We present a model to describe the on-off switching of transcriptional activity in a genetic assembly by considering the intrinsic characteristics of a giant genomic DNA molecule which can undergo a discrete structural transition between coiled and compact states. We propose a model in which the transition in the higher-order structure of DNA plays an essential role in regulating stable on-off switching and/or the oscillation of a large number of genes under the fluctuations in a living cell, where such a structural transition is caused by environmental factors. This model explains the rapid and broad transcriptional response in a genetic assembly as well as its robustness against fluctuations.

The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a given population are heterogeneous in that their natural frequencies are drawn from a given distribution, and each population has its own such distribution. The coupling among the oscillators is global, however, we permit the coupling strengths between the members of different populations to be separately specified. We determine the critical condition for the onset of coherent collective behavior, and develop the illustrative case in which the oscillator frequencies are drawn from a set of (possibly different) Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in which the collective dynamics of several interacting populations of oscillators (such as excitatory and inhibitory neurons and glia) are of interest.

Mesoscopic models for traffic flows are usually difficult to be employed because of the appearance of integro-differential terms in the models. In this work, a lattice Boltzmann model for traffic flow is introduced on the basis of the existing kinetics models by using the Bhatnagar-Gross-Krook-type approximation interaction term in the Boltzmann equation and discretizing it in time and phase space. The so-obtained model is simple while the relevant parameters are physically meaningful. Together with its discrete feature, the model can be easily used to investigate numerically the behavior of traffic flows. In consequence, the macroscopic dynamics of the model is derived using the Taylor and Chapman-Enskog expansions. For validating the model, numerical simulations are conducted under the periodic boundary conditions. It is found that the model could reasonably reproduce the fundamental diagram. Moreover, certain interesting physical phenomena can be captured by the model, such as the metastability and stop-and-go phenomena.

We investigate the consequences of delay in the iodate–arsenous acid reaction under the influence of an electric field at a constant current density. Using the charge balance condition, we show how the electric field may induce an intrinsic delay in the system, which gives rise to instability. The different instability regions in the appropriate parameter space are examined. We show how the delay incites an absolute instability in a system otherwise displaying varied wave-front characteristics, viz., convective and absolute instabilities and also stationary patterns.

A linear stability analysis of the buoyant-thermocapillary flow in open rectangular cavities with aspect ratios in the range $\Gamma =1.2$ to 8 is carried out for Prandtl number $\mathrm{Pr}=10$ and conditions of previous experiments. The results are in very good agreement with most available experimental data. The energy transfer between the basic and the perturbation flow reveals that buoyancy is not directly instrumental in the instabilities. For aspect ratios less than about three a stationary three-dimensional cellular flow arises. The instability relies on the lift-up mechanism operating in the shear layer below the free surface and it is aided by weak Marangoni forces. For larger aspect ratios Marangoni effects play a more significant role. While plane hydrothermal waves may appear a certain distance away from the hot wall for sufficiently large aspect ratios, the instability at intermediate aspect ratios is strongly influenced by the local nonparallel basic-flow structure.

We report finding a self-consistent electric field of electrons, ions, and dust grains inside an ordered dust cloud in glow discharge, and show that this field differs radically from that of an isolated grain. Besides, the screening radius coincides with the size of Wigner-Seitz cell. The value of potential necessary for containing dust particles in the direction perpendicular to the discharge axis is estimated. We show that the interaction potential energy of a system of ordered dust grains has a form characteristic of ionic crystals. Critical parameters for a liquidlike dust structure are estimated. The correlation function of dust grains obtained via this approach is compared with the measured function.

We use a lattice-Boltzmann based Brownian dynamics simulation to investigate the elongation of DNA at a convergent stagnation point trapped by a uniform attractive potential. The trapping rate of the DNA is not sensitive to the potential and, consistent with a mean field theory, scales as the Peclet number, ${\mathrm{Pe}}^{1∕3}$. Surprisingly, we find that the coiled state is favored over the stretched state at high Pe. The final elongation is determined by conformation changes during transport to the stagnation point, rather than hydrodynamic stretching at that point.

