Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time series analysis

The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. Results obtained in a previous work [M. Romero-Bastida, Phys. Rev. E {\bf69}, 056204 (2004)] suggest that the impurity does not contribute significantly to the dynamics of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. The ($r,\tau$) entropy, which measures the amount of information generated by unit time at different scales $\tau$ of time and $r$ of the observable, is numerically computed by methods of nonlinear time-series analysis using the position and momentum signals of the heavy impurity for various values of the energy density $\epsilon$ (energy per degree of freedom) of the system and some values of the impurity mass $M$. Results obtained from these two time series are compared and discussed.Comment: 7 pages, 5 figures, RevTeX4 PRE format; to be published in Phys. Rev.

Finite Temperature Spectral Densities of Momentum and R-Charge Correlators in N=4\N=4 Yang Mills Theory

We compute spectral densities of momentum and R-charge correlators in thermal $\N=4$ Yang Mills at strong coupling using the AdS/CFT correspondence. For $\omega \sim T$ and smaller, the spectral density differs markedly from perturbation theory; there is no kinetic theory peak. For large $\omega$, the spectral density oscillates around the zero-temperature result with an exponentially decreasing amplitude. Contrast this with QCD where the spectral density of the current-current correlator approaches the zero temperature result like $(T/\omega)^4$. Despite these marked differences with perturbation theory, in Euclidean space-time the correlators differ by only $\sim 10$ from the free result. The implications for Lattice QCD measurements of transport are discussed.Comment: 18 pages, 3 figure

α\alpha-Scale Decoupling of the Mechanical Relaxation and Diverging Shear Wave Propagation Lengthscale in Triphenylphosphite

We have performed depolarized Impulsive Stimulated Scattering experiments to observe shear acoustic phonons in supercooled triphenylphosphite (TPP) from $\sim$10 - 500 MHz. These measurements, in tandem with previously performed longitudinal and shear measurements, permit further analyses of the relaxation dynamics of TPP within the framework of the mode coupling theory (MCT). Our results provide evidence of $\alpha$ coupling between the shear and longitudinal degrees of freedom up to a decoupling temperature $T_c$ = 231 K. A lower bound length scale of shear wave propagation in liquids verified the exponent predicted by theory in the vicinity of the decoupling temperature

Calcium Pectinate Beads Formation: Shape and Size Analysis

The aim of this study was to investigate the inter-relationship between process variables and the size and shape of pectin solution droplets upon detachment from a dripping tip as well as Ca-pectinate beads formed after gelation via image analysis. The sphericity factor (SF) of the droplets was generally smaller than 0.05. There was no specific trend between the SF of the droplets and the pectin concentration or the dripping tip radius. The SF the beads formed from high-concentration pectin solutions and a small dripping tip was smaller than 0.05. The results show that the Reynolds number and Ohnesorge number of the droplets fall within the operating region for forming spherical beads in the shape diagram, with the exception to the lower boundary. The lower boundary of the operating region has to be revised to Oh = 2.3. This is because the critical viscosity for Ca-pectinate bead formation is higher than that of Ca-alginate beads. On the other hand, the radius of the droplets and beads increased as the dripping tip radius increased. The bead radius can easily be predicted by Tate's law equation

Dynamic correlations in stochastic rotation dynamics

The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for Stochastic Rotation Dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.Comment: 33 pages including 16 figure

Fluctuating hydrodynamic modelling of fluids at the nanoscale

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales (De Fabritiis {\it et. al}, Phys. Rev. Lett. 97, 134501 (2006)). However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as argon at arbitrary densities and water under ambient conditions. To that end, molecular dynamics simulations are used to derive the required fluid properties. The equilibrium state of the model is shown to be thermodynamically consistent and correctly reproduces linear hydrodynamics including relaxation of sound and shear modes. We also consider non-equilibrium states involving diffusion and convection in cavities with no-slip boundary conditions

