The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power-law potential, most notably the superpositioning of relaxation data as a function of the variable ${\mathrm{TV}}^{\gamma }$, where $T$ is temperature, $V$ the specific volume, and γ a material constant. A related scaling law $T_m{V}_m^{\Gamma }$, with the same exponent Γ$=$γ, links the melting temperature $T_m$ and volume $V_m$ of the model IPL liquid; liquid dynamics is then invariant at the melting point. Motivated by a similar invariance of dynamics experimentally observed at transitions of liquid crystals, we determine dynamic and melting-point scaling exponents γ and Γ for a large number of nonassociating liquids. Rigid, spherical molecules containing no polar bonds have Γ$=$γ; consequently, the reduced relaxation time, viscosity, and diffusion coefficient are each constant along the melting line. For other liquids γ > Γ always; that is, the dynamics is more sensitive to volume than is the melting point, and for these liquids the dynamics at the melting point slows down with increasing $T_{\mathrm{m}}$ (that is, increasing pressure).

In this paper, we investigate the rupture dynamics of thin liquid films driven by intermolecular forces via weakly nonlinear bifurcation analysis. The dynamic equations governing slow dynamics of the perturbation amplitude of the near-critical mode corresponding to several models describing the evolution of thin liquid films in different physical situations appear to have the same structure. When antagonistic (attractive and repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible, while the boundary of this supercritical bifurcation is determined solely by the form of the intermolecular potential. The rupture time estimate obtained in closed form shows an excellent agreement with the results of the previously reported numerical simulations of the strongly nonlinear coupled evolution equations upon fitting the amplitude of the small initial perturbation. We further extend the weakly nonlinear analysis of the film dynamics and apply the Galerkin approximation to derive the amplitude equation(s) governing the dynamics of the fastest growing linear mode far from the instability threshold. The comparison of the rupture time derived from this theory with the results of numerical simulations of the original nonlinear evolution equations shows a very good agreement without any adjustable parameters.

The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signaling activity of neurons a challenge of practical interest. Neuron models are frequently used to represent the dynamics of real neurons but hardly ever to evaluate the electrochemical energy required to maintain that dynamics. This paper discusses the interpretation of a Hodgkin-Huxley circuit as an energy model for real biological neurons and uses it to evaluate the consumption of metabolic energy in the transmission of information between neurons coupled by electrical synapses, i.e., gap junctions. We show that for a single postsynaptic neuron maximum energy efficiency, measured in bits of mutual information per molecule of adenosine triphosphate (ATP) consumed, requires maximum energy consumption. For groups of parallel postsynaptic neurons we determine values of the synaptic conductance at which the energy efficiency of the transmission presents clear maxima at relatively very low values of metabolic energy consumption. Contrary to what could be expected, the best performance occurs at a low energy cost.

This letter reports synchronization phenomena and mathematical modeling on a frustrated system of living beings, or Japanese tree frogs (Hyla japonica). While an isolated male Japanese tree frog calls nearly periodically, he can hear sounds including calls of other males. Therefore, the spontaneous calling behavior of interacting males can be understood as a system of coupled oscillators. We construct a simple but biologically reasonable model based on the experimental results of two frogs, extend the model to a system of three frogs, and theoretically predict the occurrence of rich synchronization phenomena, such as triphase synchronization and 1:2 antiphase synchronization. In addition, we experimentally verify the theoretical prediction by ethological experiments on the calling behavior of three frogs and time series analysis on recorded sound data. Note that the calling behavior of three male Japanese tree frogs is frustrated because almost perfect antiphase synchronization is robustly observed in a system of two male frogs. Thus, nonlinear dynamics of the three-frogs system should be far from trivial.

Measures of the direction and strength of the interdependence between two time series are evaluated and modified to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length, and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of a causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG) for the detection of the information flow in the brain of an epileptic patient. The performance of the measures on EEG is interpreted in view of the results from the simulation study.