We study the effect of the presence of a regular substrate pattern on the irreversible adsorption of nanosized and colloid particles. Deposition of disks of radius $r_0$ is considered, with the allowed regions for their center attachment at the planar surface consisting of square cells arranged in a square lattice pattern. We study the jammed state properties of a generalized version of the random sequential adsorption model for different values of the cell size, $a$, and cell-cell separation, $b$. The model shows a surprisingly rich behavior in the space of the two dimensionless parameters $\alpha =a∕2r_0$ and $\beta =b∕2r_0$. Extensive Monte Carlo simulations for system sizes of $500\times 500$ square lattice unit cells were performed by utilizing an efficient algorithm, to characterize the jammed state morphology.

In a coarse-grained description of a protein chain, all of the 20 amino acid residues can be broadly divided into three groups: Hydrophobic $\left(H\right)$, polar $\left(P\right)$, and electrostatic $\left(E\right)$. A protein can be described by nodes tethered in a chain with a node representing an amino acid group. Aspartic acid protease consists of 99 residues in a well-defined sequence of $H$, $P$, and $E$ nodes tethered together by fluctuating bonds. The protein chain is placed on a cubic lattice where empty lattice sites constitute an effective solvent medium. The amino groups (nodes) interact with the solvent $\left(S\right)$ sites with appropriate attractive $\left(PS\right)$ and repulsive $\left(HS\right)$ interactions with the solvent and execute their stochastic movement with the Metropolis algorithm. Variations of the root mean square displacements of the center of mass and that of its center node of the protease chain and its gyration radius with the time steps are examined for different solvent strength. The structure of the protease swells on increasing the solvent interaction strength which tends to enhance the relaxation time to reach the diffusive behavior of the chain. Equilibrium radius of gyration increases linearly on increasing the solvent strength: A slow rate of increase in weak solvent regime is followed by a faster swelling in stronger solvent. Variation of the gyration radius with the time steps suggests that the protein chain moves via contraction and expansion in a somewhat quasiperiodic pattern particularly in strong solvent.

We quantify and analyze the growth dynamics of a religious group in 140 countries for a 47-year period (1959–2005). We find that (i) the distribution of annual logarithmic growth rates exhibits the same functional form for distinct size scales and (ii) the standard deviation of growth rates scales with size as a power law. Both findings hold for distinct measures of religious activity. These results are in surprising agreement with those found in the study of economic activities and scientific research, suggesting that religious activities are governed by universal growth mechanisms. We also compare the empirical findings on religious activities with the predictions of general models recently proposed in the context of complex organizations. Our findings should provide useful information for a better understanding of the mechanisms governing the growth of religion.

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is “knocked out” (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates’ Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can—to a good approximation—be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Nanoparticles suspended in ambient air within microscale geometries form a Knudsen layer when diffusing in a Brownian fashion toward a solid wall. More specifically, the particle number density adjacent to the wall approaches a nonzero value proportional to the flux. An approximate theory for the coefficient of proportionality as a function of the particle sticking fraction at the wall and the drift velocity normal to the wall is compared to Langevin particle simulations. The resulting boundary condition enables accurate advection-diffusion simulations of nanoparticle-aerosol transport.

The influence of a slight temperature change on the correlation of multiply scattered acoustic waves is studied, and experimental results are discussed. The technique presented here, similar to diffusing-acoustic-wave spectroscopy, is based on the sensitivity of a multiply scattering medium to a slight change. Ultrasonic waves around 3 MHz are transmitted through a sample made of steel rods in water and recorded by an array of transducers at different temperatures. The cross correlations between highly scattered signals are computed. The main effect of the temperature change is a simple dilation of the times of arrival, due to a change of the sound velocity in water. But the scatterers also play a role in the progressive decorrelation of wave forms. An analysis resolved in both time and frequency shows that at some particular frequencies, the resonant behavior of the scatterers is responsible for a significantly larger decorrelation. Interestingly, the experimental results allow one to detect the presence of a small resonance that was not detected earlier on the same scatterers with classical measurement of the scattering mean free path. A simple model is proposed to interpret the experimental results.

We find a general integrable system of reduced Maxwell-Bloch equations describing the interaction of a two-component electromagnetic field with the dipole transition of a two-level medium. The anisotropy of the anisotropic dipole momentum of the transition as a permanent dipole momentum is taken into account. A solution of the model is found for a particular case by using the inverse scattering transform. The method is based on a solution of the Riemann-Hilbert problem taking into account the symmetry properties of the corresponding fundamental solutions.

An exactly solvable model is used to obtain the response to confinement of the cluster distribution of linear aggregation. A direct relevance to simulation studies of linear self-assembly in discotic solutions and in peptide tape formation is proposed. The mapping predicts, for typical simulation procedures, that a finite reservoir of solute leads to a dramatic departure from isodesmic chemical equilibria for solute-solute interaction strengths higher than only a few $k_{B}T$.

