Invaded cluster dynamics for frustrated models

The invaded cluster (IC) dynamics introduced by Machta et al. [Phys. Rev. Lett. 75, 2792 (1995)] is extended to the fully frustrated Ising model on a square lattice. The properties of the dynamics that exhibits numerical evidence of self-organized criticality are studied. The fluctuations in the IC dynamics are shown to be intrinsic of the algorithm and the fluctuation-dissipation theorem is no longer valid. The relaxation time is found to be very short and does not present a critical size dependence.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

A Thermokinetic approach to radiative heat transfer at the nanoscale

Radiative heat exchange at the nanoscale presents a challenge for several areas due to its scope and nature. Here, we provide a thermokinetic description of microscale radiative energy transfer including phonon-photon coupling manifested through a non-Debye relaxation behavior. We show that a lognormal-like distribution of modes of relaxation accounts for this non-Debye relaxation behavior leading to the thermal conductance. We also discuss the validity of the fluctuation-dissipation theorem. The general expression for the thermal conductance we obtain fits existing experimental results with remarkable accuracy. Accordingly, our approach offers an overall explanation of radiative energy transfer through micrometric gaps regardless of geometrical configurations and distances.

Theoretical Analysis and Simulations of Vertically Vibrated Granular Materials

The dynamical properties ofshaken granular materials are important in many industrial applications where the shaking is used to mix, segregate and transport them. In this work asystematic, large scale simulation study has been performed to investigate the rheology of dense granular media, in the presence of gas, in a three dimensional vertical cylinder filled with glass balls. The base wall of the cylinder is subjected to sinusoidal oscillation in the vertical direction. The viscoelastic behavior of glass balls during a collision, have been studied experimentally using a modified Newton's Cradle device. By analyzing the results of the measurements, using numerical model based on finite element method, the viscous damping coefficient was determinedfor the glass balls. To obtain detailed information about the interparticle interactions in a shaker, a simplified model for collision between particles of a granular material was proposed. In order to simulate the flow of surrounding gas, a formulation of the equations for fluid flow in a porous medium including particle forces was proposed. These equations are solved with Large Eddy Simulation (LES) technique using a subgrid-model originally proposed for compressible turbulent flows. For a pentagonal prism-shaped container under vertical vibrations, the results show that oscillon type structures were formed. Oscillons are highly localized particle-like excitations of the granular layer. This self-sustaining state was named by analogy with its closest large-scale analogy, the soliton, which was first documented by J.S. Russell in 1834. The results which has been reportedbyBordbar and Zamankhan(2005b)also show that slightly revised fluctuation-dissipation theorem might apply to shaken sand, which appears to be asystem far from equilibrium and could exhibit strong spatial and temporal variations in quantities such as density and local particle velocity. In this light, hydrodynamic type continuum equations were presented for describing the deformation and flow of dense gas-particle mixtures. The constitutive equation used for the stress tensor provides an effective viscosity with a liquid-like character at low shear rates and a gaseous-like behavior at high shear rates. The numerical solutions were obtained for the aforementioned hydrodynamic equations for predicting the flow dynamics ofdense mixture of gas and particles in vertical cylindrical containers. For a heptagonal prism shaped container under vertical vibrations, the model results were found to predict bubbling behavior analogous to those observed experimentally. This bubbling behavior may be explained by the unusual gas pressure distribution found in the bed. In addition, oscillon type structures were found to be formed using a vertically vibrated, pentagonal prism shaped container in agreement with computer simulation results. These observations suggest that the pressure distribution plays a key rolein deformation and flow of dense mixtures of gas and particles under vertical vibrations. The present models provide greater insight toward the explanation of poorly understood hydrodynamic phenomena in the field of granular flows and dense gas-particle mixtures. The models can be generalized to investigate the granular material-container wall interactions which would be an issue of high interests in the industrial applications. By following this approach ideal processing conditions and powder transport can be created in industrial systems.

