800 research outputs found
Factorised Steady States in Mass Transport Models on an Arbitrary Graph
We study a general mass transport model on an arbitrary graph consisting of
nodes each carrying a continuous mass. The graph also has a set of directed
links between pairs of nodes through which a stochastic portion of mass, chosen
from a site-dependent distribution, is transported between the nodes at each
time step. The dynamics conserves the total mass and the system eventually
reaches a steady state. This general model includes as special cases various
previously studied models such as the Zero-range process and the Asymmetric
random average process. We derive a general condition on the stochastic mass
transport rules, valid for arbitrary graph and for both parallel and random
sequential dynamics, that is sufficient to guarantee that the steady state is
factorisable. We demonstrate how this condition can be achieved in several
examples. We show that our generalized result contains as a special case the
recent results derived by Greenblatt and Lebowitz for -dimensional
hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur
Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology
The motion of a single Brownian particle in a complex fluid can reveal material behavior both at and away from equilibrium. In active microrheology, a probe particle is driven by an external force through a complex medium and its motion studied in order to infer properties of the embedding material. Most work in microrheology has focused on steady behavior and established the relationship between the motion of the probe, the microstructure, and the effective microviscosity of the medium. Transient behavior in the near-equilibrium, linear-response regime has also been studied via its connection to low-amplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium fluctuations. But important information about the basic physical aspects of structural development and relaxation in a medium is captured by startup and cessation of the imposed deformation in the nonlinear regime, where the structure is driven far from equilibrium. Here, we study theoretically and by dynamic simulation the transient behavior of a colloidal dispersion undergoing nonlinear microrheological forcing. The strength with which the probe is forced, Fext, compared to thermal forces, kT/b, governs the dynamics and defines a PĂ©clet number, Pe = F^ext/(kT/b), where kT is the thermal energy and b is the colloidal bath particle size. For large Pe, a boundary layer (in which unsteady advection balances diffusion) forms at particle contact on the time scale of the flow, a/U, where a is the probe size and U its speed, whereas the wake forms over O(Pe) diffusive time steps. Similarly, relaxation following cessation occurs over several time scales corresponding to distinct physical processes. For very short times, the time scale for relaxation is set by a boundary layer of thickness ÎŽ ⌠(a+b)/Pe, and so Ï âŒ ÎŽ^2/D_r, where Dr is the relative diffusivity between the probe of size a and a bath particle. Nearly all stress relaxation occurs during this time. At longer times, the Brownian diffusion of the bath particles acts to close the wake on a time scale set by how long it takes a bath particle to diffuse laterally across it, Ï âŒ (a+b)^2/D_r. Although the majority of the microstructural relaxation occurs during this wake-healing process, it does so with little change in the stress. Also during relaxation, the probe travels backward in the suspension; this recovered strain is proportional to the free energy stored in the compressed particle configuration, an indicator that the stress is proportional to the free energy density stored entropically in the microstructure. Theoretical results are compared with Brownian dynamics simulation where it is found that the dilute theory captures the correct behavior even for concentrated suspensions. Two modes of forcing are studied: Constant force and constant velocity. Results are compared to analogous macrorheology results for suspensions undergoing simple shear flow
Spatial structures in a simple model of population dynamics for parasite-host interactions
Spatial patterning can be crucially important for understanding the behavior
of interacting populations. Here we investigate a simple model of parasite and
host populations in which parasites are random walkers that must come into
contact with a host in order to reproduce. We focus on the spatial arrangement
of parasites around a single host, and we derive using analytics and numerical
simulations the necessary conditions placed on the parasite fecundity and
lifetime for the populations long-term survival. We also show that the parasite
population can be pushed to extinction by a large drift velocity, but,
counterintuitively, a small drift velocity generally increases the parasite
population.Comment: 6 pages, 6 figure
Construction of the factorized steady state distribution in models of mass transport
For a class of one-dimensional mass transport models we present a simple and
direct test on the chipping functions, which define the probabilities for mass
to be transferred to neighbouring sites, to determine whether the stationary
distribution is factorized. In cases where the answer is affirmative, we
provide an explicit method for constructing the single-site weight function. As
an illustration of the power of this approach, previously known results on the
Zero-range process and Asymmetric random average process are recovered in a few
lines. We also construct new models, namely a generalized Zero-range process
and a binomial chipping model, which have factorized steady states.Comment: 6 pages, no figure
Fluctuations and correlations in an individual-based model of biological coevolution
We extend our study of a simple model of biological coevolution to its
statistical properties. Staring with a complete description in terms of a
master equation, we provide its relation to the deterministic evolution
equations used in previous investigations. The stationary states of the
mutationless model are generally well approximated by Gaussian distributions,
so that the fluctuations and correlations of the populations can be computed
analytically. Several specific cases are studied by Monte Carlo simulations,
and there is excellent agreement between the data and the theoretical
predictions.Comment: 25 pages, 2 figure
Exact dynamics of a reaction-diffusion model with spatially alternating rates
We present the exact solution for the full dynamics of a nonequilibrium spin
chain and its dual reaction-diffusion model, for arbitrary initial conditions.
