82 research outputs found
Stress response inside perturbed particle assemblies
The effect of structural disorder on the stress response inside three
dimensional particle assemblies is studied using computer simulations of
frictionless sphere packings. Upon applying a localised, perturbative force
within the packings, the resulting {\it Green's} function response is mapped
inside the different assemblies, thus providing an explicit view as to how the
imposed perturbation is transmitted through the packing. In weakly disordered
arrays, the resulting transmission of forces is of the double-peak variety, but
with peak widths scaling linearly with distance from the source of the
perturbation. This behaviour is consistent with an anisotropic elasticity
response profile. Increasing the disorder distorts the response function until
a single-peak response is obtained for fully disordered packings consistent
with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte
Sensitivity of the stress response function to packing preparation
A granular assembly composed of a collection of identical grains may pack
under different microscopic configurations with microscopic features that are
sensitive to the preparation history. A given configuration may also change in
response to external actions such as compression, shearing etc. We show using a
mechanical response function method developed experimentally and numerically,
that the macroscopic stress profiles are strongly dependent on these
preparation procedures. These results were obtained for both two and three
dimensions. The method reveals that, under a given preparation history, the
macroscopic symmetries of the granular material is affected and in most cases
significant departures from isotropy should be observed. This suggests a new
path toward a non-intrusive test of granular material constitutive properties.Comment: 15 pages, 11 figures, some numerical data corrected, to appear in J.
Phys. Cond. Mat. special issue on Granular Materials (M. Nicodemi Editor
New method to study stochastic growth equations: a cellular automata perspective
We introduce a new method based on cellular automata dynamics to study
stochastic growth equations. The method defines an interface growth process
which depends on height differences between neighbors. The growth rule assigns
a probability exp for a site to
receive one particle at a time and all the sites are updated
simultaneously. Here and are two parameters and
is a function which depends on height of the site and its neighbors. Its
functional form is specified through discretization of the deterministic part
of the growth equation associated to a given deposition process. In particular,
we apply this method to study two linear equations - the Edwards-Wilkinson (EW)
equation and the Mullins-Herring (MH) equation - and a non-linear one - the
Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical
analysis of the height distributions of the profiles, we recover the values for
roughening exponents, which confirm that the processes generated by the method
are indeed in the universality classes of the original growth equations. In
addition, a crossover from Random Deposition to the associated correlated
regime is observed when the parameter is varied.Comment: 6 pages, 7 figure
Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results
We study the response of a two-dimensional hexagonal packing of massless,
rigid, frictionless spherical grains due to a vertically downward point force
on a single grain at the top layer. We use a statistical approach, where each
mechanically stable configuration of contact forces is equally likely. We show
that this problem is equivalent to a correlated -model. We find that the
response is double-peaked, where the two peaks, sharp and single-grain diameter
wide, lie on the two downward lattice directions emanating from the point of
the application of the external force. For systems of finite size, the
magnitude of these peaks decreases towards the bottom of the packing, while
progressively a broader, central maximum appears between the peaks. The
response behaviour displays a remarkable scaling behaviour with system size
: while the response in the bulk of the packing scales as , on
the boundary it is independent of , so that in the thermodynamic limit only
the peaks on the lattice directions persist. This qualitative behaviour is
extremely robust, as demonstrated by our simulation results with different
boundary conditions. We have obtained expressions of the response and higher
correlations for any system size in terms of integers corresponding to an
underlying discrete structure.Comment: Accepted for publication in JStat; 33 pages, 10 figures; Section 2.2
reorganized and rewritten; Details about the simulation procedure added in
Sec.3.1. ; A new section, summarizing the final results and the calculation
procedure adde
Response of electrically coupled spiking neurons: a cellular automaton approach
Experimental data suggest that some classes of spiking neurons in the first
layers of sensory systems are electrically coupled via gap junctions or
ephaptic interactions. When the electrical coupling is removed, the response
function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons
typically shows a decrease in dynamic range and sensitivity. In order to assess
the effect of electrical coupling in the sensory periphery, we calculate the
response to a Poisson stimulus of a chain of excitable neurons modeled by
-state Greenberg-Hastings cellular automata in two approximation levels. The
single-site mean field approximation is shown to give poor results, failing to
predict the absorbing state of the lattice, while the results for the pair
approximation are in good agreement with computer simulations in the whole
stimulus range. In particular, the dynamic range is substantially enlarged due
to the propagation of excitable waves, which suggests a functional role for
lateral electrical coupling. For probabilistic spike propagation the Hill
exponent of the response function is , while for deterministic spike
propagation we obtain , which is close to the experimental values
of the psychophysical Stevens exponents for odor and light intensities. Our
calculations are in qualitative agreement with experimental response functions
of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.
Tricritical directed percolation
We consider a modification of the contact process incorporating higher-order
reaction terms. The original contact process exhibits a non-equilibrium phase
transition belonging to the universality class of directed percolation. The
incorporated higher-order reaction terms lead to a non-trivial phase diagram.
In particular, a line of continuous phase transitions is separated by a
tricritical point from a line of discontinuous phase transitions. The
corresponding tricritical scaling behavior is analyzed in detail, i.e., we
determine the critical exponents, various universal scaling functions as well
as universal amplitude combinations
Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force
The response to a localized force provides a sensitive test for different
models of stress transmission in granular solids. The elasto-plastic models
traditionally used by engineers have been challenged by theoretical and
experimental results which suggest a wave-like (hyperbolic) propagation of the
stress, as opposed to the elliptic equations of static elasticity. Numerical
simulations of two-dimensional granular systems subject to a localized external
force are employed to examine the nature of stress transmission in these
systems as a function of the magnitude of the applied force, the frictional
parameters and the disorder (polydispersity). The results indicate that in
large systems (typically considered by engineers), the response is close to
that predicted by isotropic elasticity whereas the response of small systems
(or when sufficiently large forces are applied) is strongly anisotropic. In the
latter case the applied force induces changes in the contact network
accompanied by frictional sliding. The larger the coefficient of static
friction, the more extended is the range of forces for which the response is
elastic and the smaller the anisotropy. Increasing the degree of polydispersity
(for the range studied, up to 25%) decreases the range of elastic response.
This article is an extension of a previously published letter [1].Comment: 21 pages (PDFLaTeX), 24 figures (some of them bitmapped to save
space); submitted to Phys. Rev.
Severe Hindrance of Viral Infection Propagation in Spatially Extended Hosts
The production of large progeny numbers affected by high mutation rates is a ubiquitous strategy of viruses, as it promotes quick adaptation and survival to changing environments. However, this situation often ushers in an arms race between the virus and the host cells. In this paper we investigate in depth a model for the dynamics of a phenotypically heterogeneous population of viruses whose propagation is limited to two-dimensional geometries, and where host cells are able to develop defenses against infection. Our analytical and numerical analyses are developed in close connection to directed percolation models. In fact, we show that making the space explicit in the model, which in turn amounts to reducing viral mobility and hindering the infective ability of the virus, connects our work with similar dynamical models that lie in the universality class of directed percolation. In addition, we use the fact that our model is a multicomponent generalization of the Domany-Kinzel probabilistic cellular automaton to employ several techniques developed in the past in that context, such as the two-site approximation to the extinction transition line. Our aim is to better understand propagation of viral infections with mobility restrictions, e.g., in crops or in plant leaves, in order to inspire new strategies for effective viral control
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