Using polarizing optical microscopy we studied thin films and droplets of smectic-$A$ 4-cyano-$4^{\prime }$-n-octylbiphenyl (8CB) liquid crystal deposited in air on crystalline surfaces of muscovite mica that induce monostable planar anchoring. The competition with the homeotropic anchoring at the 8CB-air interface leads to the formation of one-dimensional (1D) patterns composed of straight, parallel defect domains that are organized in periodic arrays over areas as large as several ${\mathrm{mm}}^2$. We have developed a simple model which identifies the arrays with self-assembled “oily streaks,” comprising straight disclination lines and curvature walls. The model reproduces the observed monotonic increase of the period $p$ with the film thickness $h$ in the range $p=1–4\mu \mathrm{m}$ and $h=0.8–17\mu \mathrm{m}$. For higher values of $h$ we observed a sharp transition to a 2D lattice of fragmented focal conic domains. Despite the apparent generality of our model for hybrid planar-homeotropic anchoring conditions, periodic arrays of straight oily streaks have been observed so far only for 8CB on crystalline surfaces such as mica or $\mathrm{Mo}{\mathrm{S}}_2$. Our model indicates that this specificity is due to a particularly strong anchoring of the liquid crystal on such surfaces.

Hyperchaos occurs in a dynamical system with more than one positive Lyapunov exponent. When the equations governing the time evolution of the dynamical system are known, the transition from chaos to hyperchaos can be readily obtained when the second largest Lyapunov exponent crosses zero. If the only information available on the system is a time series, however, such method is difficult to apply. We propose the use of recurrence quantification analysis of a time series to characterize the chaos-hyperchaos transition. We present results obtained from recurrence plots of coupled chaotic piecewise-linear maps and Chua-Matsumoto circuits, but the method can be applied as well to other systems, even when one does not know their dynamical equations.

We point out that the recent discussion of nonrelativistic anti-de Sitter space and conformal field theory correspondence has a direct application in nonequilibrium statistical physics, a fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent $z=2$ and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.

We investigate the dynamics of single-stranded DNA translocation through a nanopore driven by an external force using Langevin dynamics simulations in two dimensions to study how the translocation dynamics depend on the details of the DNA sequences. We consider a coarse-grained model of DNA built from two bases $A$ and $C$, having different base-pore interactions, e.g., a strong (weak) attractive force between the pore and the base $A$ $\left(C\right)$ inside the pore. From a series of studies on hetero-DNAs with repeat units $A_m{C}_n$, we find that the translocation time decreases exponentially as a function of the volume fraction $f_C$ of the base $C$. For longer $A$ sequences with $f_C⩽0.5$, the translocation time strongly depends on the orientation of DNA, namely which base enters the pore first. Our studies clearly demonstrate that for a DNA of certain length $N$ with repeat units $A_m{C}_n$, the pattern exhibited by the waiting times of the individual bases and their periodicity can unambiguously determine the values of $m$, $n$, and $N$, respectively. Therefore, a prospective experimental realization of this phenomenon may lead to fast and efficient sequence detection.

Electrorheological (ER) fluids are a type of ‘‘smart’’ colloid capable of reversible viscosity variations, or even solidification, in response to an applied electric field. The response time can be as short as a few milliseconds. By using the ER fluid as the carrier fluid in microfluidic chips, we report the generation and manipulation of microdroplets and bubbles via integrated, digitally controlled micro-electrodes equipped with a feedback system. By utilizing the strong electric response of the ER fluid, the flow rate can be easily controlled digitally, thereby making tunable the size of the droplets generated and their separations. In particular, ordering change in a chain of droplets is demonstrated. The maneuverability presented in this paper may have potential applications in a variety of lab chips for chemical reactions, bioassays, as well as microfluidic logic computation.

Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes immigration, binary reproduction, and death. The unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution (MPD) of the population. We develop a systematic WKB theory, complemented by the van Kampen system size expansion, for the MPD and for the decay time. Important signatures of the MPD are a power-law tail (such that all the distribution moments, except the zeroth one, diverge) and the presence in the solution of two different WKB modes.

We discuss a kinetically constrained model in which real-valued local densities fluctuate in time, as introduced recently by Bertin, Bouchaud, and Lequeux. We show how the phenomenology of this model can be reproduced by an effective theory of mobility excitations propagating in a disordered environment. Both excitations and probe particles have subdiffusive motion, characterized by different exponents and operating on different time scales. We derive these exponents, showing that they depend continuously on one of the parameters of the model.

