We show how accurate kinetic information, such as the rates of protein folding and unfolding, can be extracted from replica-exchange molecular dynamics (REMD) simulations. From the brief and continuous trajectory segments between replica exchanges, we estimate short-time propagators in conformation space and use them to construct a master equation. For a helical peptide in explicit water, we determine the rates of transitions both locally between microscopic conformational states and globally for folding and unfolding. We show that accurate rates in the $\sim 1∕\left(100\mathrm{ns}\right)$ to $\sim 1∕\left(1\mathrm{ns}\right)$ range can be obtained from REMD with exchange times of $5\mathrm{ps}$, in excellent agreement with results from long equilibrium molecular dynamics.

The complex dynamics of intracellular calcium regulates cellular responses to information encoded in extracellular signals. Here we study the encoding of these external signals in the context of the Li-Rinzel model. We show that by control of biophysical parameters the information can be encoded in amplitude modulation (AM), frequency modulation (FM), or mixed (AM and FM) modulation. We briefly discuss the possible implications of this role of information encoding for astrocytes.

We consider the construction of point processes from tilings, with equal-volume tiles, of $d$-dimensional Euclidean space ${\mathbb{R}}^d$. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are “superhomogeneous” (or “hyperuniform”)—i.e., for which the structure factor $S\left(\mathbf{k}\right)$ vanishes when the wave vector $\mathbf{k}$ tends to zero. The exponent $\gamma$ characterizing the leading small-$k$ behavior, $S\left(k\to 0\right)\propto k^{\gamma }$, depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent $\gamma =4$ for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents in the range $4-d<\gamma <4$ (and thus always superhomogeneous for $d\le 4$) may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate $S\left(\mathbf{k}\right)$ exactly. Our results provide an explicit analytical construction of point processes with $\gamma >4$. Applications to condensed matter physics, and also to cosmology, are briefly discussed.

Within the capillary-wave model (CWM), the liquid-vapor interface is a hypothetical two-dimensional surface whose deviations from planarity are represented as long wavelength capillary waves. We modify the CWM for liquid-liquid interfaces and treat them as two harmonically interacting surfaces (model 1). Corrections to the model are proposed to prevent the usual divergence of the capillary-wave broadening in the thermodynamic limit by introducing a surface-bulk coupling (model 2) and to incorporate the curvature of the two surfaces (model 3). Expressions for the capillary-wave contribution to the surface tension of the interface are obtained. Molecular dynamics simulations are performed for two series of water-hydrocarbon interfacial systems (a) $n$-pentane, 2-methyl pentane, and 2,2,4-trimethyl pentane (constant chain length) and (b) $n$-octane, 2-methyl heptane, and 2,2,4-trimethyl pentane (constant molecular mass). A simple procedure to identify the molecular sites at the surface is utilized for a molecular representation of the surface. The distribution of these surface sites as well as the wave-vector dependence of surface fluctuations are analyzed in order to extract the parameters required for model 2. A small length scale is identified above which surface fluctuations correspond to capillary-wave fluctuations thereby connecting the molecular and mesoscopic scales. This approach is applied to all interfacial systems studied here and predictions based on the parameters found to be in good agreement with independent simulation results for surface tension and interfacial widths. Hydrocarbon branching has a small effect on model parameters.

For a pure material, the dynamics of the growth of one phase in a supercooled other phase for the case of a shallow temperature quench is traditionally understood via a kinetic thermal diffusion equation model or a quasistatic Laplace equation model, if order-parameter details can be neglected. In the quasistatic model, the interfacial boundary temperature $T_R$ is equal to the phase transition temperature $T_m$. In the kinetic model, however, growth is driven by a nonzero interfacial undercooling $T_m-T_R$. By assuming that the growth process occurs at small but finite, identical spatial steps, the growth laws for the cases of shallow and deep temperature quenches were derived analytically from the kinetic model in the limit of zero thermal diffusivity. For the case of a shallow temperature quench, it is shown that the apparent difference between the assumed interfacial boundary conditions of the quasistatic and the kinetic model does not exist.

We present experimental and theoretical study of colloidal interactions in quadrupolar nematic liquid crystal colloids, confined to a thin planar nematic cell. Using the laser tweezers, the particles have been positioned in the vicinity of other colloidal particles and their interactions have been determined using particle tracking video microscopy. Several types of interactions have been analyzed: (i) quadrupolar pair interaction, (ii) the interaction of an isolated quadrupole with a quadrupolar chain, and (iii) the interaction of an isolated quadrupolar colloidal particle with a two-dimensional (2D) quadrupolar crystallite. In all cases, the interactions are of the order of several $100k_{B}T$ for $2\mu \text{m}$ particles, which gives rise to relatively stable 2D colloidal crystals. The experimental results are compared to the predictions of Landau–de Gennes theory and we find a relatively good qualitative agreement.