In the present paper we report the existence of a new family of solitary waves in general one-dimensional dimer chains with elastic interactions between beads obeying a strongly nonlinear Hertzian force law. These dimers consist of pairs of “heavy” and “light” beads with no precompression. The solitary waves reported herein can be considered as analogous to the solitary waves in general homogeneous granular chains studied by Nesterenko, in the sense that they do not involve separations between beads, but rather satisfy special symmetries or, equivalently antiresonances in their intrinsic dynamics. We conjecture that these solitary waves are the direct products of a countable infinity of antiresonances in the dimer. An interesting finding is that the solitary waves in the dimer propagate faster than solitary waves in the corresponding homogeneous granular chain obtained in the limit of no mass mismatch between beads (i.e., composed of only heavy beads). This finding, which might seem counterintuitive, indicates that under certain conditions nonlinear antiresonances can increase the speed of disturbance transmission in periodic granular media, through the generation of different ways for transferring energy to the far field of these media. From a practical point of view, this result can have interesting implications in applications where granular media are employed as shock transmitters or attenuators.

We investigate the relaxation of the Ising-Glauber model on a periodic cubic lattice after a quench to zero temperature. In contrast to the conventional picture from phase-ordering kinetics, we find the following: (i) Domains at long time are highly interpenetrating and topologically complex, with average genus growing algebraically with system size. (ii) The long-time state is almost never static, but rather contains “blinker” spins that can flip ad infinitum with no energy cost. (iii) The energy relaxation is extremely slow, with a characteristic time that grows exponentially with system size.

The hydrodynamic hindering of a single-particle dynamics under total confinement is measured by optical microscopy. The three-dimensional trajectories of single-colloidal particles confined in spherical water globules of sizes only a few times the particle’s diameter are tracked as they sample the entire volume of the globule. The hydrodynamic interactions between the particle and the spherical wall produce a dependence of the short-time diffusion on the particle’s distance to the surface and an asymmetry in the radial and tangential components of the local diffusion coefficient, with the diffusion along the tangential direction being faster than along the radial direction. The latter decreasing close to the wall while the former being practically constant.

The Soret motion in binary liquids is shown to arise to a large extent from rectified velocity fluctuations. From a hard-bead model with elastic collisions in a nonuniform temperature, we derive a net force on each molecule, which is proportional to the temperature gradient and depends on the ratio of the molecular masses and moments of inertia. Our findings agree with previous numerical simulations and provide an explanation for the thermal diffusion isotope effect observed for several liquids.

In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued by infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result, the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O ($N$) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov’s theory), large-$N$ limit, and nonperturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale $p_G$, below which the perturbative approach breaks down. Even though the action of (nonrelativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O($N$) model and interacting bosons at zero temperature.

We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localized initial conditions associated with a polaron solution, in conjunction with static electron on-site potential not having inversion symmetry, constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localized initial conditions (constituted by kicked static polaron states), violation of parity prevents the existence of pairs of counterpropagating trajectories, thus allowing for a directed current despite the time reversibility of the equations of motion. Nevertheless, propagating polaron solutions associated with sets of unbiased localized initial conditions which eventually leave the region of localized initial conditions do not exhibit time reversibility. Since the initial conditions belonging to the corresponding counterpropagating, current-compensating polaron solutions are not contained in the set, this gives rise to the emergence of a current. Occurrence of long-range coherent charge transport is demonstrated.

We investigate the level density $\sigma (x)$ and the level-spacing distribution $p(s)$ of random matrices $M=\mathrm{AF}\ne M^{†}$, where $F$ is a (diagonal) inner product and $A$ is a random, real, symmetric or complex, Hermitian matrix with independent entries drawn from a probability distribution $q(x)$ with zero mean and finite higher moments. Although not Hermitian, the matrix $M$ is self-adjoint with respect to $F$ and thus has purely real eigenvalues. We find that the level density ${\sigma }_F(x)$ is independent of the underlying distribution $q(x)$ and solely characterized by $F$, and therefore generalizes the Wigner semicircle distribution ${\sigma }_W(x)$. We find that the level-spacing distributions $p(s)$ are independent of $q(x)$, and are dependent upon both the inner product $F$ and whether $A$ is real or complex, and therefore generalize the Wigner surmise for level spacing. Our results suggest $F$-dependent generalizations of the well-known Gaussian Orthogonal Ensemble and Gaussian Unitary Ensemble classes.

We studied the ionic conductance through Al${}_2$O${}_3$ nanopore transistors to probe the surface charge density and its dependence on the applied gate field. The observed conductance modulations are entirely attributable to the electrostatic field effect, and their dependence on pH, ionic strength, and gate voltage is described by a quantitative model. Importantly, these experiments revealed how reactive surface groups dominate the response of nanofluidic field-effect devices via a chemical effect called charge regulation. A quantitative understanding of this effect enables the development of new nanofluidic technologies.

