We study a chemical gelation model in two dimensions which includes both monomer aggregations and bond fluctuations. Our numerical simulation shows that a sol-gel transition occurs when an initial monomer concentration is above a critical concentration. Fractal aggregates grow until the sol-gel transition occurs. After the gelation, however, bond fluctuations break the fractal structure and an interesting inhomogeneous gel fiber network appears instead. A pore size distribution of the inhomogeneous structure shows the existence of hierarchical structures in the gel phase. It is also found that slow dynamics appear near the critical concentration.

In this paper, we report on the flexoelastic and viscoelastic ratios for a number of bimesogens compounds with the same generic structure. Values are obtained indirectly by measuring the flexoelectro-optic response in the chiral nematic phase. By varying the molecular structure we alter the bend angle, transverse dipole moment, and length of the molecule. First, to examine the influence of the bend angle we use a homologous series whereby the only alteration in the molecular structure is the number of methylene units in the aliphatic spacer, $n$. Results show that the flexoelastic ratio, $e∕K$, and the effective flexoelectric coefficient, $e$, both exhibit an odd-even effect with values for $n=\text{odd}$ being greater than that for $n=\text{even}$. This is understood in terms of an increase in the bend angle of the molecule and an increase in the transverse dipole moment. Second, in order to investigate the impact of the dipole moment, we have altered the mesogenic units so as to vary the longitudinal dipole moment and used different linkages in the aliphatic spacer in an attempt to alter the transverse dipole moment. Qualitatively, the results demonstrate that the odd-spaced bimesogen with larger transverse dipole moments exhibit larger flexoelastic ratios.

We present results from constant pressure molecular-dynamics simulations for a bead-spring model of a crystallizable polymer melt. Our model has two main features, a chemically realistic intrachain rigidity and a purely repulsive interaction between nonbonded monomers. By means of intrachain and interchain structure factors we explore polymer conformation and melt structure above and below the temperature $T_{\mathrm{crys}}^{\mathrm{hom}}$ of homogeneous crystallization. Here, we do not only determine average spatial correlations, but also site-specific correlations which depend on the position of the monomers along the polymer backbone. In the liquid phase above $T_{\mathrm{crys}}^{\mathrm{hom}}$ we find that this site dependence can be well-accounted for by known theoretical approximations, the Koyama distribution for the intrachain structure and the polymer reference interaction site model (PRISM) for the interchain structure. This is no longer true in the semicrystalline phase. Below $T_{\mathrm{crys}}^{\mathrm{hom}}$ short chains fully extend upon crystallization, whereas sufficiently long chains form chain-folded lamellae which coexist with amorphous regions. The structural features of these polymer crystals lead to violations of premises of the Koyama approximation or PRISM theory so that both theoretical approaches cannot be applied simultaneously. Furthermore, we find a violation of the Hansen-Verlet freezing criterion; our polymer melt crystallizes more easily than a simple liquid. This hints at the importance of the coupling between conformation (backbone rigidity) and density (packing constraints) for polymer crystallization.

Billiards are idealizations for systems where particles or waves are confined to cavities, or to other homogeneous regions. In billiard systems a point particle moves freely except for specular reflections from rigid walls. However, billiard walls are not always completely reflective and measurements inside can also open the billiard. Since boundary openings have been studied extensively in the literature, we rather model leakages inside the billiard. In particular, we investigate the classical dynamics of a leakage for a continuous family of billiard systems, that is, the stadium-lemon-billiard family. With a single parameter the geometry of the billiard can be tuned from stadium (being fully hyperbolic) over circle (integrable) to the lemon-shaped billiard (mixed chaotic). For the stadium billiard we found an algebraically decaying mean escape time with the linear size $ϵ$ of the leakage $⟨n_{\mathrm{esc}}⟩\sim {ϵ}^{-1}$ together with an exponential decay of the survival probability distribution. The finding is nearly independent of the position and size of the leakage, as long as the leakage is much smaller than the system size, and it is in good agreement with a stochastic map approximation of the dynamics. Due to the mixed phase space for lemon billiards, the mean escape time depends both on the position and geometry of the leakage. For systems where quasiregular motion dominates, we found a linear dependence of the mean escape time, $⟨n_{\mathrm{esc}}⟩\sim 1-ϵ$, which we refer to as flooding law. Our findings are helpful in understanding dynamics of leaking Hamiltonian systems.

