Juan Camacho

Understanding diluted dispersions of superparamagnetic particles under strong magnetic fields: a review of concepts, theory and simulations

In recent years, there has been a great progress in the development of superparamagnetic particles targeted to a wide range of applications, including fields as diverse as biotechnology or waste removal. However, the physics behind their behaviour under usual conditions (diluted dispersions and high magnetic fields) has many, fundamental, open questions. In this review, we revisit the advances in the basic physical concepts and predictive analytical and simulation tools. We focus on recent developments in the understanding and prediction of phenomena induced by magnetic fields both in uniform fields (for example, chain formation) and in magnetic gradients (cooperative magnetophoresis).

Aggregation of superparamagnetic colloids in magnetic fields: the quest for the equilibrium state

Previous experimental and simulation studies of superparamagnetic colloids in a strong external field have systematically shown a nonequilibrium aggregation process in which chains of particles steadily grow in the direction of the applied external field with the average length increasing as a power law over time. Here we show, by employing Langevin dynamics simulations, the existence of a different behavior under the effects of an external magnetic field: after a transient period of chain formation, the system attains an equilibrium state. Furthermore, a thermodynamic self-assembly theory supports the simulation results and it also predicts that the average chain length in the equilibrium state depends only on a dimensionless parameter combining the volume fraction of colloids ϕ0 and the magnetic coupling parameter Γ. The conditions under which this new behavior can be observed are discussed here.

Evolution of cooperation mediated by limiting resources: connecting resource based models and evolutionary game theory.

Recent studies have shown that constraints on available resources may play an important role in the evolution of cooperation, especially when individuals do not posses the capacity to recognize other individuals, memory or other developed abilities, as it is the case of most unicellular organisms, algae or even plants. We analyze the evolution of cooperation in the case of a limiting resource, which is necessary for reproduction and survival. We show that, if the strategies determine a prisoners dilemma, the outcome of the interactions may be modified by the limitation of resources allowing cooperators to invade the entire population. Analytic expressions for the region of cooperation are provided. Furthermore we derive expressions for the connection between fitness, as understood in evolutionary game theory, and resource exchanges, which may be of help to link evolutionary game theoretical results with resource based models.

Simulation of magnetophoretic separation processes in dispersions of superparamagnetic nanoparticles in the noncooperative regime

Magnetic separation has gained much attention due to its implications in different fields, becoming feasible as an alternative to existent technologies at the industrial and lab scale. Substantial efforts are focused to improve the magnetic particles used in these applications. Here we show how a relatively simple and low-cost simulation strategy (tracer simulations) can be employed to predict the effect of various key factors in magnetic separation processes, namely, particle properties and magnetic separator designs. For concreteness, we consider here specific problems in magnetic separation. The first one is the effect of different profiles of the magnetic field in the separation of magnetic nanoparticles, and the second one is the magnetophoresis of colloidal particles in a dispersion of magnetic nanoparticles.

Noncharacteristic half-lives in radioactive decay.

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that we explore a method for fitting power laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation.

On the thermodynamics of dilute dumbbell solutions under shear

The relation predicted by extended irreversible thermodynamics between the nonequilibrium entropy and the frequency‐dependent viscosity is confirmed from kinetic theory for dilute dumbbell solutions under shear. New relations between nonequilibrium entropy and the coefficients of the constitutive equations are discussed.

Coexistence of cooperators and defectors in well mixed populations mediated by limiting resources.

Traditionally, resource limitation in evolutionary game theory is assumed just to impose a constant population size. Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoners dilemma, and to allow for the stable coexistence between unconditional cooperators and defectors in well-mixed populations. This is a consequence of a self-organizing process that turns the interaction payoff matrix into evolutionary neutral, and represents a resource-based control mechanism preventing the spread of defectors. To our knowledge, this is the first example of coexistence in well-mixed populations with a game structure different from a snowdrift game.

On-the-fly coarse-graining methodology for the simulation of chain formation of superparamagnetic colloids in strong magnetic fields.

The aim of this work is the description of the chain formation phenomena observed in colloidal suspensions of superparamagnetic nanoparticles under high magnetic fields. We introduce a methodology based on an on-the-fly coarse-grain (CG) model. Within this approach, the coarse-grain objects of the simulation and their dynamic behavior are not fixed a priori at the beginning of the simulation but rather redefined on the fly. The motion of the CG objects (single particles or aggregates) is described by an anisotropic diffusion model and the magnetic dipole-dipole interaction is replaced by an effective short-range interaction between CG objects. The methodology correctly reproduces previous results from detailed Langevin dynamics simulations of dispersions of superparamagnetic colloids under strong fields while requiring an amount of CPU time orders of magnitude smaller. This substantial improvement in the computational requirements allows the simulation of problems in which the relevant phenomena extend to time scales inaccessible with previous simulation techniques. A relevant example is the waiting time dependence of the relaxation time T(2) of water protons observed in magnetic resonance experiments containing dispersions of superparamagnetic colloids, which is correctly predicted by our simulations. Future applications may include other popular real-world applications of superparamagnetic colloids such as the magnetophoretic separation processes.

Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations.

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.

Magnetophoresis of colloidal particles in a dispersion of superparamagnetic nanoparticles: theory and experiments

Recent works have demonstrated the exciting possibility of inducing a tunable magnetic behavior in non-magnetic colloids by immersing them in a dispersion of superparamagnetic nanoparticles (NPs). Here we show experimentally that non-magnetic latex particles in a dispersion of superparamagnetic NPs experience a nontrivial, two-step “go and come-back” motion when brought under a uniform magnetic gradient. Our theoretical analysis indicates that the observed motion is due to the combined effect of the behavior of latex particles as magnetic holes and the adsorption of NPs at the latex surface. In agreement with theory, the NPs adsorption has been confirmed in our experiments by three independent experimental techniques (EDS, SEM and electrophoresis).