The local and slow dynamics of a colloidal particle dispersed in a hyperswollen lyotropic lamellar phase was studied by passive and active microrheological methods. According to observation by a particle-tracking video microscopy, the motion of a particle follows a normal diffusion process in a lamellar phase with a large interlayer distance. However, trap-diffusion motion was also observed for a small interlayer distance. This characteristic motion was discussed by consideration of the time evolution of mean square displacement, the van Hove self-correlation function and the non-Gaussian parameter. These indicate that the dynamics of a particle becomes spatially heterogeneous in a lamellar phase whose interlayer distance is close to the size of the particle. By the measurement of local viscosity using optical tweezers, Newtonian behavior was observed at a high shear rate. In a lamellar phase with a small interlayer distance, non-Newtonian behavior was also observed at a low shear rate. The dependences of effective viscosity on the interlayer distance obtained by both methods are in agreement. The effective viscosity in the lamellar phase was found to be four to five times larger than that of water even for a large interlayer distance. Possible reasons for the increase in effective viscosity are discussed quantitatively.

It is well known that a mixture of big and small hard spheres next to a planar wall will exhibit segregation based on their size difference. The larger spheres will tend to locate next to the substrate because the overall system entropy loss per unit area is less. In the present study we determine the role of attraction between the small particles and the wall to displace the larger particles. Both fluids density-functional theory and discontinuous molecular dynamics simulations demonstrate that at a certain attractive potential, which is on the order of the thermal energy, the large particles can indeed be dislodged from the surface layer so the small particles are now the major surface component. Exploration of a range of parameters, including relative sphere size and concentration, as well as attractions between the small spheres in the bulk, shows that the phenomenon is quite robust.

The ability to design artificial genetic devices with predictable functions is critical to the development of synthetic biology. Given the highly variable requirements of biological designs, the ability to tune the behavior of a genetic device is also of key importance; such tuning will allow devices to be matched with other components into larger systems, and to be shifted into the correct parameter regimes to elicit desired behaviors. Here, we have developed a minimal synthetic genetic system that acts as a multifunction, tunable biodevice in the bacterium Escherichia coli. First, it acts as a biochemical AND gate, sensing the extracellular small molecules isopropyl $\beta \text{-D}$-1-thiogalactopyranoside and anhydrotetracycline as two input signals and expressing enhanced green fluorescent protein as an output signal. Next, the output signal of the AND gate can be amplified by the application of another extracellular chemical, arabinose. Further, the system can generate a wide range of chemically tunable single input-output response curves, without any genetic alteration of the circuit, by varying the concentrations of a set of extracellular small molecules. We have developed and parameterized a simple transfer function model for the system, and shown that the model successfully explains and predicts the quantitative relationships between input and output signals in the system.

We study long-wave Marangoni convection in a layer heated from below. Using the scaling $k=O\left(\sqrt{\text{Bi}}\right)$, where $k$ is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

An adaptive feedback method for tracking and stabilizing unknown and/or slowly varying saddle-type steady states of conservative and weakly damped dissipative dynamical systems is proposed. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. The proposed controller involves both filters working in parallel. As a specific example, the Lagrange point L2 of the Sun-Earth system is discussed and the second-order saddle model is considered. Analog simulations have been performed using an inclusive nonlinear electrical circuit, imitating dynamics of a body along the Sun-Earth line. External chaotic perturbations have been used to check the robustness of the control technique.

We present a numerical study of the statistical behavior of a two-phase flow in a two-dimensional porous medium subjected to an oscillatory acceleration transverse to the overall direction of flow. A viscous nonwetting fluid is injected into a porous medium filled with a more viscous wetting fluid. During the whole process sinusoidal oscillations of constant amplitude and frequency accelerates the porous medium sideways, perpendicular to the overall direction of flow. The invasion process displays a transient behavior where the saturation of the defending fluid decreases, before it enters a state of irreducible wetting fluid saturation, where there is no net transport of defending fluid toward the outlet of the system. In this state the distribution of sizes of the remaining clusters are observed to obey a power law with an exponential cutoff. The cutoff cluster size is found to be determined by the flow and oscillatory stimulation parameters. This cutoff size is also shown to be directly related to the extracted amount of defending fluid. Specifically, the results show that the oscillatory acceleration of the system leads to potentially a large increase in extracted wetting fluid.

Particulate dense suspensions behave as complex fluids. They do not lend themselves easily to analytical solution. We propose an analytical model to mimic this problem. Namely, we consider arrays of long parallel plates which represent a simplification of arrays of chains of spherical particles. This simplified model can be solved analytically. The effect of effective rotation of the spherical particles is taken into account by attributing different velocities on each side of the plate that mimics the fact that particles are subject to shear. This work is an extension of a previous study where particle rotation was disregarded. The flow rate, the dissipation and the apparent viscosity are studied as a function of the underlying structure. For a single plate placed out of the flow center, the viscosity is lower when rotation is taken into account. For two plates, the minimal viscosity corresponds to the situation where the particles are as close as possible to the center and arranged symmetrically with respect to the center. We compute the rheological properties for arbitrary plate positions, and exploit them for a periodic arrangement. For $N$ plates, and in a confined geometry, the viscosity is about twice as small as compared to the situation where rotation is ignored. We have conducted a numerical study of a suspension of spherical particles, and linear chains of spherical particles. The numerical study is in good qualitative and semiquantitative agreement with the analytical theory considering long plates. This agreement highlights the fact that our analytical model captures the essential features of a real suspension. The numerical study is based on a fluid dynamic particle method where the particles are represented by a scalar field having high viscosity inside.

