34 research outputs found
Numerical study of rice-pile model
A one-dimensional model of a rice-pile is numerically studied for different driving mechanisms. We found that for a sufficiently large system, there is a sharp transition between the trivial behaviour of a 1D BTW model and self-organized critical (SOC) behaviour. Depending on the driving mechanism, the self-organized critical rice-pile model belongs to two different universality classes.A one-dimensional model of a rice-pile is numerically studied for different driving mechanisms. We found that for a sufficiently large system, there is a sharp transition between the trivial behaviour of a 1D BTW model and self-organized critical (SOC) behaviour. Depending on the driving mechanism, the self-organized critical rice-pile model belongs to two different universality classes
Phase diagrams and magnetic behavior of films with amorphization and anisotropy in surfaces
The phase diagrams and magnetic behavior of thin films with two amorphous surfaces are investigated by the use of the effective field theory with correlations. The transition temperature dependence of the exchange integral at surfaces, coupling between surface and nearest-layers, film thickness, and structural fluctuations are studied. Some interesting phenomena can occur as wetting phenomena and compensation point.The phase diagrams and magnetic behavior of thin films with two amorphous surfaces are investigated by the use of the effective field theory with correlations. The transition temperature dependence of the exchange integral at surfaces, coupling between surface and nearest-layers, film thickness, and structural fluctuations are studied. Some interesting phenomena can occur as wetting phenomena and compensation point
A simulation study of an asymmetric exclusion model with disorder
On the one hand, using numerical simulations, we study the asymmetric exclusion model with open boundaries, particlewise disorder. The phase diagram in the (α , β) -plane displays high density, low density and maximum current phases, with the first order transition line between high and low density phases shifted away from the line α =β. Within the low density phase a platoon phase transition occurs, many features of which can be explained using exact results for asymmetric exclusion with particlewise disorder on the ring. In a certain region of parameter space the disorder induces a cusp in the current-density relation at maximum flow. Our simulations indicate that this does not affect the topology of the phase diagram, nor the familiar 1/Öx -decay of the density profile in the maximum current phase. On the other hand, we study the effects of defects in the road and of jumping rate ∆t on the phase diagram J−ρ, using asymmetric exclusion model with periodic boundaries. For different level of disorder, the space-time evolution of particles displays «waves» for both phases low density and high density. Besides, there exist two critical values of density, a lower critical value ρc1 and a upper critical value ρc2, in between the current is constant and reaches its maximal value Jmax which increases with increasing the jumping rate ∆t and/or the degree of disorder c. Increasing ∆t and/or c, ρc1 increases and ρc2 decreases.On the one hand, using numerical simulations, we study the asymmetric exclusion model with open boundaries, particlewise disorder. The phase diagram in the (α , β) -plane displays high density, low density and maximum current phases, with the first order transition line between high and low density phases shifted away from the line α =β. Within the low density phase a platoon phase transition occurs, many features of which can be explained using exact results for asymmetric exclusion with particlewise disorder on the ring. In a certain region of parameter space the disorder induces a cusp in the current-density relation at maximum flow. Our simulations indicate that this does not affect the topology of the phase diagram, nor the familiar 1/Öx -decay of the density profile in the maximum current phase. On the other hand, we study the effects of defects in the road and of jumping rate ∆t on the phase diagram J−ρ, using asymmetric exclusion model with periodic boundaries. For different level of disorder, the space-time evolution of particles displays «waves» for both phases low density and high density. Besides, there exist two critical values of density, a lower critical value ρc1 and a upper critical value ρc2, in between the current is constant and reaches its maximal value Jmax which increases with increasing the jumping rate ∆t and/or the degree of disorder c. Increasing ∆t and/or c, ρc1 increases and ρc2 decreases
Disorder-induced phase transition in a one-dimensional model of rice pile
We propose a one-dimensional rice-pile model which connects the 1D BTW
sandpile model (Phys. Rev. A 38, 364 (1988)) and the Oslo rice-pile model
(Phys. Rev. lett. 77, 107 (1997)) in a continuous manner. We found that for a
sufficiently large system, there is a sharp transition between the trivial
critical behaviour of the 1D BTW model and the self-organized critical (SOC)
behaviour. When there is SOC, the model belongs to a known universality class
with the avalanche exponent .Comment: 10 pages, 7 eps figure
Analytical Approach to the One-Dimensional Disordered Exclusion Process with Open Boundaries and Random Sequential Dynamics
A one dimensional disordered particle hopping rate asymmetric exclusion
process (ASEP) with open boundaries and a random sequential dynamics is studied
