To investigate the effect of quantum coherence on electronic energy transfer, which is the subject of current interest in photosynthesis, we solve the problem of transport for the simplest model of an aggregate of monomers interacting through dipole-dipole forces using both quantum and classical dynamics. We conclude that for realistic coupling strengths quantum and classical coherent transport are identical. This is demonstrated by numerical calculations for a linear chain and for the photosynthetic Fenna-Matthews-Olson complex.

Interest in understanding the interplay between noise and the response of a nonlinear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in nonlinear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous “natural” noise with a $1/f$ frequency spectrum. Specifically, we study the impact of the $1/f$ noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small steplike stimulus. For the perfect (nonleaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low-pass) filter function given by $\mathcal{F}(t,f)={\mathrm{sinc}}^2(\pi ft)$. This result elucidates the connection between low-frequency noise and disorder in neuron dynamics. Under $1/f$ noise, spike dynamics lacks a characteristic correlation time, inducing the leaky and nonleaky models, to exhibit nonergodic behavior and the Fano factor, increasing logarithmically as a function of time. We compare our results to experimental data of single neurons in vivo [Teich, Heneghan, Lowen, Ozaki, and Kaplan, J. Opt. Soc. Am. A 14, 529 (1997)] and show how the $1/f$ noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low-frequency noise, however, complicates the case for an information-coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of $1/f$ noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.

The recent availability of data describing social networks is changing our understanding of the “microscopic structure” of a social tie. A social tie indeed is an aggregated outcome of many social interactions such as face-to-face conversations or phone calls. Analysis of data on face-to-face interactions shows that such events, as many other human activities, are bursty, with very heterogeneous durations. In this paper we present a model for social interactions at short time scales, aimed at describing contexts such as conference venues in which individuals interact in small groups. We present a detailed analytical and numerical study of the model’s dynamical properties, and show that it reproduces important features of empirical data. The model allows for many generalizations toward an increasingly realistic description of social interactions. In particular, in this paper we investigate the case where the agents have intrinsic heterogeneities in their social behavior, or where dynamic variations of the local number of individuals are included. Finally we propose this model as a very flexible framework to investigate how dynamical processes unfold in social networks.

We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, $N$. When the advection term in the Vlasov equation is dominant, the convergence with $N$ of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.

It is known that randomness in dynamical systems often leads to infinite hierarchies of coupled equations for relevant probabilistic quantities. Several closure methods for truncation of the hierarchies have been proposed in the literature. In the present paper the performance of closure schemes for moment hierarchies is compared by using the well-known nonlinear equation of overdamped oscillator with additive Gaussian white noise. In the case of bistable dynamics it is shown that the closure schemes can give incorrect results despite of their good convergence properties. To overcome this deficiency new closure procedures are proposed. They are based on using the Hermite polynomials and their generalization.

We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected according to the Granger notion of predictability improvement, and is quantified in terms of information transfer. We apply the approach to simulations of deterministic and stochastic systems, showing its superiority over standard uniform embedding. Effects of quantization, data length, and noise contamination are investigated. As practical applications, we consider the assessment of cardiovascular regulatory mechanisms from the analysis of heart period, arterial pressure, and respiration time series, and the investigation of the information flow across brain areas from multichannel scalp electroencephalographic recordings.

Intrinsic oscillations are thought to play important and distinct roles in cognitive processes across nearly all regions of the brain. Their specific roles are highly dependent on their properties: low-frequency $\theta$ is thought to be important in the gating of cognitive processes, while high-frequency $\gamma$ is believed to be essential for binding and spike-timing-dependent plasticity. We investigated the role of an oscillatory drive for pattern formation of heterogeneous networks. Network heterogeneities were implemented as network regions having increased connectivity as compared to the rest of the network. We varied the properties of the oscillatory drive as well as network connectivity. We observed that the disparity in spatiotemporal patterning of activity between the structurally enhanced region and rest of the network was highly dependent on the frequency and amplitude of the oscillatory drive as well as network connectivity, generally favoring bigger enhancement of activity for high-frequency oscillations and phase locking with moderate enhancement of activity for lower-frequency oscillations. Thus, these results indicate that the specific role of the observed oscillations may depend on their dynamical interactions with the heterogeneous network.

