Similar to the Debye-Hückel plasma, charged groups of oppositely charged polyelectrolytes attract each other. We find exact expression for the correlation free energy of electrostatic attraction in polyelectrolytes within the random phase approximation. The obtained expression is shown to be valid in dilute, semidilute, concentrated solutions, and melts. In this theory we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentrations fluctuations. The existence of the critical point in $\theta$ solvent is demonstrated. The theory reproduces scaling results and describes the system beyond the scaling approximation.

Due to the migration of mobile molecules and ions, a thin diffusive layer of distributed charge—the electric double layer—forms at the interface between a polyelectrolyte gel and a liquid ionic solution. When two polyelectrolyte gels are brought closely together, the electric double layers overlap and interact with each other, resulting in an effective repulsion. The multiphysics-coupling nature of soft gels makes their surface interactions significantly different from the interactions between rigid solids. Using the recently formulated nonlinear theory, this paper develops a continuum model to study the surface interactions between two like-charged polyelectrolyte gels, accounting for the coupled electric, concentration, and deformation fields in both the gels and the liquid. Numerical solutions of the surface interactions are obtained and compared to a qualitative scaling law derived via linearization. The results suggest that the structure of double layers, as well as their interactions, depends not only on the concentration of liquid solutions, but more on the bulk properties of the gels such as stiffness and fixed-charge density. This model also provides insights to the mechanism of the low-friction phenomena on the surface of a polyelectrolyte gel.

The influence of spatial structure on the equilibrium properties of a sexual population model defined on networks is studied numerically. Using a small-world-like topology of the networks as an investigative tool, the contributions to the fitness of assortative mating and of global mutant spread properties are considered. Simple measures of nearest-neighbor correlations and speed of spread of mutants through the system have been used to confirm that both of these dynamics are important contributory factors to the fitness. It is found that assortative mating increases the fitness of populations. Quick global spread of favorable mutations is shown to be a key factor increasing the equilibrium fitness of populations.

We study spontaneous dynamics and signal transduction in a model of active hair bundle mechanics of sensory hair cells. The hair bundle motion is subjected to internal noise resulted from thermal fluctuations and stochastic dynamics of mechanoelectrical transduction ion channels. Similar to other studies we found that in the presence of noise the coherence of stochastic oscillations is maximal at a point on the bifurcation diagram away from the Andronov-Hopf bifurcation and is close to the point of maximum sensitivity of the system to weak periodic mechanical perturbations. Despite decoherent effect of noise the stochastic hair bundle oscillations can be synchronized by external periodic force of few pN amplitude in a finite range of control parameters. We then study effects of receptor potential oscillations on mechanics of the hair bundle and show that the hair bundle oscillations can be synchronized by oscillating receptor voltage. Moreover, using a linear model for the receptor potential we show that bidirectional coupling of the hair bundle and the receptor potential results in significant enhancement of the coherence of spontaneous oscillations and of the sensitivity to the external mechanical perturbations.

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $\alpha$ and death of the last particle $\delta$. The system presents a phase transition at ${\delta }_c\left(\alpha \right)$, where the average position of the last particle $⟨L⟩$ grows as $\sqrt{t}$. For $\delta >{\delta }_c$, a nonequilibrium stationary state exists while for $\delta <{\delta }_c$ the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.

Statistics of the motion of passively convected point particles in turbulent flows are studied. The database used is obtained by direct numerical solution of the Navier-Stokes equation. We estimate the probability distribution of the transit times of such particles through reference volumes with given forms and sizes. A selected position within the reference volume is moving with the local flow velocity, thus determining the motion of the entire surface. The transit time is defined as the interval between entrance and exit times of surrounding particles convected through the volume by the turbulent motions. Spherical as well as hemispherical surfaces are studied. Scale sizes in the inertial as well as in the viscous subranges of the turbulence are considered. Simple, and seemingly universal, scaling laws are obtained for the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for chemical reactions, but also for understanding details of the feeding rate of micro-organisms in turbulent waters, for instance.

By numerically solving the relativistic Boltzmann equations, we compute the time scale for relaxation to thermal equilibrium for an optically thick electron-positron plasma with baryon loading. We focus on the time scales of electromagnetic interactions. The collisional integrals are obtained directly from the corresponding QED matrix elements. Thermalization time scales are computed for a wide range of values of both the total-energy density (over 10 orders of magnitude) and of the baryonic loading parameter (over 6 orders of magnitude). This also allows us to study such interesting limiting cases as the almost purely electron-positron plasma or electron-proton plasma as well as intermediate cases. These results appear to be important both for laboratory experiments aimed at generating optically thick pair plasmas as well as for astrophysical models in which electron-positron pair plasmas play a relevant role.

We present a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by D. Achlioptas et al. [Science 323, 1453 (2009)]. We show that the following two ingredients are sufficient for obtaining an abrupt (first-order) transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting vertices in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting vertices in the same cluster). Moreover, in the extreme limit where only merging bonds are present, a complete enumeration scheme based on treelike graphs can be used to obtain an exact solution of our model that displays a first-order transition. Finally, the presented mechanism can be viewed as a generalization of standard percolation that discloses a family of models with potential application in growth and fragmentation processes of real network systems.