The equilibrium statistical properties of DNA denaturation bubbles are examined in detail within the framework of the Peyrard-Bishop-Dauxois model. Bubble formation in homogeneous DNA is found to depend crucially on the presence of nonlinear base-stacking interactions. Small bubbles extending over fewer than ten base pairs are associated with much larger free energies of formation per site than larger bubbles. As the critical temperature is approached, the free energy associated with further bubble growth becomes vanishingly small. An analysis of average displacement profiles of bubbles of varying sizes at different temperatures reveals almost identical scaled shapes in the absence of nonlinear stacking; nonlinear stacking leads to distinct scaled shapes of large and small bubbles.

We study the efficiency of the gradient mechanism of message transfer in a two-dimensional communication network of regular nodes and randomly distributed hubs. Each hub on the network is assigned some randomly chosen capacity and hubs with lower capacities are connected to the hubs with maximum capacity. The average travel times of single messages traveling on the lattice decrease rapidly as the number of hubs increase. The functional dependence of the average travel times on the hub density shows $q$-exponential behavior with a power-law tail. We also study the relaxation behavior of the network when a large number of messages are created simultaneously at random locations and travel on the network toward their designated destinations. For this situation, in the absence of the gradient mechanism, the network can show congestion effects due to the formation of transport traps. We show that if hubs of high betweenness centrality are connected by the gradient mechanism, efficient decongestion can be achieved. The gradient mechanism is less prone to the formation of traps than other decongestion schemes. We also study the spatial configurations of transport traps and propose minimal strategies for their elimination.

A type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in incomplete noise-induced synchronization in spatially extended systems are revealed analytically. Different types of model noise are considered. A very good agreement between the theoretical results and the numerically calculated data is shown.

We report on the observation of noise-free stochastic resonance in an externally driven diode resonator close to an interior crisis. At sufficiently high excitation amplitudes the diode resonator shows a strange attractor which after the collision with an unstable period-three orbit exhibits crisis-induced intermittency. In the intermittency regime the system jumps between the previously stable chaotic attractor and the phase space region which has been made accessible by the crisis. This random process can be used to amplify a weak periodic signal through the mechanism of stochastic resonance. In contrast to conventional stochastic resonance no external noise is needed. The chaotic intrinsic dynamics plays the role of the stochastic forcing. Our data obtained from the diode resonator are compared with numerical simulations of the logistic map where a similar crisis-induced intermittency is observed.

The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values $\zeta =0.5$ and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a different tecnique to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian, and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, are studied, and the non-Newtonian fluids are compared to the (previously studied) Newtonian case. We find a scaling relation between permeability and mean aperture in the low Reynolds number regime, generalizing an earlier result for Newtonian fluids. As the Reynolds number increases, we observe the same sequence of transitions to nonlinearity found in intergranular porous media. Furthermore, the permeability results may be collapsed into a master curve of friction factor vs Reynolds number, using a scaling similar to that employed for power-law fluids in porous media.

A bifurcation analysis is performed of a dc glow discharge between parallel electrodes and of a dc near-cathode space-charge sheath bordering a uniform plasma column. A model of plasma is considered with a single ion species and motion of the charged particles dominated by drift. Bifurcation points are found at which steady-state modes with spots on the cathode branch off from the abnormal mode or from the mode corresponding to the falling section of the current-density–voltage characteristic. In both discharge configurations, bifurcations in the abnormal mode have been detected; an unexpected result given that loss of stability and pattern appearance in dc gas discharges are usually associated with a negative differential resistance of the discharge. The conclusion is drawn that the two most important mechanisms governing appearance of patterns on glow cathodes, which are electrostatic mechanism and diffusion, produce competing effects: the former favors appearance of modes with multiple spots, while the latter favors appearance of a mode with one spot. This may explain the appearance in experiments of a normal spot or, alternatively, of patterns with multiple spots.

In this paper, we discuss a modification of classical electrodynamics in which “ordinary” point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector $\mathbf{k}$ and the vectors of the electromagnetic field, $\mathbf{E}$ and $\mathbf{B}$. It is shown that the vectors $\mathbf{E}$ and $\mathbf{B}$ can be defined in terms of two four-potentials and the components of $\mathbf{k}$ are the components of a four-tensor of the third rank. The Lagrangian of the modified electrodynamics is defined. The conditions are derived at which only one four-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of an electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector $\mathbf{k}$ has a discrete spectrum. The electric and magnetic fields, energy, and angular momentum of the monopole are found for different eigenvalues of $\mathbf{k}$.