Phase models are among the simplest neuron models reproducing spiking behavior, excitability, and bifurcations toward periodic firing. However, coupling among neurons has been considered only using generic arguments valid close to the bifurcation point, and the differentiation between electric and synaptic coupling remains an open question. In this work we aim to address this question and derive a mathematical formulation for the various forms of coupling. We construct a mathematical model based on a planar simplification of the Morris-Lecar model. Based on geometric arguments we then derive a phase description of a network of the above oscillators with biologically realistic electric coupling and subsequently with chemical coupling under fast synapse approximation. We demonstrate analytically that electric and synaptic coupling are differently expressed on the level of the network’s phase description with qualitatively different dynamics. Our mathematical analysis shows that a breaking of the translational symmetry in the phase flows is responsible for the different bifurcations paths of electric and synaptic coupling. Our numerical investigations confirm these findings and show excellent correspondence between the dynamics of the full network and the network’s phase description.

We present a microfluidic ratchet that exploits the deformation of individual cells through microscale funnel constrictions. The threshold pressure required to transport single cells through such constrictions is greater against the direction of taper than along the direction of taper. This physical asymmetry combined with an oscillatory excitation can enable selective and irreversible transport of individual cells in low Reynolds number flow. We devised a microfluidic device to measure the pressure asymmetry across various geometries of funnel constrictions. Using a chain of funnel constrictions, we showed that oscillatory pressure enables ratcheting transport when the pressure amplitude and oscillation period exceeds the threshold required to transport single cells. These experiments demonstrate the potential of using this mechanism to selectively transport biological cells based on their internal mechanics, and the potential to separate cells based on cell morphology or disease state.

The apparent viscosity of shear thickening fluid (STF) changes dramatically with the applied shear rate, which is a typical rheological property of STF. Such a rheological property affects the vertically vibrated dynamic property of STF. In order to get a better understanding of the vertically vibrated dynamic properties of STF, the surface instabilities in vertically vibrated STF, which was prepared by suspending polymethylmethacrylate particles in ethylene glycol, are investigated. Above a critical driving acceleration, the surface instability transforms from the disappearance to the fission of the initial hole, which is produced by applying a finite perturbation to the surface. The time required for the initial hole to disappear can be affected by the driving acceleration, vibration frequency, volume fraction, thickness, and shape and size of the perturbation. A possible model is proposed, and the expressions of hydrostatic force and viscous dissipative force are employed to clarify the relationship between disappearance of the hole and shear thickening effect. The fission and spreading follow a hexagonal arrangement. At a higher acceleration, the holes cover the entire surface in a state of disorder. The mechanism for the initial hole's evolution in vertically vibrated shear thickening fluids is discussed.

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time reverse of a black hole) by measuring the angle of the Mach cone created by an object in the “supersonic” inner flow region. We emphasize the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a “superluminal” dispersion relation, that is, that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible “trans-Planckian distortion” of black or white holes.

Frequency dependence of the subharmonic Shapiro steps has been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. As potential gets deformed, in addition to the harmonic steps, subharmonic steps appear in the number and size that increase as the frequency of the external force increases. It was found that size of both harmonic and subharmonic steps strongly depend on the frequency where in the high-amplitude limit oscillatory dependence appears. When expressed as a function of period these oscillations of the step size with frequency have the same form as the oscillations of the step size with amplitude. Deformation of the potential has strong influence on these oscillations, and as in the case of amplitude dependence, with the increase of deformation, the same three distinctive types of behavior have been classified.

We experimentally investigate the energy flux in a nonlinear electrical transmission line formed by two segments which are identical in structure but have different parameters. By consideration of the driving voltage at a frequency within the passband of one segment, the phenomenon of asymmetric energy flux caused by linear waves has been observed. The experiment shows that the possibility of creation of an asymmetric energy flux mainly depends on the nonlinear and lattice effects; namely, the asymmetric energy flux here is carried by a linear wave in the passband, instead of by a nonlinear wave out of the band. To further understand this phenomenon in the transmission line, we study both experimentally and numerically the dependency of the asymmetric energy flux on the parameters, and the key factors which affect the efficiency of the asymmetric energy flux are obtained.