We demonstrate that in the atomic-scale limit the thermal conductance $\mathcal{K}$ of the Fermi-Pasta-Ulam (FPU) model and its variants strongly deviates from the mesoscopic behavior due to the relevance of contact resistance. As a result, atomic chains follow $\text{log}\mathcal{K}=\nu \text{log}T$, where the power-law coefficient $\nu$ is exactly two times larger than the mesoscopic value. We smoothly interconnect the atomic and mesoscopic limits and demonstrate that this turnover behavior takes place in other nonlinear FPU-like models. Our results are significant for nanoscale applications, manifesting an atomic thermal conductance with temperature scaling superior to the mesoscopic limit.

The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of the volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as the particle volume fraction is reduced, consistent with recent hard-sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter ${\psi }_6$. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase-transition-like behavior in quasi-one-dimensional systems.

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate $1/f$ fluctuations are observed with noise, while $1/f^2$ fluctuations are found for the model without demographic noise.

Adaptability of the human locomotion system has been studied from the theoretical viewpoint of dynamical systems. The structure of a dynamical system consists of its time evolution rule, known simply as the dynamics, and its constraints, such as the initial states or boundary conditions that determine future convergent states. Initial state coordination by the system itself is the key to autonomous adaptive mechanisms. Exploring such mechanisms, our previous studies have focused on the variables encoding the attractor basins, called global variables. Global variables have been shown to enable the system to adapt to perturbations, by coordinating the initial states (constraints) of the system. Thus, initial state coordination by the global variables has been proposed as a mechanism for self-production of the constraints by a system. The adaptability of human locomotion extends to active integration into its locomotion of the motion of environmental objects such as walking on high-heeled shoes or on posts erected unstably. Dealing with bipedal walking on posts, this study expands the mechanism for self-production of the constraints. This study proposes a multiple structure for self-produced constraints and a framework for their description.

Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations are essential to understand the properties and behaviors of such systems. Here we present a mathematical procedure to estimate the local action of force-generating agents from the observed fluctuating displacement fields. The active agents are modeled as oriented force dipoles or isotropic compression foci, and the matrix on which they act is assumed to be either a compressible elastic continuum or a coupled network-solvent system. Correlations at a single point and between points separated by an arbitrary distance are obtained, giving a total of three independent fluctuation modes that can be tested with microrheology experiments. Since oriented dipoles and isotropic compression foci give different contributions to these fluctuation modes, ratiometric analysis allows us characterize the force generators. We also predict and experimentally find a high-frequency ballistic regime, arising from individual force-generating events in the form of the slow buildup of stress followed by rapid but finite decay. Finally, we provide a quantitative statistical model to estimate the mean filament tension from these athermal fluctuations, which leads to stiffening of active networks.

The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant. In other words, at the output of the interneuron, inharmonious signals give rise to blurry spike trains, while the harmonious signals produce more regular, less noisy, spike trains. Theoretical results are compared with numerical simulations.

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

Evaporation from porous media involves complex pore scale transport processes affecting liquid phase distribution and fluxes. Often, the initial evaporation rate is nearly constant and supplied by capillary flow from wetted zones below to the surface. Sustaining constant flow against gravity hinges on an upward capillary gradient and on liquid phase continuity with hydraulic conductivity sufficient for supplying evaporative flux. The pore scale liquid phase adjustments during evaporative displacement necessary for maintaining a constant flux have been postulated but rarely measured. In this study we employed detailed imaging using x-ray synchrotron radiation to study liquid phase distribution and dynamics at the most sensitive domain just below the surface of evaporating sand columns. Three-dimensional images at a resolution of 7 microns were obtained from sand column (mean particle size 0.6 mm) initially saturated with calcium iodide solution (4% by mass) to enhance image contrast. Detailed imaging of near-surface liquid phase distribution during evaporation confirmed phase continuity at micrometric scale and provided quantitative estimates of liquid conductance in agreement with values required to supply evaporative flux. Temporal variations in bulk salt concentrations determined from x-ray attenuation were proportional to evaporative water mass loss. Highly resolved salt concentration images revealed existence of evaporating chimneys that supply the bulk of evaporative demand. Delineated mass loss dynamics and salt distribution measured by the x-ray attenuation were in reasonable agreement with a simplified analytical convection-diffusion model for salt dynamics during evaporation from porous media.

The object of this paper is to show that a variety of dispersion and mixing phenomena induced by laminar convection and diffusion can be approached by perturbation analysis of the spectrum associated with the corresponding advection-diffusion operator. As a case study for dispersion, we consider the classical Taylor-Aris problem, whereas a prototypical model of Sturm-Liouville generalized eigenvalue problem is considered for describing mixing in open or closed bounded flows. For both cases, we show how a simplified (low-order) perturbative approach defines quantitatively the range of different mixing regimes and the associated time scales. Furthermore, we show how a complete higher-order approach cannot improve significantly the simplified low-order analysis due to the lack of analyticity of the eigenvalue branches. The perturbation analysis is also extended to models of physically realizable mixing systems (lid-driven cavity flow).

Correlation or convolution of recordings of diffuse fields at a pair of locations have been shown to result in estimates of the Green’s function between the two locations. Variously referred to as wave field or seismic interferometry in different fields of research, Green’s functions can thus be constructed between either pairs of receivers or pairs of energy sources. Proofs of these results rely on representation theorems. We show how to derive three acoustic and elastic representation theorems that unify existing correlational and convolutional approaches. We thus derive three forms of interferometry that provide Green’s functions on source-to-receiver paths, using only energy that has propagated from surrounding sources or to surrounding receivers. The three forms correspond to three possible canonical geometries. We thus allow interferometric theory and methods to be applied to commonly used source-receiver configurations.