Monte Carlo simulations in the three-dimensional (3D) Ashkin-Teller model on a cubic lattice are performed in the regions of the two-parameter space diagram where Ising-type phase transitions are expected. The scaling behavior of the Binder cumulant $Q$ and the magnetic susceptibility in the critical region are exploited. In simulations the periodic boundary conditions and the Metropolis algorithm are used. Starting from Ising critical exponents and applying the finite-size-scaling analysis of the cumulant $Q$ with nonlinear corrections, the accurate positions of the critical couplings on the continuous phase transition lines are calculated. For these couplings the critical exponent $y_h$ is calculated analyzing the magnetic susceptibility in the framework of the finite-size scaling with corrections. The values of $y_h$ agree with the 3D Ising model value along two lines determined by the order parameter $⟨s\sigma ⟩$.

Analytical and numerical simulation studies are performed on the diffusion of simple fluids in both thin slits and long cylindrical pores. In the region of large Knudsen numbers, where the wall-particle collisions outnumber the intermolecular collisions, we obtain analytical results for the self-diffusion coefficients for both slit and cylindrical pore shapes. The results show anomalous behavior of the mean square displacement and the velocity autocorrelation for the case of slits, unlike the case of cylindrical pores which shows standard Fick’s law. Molecular dynamics simulations confirm the analytical results. We further study the wall-mediated diffusion behavior conducted by a Smoluchowski thermal wall and compare with our analytical results obtained from the stochastic thermal wall model proposed by Mon and Percus.

We report the formation of stable two-dimensional clusters consisting of long-range-interacting colloidal particles with predefined magnetic moments. The symmetry and arrangement of the particles within the cluster are imposed by the magnetic frustration. By satisfying the criteria of stability, a series of magic number clusters is formed. The magic clusters are close packed and have compensating magnetic moments and chirality. Thus, the system can be regarded as a classical mesoscopic model for spin arrangements in two-dimensional triangular antiferromagnets, although the exact nature of the interactions between the macroscopic magnetic moments is different.

The role of nanoconfinement on the glass transition temperature $\left(T_g\right)$ of polymers has been extensively studied in the thin film geometry. This work looks at the $T_g$ of nanoconfined polystyrene (PS) in spherical nanoparticles $(27–200\mathrm{nm})$, individually dispersed in crosslinked polybuthylmethacrylate matrices. A reduction of $T_g$ compared to the bulk was observed in PS nanospheres via neutron scattering mechanical tests and was found to decrease with decreasing diameter for $D<50\mathrm{nm}$. The general trend of $T_g$ depression in nanospheres was found to be similar to the results on thin film geometry.

We employ a reaction diffusion equation with local dynamics specified by the Beeler-Reuter model to study the meandering of spiral waves. With the appropriate choice for the conductances of sodium and calcium channels, the trajectory of the tip of a spiral wave lies on a straight line. The phenomenon of annihilation or reflection of a spiral at the boundaries of the domain is studied. This phenomenon is analyzed in terms of the variable $j$, which controls the reactivation of the sodium channel in the Beeler-Reuter model. The results presented can have potential applications in the study of cardiac arrhythmias by providing insight on the interaction between spiral waves and obstacles in the heart.

In order to explain the empirical evidence that the dynamics of human activity may not be well modeled by Poisson processes, a model based on queuing processes was built in the literature [A. L. Barabasi, Nature (London) 435, 207 (2005)]. The main assumption behind that model is that people execute their tasks based on a protocol that first executes the high priority item. In this context, the purpose of this paper is to analyze the validity of that hypothesis assuming that people are rational agents that make their decisions in order to minimize the cost of keeping nonexecuted tasks on the list. Therefore, we build and analytically solve a dynamic programming model with two priority types of tasks and show that the validity of this hypothesis depends strongly on the structure of the instantaneous costs that a person has to face if a given task is kept on the list for more than one period. Moreover, one interesting finding is that in one of the situations the protocol used to execute the tasks generates complex one-dimensional dynamics.

We explore the effect of spatiotemporally varying substrate temperature profiles on the dynamics and the resulting reaction rate enhancement of the catalytic oxidation of CO on Pt(110). The catalytic surface is “addressed” by a focused laser beam whose motion is computer controlled. The averaged reaction rate is observed to undergo a characteristic maximum as a function of the speed of this moving laser spot. Experiments as well as modeling are used to explore and rationalize the existence of such an optimal laser speed.