The control of quantum dynamics is often concerned with finding time-dependent optimal control fields that can take a system from an initial state to a final state to attain the desired value of an observable. This paper presents a general method for formulating monotonically convergent algorithms to iteratively improve control fields. The formulation is based on a two-point boundary-value quantum control paradigm (TBQCP) expressed as a nonlinear integral equation of the first kind arising from dynamical invariant tracking control. TBQCP is shown to be related to various existing techniques, including local control theory, the Krotov method, and optimal control theory. Several accelerated monotonic convergence schemes for iteratively computing control fields are derived based on TBQCP. Numerical simulations are compared with the Krotov method showing that the new TBQCP schemes are efficient and remain monotonically convergent over a wide range of the iteration step parameters and the control pulse lengths, which is attributable to the trap-free character of the transition probability quantum dynamics control landscape.

Nonextensive statistical mechanics, pioneered by Tsallis, has recently achieved a generalization of the Gutenberg-Richter law for earthquakes. This remarkable generalization is combined here with natural time analysis, which enables the distinction of two origins of self-similarity, i.e., the process’ memory and the process’ increments infinite variance. By using also detrended fluctuation analysis for the detection of long-range temporal correlations, we demonstrate the existence of both temporal and magnitude correlations in real seismic data of California and Japan. Natural time analysis reveals that the nonextensivity parameter $q$, in contrast to some published claims, cannot be considered as a measure of temporal organization, but the Tsallis formulation does achieve a satisfactory description of real seismic data for Japan for $q=1.66$ when supplemented by long-range temporal correlations.

We study the stochastic resonance of a flexible polymer chain crossing over a piecewise linear bistable potential. The dependence of signal to noise ratio SNR on noise intensity $D$, coupling constant $k$, and polymer length $N$ is studied via two-state approximation. We find that the response of signal to the background noise strength is significant at optimum values of $D_{opt}$, $k_{opt}$, and $N_{opt}$ which suggests a means of manipulating proteins or vesicles. Furthermore, the thermally activated barrier crossing rate $r_k$ for the flexible polymer chain is studied. We find that the crossing rate $r_k$ exhibits an optimal value at an optimal coupling constant $k_{opt}$; $k_{opt}$ decreases with $N$. As the chain length $N$ increases, the escape rate for the center of mass $r_k$ monotonously decreases. On the other hand, the crossing rate for the portion of polymer segment $r_s$ increases and saturates to a constant rate as $N$ steps up.

The recently proposed method for modulating through an external field the composition of a binary fluid mixture adsorbed in a slit pore is discussed. The population inversion near the bulk (demixing) instability is first analyzed in the case of a symmetric mixture of nonadditive hard spheres, without field. It is next investigated for a mixture comprising dipolar particles subject to an external field. The influence of several factors on the adsorption curves including bulk composition, pore width, field direction, polarizability versus permanent dipoles, and temperature on this field induced population inversion is shown by Monte Carlo simulation.

We investigate the dynamics of spreading of a small liquid droplet in gas in a one-component simple fluid, where the temperature is inhomogeneous around $0.9T_c$ and latent heat is released or generated at the interface upon evaporation or condensation (with $T_c$ being the critical temperature). In the scheme of the dynamic van der Waals theory, the hydrodynamic equations containing the gradient stress are solved in the axisymmetric geometry. We assume that the substrate has a finite thickness and its temperature obeys the thermal diffusion equation. A precursor film then spreads ahead of the bulk droplet itself in the complete wetting condition. Cooling the substrate enhances condensation of gas onto the advancing film, which mostly takes place near the film edge and can be the dominant mechanism of the film growth in a late stage. The generated latent heat produces a temperature peak or a hot spot in the gas region near the film edge. On the other hand, heating the substrate induces evaporation all over the interface. For weak heating, a steady-state circular thin film can be formed on the substrate. For stronger heating, evaporation dominates over condensation, leading to eventual disappearance of the liquid region.

The generation and synchronization of bursts are studied in intrinsically spiking neurons due to stimulation with random intracellular calcium fluctuations. It is demonstrated that sufficiently strong noise could induce qualitative change in the firing patterns of a single neuron from periodic spiking to bursting modes. The dynamical mechanism of noise-induced bursting is presented based on a global bifurcation analysis. Furthermore, it is found that a pair of uncoupled and nonidentical spiking neurons, subjected to a common noise, can exhibit synchronous firing in terms of noise-induced bursting. Furthermore, the synchronization is overall enhanced with the noise intensity increasing, and synchronization transitions are exhibited at intermediate noise levels.

