764 research outputs found
Spurious phase in a model for traffic on a bridge
We present high-precision Monte Carlo data for the phase diagram of a
two-species driven diffusive system, reminiscent of traffic across a narrow
bridge. Earlier studies reported two phases with broken symmetry; the existence
of one of these has been the subject of some debate. We show that the disputed
phase disappears for sufficiently large systems and/or sufficiently low bulk
mobility.Comment: 8 pages, 3 figures, JPA styl
Drift causes anomalous exponents in growth processes
The effect of a drift term in the presence of fixed boundaries is studied for
the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism
that causes a change of exponents for a very broad class of growth processes.
This mechanism represents a relevant perturbation and therefore is important
for the interpretation of experimental and numerical results. In effect, the
mechanism leads to the roughness exponent assuming the same value as the growth
exponent. In the case of the Edwards-Wilkinson equation this implies exponents
deviating from those expected by dimensional analysis.Comment: 4 pages, 1 figure, REVTeX; accepted for publication in PRL; added
note and reference
Dynamically accelerated cover times
Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d ≥ 3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to “accelerate” or “decelerate” upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1 / f α Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d > 3 , our results for acceleration in d = 3 challenge the current understanding of the role of correlations in the cover time problem
Nonuniversal exponents in sandpiles with stochastic particle number transfer
We study fixed density sandpiles in which the number of particles transferred
to a neighbor on relaxing an active site is determined stochastically by a
parameter . Using an argument, the critical density at which an
active-absorbing transition occurs is found exactly. We study the critical
behavior numerically and find that the exponents associated with both static
and time-dependent quantities vary continuously with .Comment: Some parts rewritten, results unchanged. To appear in Europhys. Let
One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve
We derive the steady state properties of a general directed ``sandpile''
model in one dimension. Using a central limit theorem for dependent random
variables we find the precise conditions for the model to belong to the
universality class of the Totally Asymmetric Oslo model, thereby identifying a
large universality class of directed sandpiles. We map the avalanche size to
the area under a Brownian curve with an absorbing boundary at the origin,
motivating us to solve this Brownian curve problem. Thus, we are able to
determine the moment generating function for the avalanche-size probability in
this universality class, explicitly calculating amplitudes of the leading order
terms.Comment: 24 pages, 5 figure
Abelian Manna model on various lattices in one and two dimensions
We perform a high-accuracy moment analysis of the avalanche size, duration
and area distribution of the Abelian Manna model on eight two-dimensional and
four one-dimensional lattices. The results provide strong support to establish
universality of exponents and moment ratios across different lattices and a
good survey for the strength of corrections to scaling which are notorious in
the Manna universality class. The results are compared against previous work
done on Manna model, Oslo model and directed percolation. We also confirm
hypothesis of various scaling relations.Comment: 16 pages, 3 figures, 7 tables, submitted to Journal of Statistical
Mechanic
Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"
In [Braz. J. Phys. 30, 27 (2000)] Dickman et al. suggested that
self-organized criticality can be produced by coupling the activity of an
absorbing state model to a dissipation mechanism and adding an external drive.
We analyzed the proposed mechanism in [Phys. Rev. E 73, 025106R (2006)] and
found that if this mechanism is at work, the finite-size scaling found in
self-organized criticality will depend on the details of the implementation of
dissipation and driving. In the preceding comment [Phys. Rev. E XX, XXXX
(2008)] Alava et al. show that one avalanche exponent in the AS approach
becomes independent of dissipation and driving. In our reply we clarify their
findings and put them in the context of the original article.Comment: 4 pages, REVTeX (draft
Critical Behaviour of the Drossel-Schwabl Forest Fire Model
We present high statistics Monte Carlo results for the Drossel-Schwabl forest
fire model in 2 dimensions. They extend to much larger lattices (up to
) than previous simulations and reach much closer to the
critical point (up to ). They are incompatible with
all previous conjectures for the (extrapolated) critical behaviour, although
they in general agree well with previous simulations wherever they can be
directly compared. Instead, they suggest that scaling laws observed in previous
simulations are spurious, and that the density of trees in the critical
state was grossly underestimated. While previous simulations gave , we conjecture that actually is equal to the critical threshold
for site percolation in . This is however still far from
the densities reachable with present day computers, and we estimate that we
would need many orders of magnitude higher CPU times and storage capacities to
reach the true critical behaviour -- which might or might not be that of
ordinary percolation.Comment: 8 pages, including 9 figures, RevTe
A field-theoretic approach to the Wiener Sausage
The Wiener Sausage, the volume traced out by a sphere attached to a Brownian
particle, is a classical problem in statistics and mathematical physics.
Initially motivated by a range of field-theoretic, technical questions, we
present a single loop renormalised perturbation theory of a stochastic process
closely related to the Wiener Sausage, which, however, proves to be exact for
the exponents and some amplitudes. The field-theoretic approach is particularly
elegant and very enjoyable to see at work on such a classic problem. While we
recover a number of known, classical results, the field-theoretic techniques
deployed provide a particularly versatile framework, which allows easy
calculation with different boundary conditions even of higher momenta and more
complicated correlation functions. At the same time, we provide a highly
instructive, non-trivial example for some of the technical particularities of
the field-theoretic description of stochastic processes, such as excluded
volume, lack of translational invariance and immobile particles. The aim of the
present work is not to improve upon the well-established results for the Wiener
Sausage, but to provide a field-theoretic approach to it, in order to gain a
better understanding of the field-theoretic obstacles to overcome.Comment: 45 pages, 3 Figures, Springer styl
Detailed assessment of the hemodynamic response to psychosocial stress using real-time MRI
Purpose: To demonstrate that combining the Montreal Imaging Stress Task (MIST) with real-time cardiac magnetic resonance imaging (MRI) allows detailed assessment of the cardiovascular mental stress response.Materials and Methods: 22 healthy volunteers (1:1 M:F, 26-64 years) underwent MRI during rest and the MIST. Real-time spiral phase contrast MR, accelerated with sensitivity encoding (SENSE) was used to assess stroke volume (SV), and radial k-t SENSE was used to assess ventricular volumes. Simultaneous heart rate (HR) and blood pressure (BP) measures allowed calculation of cardiac output (CO), systemic vascular resistance (SVR), and arterial compliance (TAC). Endocrine responses were assessed using salivary cortisol.Results: In response to stress. BP increased due to increased CO and reduced TAC but not increased SVR, which fell. HR, not SV, determined CO increases. Greater BP responses occurred in men due to greater CO increases and relatively higher SVR. Older participants had greater BP responses due to greater falls in TAC. Greater cortisol response was correlated with greater falls In TAC but resting cortisol and TAC were not related.Conclusion: This new approach allows detailed, accurate assessment of stress physiology. Preliminary findings suggest stress exposes relationships, not seen at rest, of cardiovascular function with age, sex, and endocrine function
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