Molecular motors convert chemical energy derived from the hydrolysis of adenosine triphosphate (ATP) into mechanical energy. A well-studied model of a molecular motor is the flashing ratchet model. We show that this model exhibits a fluctuation relation known as the Gallavotti-Cohen symmetry. Our study highlights the fact that the symmetry is present only if the chemical and mechanical degrees of freedom are both included in the description.

Binary mixtures with a negative separation ratio are known to exhibit time-independent spatially localized convection when heated from below. Numerical continuation of such states in a closed two-dimensional container with experimental boundary conditions and parameter values reveals the presence of a pinning region in Rayleigh number with multiple stable localized states but no bistability between the conduction state and an independent container-filling state. An explanation for this unusual behavior is offered.

A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics and investigate emerging structural property. The model consists of an undirected weighted network of fixed mean degree and randomly diffusing particles of fixed density. The weight $w$ of an edge increases by the amount of traffics through its connecting nodes or decreases by a constant factor. Edges are removed with the probability $P_{rew}=1/\left(1+w\right)$ and replaced by new ones having $w=0$ at random locations. We find that the model exhibits a structural phase transition between the homogeneous phase characterized by an exponentially decaying degree distribution and the heterogeneous phase characterized by the presence of hubs. The hubs emerge as a consequence of a positive feedback between the particle and the edge dynamics.

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams obtained from studies in different countries. The net-time headway, however, stays approximately constant over all these different data sets. By using this fact, we demonstrate how the underlying dynamics of pedestrian crowds, naturally follows from local interactions. This means that there is no need to come up with an arbitrary fit function (with arbitrary fit parameters) as has traditionally been done. Further, by using not only the average density values but the variance as well, we show how the recently reported stop-and-go waves [Helbing et al., Phys. Rev. E 75, 046109 (2007)] emerge when local density variations take values exceeding a certain maximum global (average) density, which makes pedestrians stop.

We studied the response of a linearly growing domain of the oscillatory chemical chlorine dioxide-iodide-malonic acid (CDIMA) medium to periodic forcing at its growth boundary. The medium is Hopf-, as well as Turing-unstable and the system is convectively unstable. The results confirm numerical predictions that two distinct modes of pattern can be excited by controlling the driving frequency at the boundary, a flow-distributed-oscillation (FDO) mode of traveling waves at low values of the forcing frequency $f$, and a mode of stationary Turing patterns at high values of $f$. The wavelengths and phase velocities of the experimental patterns were compared quantitatively with results from dynamical simulations and with predictions from linear dispersion relations. The results for the FDO waves agreed well with these predictions, and obeyed the kinematic relations expected for phase waves with frequencies selected by the boundary driving frequency. Turing patterns were also generated within the predicted range of forcing frequencies, but these developed into two-dimensional structures which are not fully accounted for by the one-dimensional numerical and analytical models. The Turing patterns excited by boundary forcing persist when the forcing is removed, demonstrating the bistability of the unforced, constant size medium. Dynamical simulations at perturbation frequencies other than those of the experiments showed that in certain ranges of forcing frequency, FDO waves become unstable, breaking up into harmonic waves of different frequency and wavelength and phase velocity.

We perform numerical studies of a reaction-diffusion system that is both Turing and Hopf unstable, and that grows by addition at a moving boundary (which is equivalent by a Galilean transformation to a reaction-diffusion-advection system with a fixed boundary and a uniform flow). We model the conditions of a recent set of experiments which used a temporally varying illumination in the boundary region to control the formation of patterns in the bulk of the photosensitive medium. The frequency of the illumination variations can select patterns from among the competing instabilities of the medium. In the usual case, the waves that are excited have frequencies (as measured at a constant distance from the upstream boundary) matching the driving frequency. In contrast to the usual case, we find that both Turing patterns and flow-distributed oscillation waves can be excited by forcing at subharmonic multiples of the wave frequencies. The final waves (with frequencies at integer multiples of the driving frequency) are formed by a process in which transient wave fronts break up and reconnect. We find ratios of response to driving frequency as high as 10.

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of “snaking without bistability,” recently observed in simulations of binary fluid convection by Mercader et al. Phys. Rev. E80, 025201 (2009).

We consider phase multistability and phase synchronization phenomena in a chain of period-doubling oscillators. The synchronization in arrays of diffusively coupled self-sustained oscillators manifests itself as rotating wave regimes, which are characterized by equal amplitudes and phases in every site which are shifted by a constant value. The value of the phase shift is preserved while the shape of motion becomes more complex through a period-doubling cascade. The number of coexisting attractors increases drastically after the transition from period-one to period-two oscillations and then after every following period-doubling bifurcation. In the chaotic region, we observe a number of phase-synchronized modes with instantaneous phases locked in different values. The loss of phase synchronization with decreasing coupling is accompanied by intermittency between several synchronous regimes.

