Evaporation and coarsening dynamics with open boundaries

We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

Unraveling dynamics of human physical activity patterns in chronic pain conditions.

Chronic pain is a complex disabling experience that negatively affects the cognitive, affective and physical functions as well as behavior. Although the interaction between chronic pain and physical functioning is a well-accepted paradigm in clinical research, the understanding of how pain affects individuals' daily life behavior remains a challenging task. Here we develop a methodological framework allowing to objectively document disruptive pain related interferences on real-life physical activity. The results reveal that meaningful information is contained in the temporal dynamics of activity patterns and an analytical model based on the theory of bivariate point processes can be used to describe physical activity behavior. The model parameters capture the dynamic interdependence between periods and events and determine a 'signature' of activity pattern. The study is likely to contribute to the clinical understanding of complex pain/disease-related behaviors and establish a unified mathematical framework to quantify the complex dynamics of various human activities.

Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice

We present a theoretical study of the recently observed dynamical regimes of paramagnetic colloidal particles externally driven above a regular lattice of magnetic bubbles [P. Tierno, T. H. Johansen, and T. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007)]. An external precessing magnetic field alters the potential generated by the surface of the film in such a way to either drive the particle circularly around one bubble, ballistically through the array, or in triangular orbits on the interstitial regions between the bubbles. In the ballistic regime, we observe different trajectories performed by the particles phase locked with the external driving. Superdiffusive motion, which was experimentally found bridging the localized and delocalized dynamics, emerge only by introducing a certain degree of randomness into the bubbles size distribution.

The prediction of chemical reactivity from first principles: Collision and reaction dynamics

Aquest treball fa una revisió de mesures experimentals i càlculs teòrics sobre la dinàmica de col·lisions i reaccions moleculars. Els experiments se centren en col·lisions, a energies intermèdies, que involucren sistemes del tipus ió-àtom i iómolècula, per les quals es mesuren seccions eficaces totals, estat a estat, així com aquelles que discerneixen les diferents contribucions del moment angular d'espín. Els resultats obtinguts s'interpreten satisfactòriament en termes d'acoblaments no adiabàtics entre els diferents estats electrònics dels sistemes col·lisionants. Els càlculs teòrics utilitzen la metodologia quasiclàssica, així com metodologies mecanoquàntiques recentment desenvolupades, tant aproximades com exactes. S'han obtingut resultats totalment convergits per sistemes tipus, mentre que s'han analitzat, de manera detallada i extensiva, les característiques dinàmiques de sistemes triatòmic, tetraatòmic i pentaatòmic.

Front dynamics in turbulent media

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Resting-State Functional Connectivity Emerges from Structurally and Dynamically Shaped Slow Linear Fluctuations.

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

Dynamics of transient pattern formation in nematic liquid crystals

We analyze the dynamics of a transient pattern formation in the Fréedericksz transition corresponding to a twist geometry. We present a calculation of the time-dependent structure factor based on a dynamical model which incorporates consistently the coupling of the director field with the velocity flow and also the effect of fluctuations. The appearance and development of a characteristic periodicity is described in terms of the time dependence of the maximum of the structure factor. We find a well-defined time for the appearance of the pattern and a subsequent stage of pattern development in which the characteristic periodicity tends to an asymptotic value.

Neural networks as mechanisms to regulate division of labor.

Abstract In social insects, workers perform a multitude of tasks, such as foraging, nest construction, and brood rearing, without central control of how work is allocated among individuals. It has been suggested that workers choose a task by responding to stimuli gathered from the environment. Response-threshold models assume that individuals in a colony vary in the stimulus intensity (response threshold) at which they begin to perform the corresponding task. Here we highlight the limitations of these models with respect to colony performance in task allocation. First, we show with analysis and quantitative simulations that the deterministic response-threshold model constrains the workers' behavioral flexibility under some stimulus conditions. Next, we show that the probabilistic response-threshold model fails to explain precise colony responses to varying stimuli. Both of these limitations would be detrimental to colony performance when dynamic and precise task allocation is needed. To address these problems, we propose extensions of the response-threshold model by adding variables that weigh stimuli. We test the extended response-threshold model in a foraging scenario and show in simulations that it results in an efficient task allocation. Finally, we show that response-threshold models can be formulated as artificial neural networks, which consequently provide a comprehensive framework for modeling task allocation in social insects.

Nonlinear effects in the dynamics of transient pattern formation in nematics

A nonlinear calculation of the dynamics of transient pattern formation in the Fréedericksz transition is presented. A Gaussian decoupling is used to calculate the time dependence of the structure factor. The calculation confirms the range of validity of linear calculations argued in earlier work. In addition, it describes the decay of the transient pattern.

Dynamics of orientational fluctuations in a homeotropic Fréedericksz transition under a rotating magnetic field

We study the problem of the Fréedericksz transition under a rotating magnetic field by using a dynamical model which incorporates thermal fluctuations into the whole set of nematodynamic equations. In contrast to other geometries, nonuniform textures in the plane of the sample do not appear favored. The proper consideration of thermal noise enables us to describe the dynamics of orientational fluctuations both below and above the shifted instability.

Dynamics of transient domain structures in nematic liquid crystals: The splay Fréedericksz transition

We discuss the dynamics of the transient pattern formation process corresponding to the splay Fréedericksz transition. The emergence and subsequent evolution of the spatial periodicity is here described in terms of the temporal dependence of the wave numbers corresponding to the maxima of the structure factor. Situations of perpendicular as well as oblique field-induced stripes relative to the initial orientation of the director are both examined with explicit indications of the time scales needed for their appearance and posterior development.

Transient patterns in nematic liquid crystals: Domain-wall dynamics

We study the dynamics of the late stages of the Fréedericksz transition in which a periodic transient pattern decays to a final homogeneous state. A stability analysis of an unstable stationary pattern is presented, and equations for the evolution of the domain walls are obtained. Using results of previous theories, we analyze the effect that the specific dynamics of the problem, incorporating hydrodynamic couplings, has on the expected logarithmic domain growth law.