Precursor phenomena in frustrated systems

To understand the origin of the dynamical transition, between high-temperature exponential relaxation and low-temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in the presence of disorder) or fully frustrated Ising (in the absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.

Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.

Extreme times in financial markets.

We apply the theory of continuous time random walks (CTRWs) to study some aspects involving extreme events in financial time series. We focus our attention on the mean exit time (MET). We derive a general equation for this average and compare it with empirical results coming from high-frequency data of the U.S. dollar and Deutsche mark futures market. The empirical MET follows a quadratic law in the return length interval which is consistent with the CTRW formalism.

Self-organized evolution in a socio-economic environment

We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state.

Difussion in a titled periodic potential: Enhancement, universality, and scaling

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In comparison with the bare (potential-free) thermal diffusion, the effective diffusion coefficient in a critically tilted periodic potential may be, in principle, arbitrarily enhanced. For a realistic experimental setup, an enhancement by 14 orders of magnitude is predicted so that thermal diffusion should be observable on a macroscopic scale at room temperature.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

BEYOND THE “LEAST LIMITING WATER RANGE”: RETHINKING SOIL PHYSICS RESEARCH IN BRAZIL

As opposed to objective definitions in soil physics, the subjective term “soil physical quality” is increasingly found in publications in the soil physics area. A supposed indicator of soil physical quality that has been the focus of attention, especially in the Brazilian literature, is the Least Limiting Water Range (RLL), translated in Portuguese as "Intervalo Hídrico Ótimo" or IHO. In this paper the four limiting water contents that define RLLare discussed in the light of objectively determinable soil physical properties, pointing to inconsistencies in the RLLdefinition and calculation. It also discusses the interpretation of RLL as an indicator of crop productivity or soil physical quality, showing its inability to consider common phenological and pedological boundary conditions. It is shown that so-called “critical densities” found by the RLL through a commonly applied calculation method are questionable. Considering the availability of robust models for agronomy, ecology, hydrology, meteorology and other related areas, the attractiveness of RLL as an indicator to Brazilian soil physicists is not related to its (never proven) effectiveness, but rather to the simplicity with which it is dealt. Determining the respective limiting contents in a simplified manner, relegating the study or concern on the actual functioning of the system to a lower priority, goes against scientific construction and systemic understanding. This study suggests a realignment of the research in soil physics in Brazil with scientific precepts, towards mechanistic soil physics, to replace the currently predominant search for empirical correlations below the state of the art of soil physics.

Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

Experimental Method to Determine Some Physical Properties in Physics Classes

ABSTRACT Particle density, gravimetric and volumetric water contents and porosity are important basic concepts to characterize porous systems such as soils. This paper presents a proposal of an experimental method to measure these physical properties, applicable in experimental physics classes, in porous media samples consisting of spheres with the same diameter (monodisperse medium) and with different diameters (polydisperse medium). Soil samples are not used given the difficulty of working with this porous medium in laboratories dedicated to teaching basic experimental physics. The paper describes the method to be followed and results of two case studies, one in monodisperse medium and the other in polydisperse medium. The particle density results were very close to theoretical values for lead spheres, whose relative deviation (RD) was -2.9 % and +0.1 % RD for the iron spheres. The RD of porosity was also low: -3.6 % for lead spheres and -1.2 % for iron spheres, in the comparison of procedures – using particle and porous medium densities and saturated volumetric water content – and monodisperse and polydisperse media.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi¿Pasta¿Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters

Spontaneous aggregation and global polar ordering in squirmer suspensions

We have developed numerical simulations of three dimensional suspensions of active particles to characterize the capabilities of the hydrodynamic stresses induced by active swimmers to promote global order and emergent structures in active suspensions. We have considered squirmer suspensions embedded in a fluid modeled under a Lattice Boltzmann scheme. We have found that active stresses play a central role to decorrelate the collective motion of squirmers and that contractile squirmers develop significant aggregates.

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.