We present a mechanism to form self-assembled functional gradient superlattice structures by subjecting binary nanoparticles in an electric field. The interaction among different dipoles leads to the controllable formation of diverse structures, including particle columns with gradient material properties from inside to outside and various hierarchical layered or three-dimensional particle chain networks. We elucidate how permittivity, volume fraction, particle size, and the frequency of the electric field can be utilized to control the morphology of the induced structures, which would enable designed nanofabrication.

Electro-optical properties of deformed helix ferroelectric liquid crystal (DHFLC) cells are studied by using a general theoretical approach to polarization gratings in which the transmission and reflection matrices of diffraction orders are explicitly related to the evolution operator of equations for the Floquet harmonics. In the short-pitch approximation, a DHFLC cell is shown to be optically equivalent to a uniformly anisotropic biaxial layer where one of the optical axes is normal to the bounding surfaces. For in-plane anisotropy, orientation of the optical axes and birefringence are both determined by the voltage applied across the cell and represent the parameters that govern the transmittance of normally incident light passing through crossed polarizers. We calculate the transmittance as a function of the electric field and compare the computed curves with the experimental data. The theoretical and experimental results are found to be in good agreement.

A number of recent experiments have provided detailed observations of the configurations of long DNA strands under nano-to-micrometer-sized confinement. We therefore revisit the problem of an excluded volume polymer chain confined between two parallel plates with varying plate separation. We show that the nonmonotonic behavior of the overall size of the chain as a function of plate separation, seen in computer simulations and reproduced by earlier theories, can already be predicted on the basis of scaling arguments. However, the behavior of the size in a plane parallel to the plates, a quantity observed in recent experiments, is predicted to be monotonic, in contrast to the experimental findings. We analyze this problem in depth with a mean-field approach that maps the confined polymer onto an anisotropic Gaussian chain, which allows the size of the polymer to be determined separately in the confined and unconfined directions. The theory allows the analytical construction of a smooth crossover between the small-plate-separation de Gennes regime and the large-plate-separation Flory regime. The results show good agreement with molecular dynamics simulations in the presence of a Langevin heat bath and confirm the scaling predictions.

We present a kinetic model for flowing active suspensions and analyze the behavior of a suspension subjected to a weak steady shear. Asymptotic solutions are sought in Deborah number expansions. At the leading order, we explore the steady states and perform their stability analysis. We predict the rheology of active systems including an activity thickening or thinning behavior of the apparent viscosity and a negative apparent viscosity depending on the particle type, flow alignment, and the anchoring conditions, which can be tested on bacterial suspensions. We find remarkable dualities that show that flow-aligning rodlike contractile (extensile) particles are dynamically and rheologically equivalent to flow-aligning discoid extensile (contractile) particles for both tangential and homeotropic anchoring conditions. Another key prediction of this work is the role of the concentration of active suspensions in controlling the rheological behavior: The apparent viscosity may decrease with the increase of the concentration.

Swimming at a micrometer scale demands particular strategies. When inertia is negligible compared to viscous forces, hydrodynamics equations are reversible in time. To achieve propulsion, microswimmers must therefore deform in a way that is not invariant under time reversal. Here, we investigate dispersal properties of the microalga Chlamydomonas reinhardtii by means of microscopy and cell tracking. We show that tracked trajectories are well modeled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlation is lost and a standard random walk characterizes the trajectories. Moreover, high-speed imaging enables us to show how the back-and-forth motion of flagella at very short times affects the statistical description of the dynamics. Finally, we show how drag forces modify the characteristics of this particular random walk.

Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the von Neumann entropy of networks with given expected degree sequence. We find in different examples of network topologies that when the degree distribution contains some heterogeneity, an intriguing correlation emerges between the two entropic quantities. This results seems to suggest that heterogeneity in the expected degree distribution is implying an equivalence between a quantum and a classical description of networks, which respectively corresponds to the von Neumann and the Shannon entropy.

Motivated by recent observations in neuronal systems we investigate all-to-all networks of nonidentical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all incoming links is conserved. We find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator. In sufficiently large networks the adaptive coupling is found to develop effective network topologies dominated by one or two loops. This results in a multitude of stable splay states, which differ in their firing sequences. With increasing coupling strength their frequency increases linearly and the oscillators become less synchronized. The essential features of the two classes of states are captured analytically in perturbation analyses of the extended Kuramoto model used in the simulations.