We experimentally investigated field-induced aggregation of nonmagnetic particles confined in a magnetic fluid layer when rotating magnetic fields were applied. After application of a magnetic field rotating in the plane of the fluid layer, the single particles start to form two-dimensional clusters, like dimers, trimers, and more complex structures. These clusters aggregated again and again to form bigger clusters. During this nonequilibrium process, a broad range of cluster sizes was formed, and the scaling exponents $z$ and $z^{\prime }$ of the number of clusters $N\left(t\right)\sim t^{-z^{\prime }}$ and average cluster size $S\left(t\right)\sim t^z$ were calculated. The process could be characterized as diffusion-limited cluster-cluster aggregation. We found that all sizes of clusters that occurred during an experiment fall on a single curve, as the dynamic scaling theory predicts. However, the characteristic scaling exponents $z^{\prime },z$ and crossover exponents $\Delta$ were not universal. A particle tracking method was used to find the dependence of the diffusion coefficients $D_s$ on cluster size $s$. The cluster motions show features of Brownian motion. The average diffusion coefficients $⟨D_s⟩$ depend on the cluster size $s$ as a power law $⟨D_s⟩\propto s^{\gamma }$ where values of $\gamma$ as different as $\gamma =-0.62\pm 0.19$ and $\gamma =-2.08\pm 0.51$ were found in two of the experiments.

The effect of the attractive forces originating from van der Waals interactions on the dynamics of thin films $(⩽\sim 100\mathrm{nm})$ is often approximated in fluid dynamics as the disjoining pressure between two unbounded parallel interfaces. However, it is known that this concept of the disjoining pressure, as a force per unit area between parallel interfaces, cannot generally be extended to films of nonuniform thickness. In this paper, we derive a formula for the disjoining pressure for a film of nonuniform thickness by minimizing the total Helmholtz free energy for a thin film residing on a solid substrate. Comparing to the augmented Young-Laplace equation, the disjoining pressure for a thin film of small slope on a flat substrate is shown to take the form $\Pi =-\frac{A_{123}(4-3h_x^2+3h{h}_{xx})}{24\pi h^3}$, where $A_{123}$ is the Hamaker constant for phases 1 and 3 interacting through phase 2; $h$, $h_x$, and $h_{xx}$ are the local film thickness, slope and second order derivative, respectively. For the limiting case of parallel interfaces (e.g., $h_x=h_{xx}\equiv 0$), the disjoining pressure reduces to $\Pi =-\frac{A_{123}}{6\pi h^3}$ in agreement with the classical Lifshitz expression for the van der Waals force. The derivation can be readily extended to more general nonuniform films by constructing tangential planes at both interfaces of the films. Because of steric effects that prevent molecules from overlapping each other, the molecular size cannot be neglected when applying the mesoscopic concept of the disjoining pressure to films of thickness comparable to molecular scales.

We study nematodynamics of a mesoscopic system consisting of sheared biaxial liquid crystalline polymers using a hydrodynamical kinetic theory. We solve the governing Smoluchowski equation using the Galerkin method in selected regions of the material parameter space and a range of accessible shear rates to investigate stable mesoscopic states and robust structures. The imposed shear flow breaks the rotational symmetry in the quiescent state to induce truly biaxial flow-aligning steady states, logrolling states, out-of-plane steady states, exotic time-periodic motions, and chaotic motions in different regimes of material parameters and shear rates.

Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable $\pi$-twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times.

We present a first-order model for obligatory coassembly of block copolymers via an associative driving force in a nonselective solvent, making use of the classical self-consistent field (SCF) theory. The key idea is to use a generic associative driving force to bring two polymer blocks together into the core of the micelle and to employ one block of the copolymer(s) to provide a classical stopping mechanism for micelle formation. The driving force is generated by assuming a negative value for the relevant short-range Flory-Huggins interaction parameter. Hence, the model may be adopted to study micellization via H bonding, acceptor-donor interactions, and electrostatic interactions. Here, we limit ourselves to systems that resemble experimental ones where the mechanism of coassembly is electrostatic attraction leading to charge compensation. The resulting micelles are termed complex coacervate core micelles (CCCMs). We show that the predictions are qualitatively consistent with a wide variety of experimentally observed phenomena, even though the model does not yet account for the charges explicitly. For example, it successfully mimics the effect of salt on CCCMs. In the absence of salt CCCMs are far more stable than in excess salt, where the driving force for self-assembly is screened. The main limitations of the SCF model are related to the occurrence of soluble complexes, i.e., soluble, charged particles that coexist with the CCCMs.

A procedure to obtain the smectic translational order parameter $\Sigma$ from the temperature-dependent intensity $I$ of the fundamental (001) smectic layer peak, observed in small-angle x-ray scattering experiments, is presented. We report results obtained with this procedure on the smectic-A or chiral smectic-A phases of six different liquid crystals, among them a “de Vries”-type $2-\{4^{\prime }-[1^{″},1^{″}-\text{dihydro}-2^{″}-(2^{″}-\text{perfluorobutoxyperfluoroethoxy})-$ $\text{perfluoroethoxy}\left]\right\}\text{phenyl}-5^{\prime }-$$\text{octylpyrimidine}\left(3\text{M}8422\right)$ and the antiferroelectric $\mathrm{R}-4-(1-\text{methylheptyloxycarbonyl})\text{phenyl}-4^{\prime }-\text{octloxybiphenyl}-4-\text{carboxylate}$ (MHPOBC) materials. The smectic order parameters obtained are in the range between $0.5$ and $0.9$. For the “de Vries”-type 3M 8422 we found remarkably high values of $\Sigma$ in the order of $\sim 0.9$.

Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation are calculated theoretically. The calculated values appear to be in good agreement with those determined by numerical experiments. The relevance of our results to jamming transitions is also mentioned.

Chemical derivatives are used in the mathematical modeling of transport phenomena in equilibrium plasma flows when chemical element diffusion and mixing or demixing effects are accounted for. They measure the variation of mixture chemical composition in response to changes in element fractions, pressure, or temperature. Currently, these quantities are calculated numerically, using finite differences. This approach, other than being computationally expensive and prone to numerical error, does not provide any insight into flow physics. Our work is aimed at introducing a fully analytical method for the calculation of chemical derivatives which bypasses the computational cost. It also provides a simple means of estimating their order of magnitude.

We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-field approximation.

We show that the exactly solved low-temperature branch of the two-dimensional $\mathrm{O}\left(n\right)$ model is equivalent to an $\mathrm{O}\left(n\right)$ model with vacancies and a different value of $n$. We present analytic results for several universal parameters of the latter model, which is identified as a tricritical point. These results apply to the range $n⩽3∕2$ and include the exact tricritical point, the conformal anomaly, and a number of scaling dimensions, among which are the thermal and magnetic exponents, and the exponent associated with the crossover to ordinary critical behavior and to tricritical behavior with cubic symmetry. We describe the translation of the tricritical model in a Coulomb gas. The results are verified numerically by means of transfer-matrix calculations. We use a generalized ADE model as an intermediary and present the expression of the one-point distribution function in that language. The analytic calculations are done both for the square and the honeycomb lattice.

We compare weak- and strong-coupling theory of counterion-mediated electrostatic interactions between two asymmetrically charged plates with extensive Monte Carlo simulations. Analytical results in both weak- and strong-coupling limits compare excellently with simulations in their respective regimes of validity. The system shows a surprisingly rich structure in terms of interactions between the surfaces as well as fundamental qualitative differences in behavior in the weak- and the strong-coupling limits.

We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At its turn, each of the two players picks a move among two alternatives in order to maximize its final score, and minimize the opponent’s return. For a game of length $n$, we find that the probability distribution of the final score $S_n$ develops a traveling wave form, $\mathrm{Prob}(S_n=m)=f(m-vn)$, with the wave profile $f\left(z\right)$ decaying unusually as a double exponential for large positive and negative $z$. In addition, as the only parameter in the game is varied, we find a transition where one player is able to get its maximum theoretical score. By extending this model, we suggest that the front velocity $v$ is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially, and for which standard traveling wave theory applies.

Extensive experimental work on the response of DNA molecules to externally applied forces and on the dynamics of DNA molecules flowing in microchannels and nanochannels has been carried out over the past two decades, however, there has not been available, until now, any atomic-scale means of analyzing nonequilibrium DNA response dynamics. There has not therefore been any way to investigate how the backbone and side-chain atoms along the length of a DNA molecule interact with the molecules and ions of the flowing solvent and with the atoms of passing boundary surfaces. We report here on the application of the nonequilibrium biomolecular dynamics simulation method that we developed [G. M. Wang and W. C. Sandberg, Nanotechnology 18, 4819 (2007)] to analyze, at the atomic interaction force level, the conformational dynamics of short-chain single-stranded DNA molecules in a shear flow near a surface. This is a direct atomic computational analysis of the hydrodynamic interaction between a biomolecule and a flowing solvent. The DNA molecules are observed to exhibit conformational behaviors including coils, hairpin loops, and figure-eight shapes that have neither been previously measured experimentally nor observed computationally, as far as we know. We relate the conformational dynamics to the atomic interaction forces experienced throughout the length of a molecule as it moves in the flowing solvent past the surface boundary. We show that the DNA conformational dynamics is related to the asymmetry in the molecular environment induced by the motion of the surrounding molecules and the atoms of the passing surface. We also show that while the asymmetry in the environment is necessary, it is not sufficient to produce the observed conformational dynamics. A time variation in the asymmetry, due in our case to a shear flow, must also exist. In order to contrast these results with the usual experimental situation of purely diffusive motion in thermal equilibrium we have also carried out computations with a zero shear rate. We show that in thermal equilibrium there is asymmetry and an atomic hydrodynamic coupling between DNA molecules and the solvent molecules but there is no coil-uncoil transition.