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.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

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.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

A New open economy macroeconomic model with endogenous portfolio diversification and firms entry

This paper provides a new benchmark for the analysis of the international diversi…cation puzzle in a tractable new open economy macroeconomic model. Building on Cole and Obstfeld (1991) and Heathcote and Perri (2009), this model speci…es an equilibrium model of perfect risk sharing in incomplete markets, with endogenous portfolios and number of varieties. Equity home bias may not be a puzzle but a perfectly optimal allocation for hedging risk. In contrast to previous work, the model shows that: (i) optimal international portfolio diversi…cation is driven by home bias in capital goods, independently of home bias in consumption, and by the share of income accruing to labour. The model explains reasonably well the recent patterns of portfolio allocations in developed economies; and (ii) optimal portfolio shares are independent of market dynamics.

Labor markets and monetary policy: A new-Keynesian model with unemployement

We construct a utility-based model of fluctuations, with nominal rigidities andunemployment, and draw its implications for the unemployment-inflation trade-off and for the conduct of monetary policy.We proceed in two steps. We first leave nominal rigidities aside. We show that,under a standard utility specification, productivity shocks have no effect onunemployment in the constrained efficient allocation. We then focus on theimplications of alternative real wage setting mechanisms for fluctuations in un-employment. We show the role of labor market frictions and real wage rigiditiesin determining the effects of productivity shocks on unemployment.We then introduce nominal rigidities in the form of staggered price setting byfirms. We derive the relation between inflation and unemployment and discusshow it is influenced by the presence of labor market frictions and real wagerigidities. We show the nature of the tradeoff between inflation and unemployment stabilization, and its dependence on labor market characteristics. We draw the implications for optimal monetary policy.

Comment on "Kinetics of spinodal decomposition in the ising model with vacancy diffusion"

In a recent paper [Phys. Rev. B 50, 3477 (1994)], P. Fratzl and O. Penrose present the results of the Monte Carlo simulation of the spinodal decomposition problem (phase separation) using the vacancy dynamics mechanism. They observe that the t1/3 growth regime is reached faster than when using the standard Kawasaki dynamics. In this Comment we provide a simple explanation for the phenomenon based on the role of interface diffusion, which they claim is irrelevant for the observed behavior.

Random-field Potts model with dipolarlike interactions: Hysteresis avalanches and microstructure

A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the random-field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional microstructure formation, and on avalanche statistics.

Calibration and application of the MN2D dynamics model to the avalanches of Las Leñas (Argentina)

During the winters of 1999 and 2000 large avalanches occurred in the ski resort of Las Leñas (Los Andes, Mendoza, Argentina). On 8 September 1999 an avalanche of new, dry snow ran over a path with a 1000 m vertical drop. On 30 June and on 1 July 2000 five avalanches of similar vertical drop, which start with new snow, entrained very wet snow during their descent, and evolved into dense snow avalanches. To use the MN2D dynamics model correctly, calibration of model parameters is necessary. Also, no previous works with the use of dynamics models exist in South America. The events used to calibrate the model occurred during the winters of 1999 and 2000 and are a good sample of the kind of avalanches which can occur in this area of the Andes range. By considering the slope morphology and topography, the snow and meteorological conditions and the results of the model simulations, it was estimated that these avalanches were not extreme events with a return period greater than one hundred years. This implies that, in natural conditions, bigger, extreme avalanches could happen. In this work, the MN2D dynamics model is calibrated with two different avalanches of the same magnitude: dry and wet. The importance of the topographic data in the simulation is evaluated. It is concluded that MN2D dynamics model can be used to simulate dry extreme avalanches in Argentinean Andes but not to simulate extreme wet avalanches, which are much more sensitive to the topography.

Unemployment and wage formation in a growth model with public capital

We study the relation between public capital, employment and growth under different assumptions concerning wage formation. We show that public capital increases economic growth, and that, if there is wage inertia, employment positively depends on both economic growth and public capital.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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

On the existence of hysteresis in the Kuramoto model with bimodal frequency distributions

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Candidate quality in a Downsian Model with a continuous policy space

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a non-policy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution over the unit interval. In our equilibrium the advantaged candidate chooses the expected median voter with probability one and the disadvantaged candidate uses a mixed strategy that is symmetric around it. We show that this equilibrium exists if the number of voters is large enough relative to the size of the advantage.