Driven fragmentation of granular gases

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the longvelocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f (c)~exp (−cⁿ), with n ≈1.2, regarding less the fragmentation mechanisms

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

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.

Estudi del procés d'adsorció en carbó actiu granular per eliminar colorants tèxtils

L’objectiu principal d’aquest projecte és estudiar la capacitat d’adsorció del colorant comercial Gris Lanaset G en carbó actiu granular (GAC); per assolir aquest objectiu es compara l’eficàcia d’adsorció d’aquest carbó respecte altres adsorbents i l’eficàcia d’eliminació d’un altre colorant més simple sobre aquest carbó.

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.

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.