Biochemical reaction networks in living cells usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells, mass-action theory fails to describe the dynamics of such systems. Instead, the biochemical reactions must be treated as stochastic processes that intrinsically generate concentration fluctuations of the chemicals. We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modeling and numerically exact Monte Carlo simulation of the temporally fluctuating concentration. Depending on the parameter regime, we find for the probability density of the concentration qualitatively distinct classes of distribution functions including power-law distributions with a fractional and tunable exponent. These findings challenge the traditional view of biochemical control networks as deterministic computational systems and suggest that CMCs in cells can function as versatile and tunable noise generators.

In order to study solvation effects on protein folding, we analyze the collapse transition of a self-avoiding random walk composed of hydrophobic segments that is embedded in a lattice model of a solvent. As expected, hydrophobic interactions lead to an attractive potential of mean force among chain segments. As a consequence, the random walk in solvent undergoes a collapse transition at a higher temperature than in its absence. Chain collapse is accompanied by the formation of a region depleted of solvent around the chain. In our simulation, the depleted region at collapse is as large as our computational domain.

In most unmyelinated axons, ion channels are distributed uniformly along the axon to facilitate stable propagation of action potentials. In this case, the conduction in the axon is continuous, and the excitability along the membrane is constant. Some experimental papers show that ion channels also locate in clusters in some unmyelinated axons. In this paper, we investigate theoretically the effect of clustered ion channels along unmyelinated axon. We mainly focused on two aspects: the propagation efficiency and the propagation speed. Our results show that localization of potassium ion channels is beneficial for increasing propagation efficiency and propagation speed of action potentials; however, localization of sodium ion channels is advantageous to the propagation efficiency only when axonal parameters are in a specific range.

In this Rapid Communication we consider certain equations that arise from imposing a constant kinetic-energy constraint on a one-dimensional set of oscillators. This is a nonlinear nonholonomic constraint on these oscillators and the dynamics are consistent with Gauss’s law of least constraint. Dynamics of this sort are of interest in nonequilibrium molecular dynamics. We show that under certain choices of external potential these equations give rise to a generalization of the so-called double-bracket equations which are of interest in studying gradient flows and integrable systems such as the Toda lattice. In the case of harmonic potentials the flow is described by a symmetric bracket and periodic solutions are obtained.

The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective “adaptive inflation expectations” with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, $r\left(t\right)$, changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time $t_c$. By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, $p\left(t\right)$. One is given by the already reported form $p\left(t\right)\approx {\left(t_c-t\right)}^{-\alpha }$ (with $\alpha >0$) and the other exhibits a logarithmic divergence, $p\left(t\right)\approx \text{ln}\left[1/\left(t_c-t\right)\right]$. The singularity is a signature for an economic crash. In the present work we express $p\left(t\right)$ explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of $r\left(t\right)$ and $p\left(t\right)$ performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941–1944) and Yugoslavia (1991–1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.

The heat transfer mechanism in Rayleigh-Bénard convection in a liquid with a mean temperature close to its boiling point is studied through numerical simulations with pointlike vapor bubbles, which are allowed to grow or shrink through evaporation and condensation and which act back on the flow both thermally and mechanically. It is shown that the effect of the bubbles is strongly dependent on the ratio of the sensible heat to the latent heat as embodied in the Jakob number Ja. For very small Ja the bubbles stabilize the flow by absorbing heat in the warmer regions and releasing it in the colder regions. With an increase in Ja, the added buoyancy due to the bubble growth destabilizes the flow with respect to single-phase convection and considerably increases the Nusselt number.

We propose a practical acoustic near-field microscope, which is simply a steel slab with periodic array of subwavelength slits. The near field is transported by the coupling of the incident evanescent waves and the acoustic guided modes supported by the structured slab. The transmission coefficients of the structured slab as a function of the transverse wave vector are theoretically derived, and a theoretical model is employed to study the imaging of the proposed device. Numerical simulations are also performed to verify the theoretical results, which show that subwavelength imaging with good quality can indeed be realized.

A statistical theory is presented that allows the calculation of the stationary state achieved by a driven one-component plasma after a process of collisionless relaxation. The stationary Vlasov equation with appropriate boundary conditions is reduced to an ordinary differential equation, which is then solved numerically. The solution is then compared with the molecular-dynamics simulation. A perfect agreement is found between the theory and the simulations. The full current-voltage phase diagram is constructed.

