Transient currents of electrolytes in response to a voltage step can reveal a lot about the behavior of charges present in an electrolyte. In this paper, electrolytes with high ionic strength are considered. In the limit of small voltage steps, the interpretation is straightforward as the equations describing the transient can be linearized. However, when high ion concentrations and voltage steps of the order of $kT∕q$ are considered, we find higher-order effects that occur simultaneously with the diffuse double layer charging. In this case, the diffuse double layer and the transient diffusion layer are coupled because of the screening of the field, leading to a $-3∕2$ power law for the transient current.

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by Vernizzi, Orland, and Zee [Phys. Rev. Lett. 94, 168103 (2005)]. The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a $N\times N$ Hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement, and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of $1∕N$ as being a measure of the concentration of ${\mathrm{Mg}}^{2+}$ in solution.

Many neurons display intrinsic interspike interval correlations in their spike trains. However, the effects of such correlations on information transmission in neural populations are not well understood. We quantified signal processing using linear response theory supported by numerical simulations in networks composed of two different models: One model generates a renewal process where interspike intervals are not correlated while the other generates a nonrenewal process where subsequent interspike intervals are negatively correlated. Our results show that the fractional rate of increase in information rate as a function of network size and stimulus intensity is lower for the nonrenewal model than for the renewal one. We show that this is mostly due to the lower amount of effective noise in the nonrenewal model. We also show the surprising result that coupling has opposite effects in renewal and nonrenewal networks: Excitatory (inhibitory coupling) will decrease (increase) the information rate in renewal networks while inhibitory (excitatory coupling) will decrease (increase) the information rate in nonrenewal networks. We discuss these results and their applicability to other classes of excitable systems.

We consider the use of a running measure of power spectrum disorder to distinguish between the normal sinus rhythm of the heart and two forms of cardiac arrhythmia: atrial fibrillation and atrial flutter. This spectral entropy measure is motivated by characteristic differences in the power spectra of beat timings during the three rhythms. We plot patient data derived from ten-beat windows on a “disorder map” and identify rhythm-defining ranges in the level and variance of spectral entropy values. Employing the spectral entropy within an automatic arrhythmia detection algorithm enables the classification of periods of atrial fibrillation from the time series of patients’ beats. When the algorithm is set to identify abnormal rhythms within $6\mathrm{s}$, it agrees with 85.7% of the annotations of professional rhythm assessors; for a response time of $30\mathrm{s}$, this becomes 89.5%, and with $60\mathrm{s}$, it is 90.3%. The algorithm provides a rapid way to detect atrial fibrillation, demonstrating usable response times as low as $6\mathrm{s}$. Measures of disorder in the frequency domain have practical significance in a range of biological signals: the techniques described in this paper have potential application for the rapid identification of disorder in other rhythmic signals.

Proteins are polymerized by cyclic machines called ribosomes, which use their messenger RNA (mRNA) track also as the corresponding template, and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them—namely, the dwell time distribution—has been measured in recent single-ribosome experiments. The form of the distribution, which fits best with our simulation data, is consistent with that extracted from the experimental data. For our computations, we use a model that captures both the mechanochemistry of each individual ribosome and their steric interactions. We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. Finally, inspired by recent advances in the experimental techniques of manipulating single ribosomes, we make theoretical predictions on the force-velocity relation for individual ribosomes. In principle, all our predictions can be tested by carrying out in vitro experiments.

The spectral densities of ensembles of non-Hermitian sparse random matrices are analyzed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated. Within this approach, the generalized Girko’s law is recovered easily. We compare our results with direct diagonalisation for a number of random matrix ensembles, finding excellent agreement.

We use the standardized variance $\left({\nu }_{\mathit{st}}\right)$ of the degree distribution of a random network as an analytic measure of its heterogeneity. We show that ${\nu }_{\mathit{st}}$ accurately predicts, quantitatively, the success of cooperators in an evolutionary prisoner’s dilemma. Moreover, we show how the generating functional expression for ${\nu }_{\mathit{st}}$ suggests an intrinsic interpretation for the heterogeneity of the network that helps explain local mechanisms through which cooperators thrive in heterogeneous populations. Finally, we give a simple relationship between ${\nu }_{\mathit{st}}$, the cooperation level, and the epidemic threshold of a random network that reveals an appealing connection between epidemic disease models and the evolutionary prisoner’s dilemma.