analytically. Combining the exact results of the steady states in the pure case
with a perturbative mean field-like approach the broken particle-hole symmetry
is highlighted and the phase diagram is studied in the parameter space
, where and represent respectively the
injection rate and the extraction rate of particles. The model displays, as in
the pure case, high-density, low-density and maximum-current phases. All
critical lines are determined analytically showing that the high-density
low-density first order phase transition occurs at . We show
that the maximum-current phase extends its stability region as the disorder is
increased and the usual -decay of the density profile in this
phase is universal. Assuming that some exact results for the disordered model
on a ring hold for a system with open boundaries, we derive some analytical
results for platoon phase transition within the low-density phase and we give
an analytical expression of its corresponding critical injection rate
. As it was observed numerically, we show that the quenched
disorder induces a cusp in the current-density relation at maximum flow in a
certain region of parameter space and determine the analytical expression of
its slope. The results of numerical simulations we develop agree with the
analytical ones.Comment: 23 pages, 7 figures. to appear in J. Stat. Phy
fluctuations in a ricepile model
The temporal fluctuation of the average slope of a ricepile model is
investigated. It is found that the power spectrum scales as
with when grains of rice are added only to
one end of the pile. If grains are randomly added to the pile, the power
spectrum exhibits behaviour. The profile fluctuations of the pile under
different driving mechanisms are also discussed.Comment: 4 pages, 4 eps figures; Revtex format, published versio
Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
Recent work on stochastic interacting particle systems with two particle
species (or single-species systems with kinematic constraints) has demonstrated
the existence of spontaneous symmetry breaking, long-range order and phase
coexistence in nonequilibrium steady states, even if translational invariance
is not broken by defects or open boundaries. If both particle species are
conserved, the temporal behaviour is largely unexplored, but first results of
current work on the transition from the microscopic to the macroscopic scale
yield exact coupled nonlinear hydrodynamic equations and indicate the emergence
of novel types of shock waves which are collective excitations stabilized by
the flow of microscopic fluctuations. We review the basic stationary and
dynamic properties of these systems, highlighting the role of conservation laws
and kinetic constraints for the hydrodynamic behaviour, the microscopic origin
of domain wall (shock) stability and the coarsening dynamics of domains during
phase separation.Comment: 72 pages, 6 figures, 201 references (topical review for J. Phys. A:
Math. Gen.
Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments
The phenomenon of protein synthesis has been modeled in terms of totally
asymmetric simple exclusion processes (TASEP) since 1968. In this article, we
provide a tutorial of the biological and mathematical aspects of this approach.
We also summarize several new results, concerned with limited resources in the
cell and simple estimates for the current (protein production rate) of a TASEP
with inhomogeneous hopping rates, reflecting the characteristics of real genes.Comment: 25 pages, 7 figure
Traffic and Related Self-Driven Many-Particle Systems
Since the subject of traffic dynamics has captured the interest of
physicists, many astonishing effects have been revealed and explained. Some of
the questions now understood are the following: Why are vehicles sometimes
stopped by so-called ``phantom traffic jams'', although they all like to drive
fast? What are the mechanisms behind stop-and-go traffic? Why are there several
different kinds of congestion, and how are they related? Why do most traffic
jams occur considerably before the road capacity is reached? Can a temporary
reduction of the traffic volume cause a lasting traffic jam? Under which
conditions can speed limits speed up traffic? Why do pedestrians moving in
opposite directions normally organize in lanes, while similar systems are
``freezing by heating''? Why do self-organizing systems tend to reach an
optimal state? Why do panicking pedestrians produce dangerous deadlocks? All
these questions have been answered by applying and extending methods from
statistical physics and non-linear dynamics to self-driven many-particle
systems. This review article on traffic introduces (i) empirically data, facts,
and observations, (ii) the main approaches to pedestrian, highway, and city
traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and
macroscopic (fluid-dynamic) models. Attention is also paid to the formulation
of a micro-macro link, to aspects of universality, and to other unifying
concepts like a general modelling framework for self-driven many-particle
systems, including spin systems. Subjects such as the optimization of traffic
flows and relations to biological or socio-economic systems such as bacterial
colonies, flocks of birds, panics, and stock market dynamics are discussed as
well.Comment: A shortened version of this article will appear in Reviews of Modern
Physics, an extended one as a book. The 63 figures were omitted because of
storage capacity. For related work see http://www.helbing.org