Thermodiffusion in model nanofluids by molecular dynamics simulations

In this work, a new algorithm is proposed to compute single particle (infinite dilution) thermodiffusion using Non-Equilibrium Molecular Dynamics simulations through the estimation of the thermophoretic force that applies on a solute particle. This scheme is shown to provide consistent results for simple Lennard-Jones fluids and for model nanofluids (spherical non-metallic nanoparticles + Lennard-Jones fluid) where it appears that thermodiffusion amplitude, as well as thermal conductivity, decrease with nanoparticles concentration. Then, in nanofluids in the liquid state, by changing the nature of the nanoparticle (size, mass and internal stiffness) and of the solvent (quality and viscosity) various trends are exhibited. In all cases the single particle thermodiffusion is positive, i.e. the nanoparticle tends to migrate toward the cold area. The single particle thermal diffusion 2 coefficient is shown to be independent of the size of the nanoparticle (diameter of 0.8 to 4 nm), whereas it increases with the quality of the solvent and is inversely proportional to the viscosity of the fluid. In addition, this coefficient is shown to be independent of the mass of the nanoparticle and to increase with the stiffness of the nanoparticle internal bonds. Besides, for these configurations, the mass diffusion coefficient behavior appears to be consistent with a Stokes-Einstein like law

DNA binding shifts the redox potential of the transcription factor SoxR

Electrochemistry measurements on DNA-modified electrodes are used to probe the effects of binding to DNA on the redox potential of SoxR, a transcription factor that contains a [2Fe-2S] cluster and is activated through oxidation. A DNA-bound potential of +200 mV versus NHE (normal hydrogen electrode) is found for SoxR isolated from Escherichia coli and Pseudomonas aeruginosa. This potential value corresponds to a dramatic shift of +490 mV versus values found in the absence of DNA. Using Redmond red as a covalently bound redox reporter affixed above the SoxR binding site, we also see, associated with SoxR binding, an attenuation in the Redmond red signal compared with that for Redmond red attached below the SoxR binding site. This observation is consistent with a SoxR-binding-induced structural distortion in the DNA base stack that inhibits DNA-mediated charge transport to the Redmond red probe. The dramatic shift in potential for DNA-bound SoxR compared with the free form is thus reconciled based on a high-energy conformational change in the SoxR–DNA complex. The substantial positive shift in potential for DNA-bound SoxR furthermore indicates that, in the reducing intracellular environment, DNA-bound SoxR is primarily in the reduced form; the activation of DNA-bound SoxR would then be limited to strong oxidants, making SoxR an effective sensor for oxidative stress. These results more generally underscore the importance of using DNA electrochemistry to determine DNA-bound potentials for redox-sensitive transcription factors because such binding can dramatically affect this key protein property

Solidity of viscous liquids. IV. Density fluctuations

This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event (a jump between two energy minima in configuration space) are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k-space of the form $\Gamma_0+Dk^2$ with $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) may be taken to be ultra local. As an illustration of the theory the case with the simplest non-trivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an $\omega^{-1/2}$ decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed

Escort mean values and the characterization of power-law-decaying probability densities

Escort mean values (or $q$-moments) constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like {\it power laws}. They naturally appear in the study of many complex dynamical systems, particularly those obeying nonextensive statistical mechanics, a current generalization of the Boltzmann-Gibbs theory. They recover standard mean values (or moments) for $q=1$. Here we discuss the characterization of a (non-negative) probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities, provided that all of them converge. This opens the door to a natural extension of the well known characterization, for the $q=1$ instance, of a distribution in terms of the standard moments, provided that {\it all} of them have {\it finite} values. This question would be specially relevant in connection with probability densities having {\it divergent} values for all nonvanishing standard moments higher than a given one (e.g., probability densities asymptotically decaying as power-laws), for which the standard approach is not applicable. The Cauchy-Lorentz distribution, whose second and higher even order moments diverge, constitutes a simple illustration of the interest of this investigation. In this context, we also address some mathematical subtleties with the aim of clarifying some aspects of an interesting non-linear generalization of the Fourier Transform, namely, the so-called $q$-Fourier Transform.Comment: 20 pages (2 Appendices have been added