12,037 research outputs found
Flocking Regimes in a Simple Lattice Model
We study a one-dimensional lattice flocking model incorporating all three of
the flocking criteria proposed by Reynolds [Computer Graphics vol.21 4 (1987)]:
alignment, centring and separation. The model generalises that introduced by O.
J. O' Loan and M. R. Evans [J. Phys. A. vol. 32 L99 (1999)]. We motivate the
dynamical rules by microscopic sampling considerations. The model exhibits
various flocking regimes: the alternating flock, the homogeneous flock and
dipole structures. We investigate these regimes numerically and within a
continuum mean-field theory.Comment: 24 pages 7 figure
Nonlinear rheological properties of dense colloidal dispersions close to a glass transition under steady shear
The nonlinear rheological properties of dense colloidal suspensions under
steady shear are discussed within a first principles approach. It starts from
the Smoluchowski equation of interacting Brownian particles in a given shear
flow, derives generalized Green-Kubo relations, which contain the transients
dynamics formally exactly, and closes the equations using mode coupling
approximations. Shear thinning of colloidal fluids and dynamical yielding of
colloidal glasses arise from a competition between a slowing down of structural
relaxation, because of particle interactions, and enhanced decorrelation of
fluctuations, caused by the shear advection of density fluctuations. The
integration through transients approach takes account of the dynamic
competition, translational invariance enters the concept of wavevector
advection, and the mode coupling approximation enables to quantitatively
explore the shear-induced suppression of particle caging and the resulting
speed-up of the structural relaxation. Extended comparisons with shear stress
data in the linear response and in the nonlinear regime measured in model
thermo-sensitive core-shell latices are discussed. Additionally, the single
particle motion under shear observed by confocal microscopy and in computer
simulations is reviewed and analysed theoretically.Comment: Review submited to special volume 'High Solid Dispersions' ed. M.
Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009);
some figures slightly cu
The influence of dispersal on a predator-prey system with two habitats
Dispersal between different habitats influences the dynamics and stability of
populations considerably. Furthermore, these effects depend on the local
interactions of a population with other species. Here, we perform a general and
comprehensive study of the simplest possible system that includes dispersal and
local interactions, namely a 2-patch 2-species system. We evaluate the impact
of dispersal on stability and on the occurrence of bifurcations, including
pattern forming bifurcations that lead to spatial heterogeneity, in 19
different classes of models with the help of the generalized modelling
approach. We find that dispersal often destabilizes equilibria, but it can
stabilize them if it increases population losses. If dispersal is nonrandom,
i.e. if emigration or immigration rates depend on population densities, the
correlation of stability with migration rates is positive in part of the
models. We also find that many systems show all four types of bifurcations and
that antisynchronous oscillations occur mostly with nonrandom dispersal
Money and Goldstone modes
Why is ``worthless'' fiat money generally accepted as payment for goods and
services? In equilibrium theory, the value of money is generally not
determined: the number of equations is one less than the number of unknowns, so
only relative prices are determined. In the language of mathematics, the
equations are ``homogeneous of order one''. Using the language of physics, this
represents a continuous ``Goldstone'' symmetry. However, the continuous
symmetry is often broken by the dynamics of the system, thus fixing the value
of the otherwise undetermined variable. In economics, the value of money is a
strategic variable which each agent must determine at each transaction by
estimating the effect of future interactions with other agents. This idea is
illustrated by a simple network model of monopolistic vendors and buyers, with
bounded rationality. We submit that dynamical, spontaneous symmetry breaking is
the fundamental principle for fixing the value of money. Perhaps the continuous
symmetry representing the lack of restoring force is also the fundamental
reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure
Money and Goldstone modes
Why is ``worthless'' fiat money generally accepted as payment for goods and
services? In equilibrium theory, the value of money is generally not
determined: the number of equations is one less than the number of unknowns, so
only relative prices are determined. In the language of mathematics, the
equations are ``homogeneous of order one''. Using the language of physics, this
represents a continuous ``Goldstone'' symmetry. However, the continuous
symmetry is often broken by the dynamics of the system, thus fixing the value
of the otherwise undetermined variable. In economics, the value of money is a
strategic variable which each agent must determine at each transaction by
estimating the effect of future interactions with other agents. This idea is
illustrated by a simple network model of monopolistic vendors and buyers, with
bounded rationality. We submit that dynamical, spontaneous symmetry breaking is
the fundamental principle for fixing the value of money. Perhaps the continuous
symmetry representing the lack of restoring force is also the fundamental
reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure
Temporal signatures of leptohadronic feedback mechanisms in compact sources
The hadronic model of Active Galactic Nuclei and other compact high energy
astrophysical sources assumes that ultra-relativistic protons,
electron-positron pairs and photons interact via various hadronic and
electromagnetic processes inside a magnetized volume, producing the
multiwavelength spectra observed from these sources. A less studied property of
such systems is that they can exhibit a variety of temporal behaviours due to
the operation of different feedback mechanisms. We investigate the effects of
one possible feedback loop, where \gamma-rays produced by photopion processes
are being quenched whenever their compactness increases above a critical level.
This causes a spontaneous creation of soft photons in the system that result in
further proton cooling and more production of \gamma-rays, thus making the loop
operate. We perform an analytical study of a simplified set of equations
describing the system, in order to investigate the connection of its temporal
behaviour with key physical parameters. We also perform numerical integration
of the full set of kinetic equations verifying not only our analytical results
but also those of previous numerical studies. We find that once the system
becomes `supercritical', it can exhibit either a periodic behaviour or a damped
oscillatory one leading to a steady state. We briefly point out possible
implications of such a supercriticality on the parameter values used in Active
Galactic Nuclei spectral modelling, through an indicative fitting of the VHE
emission of blazar 3C 279.Comment: 19 pages, 20 figures, accepted for publication in MNRA
Network Inoculation: Heteroclinics and phase transitions in an epidemic model
In epidemiological modelling, dynamics on networks, and in particular
adaptive and heterogeneous networks have recently received much interest. Here
we present a detailed analysis of a previously proposed model that combines
heterogeneity in the individuals with adaptive rewiring of the network
structure in response to a disease. We show that in this model qualitative
changes in the dynamics occur in two phase transitions. In a macroscopic
description one of these corresponds to a local bifurcation whereas the other
one corresponds to a non-local heteroclinic bifurcation. This model thus
provides a rare example of a system where a phase transition is caused by a
non-local bifurcation, while both micro- and macro-level dynamics are
accessible to mathematical analysis. The bifurcation points mark the onset of a
behaviour that we call network inoculation. In the respective parameter region
exposure of the system to a pathogen will lead to an outbreak that collapses,
but leaves the network in a configuration where the disease cannot reinvade,
despite every agent returning to the susceptible class. We argue that this
behaviour and the associated phase transitions can be expected to occur in a
wide class of models of sufficient complexity.Comment: 26 pages, 11 figure
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