We study a fully connected network (cluster) of interacting two-state units as a model of cooperative decision making. Each unit in isolation generates a Poisson process with rate $g$. We show that when the number of nodes is finite, the decision-making process becomes intermittent. The decision-time distribution density is characterized by inverse power-law behavior with index $\mu =1.5$ and is exponentially truncated. We find that the condition of perfect consensus is recovered by means of a fat tail that becomes more and more extended with increasing number of nodes $N$. The intermittent dynamics of the global variable are described by the motion of a particle in a double well potential. The particle spends a portion of the total time ${\tau }_S$ at the top of the potential barrier. Using theoretical and numerical arguments it is proved that ${\tau }_S\propto \left(1/g\right)\text{ln}\left(\text{const}\times N\right)$. The second portion of its time, ${\tau }_K$, is spent by the particle at the bottom of the potential well and it is given by ${\tau }_K=\left(1/g\right)\text{exp}\left(\text{const}\times N\right)$. We show that the time ${\tau }_K$ is responsible for the Kramers fat tail. This generates a stronger ergodicity breakdown than that generated by the inverse power law without truncation. We establish that the condition of partial consensus can be transmitted from one cluster to another provided that both networks are in a cooperative condition. No significant information transmission is possible if one of the two networks is not yet self-organized. We find that partitioning a large network into a set of smaller interacting clusters has the effect of converting the fat Kramers tail into an inverse power law with $\mu =1.5$.

A theoretical framework for analyzing stochastic data from single-particle tracking in viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation, we found analytical expressions for the two-time dynamics of a particle subjected to a harmonic potential. The mean-square displacement and the velocity autocorrelation function of the diffusing particle are given in terms of the time lag. In particular, we investigate the subdiffusive case. Using a power-law memory kernel, exact expressions for the mean-square displacement and the velocity autocorrelation function are obtained in terms of Mittag-Leffler functions and their derivatives. The behaviors for short-, intermediate-, and long-time lags are investigated in terms of the involved parameters. Finally, the validity of usual approximations is examined.

A simple model composed of two rigid macromolecules (adsorbents) immersed in a large number of small molecules (adsorbates) is used to study entropy-driven association processes. The surfaces of the adsorbents are capable of adsorbing the smaller adsorbates. The partition function of the model is obtained analytically. The probability of dimerization and the number of adsorbed molecules are shown to depend on the enthalpy and the entropy differences between the assembled and the disassembled states. Under certain conditions, dimerization of the macromolecules occurs with increasing temperature. This entropy-driven self-assembly is originated from an overall entropy gain due to the release of the adsorbed small molecules, leading to a large peak in the heat capacity due to the dimer formation. The desorption of the adsorbates induces a sharp change in the first-order derivative of the free energy, resulting in another large peak in the heat capacity. A temperature-induced re-entrance into the dimer state is also contained in the model.

The cluster-cluster aggregation processes of Ising dipolar particles under thermal noise are investigated in the dilute condition. As the temperature increases, changes in the typical structures of clusters are observed from chainlike $\left(D\simeq 1\right)$ to crystalline $\left(D\simeq 2\right)$ through fractal structures $\left(D\simeq 1.45\right)$, where $D$ is the fractal dimension. By calculating the bending energy of the chainlike structure, it is found that the transition temperature is associated with the energy gap between the chainlike and crystalline configurations. The aggregation dynamics changes from being dominated by attraction to diffusion involving changes in the dynamic exponent $z=0.2$ to 0.5. In the region of temperature where the fractal clusters grow, different growth rates are observed between charged and neutral clusters. Using the Smoluchowski equation with a twofold kernel, this hetero-aggregation process is found to result from two types of dynamics: the diffusive motion of neutral clusters and the weak attractive motion between charged clusters. The fact that changes in structures and dynamics take place at the same time suggests that transitions in the structure of clusters involve marked changes in the dynamics of the aggregation processes.

We use computer simulations to study the glass transition of dense fluids made of polydisperse repulsive spheres. For hard particles, we vary the volume fraction, $\phi$, and use compressible particles to explore finite temperatures, $T>0$. In the hard sphere limit, our dynamic data show evidence of an avoided mode-coupling singularity near ${\phi }_{\text{MCT}}\approx 0.592$; they are consistent with a divergence of equilibrium relaxation times occurring at ${\phi }_0\approx 0.635$, but they leave open the existence of a finite temperature singularity for compressible spheres at volume fraction $\phi >{\phi }_0$. Using direct measurements and a scaling procedure, we estimate the equilibrium equation of state for the hard sphere metastable fluid up to ${\phi }_0$, where pressure remains finite, suggesting that ${\phi }_0$ corresponds to an ideal glass transition. We use nonequilibrium protocols to explore glassy states above ${\phi }_0$ and establish the existence of multiple equations of state for the unequilibrated glass of hard spheres, all diverging at different densities in the range $\phi ∊\left[0.642,0.664\right]$. Glassiness thus results in the existence of a continuum of densities where jamming transitions can occur.

