Kirkwood-Buff (KB) solution theory is a means to obtain certain thermodynamic derivatives from knowledge of molecular distributions. In actual practice the required integrals over radial distribution functions suffer inaccuracies due to finite-distance truncation effects and their use in closed systems. In this work we discuss how best to minimize these inaccuracies under traditional KB theory. In addition we implement a method for calculating KB quantities in molecular simulations with periodic boundary conditions and particularly within the canonical ensemble. The method is based on a finite-Fourier-series expansion of molecular concentration fluctuations and leads to more reliable results for a given computational effort. The procedure is validated and compared to the original method for a nonideal liquid mixture of Lennard-Jones particles intended to imitate a real system, carbon tetrafluoride, and methane.

The nucleation and growth of compact two-dimensional islands having a regular shape and edges consisting of atomically straight kink-free segments is studied analytically and with kinetic Monte Carlo (KMC) simulations. In the analytical model the islands grow by a cyclic process of deposition of single atomic rows along the island edges. Two ends of an incomplete row are the kink sites where adatoms incorporate into the crystal. Adatoms attached to the island edge are able to migrate along the edge and detach back to the terrace before reaching the kinks. Completion of the rows corresponds to a sequence of the magic island sizes. It is assumed that a one-dimensional nucleus of the next atomic row (a pair of kinks) forms when two adatoms meet each other at the edge of the magic island. It follows from the model that at certain growth conditions the island density is independent of the deposition flux and increases with the increasing growth temperature. The predictions of the analytical model are in good agreement with results of KMC simulations. Computer simulations also show that the island size distribution gradually changes with the increasing detachment probability from the monomodal distribution with a peak around the mean island size to a sequence of monotonously decreasing peaks at magic sizes.

Most integrodifference models of biological invasions are based on the nonoverlapping-generations approximation. However, the effect of multiple reproduction events (overlapping generations) on the front speed can be very important (especially for species with a long life spam). Only in one-dimensional space has this approximation been relaxed previously, although almost all biological invasions take place in two dimensions. Here we present a model that takes into account the overlapping generations effect (or, more generally, the stage structure of the population), and we analyze the main differences with the corresponding nonoverlapping-generations results.

Precipitation patterns emerging in a two-dimensional moving front are investigated on the example of NaOH diffusing into a gel containing ${\text{AlCl}}_3$. The time evolution of the precipitate $\text{Al}{\left(\text{OH}\right)}_3$ can be observed since the precipitate redissolves in the excess outer electrolyte NaOH and thus it exists only in a narrow optically accessible region of the reaction front. The patterns display self-similar coarsening with a characteristic length $\xi$ increasing with time as $\xi \left(t\right)\sim \sqrt{t}$. A theory based on the Cahn-Hilliard phase-separation dynamics, including redissolution, is shown to yield agreement with the experiments.

We studied spatial Prisoner’s Dilemma and Stag Hunt games where both the strategy distribution and the players’ individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single $K$ (temperaturelike) parameter describing how strongly adoptions depend on the payoff difference. If we start the system from a random strategy distribution with many different player specific $K$ parameters, the simultaneous evolution of strategies and $K$ parameters drives the system to a final stationary state where only one $K$ value remains. In the coexistence phase of cooperator and defector strategies the surviving $K$ parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform $K$ is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.

The statistical physics properties of regular and irregular Sourlas codes are investigated in this paper by the cavity method. At finite temperatures, the free-energy density of these coding systems is derived and compared with the result obtained by the replica method. In the zero-temperature limit, the Shannon’s bound is recovered in the case of infinite-body interactions while the code rate is still finite. However, the decoding performance as obtained by the replica theory has not considered the zero-temperature entropic effect. The cavity approach is able to consider the ground-state entropy. It leads to a set of evanescent cavity fields propagation equations which further improve the decoding performance as confirmed by our numerical simulations on single instances. For the irregular Sourlas code, we find that it takes the trade-off between good dynamical property and high performance of decoding. In agreement with the results found from the algorithmic point of view, the decoding exhibits a first-order phase transition as occurs in the regular code system with three-body interactions. The cavity approach for the Sourlas code system can be extended to consider first-step replica symmetry breaking.