Considering the accumulation phenomenon in public places, we investigate how the condensation of moving bosonic particles influences the epidemic spreading in scale-free metapopulation networks. Our mean-field theory shows that condensation can significantly enhance the effect of epidemic spreading and reduce the threshold for epidemic to survive, in contrast to the case of without condensation. In the stationary state, the number of infected particles increases with the degree $k$ linearly when $k<k_c$ and nonlinearly when $k>k_c$, where $k_c$ denotes the crossover degree of the nodes with unity particle. The dependence of critical infective rate ${\beta }_c$ on the parameters $k_{\max }$, $\mu$, and $\delta$, is figured out, where $k_{\max }$, $\mu$, and $\delta$ denote the largest degree, recovery rate, and jumping exponent, respectively. Numerical simulations have confirmed the theoretical predictions.

Many real oscillators are coupled to other oscillators, and the coupling can affect the response of the oscillators to stimuli. We investigate phase-response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the system. Through simulation and analytic methods, the PRCs for globally coupled oscillators are also discussed.

Statistical properties of topological defects in defect-mediated turbulence due to the Doppler instability are examined experimentally in the Belousov-Zhabotinsky reaction. By applying the phase space reconstruction approach, processes of defect creation, annihilation, and defect movement are analyzed. The defect dynamics can be well interpreted within the framework of stochastic Markovian process. In contrast to previous studies that made direct measure of the gain and loss rates, which is practically difficult, we demonstrate that the rates can be obtained directly from the analysis of the time series of defects, and the shape of the probability distribution function can be reproduced in a simple way.

The author proposes an interface matching method for solving surface plasmon modes with damping in plasmonic crystals. The damping constant is considered a crucial parameter instead of a small perturbation to the undamped system. The damping effect is manifest on the complex nature of the eigenfrequency as well as on the eigenfield. For periodic layered structures, the decay factors of the two fundamental modes asymptotically approach $\gamma ∕2$ in the large-wave-number limit. For two-dimensional plasmonic crystals, the decay factors of surface plasmon modes are gathered around and bounded by $\gamma ∕2$.

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\mathcal{S}$-species hard-core lattice gas. On introducing $\mathcal{S}$ spherical constraints, the free energy may be expressed generally in terms of an $\mathcal{S}\times \mathcal{S}$ matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected “demagnetization effect” suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an $XY$ spin system below criticality.

We use light microscopy to investigate the aging dynamics of a glass made of closely packed soft spheres, following a rapid transition from a fluid to a solidlike state. By measuring time-resolved, coarse-grained displacement fields, we identify two classes of dynamical events, corresponding to reversible and irreversible rearrangements, respectively. The reversible events are due to the small, experimentally unavoidable fluctuations of the temperature imposed to the sample, leading to transient thermal expansions and contractions that cause shear deformations. The irreversible events are plastic rearrangements, induced by the repeated shear cycles. We show that the displacement due to the irreversible rearrangements grows linearly with time, both on average and at a local level. The velocity associated with this ballistic motion decreases exponentially with sample age, accounting for the observed slowing down of the dynamics. The displacement field due to the irreversible rearrangements has a vortexlike structure and is spatially correlated over surprisingly long distances.

Molecular dynamics computer simulations have been carried out in the smectic-$A$ phase of stiff wormlike rods. The analysis of the long trajectories generated has allowed for a detailed insight into that diffusion mechanism which is operative in the above-mentioned liquid-crystalline phase, as recently visualized in a system of colloidal virus rods. Fast particles, i.e., those able to move abruptly out from one into an adjacent layer, have been identified. Their properties, such as the velocity autocorrelation function and the orientational distribution function, have been determined and compared to the corresponding quantities valid for a generic rod.

We investigate Turing bifurcations in a neural field model with one spatial dimension. For some parameter values the resulting Turing patterns are stable, while for others the patterns appear transiently. We show that this difference is due to the relative position in parameter space of the saddle-node bifurcation of a spatially periodic pattern and the Turing bifurcation point. By varying parameters we are able to observe transient patterns whose duration scales in the same way as type-I intermittency. Similar behavior occurs in two spatial dimensions.