We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins. Curiously we find that it can produce results that are a very good good match to the data in the Protein Data Bank.

We study a model of opinion formation where the collective decision of a group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a critical mass. We find that there exists a unique nontrivial critical mass giving the most efficient convergence to consensus. In addition, we observe that for small critical masses, the characteristic time scale for the relaxation to consensus splits into two. The shorter time scale corresponds to a direct relaxation and the longer one can be explained by the existence of intermediate metastable states similar to those found in [P. Chen and S. Redner, Phys. Rev. E 71, 036101 (2005)]. This longer time scale is dependent on the precise condition for consensus—with a modification of the condition it can go away.

The conventional master equation is generalized to include Bose and Fermi moves. The obtained equation describes the time evolution of a system with mixed Bose-Fermi statistics which are controlled by the fraction of Fermi moves $\left(\alpha \right)$; the latter plays a role of an exploratory tendency (ET) factor. The theoretical consideration is illustrated with numerical results for navigation through a model scale-free network. Depending on the ET factor and the number of participants involved in the navigation $\left(N_{\text{tot}}\right)$, a broad variety of the behavior scenarios has been observed. The cases of $N_{\text{tot}}=1$ and $N_{\text{tot}}⪢1$ have been found drastically different. Of particular interest is the case of $N_{\text{tot}}⪢1$, when the participants interfere with each other’s motion, which is characteristic of many real systems (urban traffic, Internet, epidemic spreading, etc.). It has been found that at $\alpha <1$ all participants reach a preselected (target) state but an excessive intention to try detour routes $\left(\alpha \to 1\right)$ leads to a critical slowdown in their passage to this state. At the same time, if $\alpha =1$ (solely Fermi moves, no possibility to return to a previously visited state), only one of the participants attains the target state but it does it much faster than when a single copy navigates through the network $\left(N_{\text{tot}}=1\right)$, i.e., this one optimizes the way to the target state at the expense of other participants. The procedure used to include Bose and Fermi moves in the master equation offers a framework for derivation of kinetic equations for more complex and general statistics.

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.

We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg model on a finite system of length $L$ with open boundary conditions and parallel updates. We find numerically that in both the high and low density regimes the autocorrelation function of the system density behaves like $1-\left|t\right|/\tau$ with a finite support $\left[-\tau ,\tau \right]$. This is in contrast to the usual exponential decay typical of equilibrium systems. Furthermore, our results suggest that in fact $\tau =L/c$, and in the special case of maximum velocity $v_{\text{max}}=1$ (corresponding to the totally asymmetric simple exclusion process) we can identify the exact dependence of $c$ on the input, output and hopping rates. We also emphasize that the parameter $\tau$ corresponds to the integrated autocorrelation time, which plays a fundamental role in quantifying the statistical errors in Monte Carlo simulations of these models.

We investigate the kinetics of bimolecular chemical reactions $A+A\to 0$ and $A+B\to 0$ on weighted scale-free networks (WSFNs) with degree distribution $P\left(k\right)\sim k^{-\gamma }$. On WSFNs, a weight $w_{ij}$ is assigned to the link between node $i$ and $j$. We consider the symmetric weight given as $w_{ij}={\left(k_i{k}_j\right)}^{\mu }$, where $k_i$ and $k_j$ are the degree of node $i$ and $j$. The hopping probability $T_{ij}$ of a particle from node $i$ to $j$ is then given as $T_{ij}\propto {\left(k_i{k}_j\right)}^{\mu }$. From a mean-field analysis, we analytically show in the thermodynamic limit that the kinetics of $A+A\to 0$ and $A+B\to 0$ are identical and there exist two crossover $\mu$ values, ${\mu }_{1c}=\gamma -2$ and ${\mu }_{2c}=\left(\gamma -3\right)/2$. The density of particles $\rho \left(t\right)$ algebraically decays in time $t$ as $t^{-\alpha }$ with $\alpha =1$ for $\mu <{\mu }_{2c}$ and $\alpha =\left(\mu +1\right)/\left(\gamma -\mu -2\right)$ for ${\mu }_{2c}\le \mu <{\mu }_{1c}$. For $\mu \ge {\mu }_{1c}$, $\rho$ decays exponentially. With the mean-field rate equation for $\rho \left(t\right)$, we also analytically show that the kinetics on the WSFNs is mapped onto that on unweighted SFNs with $P\left(k\right)\sim k^{-{\gamma }^{\prime }}$ with ${\gamma }^{\prime }=\left(\mu +\gamma \right)/\left(\mu +1\right)$.

This paper establishes a universal mechanism for the generation of $1/f$ noises. The mechanism is based on a signal-superposition model, which superimposes signals transmitted from independent sources. All sources transmit a statistically common—yet arbitrary—stochastic signal pattern; each source has its own random transmission parameters—amplitude, frequency, and initiation epoch. We explore randomizations of the transmission parameters which render the power spectrum of the super-imposed signal invariant with respect of the stochastic signal pattern transmitted. Analysis shows that the aforementioned randomizations yield superimposed signals which are $1/f$ noises. The result obtained is, in effect, a randomized central limit theorem for $1/f$ noises.