Understanding the behaviors of molecules in tight confinement is a challenging task. Standard simulation tools like kinetic Monte Carlo have proven to be very effective in the study of adsorption and diffusion phenomena in microporous materials, but they turn out to be very inefficient when simulation time and length scales are extended. In this paper we have explored the possibility of application of a discrete version of the synchronous parallel kinetic Monte Carlo algorithm introduced by Martínez et al. [J. Comput. Phys. 227, 3804 (2008)] to the study of aromatic hydrocarbons diffusion in zeolites. The efficiency of this algorithm is investigated as a function of the number of processors and domain size. We show that with an accurate choice of domains size it is possible to achieve very good efficiencies thus permitting us to effectively extend space and time scales of the simulated system.

Combining simulations and theory I study the interplay between bundle elastic degrees of freedom and crosslink binding propensity. By slowly driving bundles into a deformed configuration, and depending on the mechanical stiffness of the crosslinking agent, the binding affinity is shown to display a sudden and discontinuous drop. This indicates a cooperative unbinding process that involves the crossing of a free-energy barrier. Choosing the proper crosslinker therefore not only allows us to change the composite elastic properties of the bundle but also the relevant time scales which can be tuned from the single crosslink binding rate to the much longer escape time over the free-energy barrier.

The free-energy difference between coexisting solid and liquid phases is studied in the context of classical density functional theory (DFT). A bridge function is used to represent the higher-order ($n>2$) terms in the perturbative expansion of the excess Helmholtz free energy, and the values of this bridge function within the solid lattice are determined by inversion using literature Monte Carlo simulation results. Four potential models, specifically hard-sphere and inverse twelfth-, sixth-, and fourth-power repulsive, are studied. The face-centered cubic (fcc) solid is considered for the hard-sphere and inverse twelfth- and sixth-power potentials, while the body-centered cubic (bcc) solid is considered for the inverse sixth- and fourth-power potentials. For a given solid structure there is a remarkable similarity among the bridge functions for different potentials that is analogous to the universality in the sum of elementary diagrams, or bridge functions, of liquid-state theory as originally observed by Rosenfeld and Ashcroft [Phys. Rev. A 20, 1208 (1979)]. In further analogy with liquid-state theory, the bridge functions in the present problem are plotted as functionals of the second-order convolution term in the perturbative expansion. In each case, the plot indicates a unique functionality in the dense regions of the solid near the lattice sites but a scattered and nonunique behavior in the void regions. Interestingly, knowledge of the functional relationship in the unique region near the lattice sites seems to be sufficient to quantitatively model the solid-fluid phase transition. These qualitative observations are true for both fcc and bcc solid phases, although there are some quantitative differences between them. The findings suggest that pursuit of a closure-based DFT of solid-fluid transitions may be profitable.

We provide a detailed discussion of out-of-equilibrium phase transitions in the Hamiltonian mean-field (HMF) model in the framework of Lynden-Bell’s statistical theory of the Vlasov equation. For two-level initial conditions, the caloric curve $\beta (E)$ only depends on the initial value $f_0$ of the distribution function. We evidence different regions in the parameter space where the nature of the phase transitions between magnetized and nonmagnetized states changes: (i) For $f_0>0.109\hspace{0.5em}65$, the system displays a second-order phase transition; (ii) for $0.109\hspace{0.5em}497<f_0<0.109\hspace{0.5em}65$, the system displays a second-order phase transition and a first-order phase transition; (iii) for $0.109\hspace{0.5em}47<f_0<0.109\hspace{0.5em}497$, the system displays two second-order phase transitions; and (iv) for $f_0<0.109\hspace{0.5em}47$, there is no phase transition. The passage from a first-order to a second-order phase transition corresponds to a tricritical point. The sudden appearance of two second-order phase transitions from nothing corresponds to a second-order azeotropy. This is associated with a phenomenon of phase reentrance. When metastable states are taken into account, the problem becomes even richer. In particular, we find another situation of phase reentrance. We consider both microcanonical and canonical ensembles and report the existence of a tiny region of ensemble inequivalence. We also explain why the use of the initial magnetization $M_0$ as an external parameter, instead of the phase level $f_0$, may lead to inconsistencies in the thermodynamical analysis. Finally, we mention different causes of incomplete relaxation that could be a limitation to the application of Lynden-Bell’s theory.