The spin chain is driven out of equilibrium by coupling alternating spins to
two thermal baths at different temperatures. In the reaction-diffusion model,
this translates into spatially alternating rates for particle creation and
annihilation, and even negative ``temperatures'' have a perfectly natural
interpretation. Observables of interest include the magnetization, the particle
density, and all correlation functions for both models. Two generic types of
time-dependence are found: if both temperatures are positive, the
magnetization, density and correlation functions decay exponentially to their
steady-state values. In contrast, if one of the temperatures is negative,
damped oscillations are observed in all quantities. They can be traced to a
subtle competition of pair creation and annihilation on the two sublattices. We
comment on the limitations of mean-field theory and propose an experimental
realization of our model in certain conjugated polymers and linear chain
compounds.Comment: 13 pages, 1 table, revtex4 format (few minor typos fixed). Published
in Physical Review
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
Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions
In active, nonlinear microrheology, a Brownian âprobeâ particle is driven through a complex fluid and its motion tracked in order to infer the mechanical properties of the embedding material. In the absence of external forcing, the probe and background particles form an equilibrium microstructure that fluctuates thermally. Probe motion through the medium distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, F^(ext), compared to thermal forces, kT/b, defining a PĂ©clet number, Pe = F^(ext)/(kT/b), where kT is the thermal energy and b is the characteristic microstructural length scale. Recent studies showed that the mean probe speed can be interpreted as the effective material viscosity, whereas fluctuations in probe velocity give rise to an anisotropic force-induced diffusive spread of its trajectory. The viscosity and diffusivity can thus be obtained by two simple quantitiesâmean and mean-square displacement of the probe. The notion that diffusive flux is driven by stress gradients leads to the idea that the stress can be related directly to the microdiffusivity, and thus the anisotropy of the diffusion tensor reflects the presence of normal stress differences in nonlinear microrheology. In this study, a connection is made between diffusion and stress gradients, and a relation between the particle-phase stress and the diffusivity and viscosity is derived for a probe particle moving through a colloidal dispersion. This relation is shown to agree with two standard micromechanical definitions of the stress, suggesting that the normal stresses and normal stress differences can be measured in nonlinear microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in Pe for Peâ«1 and vanishes as Pe^4 for PeâȘ1. The expression obtained for stress-induced migration can be viewed as a generalized nonequilibrium StokesâEinstein relation. A final connection is made between the stress and an âeffective temperatureâ of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a ânonequilibrium equation of state.
Fluctuation relations and coarse-graining
We consider the application of fluctuation relations to the dynamics of
coarse-grained systems, as might arise in a hypothetical experiment in which a
system is monitored with a low-resolution measuring apparatus. We analyze a
stochastic, Markovian jump process with a specific structure that lends itself
naturally to coarse-graining. A perturbative analysis yields a reduced
stochastic jump process that approximates the coarse-grained dynamics of the
original system. This leads to a non-trivial fluctuation relation that is
approximately satisfied by the coarse-grained dynamics. We illustrate our
results by computing the large deviations of a particular stochastic jump
process. Our results highlight the possibility that observed deviations from
fluctuation relations might be due to the presence of unobserved degrees of
freedom.Comment: 19 pages, 6 figures, very minor change
Biological activities of Rumex dentatus L: Evaluation of methanol and hexane extracts
Rumex dentatus L. (Plygonaceae) extracts were evaluated for antibacterial, antifungal, cytotoxic, antitumor and allopathic potential. The leaf, stem and root extracts were prepared in methanol and hexane by simple maceration. The methanol extracts of root and shoot were found effective against all the bacterial strains tested. Zone of inhibition ranged between 9.7 to 12.1 mm. While the hexane extracts inhibited fungal growth (up to 80%) more efficiently than the methanol extracts. Concentration of different the extracts of R. dentatus effectively inhibited tumor induction on the potato discs produced by wild type Agrobacterium strains At10 and At6. The root extracts either in methanol or hexane showed LD50 values below 1000 ppm in brine shrimp mortality assay. The methanol extracts of leaf and stem inhibited radish seed germination (70 and 61% respectively) and root length more than the hexane extracts. The R. dentatus methanol extract showed presence of alkaloids, saponins, anthraquinones and tannins while flavonoids were also found in both methanol as well as hexane extract
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