Renormalization-group theory for finite-size scaling in extreme statistics.

We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.

Width of reaction zones in A+B-->C type reaction-diffusion processes: effects of an electric current.

We investigate the effects of an electric current on the width of a stationary reaction zone in an irreversible A(-)+B(+)-->C reaction-diffusion process. The ion dynamics of electrolytes A identical with (A(+),A(-)) and B identical with (B(+),B(-)) is described by reaction-diffusion equations obeying local electroneutrality and the stationary state is obtained by employing reservoirs of fixed electrolyte concentrations at the opposite ends of a finite domain. We find that the width of the reaction zone decreases when the current drives the reacting ions toward the reaction zone while it increases in the opposite case. The linear response of the width to the current is estimated by developing a phenomenological theory based on conservation laws and on electroneutrality. The theory is found to reproduce numerical solutions to a good accuracy.

Designed patterns: flexible control of precipitation through electric currents.

Understanding and controlling precipitation patterns formed in reaction-diffusion processes is of fundamental importance with high potential for technical applications. Here we present a theory showing that precipitation resulting from reactions among charged agents can be controlled by an appropriately designed, time-dependent electric current. Examples of current dynamics yielding periodic bands of prescribed wavelength, as well as more complicated structures are given. The pattern control is demonstrated experimentally using the reaction-diffusion process 2AgNO3 + K2Cr2O7-->under Ag2Cr2O7 + 2KNO3.

Guiding fields for phase separation: controlling Liesegang patterns.

Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicrometer length scales. Thus they have significant potential for technological applications provided adequate methods of control can be devised. Here we describe a simple, physically realizable pattern control based on the notion of driven precipitation, meaning that the phase separation is governed by a guiding field such as, for example, a temperature or pH field. The phase separation is modeled through a nonautonomous Cahn-Hilliard equation whose spinodal is determined by the evolving guiding field. Control over the dynamics of the spinodal gives control over the velocity of the instability front that separates the stable and unstable regions of the system. Since the wavelength of the pattern is largely determined by this velocity, the distance between successive precipitation bands becomes controllable. We demonstrate the above ideas by numerical studies of a one-dimensional system with a diffusive guiding field. We find that the results can be accurately described by employing a linear stability analysis (pulled-front theory) for determining the velocity-local-wavelength relationship. From the perspective of the Liesegang theory, our results indicate that the so-called revert patterns may be naturally generated by diffusive guiding fields.

Formation of Liesegang patterns in the presence of an electric field.

The effects of an external electric field on the formation of Liesegang patterns are investigated. The patterns are assumed to emerge from a phase separation process in the wake of a diffusive reaction front. The dynamics is described by a Cahn-Hilliard equation with a moving source term representing the reaction zone, and the electric field enters through its effects on the properties of the reaction zone. We employ our previous results [I. Bena, F. Coppex, M. Droz, and Z. Rácz, J. Chem. Phys. 122, 024512 (2005)] on how the electric field changes both the motion of the front, as well as the amount of reaction product left behind the front, and our main conclusion is that the number of precipitation bands becomes finite in a finite electric field. The reason for the finiteness in case when the electric field drives the reagents towards the reaction zone is that the width of consecutive bands increases so that, beyond a distance l(+), the precipitation is continuous (plug is formed). In case of an electric field of opposite polarity, the bands emerge in a finite interval l(-), since the reaction product decreases with time and the conditions for phase separation cease to exist. We give estimates of l(+/-) in terms of measurable quantities and thus present an experimentally verifiable prediction of the "Cahn-Hilliard equation with a moving source" description of Liesegang phenomena.

Front motion in an A+B-->C type reaction-diffusion process: effects of an electric field.

We study the effects of an external electric field on both the motion of the reaction zone and the spatial distribution of the reaction product, C, in an irreversible A- + B+ -->C reaction-diffusion process. The electrolytes A identical with (A+,A-) and B identical with (B+,B-) are initially separated in space and the ion-dynamics is described by reaction-diffusion equations obeying local electroneutrality. Without an electric field, the reaction zone moves diffusively leaving behind a constant concentration of C's. In the presence of an electric field which drives the reagents towards the reaction zone, we find that the reaction zone still moves diffusively but with a diffusion coefficient which slightly decreases with increasing field. The important electric field effect is that the concentration of C's is no longer constant but increases linearly in the direction of the motion of the front. The case of an electric field of reversed polarity is also discussed and it is found that the motion of the front has a diffusive as well as a drift component. The concentration of C's decreases in the direction of the motion of the front, up to the complete extinction of the reaction. Possible application of the above results to the understanding of the formation of Liesegang patterns in an electric field is briefly outlined.

Extinction dynamics of Lotka-Volterra ecosystems on evolving networks.

We study a model of a multispecies ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law distribution of intervals between extinctions, but only for ecosystems with sufficient variability of species and with networks of connectivity above certain threshold that is very close to the percolation threshold of the network. The effect of slow environmental changes on extinction dynamics, degree distribution of the network of interspecies interactions, and some emergent properties of our model are also examined.

Yang-Lee zeros for an urn model for the separation of sand.

We apply the Yang-Lee theory of phase transitions to an urn model for the separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity z. Numerical calculations show that in the thermodynamic limit the zeros of the effective partition function are located on the unit circle in the complex z plane. In the complex plane of the actual control parameter, certain roots converge to the transition point of the model. Thus, the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.

Roughness distributions for 1/f alpha signals.