Single-frequency operation or locking in a lateral array of three laser oscillators is studied within the composite-cavity-mode approach. We compute the regions of stable locking, which have a nontrivial shape in the plane of coupling strength versus frequency detuning. The locking regions depend drastically on the amount of amplitude-phase coupling of the lasing field that is quantified by the $\alpha$ parameter. For small $\alpha$, locking is possible for arbitrary coupling, but only if the middle laser has sufficient frequency detuning from the two outer lasers. In contrast, for larger $\alpha$, locking is only possible for weak to moderate coupling, provided that all three lasers have similar frequencies.

A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes quantum phase transition (QPT). We find that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is nonintegrable. We show that the assertion in the context of the standard Dicke model that QPT is a precursor to a change in the level statistics is not valid in general.

The spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect is investigated by carrying out fully nonlinear two-dimensional numerical simulations initiated by a pulselike disturbance. The traveling wave packets for positive as well as negative separation factors $\psi$ are obtained numerically for ethanol-water-like mixtures (Prandtl number $\text{Pr}=10$, Lewis number $\text{Le}=0.01$) and selected combinations of Rayleigh and Reynolds numbers at $\psi =0.01$, 0.1 and $\psi =-0.1$. The characteristics of the wave fronts and the transitions observed between absolute and convective instabilities when changing the parameters are compared with the results previously obtained by linear spatiotemporal stability analysis. The simulations are in very good agreement with the stability results, which confirms the validity of both approaches. Finally, in order to characterize the possible interaction between the two wave packets of the so-called downstream and upstream modes for $\psi <0$, the spatiotemporal stability analysis is used to detect a boundary curve in the (Re, Ra) parameter region beyond which the two wave packets will never completely separate. Numerical simulations illustrate the different evolutions of the wave packets on both sides of this boundary.

We present a simple mathematical model of glassy dynamics seen as a random walk in a directed weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies focusing on particular examples of energy landscapes obtained by sampling energy minima and saddles of small systems. We point out how the relation between the energies of the minima and their number of neighbors should be studied in connection with the network’s global topology and show how the tools developed in complex network theory can be put to use in this context.

We measure surface thermal fluctuation spectra of liquids, solids, complex fluids, and biological matter using reflected light measurements down to $\sim {10}^{-17}{\text{rad}}^2/\text{Hz}$ in inclinations or $\sim {10}^{-29}{\text{m}}^2/\text{Hz}$ in vertical displacement. The random thermal fluctuations are delineated from random noise at sub-shot noise levels. The principle of the measurement is not limited to surface measurements. The dynamical evolution of the surface properties is also investigated. The measurement time is short, passive, and applicable to a wide variety of surfaces.

Shear viscosities of supercritical carbon dioxide have been measured to 673 K and 8 GPa (80 kbar). Measurements were made in a diamond-anvil cell with a rolling-ball technique. Individual isotherms are well fit by a modified free-volume equation. The data demonstrate a close relation between viscosity and residual entropy.

From dumbbells to fcc crystals, we study the self-assembly pathway of amphiphatic spherical colloidal particles as a function of the size of the hydrophobic region using molecular-dynamics simulations. Specifically, we analyze how local interparticle interactions correlate to the final self-assembled aggregate and how they affect the dynamical pathway of structure formation. We present a detailed diagram separating the many phases that we find for different sizes of the hydrophobic area and uncover a narrow region where particles self-assemble into hollow faceted cages that could potentially find interesting engineering applications.

We study a model of growth of polymer films using numerical simulations and scaling concepts. During the deposition, each new monomer flows in a direction perpendicular to the substrate, aggregates at the first contact with the deposit and executes up to $G$ steps along the polymers, propagating an existing chain or nucleating of a new polymer. Some qualitative results agree with those of a previous model for vapor deposition polymerization (VDP) with collective diffusion, such as the roughness increase and density decrease with $G$. This supports the interpretation of $G$ as a ratio between diffusion coefficient and monomer flux. We perform a systematic study of scaling properties of the outer surface roughness and of polymer size and shape. For large $G$, the polymers are stretched in the direction perpendicular to the substrate and have typical size increasing as $G^{1/2}$. This is explained by the solution of the problem of random walk trapping, which illustrates the connection of surface processes and bulk properties. The distributions of polymer sizes are monotonically decreasing for all $G$ and very broad, thus a large number of small chains and of chains much larger than the average is found in typical samples. The outer surface roughness obeys Kardar-Parisi-Zhang scaling, in contrast to the apparent anomalous scaling of previous VDP models with oblique monomer flux. However, the calculation of reliable exponents requires accounting for huge finite-size corrections. Possible applications and extensions of this model are discussed.

