Weakly linked binary mixtures of F = 1 87Rb Bose-Einstein condensates

We present a study of binary mixtures of Bose-Einstein condensates confined in a double-well potential within the framework of the mean field Gross-Pitaevskii (GP) equation. We re-examine both the single component and the binary mixture cases for such a potential, and we investigate what are the situations in which a simpler two-mode approach leads to an accurate description of their dynamics. We also estimate the validity of the most usual dimensionality reductions used to solve the GP equations. To this end, we compare both the semi-analytical two-mode approaches and the numerical simulations of the one-dimensional (1D) reductions with the full 3D numerical solutions of the GP equation. Our analysis provides a guide to clarify the validity of several simplified models that describe mean-field nonlinear dynamics, using an experimentally feasible binary mixture of an F = 1 spinor condensate with two of its Zeeman manifolds populated, m = ±1.

Energy relaxation in nonlinear one-dimensional lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Predicting spinor condensate dynamics from simple principles

We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these nonlinear systems is explained by surprisingly simple principles: minimization of energy at zero temperature and maximization of entropy at high temperature. Our analytical results for the homogeneous case are corroborated by numerical simulations for confined condensates in a wide variety of initial conditions. These predictions compare qualitatively well with recent experimental observations and can, therefore, serve as a guidance for ongoing experiments.

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

Models of social networks based on social distance attachment

We propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance. Social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space. We derive analytical results (corroborated by extensive numerical simulations), showing that the model reproduces the main statistical characteristics of real social networks: large clustering coefficient, positive degree correlations, and the emergence of a hierarchy of communities. The model is confronted with the social network formed by people that shares confidential information using the Pretty Good Privacy (PGP) encryption algorithm, the so-called web of trust of PGP.

Understanding and modulating the competitive surface-adsorption of proteins through coarse-grained molecular dynamics simulations

It is now well accepted that cellular responses to materials in a biological medium reflect greatly the adsorbed biomolecular layer, rather than the material itself. Here, we study by molecular dynamics simulations the competitive protein adsorption on a surface (Vroman effect), i.e. the non-monotonic behavior of the amount of protein adsorbed on a surface in contact with plasma as functions of contact time and plasma concentration. We find a complex behavior, with regimes during which small and large proteins are not necessarily competing between them, but are both competing with others in solution ("cooperative" adsorption). We show how the Vroman effect can be understood, controlled and inverted.

Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving.

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)].

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

The role of intramolecular barriers on the glass transition of polymers: computer simulations versus mode coupling theory

We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are analyzed within the framework of the mode coupling theory (MCT). Critical nonergodicity parameters, critical temperatures, and dynamic exponents are obtained from consistent fits of simulation data to MCT asymptotic laws. The so-obtained MCT λ-exponent increases from standard values for fully flexible chains to values close to the upper limit for stiff chains. In analogy with systems exhibiting higher-order MCT transitions, we suggest that the observed large λ-values arise form the interplay between two distinct mechanisms for dynamic arrest: general packing effects and polymer-specific intramolecular barriers. We compare simulation results with numerical solutions of the MCT equations for polymer systems, within the polymer reference interaction site model (PRISM) for static correlations. We verify that the approximations introduced by the PRISM are fulfilled by simulations, with the same quality for all the range of investigated barrier strength. The numerical solutions reproduce the qualitative trends of simulations for the dependence of the nonergodicity parameters and critical temperatures on the barrier strength. In particular, the increase in the barrier strength at fixed density increases the localization length and the critical temperature. However the qualitative agreement between theory and simulation breaks in the limit of stiff chains. We discuss the possible origin of this feature.

Nonlinear prediction based on score function

The linear prediction coding of speech is based in the assumption that the generation model is autoregresive. In this paper we propose a structure to cope with the nonlinear effects presents in the generation of the speech signal. This structure will consist of two stages, the first one will be a classical linear prediction filter, and the second one will model the residual signal by means of two nonlinearities between a linear filter. The coefficients of this filter are computed by means of a gradient search on the score function. This is done in order to deal with the fact that the probability distribution of the residual signal still is not gaussian. This fact is taken into account when the coefficients are computed by a ML estimate. The algorithm based on the minimization of a high-order statistics criterion, uses on-line estimation of the residue statistics and is based on blind deconvolution of Wiener systems [1]. Improvements in the experimental results with speech signals emphasize on the interest of this approach.

Estimating 750 years of temperature variations and uncertainties in the Pyrenees by tree-ring reconstructions and climate simulations.

Past temperature variations are usually inferred from proxy data or estimated using general circulation models. Comparisons between climate estimations derived from proxy records and from model simulations help to better understand mechanisms driving climate variations, and also offer the possibility to identify deficiencies in both approaches. This paper presents regional temperature reconstructions based on tree-ring maximum density series in the Pyrenees, and compares them with the output of global simulations for this region and with regional climate model simulations conducted for the target region. An ensemble of 24 reconstructions of May-to-September regional mean temperature was derived from 22 maximum density tree-ring site chronologies distributed over the larger Pyrenees area. Four different tree-ring series standardization procedures were applied, combining two detrending methods: 300-yr spline and the regional curve standardization (RCS). Additionally, different methodological variants for the regional chronology were generated by using three different aggregation methods. Calibration verification trials were performed in split periods and using two methods: regression and a simple variance matching. The resulting set of temperature reconstructions was compared with climate simulations performed with global (ECHO-G) and regional (MM5) climate models. The 24 variants of May-to-September temperature reconstructions reveal a generally coherent pattern of inter-annual to multi-centennial temperature variations in the Pyrenees region for the last 750 yr. However, some reconstructions display a marked positive trend for the entire length of the reconstruction, pointing out that the application of the RCS method to a suboptimal set of samples may lead to unreliable results. Climate model simulations agree with the tree-ring based reconstructions at multi-decadal time scales, suggesting solar variability and volcanism as the main factors controlling preindustrial mean temperature variations in the Pyrenees. Nevertheless, the comparison also highlights differences with the reconstructions, mainly in the amplitude of past temperature variations and in the 20th century trends. Neither proxy-based reconstructions nor model simulations are able to perfectly track the temperature variations of the instrumental record, suggesting that both approximations still need further improvements.

Networks of noisy oscillators with correlated degree and frequency dispersion

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erdös-Rényi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.

Accounting for adsorption and desorption in Lattice Boltzmann simulations

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

Feature selection for automatic analysis of emotional response based on nonlinear speech modeling suitable for diagnosis of Alzheimer׳s disease

Alzheimer׳s disease (AD) is the most common type of dementia among the elderly. This work is part of a larger study that aims to identify novel technologies and biomarkers or features for the early detection of AD and its degree of severity. The diagnosis is made by analyzing several biomarkers and conducting a variety of tests (although only a post-mortem examination of the patients’ brain tissue is considered to provide definitive confirmation). Non-invasive intelligent diagnosis techniques would be a very valuable diagnostic aid. This paper concerns the Automatic Analysis of Emotional Response (AAER) in spontaneous speech based on classical and new emotional speech features: Emotional Temperature (ET) and fractal dimension (FD). This is a pre-clinical study aiming to validate tests and biomarkers for future diagnostic use. The method has the great advantage of being non-invasive, low cost, and without any side effects. The AAER shows very promising results for the definition of features useful in the early diagnosis of AD.