_1,r_2). We show that for local variational models there exist two
non-trivial identities relating both the transverse Fourier transform G(z_\mu,
z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2
and z_3. These relations form an algebra which severely restricts the possible
form of the function G_0(z_\mu,z_\nu). For the common situations in which the
equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an
odd or even reflection symmetry in the z=L/2 plane the algebra simplifies
considerably and is used to relate the correlation function to the finite-size
excess free-energy \gamma(L). We rederive non-trivial scaling expressions for
the finite-size contribution to the free-energy at bulk criticality and for
systems where large scale interfacial fluctuations are present. Extensions to
non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte
Critical phase in non-conserving zero-range processes and equilibrium networks
Zero-range processes, in which particles hop between sites on a lattice, are
closely related to equilibrium networks, in which rewiring of links take place.
Both systems exhibit a condensation transition for appropriate choices of the
dynamical rules. The transition results in a macroscopically occupied site for
zero-range processes and a macroscopically connected node for networks.
Criticality, characterized by a scale-free distribution, is obtained only at
the transition point. This is in contrast with the widespread scale-free
real-life networks. Here we propose a generalization of these models whereby
criticality is obtained throughout an entire phase, and the scale-free
distribution does not depend on any fine-tuned parameter.Comment: 4 pages, 4 figure
Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process
In this paper, we propose a general way of computing expectation values in
the zero-range process, using an exact form of the partition function. As an
example, we provide the fundamental diagram (the flux-density plot) of the
asymmetric exclusion process corresponding to the zero-range process.We express
the partition function for the steady state by the Lauricella hypergeometric
function, and thereby have two exact fundamental diagrams each for the parallel
and random sequential update rules. Meanwhile, from the viewpoint of
equilibrium statistical mechanics, we work within the canonical ensemble but
the result obtained is certainly in agreement with previous works done in the
grand canonical ensemble.Comment: 12 pages, 2 figure
Space Station Technology Summary
The completion of the Space Station Propulsion Advanced Technology Programs established an in-depth data base for the baseline gaseous oxygen/gaseous hydrogen thruster, the waste gas resistojet, and the associated system operations. These efforts included testing of a full end-to-end system at National Aeronautics and Space Administration (NASA)-Marshall Space Flight Center (MSFC) in which oxygen and hydrogen were generated from water by electrolysis at 6.89 MPa (1,000 psia), stored and fired through the prototype thruster. Recent end-to-end system tests which generate the oxygen/hydrogen propellants by electrolysis of water at 20.67 MPa (3,000 psia) were completed on the Integrated Propulsion Test Article (IPTA) at NASA-Johnson Space Center (JSC). Resistojet testing has included 10,000 hours of life testing, plume characterization, and electromagnetic interference (EMI) testing. Extensive 25-lbf thruster testing was performed defining operating performance characteristics across the required mixture ratio and thrust level ranges. Life testing has accumulated 27 hours of operation on the prototype thruster. A total of seven injectors and five thrust chambers were fabricated to the same basic design. Five injectors and three thrust chambers designed to incorporate improved life, performance, and producibility characteristics are ready for testing. Five resistojets were fabricated and tested, with modifications made to improve producibility. The lessons learned in the area of producibility for both the O2/H2 thrusters and for the resistojet have resolved critical fabrication issues. The test results indicate that all major technology issues for long life and reliability for space station application were resolved
Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site
Condensation occurs in nonequilibrium steady states when a finite fraction of
particles in the system occupies a single lattice site. We study condensation
transitions in a one-dimensional zero-range process with a single defect site.
The system is analysed in the grand canonical and canonical ensembles and the
two are contrasted. Two distinct condensation mechanisms are found in the grand
canonical ensemble. Discrepancies between the infinite and large but finite
systems' particle current versus particle density diagrams are investigated and
an explanation for how the finite current goes above a maximum value predicted
for infinite systems is found in the canonical ensemble.Comment: 18 pages, 4 figures, revtex
Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process
It has been recently suggested that a totally asymmetric exclusion process
with two species on an open chain could exhibit spontaneous symmetry breaking
in some range of the parameters defining its dynamics. The symmetry breaking is
manifested by the existence of a phase in which the densities of the two
species are not equal. In order to provide a more rigorous basis to these
observations we consider the limit of the process when the rate at which
particles leave the system goes to zero. In this limit the process reduces to a
biased random walk in the positive quarter plane, with specific boundary
conditions. The stationary probability measure of the position of the walker in
the plane is shown to be concentrated around two symmetrically located points,
one on each axis, corresponding to the fact that the system is typically in one
of the two states of broken symmetry in the exclusion process. We compute the
average time for the walker to traverse the quarter plane from one axis to the
other, which corresponds to the average time separating two flips between
states of broken symmetry in the exclusion process. This time is shown to
diverge exponentially with the size of the chain.Comment: 42 page
Factorised Steady States in Mass Transport Models
We study a class of mass transport models where mass is transported in a
preferred direction around a one-dimensional periodic lattice and is globally
conserved. The model encompasses both discrete and continuous masses and
parallel and random sequential dynamics and includes models such as the
Zero-range process and Asymmetric random average process as special cases. We
derive a necessary and sufficient condition for the steady state to factorise,
which takes a rather simple form.Comment: 6 page
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