Chemoresponsive gels undergoing the Belousov-Zhabotinsky (BZ) reaction exhibit self-sustained pulsations, which can be harnessed to perform mechanical work. In technological applications, the gels would typically be confined between hard surfaces and thus, it is essential to establish how confinement affects these distinctive oscillations. Using theory and simulation, we pinpoint regions in phase space where the dynamic behavior of BZ gels critically depends on the presence of confining walls. We then illustrate how the wave propagation within thin samples can be tailored by selectively introducing “cut outs” in the bounding surfaces. The oscillations in the latter films are localized in specified areas, so the system contains well-defined oscillatory and nonoscillatory regions. The cut outs provide an effective means of tuning the mechanical action within the film and provide a route for tailoring the functionality of the material.

We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry, or fourfold symmetry. In this work—the first of a pair of articles—we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot’s internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields, and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter ${\gamma }_{\text{asym}}$. However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot’s boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot’s boundary smaller than a lead-width is deformed an arbitrarily large distance.

In this work—the second of a pair of articles—we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry. We use the semiclassical theory of transport to find the symmetry-induced contributions to weak localization corrections and universal conductance fluctuations for dots with left-right, up-down, inversion, and fourfold symmetries. We show that all these contributions are suppressed by asymmetric leads; however, they remain finite whenever leads intersect with their images under the symmetry operation. For an up-down symmetric dot, this means that the contributions can be finite even if one of the leads is completely asymmetric. We find that the suppression of the contributions to universal conductance fluctuations is the square of the suppression of contributions to weak localization. Finally, we develop a random-matrix theory model which enables us to numerically confirm these results.

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded-volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state solution is constructed in a slightly arranged matrix product form of the open TASEP. We obtain the critical line that separates the parameter space depending on whether the model has the stationary state. We calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state. We also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the M/M/1 queueing process and the open TASEP.

A wide variety of real-life networks share two remarkable generic topological properties: scale-free behavior and modular organization, and it is natural and important to study how these two features affect the dynamical processes taking place on such networks. In this paper, we investigate a simple stochastic process—trapping problem, a random walk with a perfect trap fixed at a given location, performed on a family of hierarchical networks that exhibit simultaneously striking scale-free and modular structure. We focus on a particular case with the immobile trap positioned at the hub node having the largest degree. Using a method based on generating functions, we determine explicitly the mean first-passage time (MFPT) for the trapping problem, which is the mean of the node-to-trap first-passage time over the entire network. The exact expression for the MFPT is calculated through the recurrence relations derived from the special construction of the hierarchical networks. The obtained rigorous formula corroborated by extensive direct numerical calculations exhibits that the MFPT grows algebraically with the network order. Concretely, the MFPT increases as a power-law function of the number of nodes with the exponent much less than 1. We demonstrate that the hierarchical networks under consideration have more efficient structure for transport by diffusion in contrast with other analytically soluble media including some previously studied scale-free networks. We argue that the scale-free and modular topologies are responsible for the high efficiency of the trapping process on the hierarchical networks.

Anomalous transport of non-Markovian thermal Brownian particle dynamics in spatially periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is modeled by a generalized Langevin equation with exponentially correlated Gaussian thermal noise, obeying the fluctuation-dissipation theorem. We study the role of nonzero correlation time of thermal fluctuations for the occurrence of absolute negative (linear) mobility (ANM) near zero bias, negative-valued, nonlinear mobility (NNM), and negative differential mobility (NDM) at finite bias away from equilibrium. We detect that a nonzero thermal correlation time can either enhance or also diminish the value of ANM. Moreover, finite thermal noise correlation can induce NDM and NNM in regions of parameter space for which such ANM and NNM behaviors are distinctly absent for limiting white thermal noise. In parts of the parameter space, we find a complex structure of regions of linear and nonlinear negative mobility: islands and tongues which emerge and vanish under parameters manipulation. While certain such anomalous transport regimes fade away with increasing temperature some specific regions interestingly remain rather robust. Outside those regimes with anomalous mobility, the ac/dc driven transport is either normal or the driven Brownian particles are not transported at all.

In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasistationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.

Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein functionality is often dominated by long-range hydro(phobic/philic) interactions, which both drive protein compaction and mediate protein-protein interactions. In contrast to previous reductionist short-range hydrophobicity scales, the holistic Moret-Zebende hydrophobicity scale [Phys. Rev. E 75, 011920 (2007)] represents a hydroanalytic tool that bioinformatically quantifies SOC in a way fully compatible with evolution. Hydroprofiling identifies chemical trends in the activities and substrate binding abilities of model enzymes and antibiotic animal lysozymes $c$, as well as defensins, which have been the subject of tens of thousands of experimental studies. The analysis is simple and easily performed and immediately yields insights not obtainable by traditional methods based on short-range real-space interactions, as described either by classical force fields used in molecular-dynamics simulations, or hydrophobicity scales based on transference energies from water to organic solvents or solvent-accessible areas.

Ventricular fibrillation (VF) is known to be the most dangerous cardiac arrhythmia, frequently leading to sudden cardiac death (SCD). During VF, cardiac output drops to nil and, unless the fibrillation is promptly halted, death usually ensues within minutes. While delivering life saving electrical shocks is a method of preventing SCD, it has been recognized that some, though not many, VF episodes are self-terminating, and understanding the mechanism of spontaneous defibrillation might provide newer therapeutic options for treatment of this otherwise fatal arrhythmia. Using the phase statistics approach, recently developed to study financial and physiological time series, here, we reveal the timing characteristics of transient features of ventricular tachyarrhythmia (mostly VF) electrocardiogram (ECG) and find that there are three distinct types of probability density function (PDF) of phase distributions: uniform (UF), concave (CC), and convex (CV). Our data show that VF patients with UF or CC types of PDF have approximately the same probability of survival and nonsurvival, while VF patients with CV type PDF have zero probability of survival, implying that their VF episodes are never self-terminating. Our results suggest that detailed phase statistics of human ECG data may be a key to understanding the mechanism of spontaneous defibrillation of fatal VF.

We investigate the capillary filling of three-dimensional microchannels with surfaces patterned by posts of square cross section. We show that pinning on the edges of the posts suppresses and can halt capillary filling. We stress the importance of the channel walls in controlling whether filling can occur. In particular for channels higher than the distance between adjacent posts, filling occurs for contact angles less than a threshold angle of $\sim 55°$, independent of the height of the channel.

It has been proposed [J. De Rosny, Ph.D. thesis, Université Paris VI, 2000] that the performance of time reversal at recreating a coherent pulse in a strongly reverberating medium is directly proportional to the number of resonant modes $M$ actively taking part at the transmission of energy. This idea is here tested against experimental results showing that as soon as losses are taken into account, the quality of the focused pulse is a sublinear function of $M$ leading to a saturation phenomenon that was previously unacknowledged. This is here proven to be caused by mutual coupling between lossy resonant modes, thanks to a statistical modal description of the transmission of signals through the medium. Closed-form relationships are proposed for the first two moments of the pulse signal-to-noise ratio linking them to the occupied bandwidth, the number of active modes, and the degree of resonance of the medium. These formulas, supported by experimental and numerical results, prove that the performance of time reversal can be affected by a strong statistical dispersion. The proposed analysis also predicts that time reversal is a self-averaging process when applied to a reverberating medium, thus, allowing the use of models developed in an ensemble-average framework.

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one.

We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps $N$, the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as $N^{1/3}$, for large $N$, and the width of the boundary region grows as $N^{\alpha /3}$, with $\alpha =0.40\pm 0.06$. If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, $⟨R_N^2⟩\sim N^{2\nu }$, shows a crossover from the Eulerian $\left(\nu =1/3\right)$ to a simple random-walk $\left(\nu =1/2\right)$ behavior.

We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high-frequency regime. In addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude $g_{syn}$. The amplitude of the voltage spikes decreases approximately linearly with $g_{syn}$. In some regions of parameter space the response is irregular, probably chaotic. In the chaotic regime between the mode-locked regions 3:1 and 2:1 near the lower excitation threshold, the output interspike interval histogram (ISIH) undergoes a sharp transition. If the driving period is below the critical value, $T_i<T^{\ast }$, the output histogram contains only odd multiples of $T_i$. For $T_i>T^{\ast }$ even multiples of $T_i$ also appear in the histogram, starting from the largest values. Near $T^{\ast }$ the ISIH scales logarithmically on both sides of the transition. The coefficient of variation of ISIH has a cusp singularity at $T^{\ast }$. The average response period has a maximum slightly above $T^{\ast }$. Near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 Hz.