Coarse-graining and thermodynamics in far-from-equilibrium systems

Lying at the core of statistical physics is the need to reduce the number of degrees of freedom in a system. Coarse-graining is a frequently-used procedure to bridge molecular modeling with experiments. In equilibrium systems, this task can be readily performed; however in systems outside equilibrium, a possible lack of equilibration of the eliminated degrees of freedom may lead to incomplete or even misleading descriptions. Here, we present some examples showing how an improper coarse-graining procedure may result in linear approaches to nonlinear processes, miscalculations of activation rates and violations of the fluctuation-dissipation theorem.

Heat transfer between nanoparticles: Thermal conductance for near-field interactions

We analyze the heat transfer between two nanoparticles separated by a distance lying in the near-field domain in which energy interchange is due to the Coulomb interactions. The thermal conductance is computed by assuming that the particles have charge distributions characterized by fluctuating multipole moments in equilibrium with heat baths at two different temperatures. This quantity follows from the fluctuation-dissipation theorem for the fluctuations of the multipolar moments. We compare the behavior of the conductance as a function of the distance between the particles with the result obtained by means of molecular dynamics simulations. The formalism proposed enables us to provide a comprehensive explanation of the marked growth of the conductance when decreasing the distance between the nanoparticles.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Portadores quentes: modelo browniano

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Study of Heavy-ion Induced Fission for Heavy Element Synthesis

Fission fragment mass distributions were measured in heavy-ion induced fission of 238U. The mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and quasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model for the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that sub-barrier energies can be used for heavy element synthesis.

Revisiting the Classics to recover the Physical Sense in electrical noise

This paper shows a physically cogent model for electrical noise in resistors that has been obtained from Thermodynamical reasons. This new model derived from the works of Johnson and Nyquist also agrees with the Quantum model for noisy systems handled by Callen and Welton in 1951, thus unifying these two Physical viewpoints. This new model is a Complex or 2-D noise model based on an Admittance that considers both Fluctuation and Dissipation of electrical energy to excel the Real or 1-D model in use that only considers Dissipation. By the two orthogonal currents linked with a common voltage noise by an Admittance function, the new model is shown in frequency domain. Its use in time domain allows to see the pitfall behind a paradox of Statistical Mechanics about systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale and also shows how to use properly the Fluctuation-Dissipation Theorem.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Photosynthesis and water relations of well-watered orange plants as affected by winter and summer conditions

The aim of this study was to evaluate how the summer and winter conditions affect the photosynthesis and water relations of well-watered orange trees, considering the diurnal changes in leaf gas exchange, chlorophyll (Chl) fluorescence, and leaf water potential (I) of potted-plants growing in a subtropical climate. The diurnal pattern of photosynthesis in young citrus trees was not significantly affected by the environmental changes when compared the summer and winter seasons. However, citrus plants showed higher photosynthetic performance in summer, when plants fixed 2.9 times more CO(2) during the diurnal period than in the winter season. Curiously, the winter conditions were more favorable to photosynthesis of citrus plants, when considering the air temperature (< 29 A degrees C), leaf-to-air vapor pressure difference (< 2.4 kPa) and photon flux density (maximum values near light saturation) during the diurnal period. Therefore, low night temperature was the main environmental element changing the photosynthetic performance and water relations of well-watered plants during winter. Lower whole-plant hydraulic conductance, lower shoot hydration and lower stomatal conductance were noticed during winter when compared to the summer season. In winter, higher ratio between the apparent electron transport rate and leaf CO(2) assimilation was verified in afternoon, indicating reduction in electron use efficiency by photosynthesis. The high radiation loading in the summer season did not impair the citrus photochemistry, being photoprotective mechanisms active. Such mechanisms were related to increases in the heat dissipation of excessive light energy at the PSII level and to other metabolic processes consuming electrons, which impede the citrus photoinhibition under high light conditions.