We have determined the diffusion, thermal diffusion, and Soret coefficients of a poly(dimethyl siloxane)/poly(ethyl-methyl siloxane) (PDMS/PEMS) polymer blend as a function of composition and temperature within the homogeneous phase. The critical slowing down of the diffusion and the corresponding critical divergence of the Soret coefficient are described within the pseudospinodal concept both for critical and off-critical compositions. These data are used to model in detail the channel-like structures that form due to the Soret effect when a focused laser beam is scanned across a polymer film of $100\mu \mathrm{m}$ thickness. A moderate vertical asymmetry is attributed to solutal convection. Although heat rapidly diffuses away from the laser focus, the composition distribution in the early stage resembles the sharp profile of the laser beam. PDMS accumulates within the center of the structures, whereas a thin PEMS-rich layer is formed that isolates the central core from the windows. Experimentally, the structures are analyzed by means of phase contrast microscopy. Possible applications as rewritable optical waveguides or tunable phase plates are briefly discussed.

Counterions in a biological system are charged in water and interact with charged macroions, which are generally made up of hydrocarbons. The dielectric difference between water and the hydrocarbon substrates occurs naturally, and may greatly affect the electrostatic properties of biological systems. Particularly for a slab geometry, bulk counterions that are dissolved in water are driven to the midplane of the slab because of their repulsive interaction with their image charges. The pressure between two charged plates becomes less repulsive since the low dielectric constant of the hydrocarbon substrate creates stronger association between counterions and surface charges as compared to the case of no dielectric discontinuity.

Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along a contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the membrane. Symmetric two-particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime; in particular, the problem may be solved exactly in the case of two membrane-bound parallel cylinders. This apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane-mediated interactions.

We present a detailed numerical study of creeping solitons in dissipative systems. A bifurcation diagram has been constructed for the region of transition between solitons and fronts. It shows a rich variety of transitions between various types of localized solutions. For the first time, we have found a sequence of period-doubling bifurcations of creeping solitons, and also a symmetry-breaking instability of creeping solitons. Creeping solitons may involve many frequencies in their dynamics, and this can result, in particular, in a multiplicity of zig-zag motions.

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

The critical and post-critical behavior of coagulating systems, where the coagulation efficiency grows with the masses of colliding particles $g$ and $l$ as $K(g,l)=0.5(g^{\alpha }{l}^{\beta }+g^{\beta }{l}^{\alpha }$), $\lambda =\alpha +\beta >1,\mu =\mid \alpha -\beta \mid <1$ is studied. The instantaneous sink that removes the particles with masses exceeding $G$ is introduced which allows one to describe the coagulation kinetics by a finite set of equations and define the gel as the deposit of particles with masses between $G+1$ and $2G$. This system displays the critical behavior (the sol-gel transition) in the limit $G\to \infty$ if $\lambda =\alpha +\beta >1$. The exact post-critical particle mass spectrum is shown to be an algebraic function of $g$ times a growing exponent. All critical parameters of the systems are determined as the functions of $\alpha$ and $\beta$.

The structure of granular deposits growing by arriving particles is analyzed using three-dimensional on-lattice Monte Carlo modeling of convective-diffusive particle deposition. The deposit density profile $\rho \left(h\right)$ depends on the particle dynamics and becomes formed by three different regions: a denser near-wall region at the deposit bottom in contact with the original plain surface, a middle uniform region with constant mean density, and an open and lighter active-growth region at the deposit outer surface. Fitting expressions for $\rho \left(h\right)$ valid in each region are proposed, based on the known features of deposits formed in the two limiting cases: ballistic deposition and diffusion-limited deposition. Also, a composite expression for $\rho \left(h\right)$ fitting the density profile throughout the deposit is given. All these expressions are written in terms of a length scale $l\left(\mathrm{Pe}\right)$ dependent on the particle Péclet number, which provides the relative importance of the convective motion to the diffusive transport for the particle.

We investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including nonexponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dynamics in line with the established methods in supercooled liquids, we construct a relaxation time versus scaled inverse temperature plot and demonstrate that one can indeed define a “fragility index” for thermotropic liquid crystals that depends on density and aspect ratio. The values of the fragility parameter are surprisingly in the range observed for glass-forming liquids. A plausible correlation between the energy landscape features and the observed fragility is discussed.

X-ray diffraction diagrams of undulated smectic phases in bent-core liquid crystals have been theoretically studied. The intensities of the reflections have been obtained for different layer modulations, and a general expression has been deduced for orthogonal cells in terms of the different harmonics of the distortion. The case of sinusoidal modulation is especially simple and has been studied also in oblique cells. High-quality x-ray measurements of three compounds reported in the literature have been analyzed as examples. In all cases it has been deduced that the modulation is sinusoidal and its amplitude has been easily obtained by fitting the experimental intensities. Equatorial $\left(h0\right)$ reflections have been also considered to obtain information about the structure of defects at the maxima and minima of the undulation.

We study the dynamics of gene activities in relatively small size biological networks (up to a few tens of nodes), e.g., the activities of cell-cycle proteins during the mitotic cell-cycle progression. Using the framework of deterministic discrete dynamical models, we characterize the dynamical modifications in response to structural perturbations in the network connectivities. In particular, we focus on how perturbations affect the set of fixed points and sizes of the basins of attraction. Our approach uses two analytical measures: the basin entropy $H$ and the perturbation size $\Delta$, a quantity that reflects the distance between the set of fixed points of the perturbed network and that of the unperturbed network. Applying our approach to the yeast-cell-cycle network introduced by Li et al. [Proc. Natl. Acad. Sci. U.S.A. 101, 4781 (2004)] provides a low-dimensional and informative fingerprint of network behavior under large classes of perturbations. We identify interactions that are crucial for proper network function, and also pinpoint functionally redundant network connections. Selected perturbations exemplify the breadth of dynamical responses in this cell-cycle model.

Cytoskeletal (CSK) dynamics such as remodeling and reorganization can be studied by tracking the spontaneous motion of CSK-bound particles. Particle motion is thought to be driven by local, ATP-dependent intracellular force fluctuations due to polymerization processes and motor proteins, and to be impeded by a viscoelastic, metastable cytoskeletal network. The mechanisms that link particle motion to force fluctuations and the CSK dynamics remain unclear. We report simultaneous measurements of the spontaneous motion of CSK-bound particles and of cellular force fluctuations. Cellular force fluctuations were measured by tracking fluorescent markers embedded in an elastic polyacrylamide hydrogel substrate that served as an extracellular matrix (ECM). The motion of CSK-bound particles and markers embedded in the ECM showed both persistence and superdiffusive behavior. Moreover, the movements of CSK-bound beads were temporally and spatially correlated with force fluctuations in the ECM. The findings suggest that the spontaneous motion of CSK-bound beads is driven not by random, local stress fluctuations within a viscoelastic continuum or cage, but rather by stress fluctuations within a tensed and constantly remodeling CSK network that transmits stresses over considerable distances to the ECM.

The search strategies of many organisms play a fundamental role in their competition to survive in a given environment. In this context, the propulsion systems of microorganisms have evolved during life history, to optimize the suitable use of energy they take from nutrients. Starting from a model for the motion of Brownian objects with internal energy depot, we show that the propulsion system of microorganisms has an optimal regimen while searching for new sources of food. Bacteria with a too low or too high energy expenditure in propulsion, moving in a nutrient-depleted environment, do not reach remote distances. In this sense, the mean square displacement has a maximum for a finite value of the propulsion rate. Species using the most efficient locomotion system have a considerable advantage for survival in hostile environments, a common situation in the ocean. Moreover, we found the existence of a lower size limit for useful locomotion. This suggests that, for organisms whose linear dimensions are below a certain threshold, it is advantageous not to use any propulsion mechanism at all, a result that is in agreement with what is observed in nature.

