Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Magnetic relaxation of a one-dimensional model for small particle systems with dipolar interactions: Monte Carlo simulation

Atribution as a function of the time are analyzed and this study leads to a deeper knowledge of the microscopic processes involved in the magnetic relaxation

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids

We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be almost independent of the molecular structures and viscosity of the liquids (at seventy-fold change) used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.

A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness. (C) 2009 Elsevier B.V. All rights reserved.

Dynamics of Bose-Einstein condensates with atomic pumping and dissipative processes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Relaxation and tunnelling of structural units within the LTO phase of La2CuO4

The anelastic relaxation (elastic energy loss and Young modulus) of nearly stoichiometric La2CuO4+delta with LTO structure was measured. Extraordinarily intense effects are present below room temperature in the elastic dynamic susceptibility, indicating relaxational dynamics of a relevant fraction of the lattice. The involved degrees of freedom are identified as rotations of the CuO6 octahedra. Two distinct processes are found at frequencies around 1 kKz: one is observed around 150 K and is characterized by a mean activation energy of 2800 K; the second one occurs below 30 K and is governed by atomic tunnelling. Two explanations are proposed for the faster process: i) formation of fluctuating LTT domains on a scale of few atomic cells; ii) the LTO phase is a dynamical Jahn-Teller phase with all the octahedra tunneling between two LTT-like tilts. In both cases there would be important implications regarding the mechanisms giving rise to charge nanophase separation and strong electron-phonon coupling.

Thermal annealing-induced electric dipole relaxation in natural alexandrite

Electrical properties of natural alexandrite (BeAl2O4:Cr3+) are investigated by the thermally stimulated depolarization current (TSDC) technique. Samples are submitted to consecutive annealing processes and TSDC is carried out after each annealing, yielding bands with different parameters. These bands are fitted by a continuous distribution of relaxation parameters: activation energy and pre-exponential factor of the Arrhenius equation. It has been observed that annealing influences the dipole relaxation behavior, since it promotes a modification of Fe3+ and C3+ impurity distributions on sites of distinct symmetry: Al-1 and Al-2. In order to have a reference for comparison, TSDC is also carried out on a synthetic alexandrite sample, where the only impurity present is Cr3+ ion.

A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Luminescence and non-radiative processes in lanthanide squarate hydrates

The luminescence properties of solid hydrated lanthanide squarates (Ln2(C4O4)3(H2O) x; x = 8 or 13;Ln3+ = Gd, La, Eu, Tb, Pr) are reported for temperatures down to 4.2K. The luminescence of the squarate group is observed for the Gd3+ and La3+ compounds at low temperatures (below 150K). The Pr3+ compound does not show any emission at all, not even at 4.2K. This is ascribed to the quenching of the Pr3+ emission by multiphonon relaxation and/or concentration quenching. The quantum efficiencies of the 5D0 emission of Eu3+ and of the 5D4 emission of Tb3+ in these squarate complexes are strikingly different. Whereas the Tb3+ emission shows a temperature independent quantum efficiency of 50% upon ligand excitation, the Eu3+ emission is strongly quenched, showing a temperature dependent quantum efficiency of 0.8% at 4.2K upon ligand excitation. This quenching is ascribed to the low energy position of the charge-transfer state of Eu3+ in these compounds.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

Dielektrische Relaxation und Retardation lokaler Prozesse in glasbildenden Materialien

Lokale sekundäre Prozesse in glasbildenden Materialien sind wegen ihrer Wechselwirkung mit der primären Relaxation von besonderem Interesse. Für D-Sorbitol wurde die beta-Relaxation mit drei verschiedenen dielektrischen Meßtechniken untersucht und die Ergebnisse miteinander verglichen. Im Gegensatz zu konventionellen Messungen der dielektrischen Retardation, detektiert eine echte dielektrische Relaxationsmessung den Zerfall des elektrischen Feldes unter der Bedingung einer konstanten dielektrischen Verschiebung. Eine weitere dielektrische Relaxationsmethode ist die Solvatationsdynamik. Sie detektiert die dielektrische Relaxation in der direkten Umgebung eines Farbstoffmoleküls. Die Übereinstimmung der lokal ermittelten und der makroskopisch gemittelten Ergebnisse für den Glaszustand weisen darauf hin, daß die Sekundärrelaxation in D-Sorbitol eine räumlich homogene Eigenschaft ist. Im Gegensatz zu beta-Prozessen anderer Materialien, zeigt nur der abgeschreckte Glaszustand von ortho-Terphenyl einen sekundären Prozeß. Es wurde beobachtet, daß die beta-Amplitude beim Ausheilen langsam abnimmt und im Gleichgewichtszustand der Flüssigkeit oberhalb der Glasübergangstemperatur völlig verschwindet. Viele glasbildende Materialien, wie z. B. Salol zeigen keinen dielektrischen beta-Prozeß. Im Gegensatz zu Messungen mit Standardkühlraten, zeigt eine stark abgeschreckte Salol-Probe eine symmetrische dielektrische Sekundärrelaxation. Diese neuartige Eigenschaft von Salol verschwindet irreversibel, wenn sich die Temperatur der Glasübergangstemperatur nähert.

Relaxation of species-specific neighborhood effects in Bornean rain forest under climatic perturbation

Evidence of negative conspecific density dependence (NDD) operating on seedling survival and sapling recruitment has accumulated recently. In contrast, evidence of NDD operating on growth of trees has been circumstantial at best. Whether or not local NDD at the level of individual trees leads to NDD at the level of the community is still an open question. Moreover, whether and how perturbations interfere with these processes have rarely been investigated. We applied neighborhood models to permanent plot data from a Bornean dipterocarp forest censused over two 10-11 year periods. Although the first period was only lightly perturbed, a moderately strong El Nino event causing severe drought occurred in the first half of the second period. Such events are an important component of the environmental stochasticity affecting the region. We show that local NDD on growth of small-to-medium-sized trees may indeed translate to NDD at the level of the community. This interpretation is based on increasingly negative effects of bigger conspecific neighbors on absolute growth rates of individual trees with increasing basal area across the 18 most abundant overstory species in the first period. However, this relationship was much weaker in the second period. We interpreted this relaxation of local and community-level NDD as a consequence of increased light levels at the forest floor due to temporary leaf and twig loss of large trees in response to the drought event. Mitigation of NDD under climatic perturbation acts to decrease species richness, especially in forest overstory and therefore has an important role in determining species relative abundances at the site.