-
Carlos Escudero
[show abstract]
[hide abstract]
ABSTRACT: The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth, dilution, which spatially reorders the incoming matter, is responsible for the transmission of correlations. Its effects include the erasing of memory with respect to the initial condition, a partial attenuation of geometrically originated instabilities, and the restoration of universality in some special cases in which the critical exponents depend on the parameters of the equation of motion. In this sense, dilution rends the dynamics more similar to the usual one of planar systems. This fast growth regime is also characterized by the spatial decorrelation of the interface, which, in the case of radially growing interfaces, naturally originates rapid roughening and scale-dependent fractality, and suggests the advent of a self-similar fractal dimension. The center-of-mass fluctuations of growing clusters are also studied, and our analysis suggests the possible nonapplicability of usual scalings to the long-range surface fluctuations of the radial Eden model. In fact, our study points to the fact that this model belongs to a dilution-free universality class.
Physical Review E 09/2011; 84(3 Pt 1):031131. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group's direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation.
Physical Review E 07/2010; 82(1 Pt 1):011926. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different macroscopic patterns. The crucial technical point is extending the usual one species coagulation dynamics to the two species one. This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning. The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions. The possible applications of our results to some topics in which consensus reaching is fundamental, such as collective animal motion and opinion spreading dynamics, are also outlined.
Physical Review E 07/2010; 82(1 Pt 2):016113. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker-Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker-Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker-Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker-Planck equation coefficient estimation approach, can be implemented in the self-propelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.
Proceedings of the National Academy of Sciences 05/2009; 106(14):5464-9. · 9.68 Impact Factor
-
Carlos Escudero
Physical Review Letters 05/2009; 102(13):139602. · 7.37 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We consider the switching rate of a metastable reaction scheme, which includes reactions with arbitrary steps, e.g., kA<-->(k+r)A (both forward and reverse reaction steps are allowed to happen). Employing a WKB approximation, controlled by a large system size, we evaluate both the exponent and the preexponential factor for the rate. The results are illustrated on a number of examples.
Physical Review E 04/2009; 79(4 Pt 1):041149. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We consider a switching rate of a meta-stable reaction scheme, which includes reactions with arbitrary steps, e.g. $kA\to(k+r)A$. Employing WKB approximation, controlled by a large system size, we evaluate both the exponent and the pre-exponential factor for the rate. The results are illustrated on a number of examples.
11/2008;