Complex networks are constructed in the evolution process of traffic flow, and the states of traffic flow are represented by nodes in the network. The traffic dynamics can then be studied by investigating the statistical properties of those networks. According to Kerner’s three-phase theory, there are two different phases in congested traffic, synchronized flow and wide moving jam. In the framework of this theory, we study different properties of synchronized flow and moving jam in relation to complex network. Scale-free network is constructed in stop-and-go traffic, i.e., a sequence of moving jams [Chin. Phys. Lett. 10, 2711 (2005)]. In this work, the networks generated in synchronized flow are investigated in detail. Simulation results show that the degree distribution of the networks constructed in synchronized flow has two power law regions, so the distinction in topological structure can really reflect the different dynamics in traffic flow. Furthermore, the real traffic data are investigated by this method, and the results are consistent with the simulations.

In this paper we analyze in detail the secondary bifurcations of stationary hexagonal patterns in a prototype model of nonlinear optics. Hexagonal pattern solutions with all allowed wave numbers are computed and their linear stability is studied by means of a Bloch analysis. Depending on the wave number of the selected pattern we predict and numerically observe phase instabilities, amplitude instabilities, both stationary and oscillatory, and oscillatory finite wavelength bifurcations. The results presented here illustrate a typical bifurcation scenario for patterns with different wave numbers in self-focusing systems.

We present experimental observations and quantified theoretical predictions of the nanoscale hydrodynamics induced by nanorod precession emulating primary cilia motion in developing embryos. We observe phenomena including micron size particles which exhibit epicyclic orbits with coherent fluctuations distinguishable from comparable amplitude thermal noise. Quantifying the mixing and transport physics of such motions on small scales is critical to understanding fundamental biological processes such as extracellular redistribution of nutrients. We present experiments designed to quantify the trajectories of these particles, which are seen to consist of slow orbits about the rod, with secondary epicycles quasicommensurate with the precession rate. A first-principles theory is developed to predict trajectories in such time-varying flows. The theory is further tested using a dynamically similar macroscale experiment to remove thermal noise effects. The excellent agreement between our theory and experiments confirms that the continuum hypothesis applies all the way to the scales of such submicron biological motions.

We consider stochastic excitable units with three discrete states. Each state is characterized by a waiting time density function. This approach allows for a non-Markovian description of the dynamics of separate excitable units and of ensembles of such units. We discuss the emergence of oscillations in a globally coupled ensemble with excitatory coupling. In the limit of a large ensemble we derive the non-Markovian mean-field equations: nonlinear integral equations for the populations of the three states. We analyze the stability of their steady solutions. Collective oscillations are shown to persist in a large parameter region beyond supercritical and subcritical Hopf bifurcations. We compare the results with simulations of discrete units as well as of coupled FitzHugh-Nagumo systems.

The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $\beta$. The heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates. Two analytical approaches based on nested Padé approximants and partial differential approximants were used in the case of expansions with respect to two variables (two recovery rates) for the evaluation of the critical values and critical exponents. The critical exponents in heterogeneous systems are very close to those for the homogeneous contact process thus confirming that the contact process in periodic heterogeneous environment belongs to the directed percolation universality class. The disordered systems, in contrast, seem to have continuously varying critical exponents.

We present the basic equations necessary to interpret heterodyne-detected transient-grating experiments performed on a supercooled liquid composed of anisotropic molecules. The final expressions are given under a form suitable for their direct application to a test case.

This paper reports the first detailed analysis of a transient grating (TG) experiment on a supercooled molecular liquid, $m$-toluidine, from $330\mathrm{K}$ $\left(1.75T_g\right)$ to $190\mathrm{K}$ $\left(1.01T_g\right)$ based on the theoretical model presented in Paper I of this series. This method allows one to give a precise description, over a wide dynamical range, of the different physical phenomena giving rise to the signals. Disentangling the isotropic and the anisotropic parts of the TG response, a careful fitting analysis yields detailed information on the rotation-translation coupling function. We also extract the structural relaxation times related to the “longitudinal” viscosity over almost 10 decades in time and the corresponding stretching coefficient. The value of some other parameters and information on their thermal behavior is also reported.