We propose a general framework of pressure effects on the structures formed by the self-assembly of solute molecules immersed in solvent. The integral equation theory combined with the morphometric approach is employed for a hard-body model system. Our picture is that protein folding and ordered association of proteins are driven by the solvent entropy: At low pressures, the structures almost minimizing the excluded volume (EV) generated for solvent particles are stabilized. Such structures appear to be even more stabilized at high pressures. However, it is experimentally known that the native structure of a protein is unfolded, and ordered aggregates such as amyloid fibrils and actin filaments are dissociated by applying high pressures. This initially puzzling result can also be elucidated in terms of the solvent entropy. A clue to the basic mechanism is in the phenomenon that, when a large hard-sphere solute is immersed in small hard spheres forming the solvent, the small hard spheres are enriched near the solute and this enrichment becomes greater as the pressure increases. We argue that “attraction” is entropically provided between the solute surface and solvent particles, and the attraction becomes higher with rising pressure. Due to this effect, at high pressures, the structures possessing the largest possible solvent-accessible surface area together with sufficiently small EV become more stable in terms of the solvent entropy. To illustrate this concept, we perform an analysis of pressure denaturation of three different proteins. It is shown that only the structures that have the characteristics described above exhibit interesting behavior. They first become more destabilized relative to the native structure as the pressure increases, but beyond a threshold pressure the relative instability begins to decrease and they eventually become more stable than the native structure.

We propose a model for DNA dynamics by introducing the helical structure through twist deformation in analogy with the structure of a helimagnet and a cholesteric liquid-crystal system. The dynamics in this case is found to be governed by the completely integrable sine Gordon equation, which admits kink-antikink solitons with increased width, representing a wide base-pair opening configuration in DNA. The results show that the helicity introduces a length-scale variation and thus provides a better representation of the base-pair opening in DNA.

Using a homotopic family of boundary eigenvalue problems for the mean-field ${\alpha }^2$ dynamo with helical turbulence parameter $\alpha \left(r\right)={\alpha }_0+\gamma \Delta \alpha \left(r\right)$ and homotopy parameter $\beta ∊[0,1]$, we show that the underlying network of diabolical points for Dirichlet (idealized, $\beta =0$) boundary conditions substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for Robin (physically realistic, $\beta =1$) boundary conditions. In the $({\alpha }_0,\beta ,\gamma )$ space the Arnold tongues of oscillatory solutions at $\beta =1$ end up at the diabolical points for $\beta =0$. In the vicinity of the diabolical points the space orientation of the three-dimensional tongues, which are cones in first-order approximation, is determined by the Krein signature of the modes involved in the diabolical crossings at the apexes of the cones. The Krein space-induced geometry of the resonance zones explains the subtleties in finding $\alpha$ profiles leading to spectral exceptional points, which are important ingredients in recent theories of polarity reversals of the geomagnetic field.

A full-scale nonlinear stability analysis is performed on a reaction-diffusion system that includes a cubic polynomial source term and Cattaneo’s modification of Fick’s law of diffusion. This modification incorporates the effect of a small, finite relaxation time of flux at the macroscopic level of the description of the process. While linear stability analysis predicts the decay of small wavelength perturbations on a homogeneous steady state for large reaction time, consideration of finite perturbations leads to a spatiotemporal instability, resulting in an interesting phenomenon of periodic collapse and revival of spatial patterns. This instability is relaxation (time) driven, and the time period is determined by self-sustaining oscillations due to the limit cycle of the underlying dynamics. The nonlinear dynamics of finite perturbations may thus be generically different from what is expected from a linear stability analysis.

We investigate homogeneous and inhomogeneous sine-Gordon ratchet systems in which a temporal symmetry and the spatial symmetry, respectively, are broken. We demonstrate that in the inhomogeneous systems with ac driving the soliton dynamics is chaotic in certain parameter regions, although the soliton motion is unidirectional. This is qualitatively explained by a one-collective-coordinate theory which yields an equation of motion for the soliton that is identical to the equation of motion for a single particle ratchet which is known to exhibit chaotic transport in its underdamped regime. For a quantitative comparison with our simulations we use a two-collective-coordinate (2CC) theory. In contrast to this, homogeneous sine-Gordon ratchets with biharmonic driving, which breaks a temporal shift symmetry, do not exhibit chaos. This is explained by a 2CC theory which yields two ODEs: one is linear, the other one describes a parametrically driven oscillator which does not exhibit chaos. The latter ODE can be solved by a perturbation theory which yields a hierarchy of linear equations that can be solved exactly order by order. The results agree very well with the simulations.