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f(alpha) noise signals is studied. Our starting point is the generalization of the model of Gaussian, time periodic, 1/f noise, discussed in our recent Letter [Phys. Rev. Lett. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions (alpha < or = 1/2, 1/2 < alpha < or = 1, and 1< alpha), distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also nonperiodic, thus experimentally more relevant, signals on relatively short intervals embedded in the full period. We find that for alpha < or = 1/2 the scaled PDFs in both the periodic and the nonperiodic cases are Gaussian, but for alpha > 1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha = 2 and alpha-->infinity, in the latter limit the scaling function of the PDF being finite for periodic signals, but developing a singularity for the aperiodic ones. Finally, an overview is given for the scaling of cumulants of the roughness and the various scaling regions in arbitrary dimensions. We suggest that our theoretical and numerical results open a different perspective on the data analysis of 1/f(alpha) processes.

1/f noise and extreme value statistics.

We study finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions, the Fisher-Tippett-Gumbel (FTG) distribution, emerges as the scaling function when boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the FTG distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.

Criticality of natural absorbing states.

We study a recently introduced ladder model that undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behavior of the model is the same as that of the branching-annihilating random walk with N>/=2 species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power-law singularities that signal the approach of the critical point. These results are also explained using random-walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum-finding procedure, it has the best efficiency very close to the critical point.

Critical behavior of a lattice prey-predator model.

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolationlike transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward an infinite number of absorbing states, and the corresponding steady-state exponents are mean-field-like. The critical behavior of the special point T (bicritical point), where the two transition lines meet, belongs to a different universality class. A particular strategy for preparing the initial states used for the dynamical Monte Carlo method is devised to correctly describe the physics of the system near the second transition line. Relationships with a forest fire model with immunization are also discussed.

Coexistence in a predator-prey system.

We propose a lattice model of two populations, predators and prey. The model is solved via Monte Carlo simulations. Each species moves randomly on the lattice and can live only a certain time without eating. The lattice cells are either grass (eaten by prey) or tree (giving cover for prey). Each animal has a reserve of food that is increased by eating (prey or grass) and decreased after each Monte Carlo step. To breed, a pair of animals must be adjacent and have a certain minimum of food supply. The number of offspring produced depends on the number of available empty sites. We show that such a predator-prey system may finally reach one of the following three steady states: coexisting, with predators and prey; pure prey; or an empty one, in which both populations become extinct. We demonstrate that the probability of arriving at one of the above states depends on the initial densities of the prey and predator populations, the amount of cover, and the way it is spatially distributed.

Phase transitions and oscillations in a lattice prey-predator model.

A coarse grained description of a two-dimensional prey-predator system is given in terms of a simple three-state lattice model containing two control parameters: the spreading rates of prey and predator. The properties of the model are investigated by dynamical mean-field approximations and extensive numerical simulations. It is shown that the stationary state phase diagram is divided into two phases: a pure prey phase and a coexistence phase of prey and predator in which temporal and spatial oscillations can be present. Besides the usual directed percolationlike transition, the system exhibits an unexpected, different type of transition to the prey absorbing phase. The passage from the oscillatory domain to the nonoscillatory domain of the coexistence phase is described as a crossover phenomena, which persists even in the infinite size limit. The importance of finite size effects are discussed, and scaling relations between different quantities are established. Finally, physical arguments, based on the spatial structure of the model, are given to explain the underlying mechanism leading to local and global oscillations.

Spatial evolutionary prisoner's dilemma game with three strategies and external constraints

The emergency of mutual cooperation is studied in a spatially extended evolutionary prisoner's dilemma game in which the players are located on the sites of cubic lattices for dimensions d=1, 2, and 3. Each player can choose one of the three following strategies: cooperation (C), defection (D) or "tit for tat" (T). During the evolutionary process the randomly chosen players adopt one of their neighboring strategies if the chosen neighbor has a higher payoff. Moreover, an external constraint imposes that the players always cooperate with probability p. The stationary state phase diagram is computed by both using generalized mean-field approximations and Monte Carlo simulations. Nonequilibrium second-order phase transitions associated with the extinction of one of the possible strategies are found and the corresponding critical exponents belong to the directed percolation universality class. It is shown that externally forcing the collaboration does not always produce the desired result.

Acute adrenal crisis in a patient treated with intraarticular steroid therapy.

Intraarticular therapy with corticosteroids can cause systemic effects such as decreased concentration of plasma cortisol, but whether this might place a patient at risk from stress induced acute adrenal failure is not known. We describe a patient who presented with lethargy, hyponatremia, and then with acute abdomen. The diagnosis of acute adrenal crisis was related to suppression of the hypothalamic-pituitary-adrenal axis by intraarticular use of corticosteroid. This was confirmed by a low basal cortisol concentration and by a short Synacthen test that elicited an increase in plasma cortisol concentration from 36 to 481 nmol/l. Within 24 h of receiving 37.5 mg of hydrocortisone, the patient rapidly improved.

[Co-trimoxazole administration: a rare cause of hypoglycemia in elderly persons]. / Prise de co-trimoxazole: une cause rare d'hypoglycémie chez la personne âgée.

We report a case of severe hypoglycaemia following co-trimoxazole therapy. An 88-year-old woman was admitted with urinary tract infection and treated with co-trimoxazole (960 mg bid). Seven days after initiation of the treatment she became comatose. Blood sugar was 1.3 mmol/l and C-peptide at the upper limit of normal range. Glucose infusion restored normal consciousness and no hypoglycaemia recurred after interruption of co-trimoxazole therapy. Advanced aged was the only risk factor identified. Other risk factors described in previous case reports are renal failure, poor nutritional state and high doses of co-trimoxazole.