R. Escobedo

Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations

We have produced computational simulations of multi-agent systems in which wolf agents chase prey agents. We show that two simple decentralized rules controlling the movement of each wolf are enough to reproduce the main features of the wolf-pack hunting behavior: tracking the prey, carrying out the pursuit, and encircling the prey until it stops moving. The rules are (1) move towards the prey until a minimum safe distance to the prey is reached, and (2) when close enough to the prey, move away from the other wolves that are close to the safe distance to the prey. The hunting agents are autonomous, interchangeable and indistinguishable; the only information each agent needs is the position of the other agents. Our results suggest that wolf-pack hunting is an emergent collective behavior which does not necessarily rely on the presence of effective communication between the individuals participating in the hunt, and that no hierarchy is needed in the group to achieve the task properly.

Generalized drift-diffusion model for miniband superlattices

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a Bhatnagar-Gross-Krook collision term. We use a consistent Chapman-Enskog method to analyze the hyperbolic limit, at which collision and electric-field terms dominate the other terms in the Boltzmann equation. The reduced equation is of the drift-diffusion type, but it includes additional terms, and diffusion and drift do not obey the Einstein relation except in the limit of high temperatures.

Group size, individual role differentiation and effectiveness of cooperation in a homogeneous group of hunters

The emergence of cooperation in wolf-pack hunting is studied using a simple, homogeneous, particle-based computational model. Wolves and prey are modelled as particles that interact through attractive and repulsive forces. Realistic patterns of wolf aggregation readily emerge in numerical simulations, even though the model includes no explicit wolf–wolf attractive forces, showing that the form of cooperation needed for wolf-pack hunting can take place even among strangers. Simulations are used to obtain the stationary states and equilibria of the wolves and prey system and to characterize their stability. Different geometric configurations for different pack sizes arise. In small packs, the stable configuration is a regular polygon centred on the prey, while in large packs, individual behavioural differentiation occurs and induces the emergence of complex behavioural patterns between privileged positions. Stable configurations of large wolf-packs include travelling and rotating formations, periodic oscillatory behaviours and chaotic group behaviours. These findings suggest a possible mechanism by which larger pack sizes can trigger collective behaviours that lead to the reduction and loss of group hunting effectiveness, thus explaining the observed tendency of hunting success to peak at small pack sizes. They also explain how seemingly complex collective behaviours can emerge from simple rules, among agents that need not have significant cognitive skills or social organization.

MOVING BANDS AND MOVING BOUNDARIES WITH DECREASING SPEED IN POLYMER CRYSTALLIZATION

A deterministic model of polymer crystallization, derived from a previous stochastic one, is considered. The model describes the crystallization process of a rectangular sample of a material cooled at one of its sides. It is a reaction–diffusion system, composed of a PDE for the temperature and an ODE for the phase change of a polymer melt from liquid to crystal. The two equations are strongly coupled since the evolution of temperature depends on a source term, due to the latent heat developed during the phase change, the nucleation and growth rates are functions of the local (in time and space) temperature. The main difference with respect to the previous model is the introduction of a critical temperature of freezing in these functions. The paper does not contain detailed analytical aspects, that are left to subsequent investigations. A qualitative analysis of the proposed model is carried out, based on numerical simulations. An interesting feature shown by the simulations is that the solution exhibits an advancing moving band of crystallization in the mass distribution, as well as a moving boundary in the temperature field, both advancing with the same decreasing velocity. For some values of the parameters, which are typical of the physical problem, the advance takes place by jumps due to regular stops of the most advanced point of crystallization. The duration of these halts increases as the applied temperature decreases. This may indicate that the crystallization time is not a monotone function of the applied temperature. A simplified mathematical model is eventually proposed which reproduces the same patterns.

WIGNER–POISSON AND NONLOCAL DRIFT-DIFFUSION MODEL EQUATIONS FOR SEMICONDUCTOR SUPERLATTICES

A Wigner–Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are assumed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron–electron interaction is treated in the Hartree approximation. There are elastic collisions with impurities and inelastic collisions with phonons, imperfections, etc. The latter are described by a modified BGK (Bhatnagar–Gross–Krook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal drift-diffusion equations are derived systematically from the kinetic Wigner–Poisson–BGK system by means of the Chapman–Enskog method. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical solutions of the latter equations show self-sustained oscillations of the current through a voltage biased superlattice, in agreement with known experiments.

Multi-quantum-well spin oscillator

A dc voltage biased II-VI semiconductor multi-quantum-well structure attached to normal contacts exhibits self-sustained spin polarized current oscillations if one or more of its wells are doped with Mn. Without magnetic impurities, the only configurations appearing in these structures are stationary. Analysis and numerical solution of a nonlinear spin transport model yield the minimal number of wells (four) and the ranges of doping density and spin splitting needed to find oscillations.

Miniband transport and oscillations in semiconductor superlattices

We present and analyse solutions of a recent derivation of a drift-diffusion model of miniband transport in strongly coupled superlattices. The model is obtained from a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term by means of a consistent Chapman-Enskog expansion. The reduced drift-diffusion equation is solved numerically and travelling field domains and current oscillations are obtained. A broad range of frequencies can be achieved, depending on the model parameters, in good agreement with available experiments on GaAs/AlAs superlattices.

Self-sustained spin-polarized current oscillations in multiquantum well structures

Nonlinear transport through diluted magnetic semiconductor nanostructures is investigated. We have considered a II-VI multiquantum well nanostructure whose wells are selectively doped with Mn. The response to a dc voltage bias may be either a stationary or an oscillatory current. We have studied the transition from stationary to time-dependent current as a function of the doping density and the number of quantum wells. Analysis and numerical solution of a nonlinear spin transport model shows that the current in a structure without magnetic impurities is stationary, whereas current oscillations may appear if at least one well contains magnetic impurities. For long structures having two wells with magnetic impurities, a detailed analysis of nucleation of charge dipole domains shows that self-sustained current oscillations are caused by repeated triggering of dipole domains at the magnetic wells and motion towards the collector. Depending on the location of the magnetic wells and the voltage, dipole domains may be triggered at both wells or at only one. In the latter case, the well closer to the collector may inhibit domain motion between the first and the second well inside the structure. Our study could allow design of oscillatory spin-polarized current injectors.

Axisymmetric pulse recycling and motion in bulk semiconductors

The Kroemer model for the Gunn effect in a circular geometry (Corbino disks) has been numerically solved. The results have been interpreted by means of asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric pulses of the electric field are periodically shed by an inner circular cathode. These pulses decay as they move towards the outer anode, which they may not reach. As a pulse advances, the external current increases continuously until a new pulse is generated. Then the current abruptly decreases, in agreement with existing experimental results. Depending on the bias, more complex patterns with multiple pulse shedding are possible.

Optimal cooling strategies in polymer crystallization

An optimal control problem for cooling strategies in polymer crystallization processes described by a deterministic model is solved in the framework of a free boundary problem. The strategy of cooling both sides of a one dimensional sample is introduced for the first time in this model, and is shown to be well approximated by the sum of the solutions of two one-phase Stefan problems, even for arbitrary applied temperature profiles. This result is then used to show that cooling both sides is always more effective in polymer production than injecting the same amount of cold through only one side. The optimal cooling strategy, focused in avoiding low temperatures and in shortening cooling times, is derived, and consists in applying the same constant temperature at both sides. Explicit expressions of the optimal controls in terms of the parameters of the material are also obtained.