The technique of modulated luminescence of bones was developed experimentally and theoretically and was subsequently used to interpret measurements performed on the cortical layer of human skull bones. The photophysical theory is based on the optical excitation and decay rate equations of the fluorescent endogenous chromophore and on the molecular interaction parameter with the photon field density in the matrix of the bone. An effective mean relaxation lifetime, ${\tau }_M$, of skull cortical bone was derived theoretically and was found to depend on the endogenous chromophore decay lifetime, ${\tau }_2$, in the upper energy state, on the generated luminescence field density through its dependence on the incident photon field density and on the thickness of the bone. A linear dependence of ${\tau }_M$ on laser beam intensity, $I_0$, was found and sensitivity of the value of ${\tau }_M$ to bone thickness, $L$, was observed for $L\le 6.2\text{mm}$. Both experimental dependencies of ${\tau }_M$ on $I_0$ and $L$ were in excellent agreement with the theoretical model. The unusually long relaxation luminescence lifetime was accounted for theoretically by means of an excited-state manifold invoking intersystem crossing to a forbidden state followed by decay to the ground state of the chromophore. Best fits to the data were able to yield measurements of the following chromophore and photon field parameters: ${\tau }_2=19.7\text{ms}$, optical scattering coefficient ${\mu }_s\left(659\text{nm}\right)=44340{\text{m}}^{-1}$, optical absorption coefficient ${\mu }_a\left(659\text{nm}\right)=13{\text{m}}^{-1}$, and coupling coefficient $B_{21}=1.6\times {10}^4{\text{m}}^3{\text{J}}^{-1}{\text{s}}^{-1}$, the decay coupling coefficient of the endogenous chromophore participating in the optical interaction in the form of stimulated luminescence emission mediated by the luminescence photon field between the long-lived excited state $E_2$ and the lower (ground) state $E_1$. The method of modulated luminescence can be used to measure photophysical properties of the chromophore in cortical skull bones, being a sensitive marker of bone diseases, namely, osteoporosis and cancer.

To reveal the underlying hydrodynamic mechanism for the directed propulsion of the bacterium Spiroplasma, we formulate a coarse-grained elastic polymer model with domains of alternating helicities along the contour. Using hydrodynamic simulations and analytic arguments, we show that the propagation of helical domain walls leads to the directed propulsion of the cell body opposite to the domain-wall traveling direction. Several key features of Spiroplasma motility are reproduced by our model. We in particular show that the helical pitch angle observed for Spiroplasma meliferum, $\psi =35°$, is optimized for maximal swimming speed and energy-conversion efficiency. Our analytic theory based on the slender-body hydrodynamic approximation agrees very well with our numerical data demonstrating how the chirality switch propagating along the helical cell body is converted to a translational thrust for the cell body itself. We in detail consider thermal effects on the propulsion efficiency in the form of orientational fluctuations and conformational fluctuations of the helix shape. The body length dependence of the cell motility is studied numerically and compared to our approximate analytic theory. For fixed pitch angle $\psi =35°$, the swimming speed is maximized at a ratio of cell-body length to domain length of about 2–3, which are typical values for real cells. We also propose simple analytic arguments for an enhancement of the swimming velocity with increasing solution viscosity by taking into account the effects of transient confinement of a helical cell body in a polymeric meshwork. Comparison with a generalized theory for the swimming speed of flagellated bacteria in polymeric meshworks shows that the presence of a finite-sized bacterial head gives rise to a maximal swimming speed at a finite solution viscosity, whereas in the absence of a head the swimming speed monotonically increases with increasing viscosity.

We investigate a stochastic model of infection dynamics based on the Susceptible-Infective-Recovered (SIR) model, where the distribution of the recovery times can be tuned, interpolating between exponentially distributed recovery times, as in the standard SIR model, and recovery after a fixed infectious period. This is achieved by introducing $L$ infective classes, as compared to 1 in the standard model. For large populations, the spectrum of fluctuations around the deterministic limit of the model can be computed analytically. The demographic stochasticity has the effect of transforming the decaying oscillations of the deterministic model into sustained oscillations in the stochastic formulation. We find that the amplification of these stochastic oscillations increases with $L$, as well as their coherence in frequency. For large values of $L$ (of the order of 10 and greater), the height and position of the peak of the power spectra changes little and is described well by the model with fixed recovery period $\left(L\to \infty \right)$. In this limit we give a closed-form expression for the power spectrum of fluctuations of infective individuals.

A fast algorithm for computing the motion of solid particles suspended in fluid is presented. The motion of solid particles suspended in Stokes flow can be calculated without fully calculating the fluid motion. When the steady-state simulation is sufficient, this algorithm can greatly accelerate the simulation of solid particle suspension in Stokes flow.