Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity

It is found that crystals of molecular nanomagnets exhibit enhanced magnetic relaxation when placed inside a resonant cavity. A strong dependence of the magnetization curve on the geometry of the cavity has been observed, providing indirect evidence of the coherent microwave radiation by the crystals. A similar dependence has been found for a crystal placed between the Fabry-Perot superconducting mirrors.

Percolation and cluster Monte Carlo dynamics for spin models

A general scheme for devising efficient cluster dynamics proposed in a previous paper [Phys. Rev. Lett. 72, 1541 (1994)] is extensively discussed. In particular, the strong connection among equilibrium properties of clusters and dynamic properties as the correlation time for magnetization is emphasized. The general scheme is applied to a number of frustrated spin models and the results discussed.

Relaxation dynamics in suspensions of ferromagnetic particles

We have studied the relaxation dynamics of a dilute assembly of ferromagnetic particles in suspension. A formalism based on the Smoluchowski equation, describing the evolution of the probability density for the directions of the magnetic moment and of the axis of easy magnetization of the particles, has been developed. We compute the rotational viscosity from a Green-Kubo formula and give an expression for the relaxation time of the particles which comes from the dynamic equations of the correlation functions. Concerning the relaxation time for the particles, our results agree quite well with experiments performed on different samples of ferromagnetic particles for which the magnetic energy, associated with the interaction between the magnetic moments and the external field, or the energy of anisotropy plays a dominant role.

Firm Size and Short-Term Dynamics in Aggregate Entry and Exit

Much of the research on industry dynamics focuses on the interdependence between the sectorial rates of entry and exit. This paper argues that the size of firms and the reaction-adjustment period are important conditions missed in this literature. I illustrate the effects of this omission using data from the Spanish manufacturing industries between 1994 and 2001. Estimates from systems of equations models provide evidence of a conical revolving door phenomenon and of partial adjustments in the replacement-displacement of large firms. KEYWORDS: aggregation, industry dynamics, panel data, symmetry, simultaneity. JEL CLASSIFICATION: C33, C52, L60, L11

Chaotic dynamics in credit constrained emerging economies

This paper analyzes the role of financial development as a source of endogenous instability in small open economies. By assuming that firms face credit constraints, our model displays a complex dynamic behavior for intermediate values of the parameter representing the level of financial development of the economy. The basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies. Our instability concept means that small shocks have a persistent effect on the long run behavior of the model and also that economies can exhibit cycles with a very high period or even chaotic dynamic patterns.

Long-run Inflation-Unemployment Dynamics: The Spanish Phillips Curve and Economic Policy

This paper takes a new look at the long-run dynamics of inflation and unemployment in response to permanent changes in the growth rate of the money supply. We examine the Phillips curve from the perspective of what we call "frictional growth", i.e. the interaction between money growth and nominal frictions. After presenting theoretical models of this phenomenon, we construct an empirical model of the Spanish economy and, in this context, we evaluate the long-run inflation-unemployment trade for Spain and examine how recent policy changes have afected it.

Dynamics of the third order Lyness' difference equation

"Vegeu el resum a l'inici del document del fitxer adjunt"

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Modelling of bird distribution under complex mediterranean landscape dynamics: open habitat birds and fire (MEDFIRE)

Report for the scientific sojourn at the Simon Fraser University, Canada, from July to September 2007. General context: landscape change during the last years is having significant impacts on biodiversity in many Mediterranean areas. Land abandonment, urbanisation and specially fire are profoundly transforming large areas in the Western Mediterranean basin and we know little on how these changes influence species distribution and in particular how these species will respond to further change in a context of global change including climate. General objectives: integrate landscape and population dynamics models in a platform allowing capturing species distribution responses to landscape changes and assessing impact on species distribution of different scenarios of further change. Specific objective 1: develop a landscape dynamic model capturing fire and forest succession dynamics in Catalonia and linked to a stochastic landscape occupancy (SLOM) (or spatially explicit population, SEPM) model for the Ortolan bunting, a species strongly linked to fire related habitat in the region. Predictions from the occupancy or spatially explicit population Ortolan bunting model (SEPM) should be evaluated using data from the DINDIS database. This database tracks bird colonisation of recently burnt big areas (&50 ha). Through a number of different SEPM scenarios with different values for a number of parameter, we should be able to assess different hypothesis in factors driving bird colonisation in new burnt patches. These factors to be mainly, landscape context (i.e. difficulty to reach the patch, and potential presence of coloniser sources), dispersal constraints, type of regenerating vegetation after fire, and species characteristics (niche breadth, etc).

Dynamics in Thompson's group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

The Black Box of Business Dynamics

Research in business dynamics has been advancing rapidly in the last years but the translation of the new knowledge to industrial policy design is slow. One striking aspect in the policy area is that although research and analysis do not identify the existence of an specific optimal rate of business creation and business exit, governments everywhere have adopted business start-up support programs with the implicit principle that the more the better. The purpose of this article is to contribute to understand the implications of the available research for policy design. Economic analysis has identified firm heterogeneity as being the most salient characteristic of industrial dynamics, and so a better knowledge of the different types of entrepreneur, their behavior and their specific contribution to innovation and growth would enable us to see into the ‘black box’ of business dynamics and improve the design of appropriate public policies. The empirical analysis performed here shows that not all new business have the same impact on relevant economic variables, and that self-employment is of quite a different economic nature to that of firms with employees. It is argued that public programs should not promote indiscriminate entry but rather give priority to able entrants with survival capacities. Survival of entrants is positively related to their size at birth. Innovation and investment improve the likelihood of survival of new manufacturing start-ups. Investment in R&D increases the risk of failure in new firms, although it improves the competitiveness of incumbents.