José L. Mateos

Lévy walk patterns in the foraging movements of spider monkeys ( Ateles geoffroyi )

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other, nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns closely resemble what physicists know as Lévy walks. First, the length of a trajectory’s constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Lévy walk model to be an optimal strategy to search for scarce resources distributed at random. Second, the frequency distribution of the duration of stops or waiting times also approximates to a power-law function. Finally, the mean square displacement during the monkeys’ first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Lévy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own and when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.

Scale-free foraging by primates emerges from their interaction with a complex environment

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree-size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with field observations of tree-size variation and spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.

Chaotic transport and current reversal in deterministic ratchets

We address the problem of the classical deterministic dynamics of a particle in a periodic asymmetric potential of the ratchet type. We take into account the inertial term in order to understand the role of the chaotic dynamics in the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the current reversal as a bifurcation from a chaotic to a periodic regime. Close to this bifurcation, we observed trajectories revealing intermittent chaos and anomalous deterministic diffusion.

Anticipated synchronization in coupled inertial ratchets with time-delayed feedback: A numerical study

We investigate anticipated synchronization between two periodically driven deterministic, dissipative inertial ratchets that are able to exhibit directed transport with a finite velocity. The two ratchets interact through a unidirectional delay coupling, one is acting as a master system while the other one represents the slave system. Each of the two dissipative deterministic ratchets is driven externally by a common periodic force. The delay coupling involves two parameters, the coupling strength and the (positive-valued) delay time. We study the synchronization features for the unbounded, current carrying trajectories of the master and the slave, respectively, for four different strengths of the driving amplitude. These in turn characterize differing phase space dynamics of the transporting ratchet dynamics, regular, intermittent and a chaotic transport regime. We find that the slave ratchet can respond in exactly the same way as the master will respond in the future, thereby anticipating the nonlinear directed transport.

Experimental Control of Transport and Current Reversals in a Deterministic Optical Rocking Ratchet

We present an experimental demonstration of a deterministic optical rocking ratchet. A periodic and asymmetric light pattern is created to interact with dielectric microparticles in water, giving rise to a ratchet potential. The sample is moved with respect to the pattern with an unbiased time-periodic rocking function, which tilts the potential in alternating opposite directions. We obtain a current of particles whose direction can be controlled in real time and show that particles of different sizes may experience opposite currents. Moreover, we observed current reversals as a function of the magnitude and period of the rocking force.

Current reversals in deterministic ratchets: points and dimers

We address the problem of the chaotic transport of point particles and rigid dimers in an asymmetric periodic ratchet potential. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the multiple current reversals as bifurcations, usually from a chaotic to a periodic regime. We consider the dynamics of rigid dimers, as a function of size, extending in this way our previous results for point particles.

AC-driven Brownian motors: A Fokker-Planck treatment

We consider a model of AC-driven Brownian motors consisting of a classical particle which is placed in a potential that is periodic in space and time and which is coupled to a heat bath. The effects of fluctuations and dissipation are studied by a time-dependent Fokker-Planck equation. The approach lets us map the original stochastic problem onto a system of ordinary linear algebraic equations. The solution of the equations provides complete information about ratchet transport, avoiding the disadvantages of direct stochastic calculations such as long transients and large statistical fluctuations. The Fokker-Planck approach to dynamical ratchets opens the possibility for further generalizations.

THz operation of self-switching nano-diodes and nano-transistors

By means of the microscopic transport description supplied by a semiclassical 2D Monte Carlo simulator, we provide an in depth explanation of the operation (based on electrostatic effects) of the nanoscale unipolar rectifying diode, so called self-switching diode (SSD), recently proposed in [A. M. Song, M. Missous, P. Omling, A. R. Peaker, L. Samuelson, and W. Seifert, Appl. Phys. Lett. 83, 1881 (2003)]. This device provides a rectifying behavior without the use of any doping junction or barrier structure (like in p-n or Schottky barrier diodes) and can be fabricated with a simple single-step lithographic process. The simple downscaling of this device and the use of materials providing high electron velocity (like high In content InGaAs channels) allows to envisage the fabrication of structures working in the THz range. With a slight modification of the geometry of the SSD, a lateral gate contact can be added, so that a nanometer self-switching transistor (SST) can be easily fabricated. We analyze the high frequency performance of the diodes and transistors and provide design considerations for the optimization of the downscaling process.

Phase synchronization in tilted deterministic ratchets

We study phase synchronization for a ratchet system. We consider the deterministic dynamics of a particle in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues, which represent regions of synchronization in parameter space, and discuss their implications for transport in ratchets.

A random walker on a ratchet

We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet that are represented as two particles coupled nonlinearly through a bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics, where the ordering of the particles can alternate during the walking. The transitions between the two stable states on the bistable potential correspond to a walking with alternating particles. We distinguish between two main walking styles: alternating and no alternating, resembling the hand-over-hand and the inchworm walking in motor proteins, respectively. When the equilibrium distance between the two particles divided by the periodicity of the ratchet is an integer, we obtain a maximum for the current, indicating optimal transport.