We study the influence of composition changes on the glass transition of binary hard disk and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard disks strongly resembles the random close packing diagram. Compared to three dimensions from previous studies, the extension of the glass regime due to mixing is much more pronounced in two dimensions where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size ratio from unity.

In this study we develop a formalism to describe the organization of DNA inside bacteriophage capsids during genome packaging. We have previously shown that DNA inside bacteriophage phi29 (ϕ29) is organized into folded toroids [A. S. Petrov and S. C. Harvey, Structure 15, 21 (2007)], whereas epsilon15 (ε15) reveals the coaxial organization of the genetic material [A. S. Petrov, K. Lim-Hing, and S. C. Harvey, Structure 15, 807 (2007)]. We now show that each system undergoes two consecutive transitions. The first transition corresponds to the formation of global conformations and is analogous to a disorder-order conformational transition. The second transition is characterized by a significant loss of DNA mobility at the local level leading to glasslike dynamic behavior. Packing genetic material inside bacteriophages can be used as a general model to study the behavior of semiflexible chains inside confined spaces, and the proposed formalism developed here can be used to study other systems of linear polymer chains confined to closed spaces.

Electromagnetically induced transparency is a well-known quantum phenomena that electromagnetic wave controls the refractive index of medium. It enables us to create a passband for low-frequency electromagnetic wave in a dense plasma even if the plasma is opaque for the electromagnetic wave. This technique can be used to prove the ion acoustic wave because the ion acoustic frequency is lower than the plasma frequency. We have investigated a feasibility of electromagnetic radiation at THz region corresponding to the ion acoustic frequency from a dense plasma. We confirmed that the passband is created at about 7.5 THz corresponding to the ion acoustic frequency in the electron plasma density of ${10}^{21}{\text{cm}}^{-3}$ with a Ti:Sapphire laser with the wavelength of 800 nm and the laser intensity of ${10}^{17}\text{W}/{\text{cm}}^2$. The estimated radiation power is around 1 MW, which is expected to be useful for nonlinear THz science and applications.

Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutation spreads through the whole population tips the balance in favor of natural selection. The probability that the spread occurs, known as the fixation probability, depends heavily on how the population is structured. Certain topologies, albeit highly artificially contrived, have been shown to exist that favor fixation. We present a randomized mechanism for network growth that is loosely inspired in some of these topologies’ key properties and demonstrate, through simulations, that it is capable of giving rise to structured populations for which the fixation probability significantly surpasses that of an unstructured population. This discovery provides important support to the notion that natural selection can be enhanced over random drift in naturally occurring population structures.

We show that an environment composed by $N$ bosons coupled through cross-Kerr interaction to an oscillator of interest can be effective at destroying quantum coherences at short times and around the revival times even if $N=1$. It is analytically shown for this model that the effective Hilbert-space size is a relevant parameter for decoherence process. Based on numerical results, we investigate the long time dynamics and the classical limit. Since we are dealing with a phase reservoir, the model does not describe dissipation.

We consider flow in a Hele-Shaw cell for which the upper plate moves up and down, making the fluid-fluid interface be driven periodically. To study such a flow we employ a mode-coupling approach, which allows the analytical assessment of important aspects about the stability and morphology of the evolving interface. At the linear level, it is shown that both the amplitude and the frequency of the drive have a significant role in determining the ultimate number of fingers formed. The influence of these factors on the mechanisms of finger competition and finger tip behavior at the onset of nonlinear effects is also studied.

We investigate the statistics of flat-top solitary wave parameters in the presence of weak multiplicative dissipative disorder. We consider first propagation of solitary waves of the cubic-quintic nonlinear Schrödinger equation (CQNLSE) in the presence of disorder in the cubic nonlinear gain. We show by a perturbative analytic calculation and by Monte Carlo simulations that the probability-density function (PDF) of the amplitude $\eta$ exhibits loglognormal divergence near the maximum possible amplitude ${\eta }_m$, a behavior that is similar to the one observed earlier for disorder in the linear gain [A. Peleg et al., Phys. Rev. E 72, 027203 (2005)]. We relate the loglognormal divergence of the amplitude PDF to the superexponential approach of $\eta$ to ${\eta }_m$ in the corresponding deterministic model with linear/nonlinear gain. Furthermore, for solitary waves of the derivative CQNLSE with weak disorder in the linear gain both the amplitude and the group velocity $\beta$ become random. We therefore study analytically and by Monte Carlo simulations the PDF of the parameter $p$, where $p=\eta /\left(1-{\epsilon }_s\beta /2\right)$ and ${\epsilon }_s$ is the self-steepening coefficient. Our analytic calculations and numerical simulations show that the PDF of $p$ is loglognormally divergent near the maximum $p$ value.