Drying processes of polymer solutions on a solid substrate are studied, based on the two-fluid model for polymer solutions or gels. A simplified model which can describe a skin formation process is proposed to examine the diffusion process of polymers and the evaporation process of solvent. The authors show that when a skin (gel phase) is formed, the collective diffusion coefficient is greatly enhanced whereas the evaporation of solvent is considerably reduced. These two results originate from the bulk elasticity of polymer gels.

We examine numerically the three-way relationships among structure, Laplacian spectra, and frequency synchronization dynamics on complex networks. We study the effects of clustering, degree distribution, and a particular type of coupling asymmetry (input normalization), all of which are known to have effects on the synchronizability of oscillator networks. We find that these topological factors produce marked signatures in the Laplacian eigenvalue distribution and in the localization properties of individual eigenvectors. Using a set of coordinates based on the Laplacian eigenvectors as a diagnostic tool for synchronization dynamics, we find that the process of frequency synchronization can be visualized as a series of quasi-independent transitions involving different normal modes. Particular features of the partially synchronized state can be understood in terms of the behavior of particular modes or groups of modes. For example, there are important partially synchronized states in which a set of low-lying modes remain unlocked while those in the main spectral peak are locked. We find therefore that spectra are correlated with dynamics in ways that go beyond results relating a single threshold to a single extremal eigenvalue.

The continuous Gaussian ensemble, also known as the $\nu$-Gaussian or $\nu$-Hermite ensemble, is a natural extension of the classical Gaussian ensembles of real $\left(\nu =1\right)$, complex $\left(\nu =2\right)$, or quaternion $\left(\nu =4\right)$ matrices, where $\nu$ is allowed to take any positive value. From a physical point of view, this ensemble may be useful to describe transitions between different symmetries or to describe the terrace-width distributions of vicinal surfaces. Moreover, its simple form allows one to speed up and increase the efficiency of numerical simulations dealing with large matrix dimensions. We analyze the long-range spectral correlations of this ensemble by means of the ${\delta }_n$ statistic. We derive an analytical expression for the average power spectrum of this statistic, $\overline{P_k^{\delta }}$, based on approximated forms for the two-point cluster function and the spectral form factor. We find that the power spectrum of ${\delta }_n$ evolves from $\overline{P_k^{\delta }}\propto 1/k$ at $\nu =1$ to $\overline{P_k^{\delta }}\propto 1/k^2$ at $\nu =0$. Relevantly, the transition is not homogeneous with a $1/f^{\alpha }$ noise at all scales, but heterogeneous with coexisting $1/f$ and $1/f^2$ noises. There exists a critical frequency $k_c\propto \nu$ that separates both behaviors: below $k_c$, $\overline{P_k^{\delta }}$ follows a $1/f$ power law, while beyond $k_c$, it transits abruptly to a $1/f^2$ power law. For $\nu >1$ the $1/f$ noise dominates through the whole frequency range, unveiling that the $1/f$ correlation structure remains constant as we increase the level repulsion and reduce to zero the amplitude of the spectral fluctuations. All these results are confirmed by stringent numerical calculations involving matrices with dimensions up to ${10}^5$.

We present an approach to the estimate of the potential of mean force along a generic reaction coordinate based on maximum likelihood methods and path-ensemble averages in systems driven far from equilibrium. Following similar arguments, various free energy estimators can be recovered, all providing comparable computational accuracy. The method, applied to the unfolding process of the $\alpha$-helix form of an alanine decapeptide, gives results in good agreement with thermodynamic integration.

We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency of energy minima whereas the disconnectivity network tells us about the heights of the energy barriers. Both graphs are constructed by the exact enumeration of a two-dimensional square lattice of a frustrated spin glass with nearest-neighbor interactions up to the size of 27 spins. The enumeration of the energy-landscape minima as well as the analytical mean-field approximation show that these minima have a Gaussian distribution, and the connectivity graph has a log-Weibull degree distribution of shape $\kappa =8.22$ and scale $\lambda =4.84$. To study the effect of frustration on these results, we introduce an unfrustrated spin-glass model and demonstrate that the degree distribution of its connectivity graph shows a power-law behavior with the −3.46 exponent, which is similar to the behavior of proteins and Lennard-Jones clusters in its power-law form.