The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in thermal equilibrium are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the chain in thermal equilibrium can be effectively described by a system of weakly interacting renormalized nonlinear waves that possess (i) the Rayleigh-Jeans distribution and (ii) zero correlations between waves, just as noninteracting free waves would. This renormalization is achieved through a set of canonical transformations. The renormalized linear dispersion of these renormalized waves is obtained and shown to be in excellent agreement with numerical experiments. Moreover, a dynamical interpretation of the renormalization of the dispersion relation is provided via a self-consistency, mean-field argument. It turns out that this renormalization arises mainly from the trivial resonant wave interactions, i.e., interactions with no momentum exchange. Furthermore, using a multiple time-scale, statistical averaging method, we show that the interactions of near-resonant waves give rise to the broadening of the resonance peaks in the frequency spectrum of renormalized modes. The theoretical prediction for the resonance width for the thermalized $\beta$-FPU chain is found to be in very good agreement with its numerically measured value.

The self-organization of particles in a two phase system in the coexistence region through a diffusive mechanism is known as Ostwald ripening. The late stage of Ostwald ripening is studied here through the use of a mesoscopic model in conjunction with a special configuration that allows for the direct measurement of system characteristics such as domain size. The mesoscopic model is a stochastic partial integrodifferential equation and is studied through the use of recently developed and benchmarked spectral schemes. The size of the growing region is not observed to increase as a power law in this model during the late stages of self-organization in contrast to the power law growth observed in simulations of the earlier stages of self-organization. The results included here also demonstrate the effect of adjusting the interparticle interaction on the morphological evolution of the system.

The nonlinear dynamics of a cylindrical pinion that is kept at a distance from a vibrating rack is studied, and it is shown that the lateral Casimir force between the two corrugated surfaces can be rectified. The effects of friction and external load are taken into account, and it is shown that the pinion can do work against loads of up to a critical value, which is set by the amplitude of the lateral Casimir force. We present a phase diagram for the rectified motion that could help its experimental investigations, as the system exhibits a chaotic behavior in a large part of the parameter space.

Usually one finds that dissipation tends to make a quantum system more classical in nature. We study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bilinearly to the momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we find that the position and momentum variances for momentum coupling are, respectively, identical to momentum and position variances for spatial friction. This implies that momentum coupling leads to an increase in the fluctuations in position as the temperature is lowered, exactly the opposite of the classical-like localization of the oscillator, found with spatial friction. For a parabolic barrier, momentum coupling causes an increase in the unstable normal mode barrier frequency, as compared to the lowering of the barrier frequency in the presence of purely spatial coupling. This increase in the frequency leads to an enhancement of the thermal tunneling flux, which below the crossover temperature becomes exponentially large. The crossover temperature between tunneling and thermal activation increases with momentum friction so that quantum effects in the escape are relevant at higher temperatures.

In a previous paper [Bag and Hu, Phys. Rev. E 73, 061107 (2006)], we studied the mean lifetime (MLT) for the escape of a Brownian particle through an unstable limit cycle driven by multiplicative colored Gaussian and additive Gaussian white noises and found resonant activation (RA) behavior. In the present paper we switch from Gaussian to non-Gaussian multiplicative colored noise. We find that in the RA phenomenon, the minimum appears at a smaller noise correlation time $\left(\tau \right)$ for non-Gaussian noises compared to Gaussian noises in the plot of MLT vs $\tau$ for a fixed noise variance; the same plot for a given noise strength increases linearly and the increasing rate is smaller for non-Gaussian noises than for the Gaussian noises; the plot of logarithm of inverse of MLT vs inverse of the strength of additive noise is Arrhenius-like for Gaussian colored noise and it becomes similar to the quantum-Kramers rate if the multiplicative noise is non-Gaussian.

The temperature dependence of the thickness of thick free-standing films is studied using a high-resolution film thickness measurement technique. A small discontinuity in the temperature dependence of the smectic layer thickness at every phase transition between ferro-, ferri-, and antiferroelectric phases is observed. We show that the major contribution to it arises from a change in the smectic tilt angle.

We present an analysis of mapped surfaces obtained from configurations of two classical statistical-mechanical spin models in the square lattice: the $q$-state Potts model and the spin-1 Blume-Capel model. We carry out a study of the phase transitions in these models using the Monte Carlo method and a mapping of the spin configurations to a solid-on-solid growth model. The first- and second-order phase transitions and the tricritical point happen to be relevant in the kinetic roughening of the surface growth process. At the low and high temperature phases the roughness $W$ grows indefinitely with the time, with growth exponent ${\beta }_w\simeq 0.50(W\sim t^{{\beta }_w})$. At criticality the growth presents a crossover at a characteristic time $t_c$, from a correlated regime (with ${\beta }_w\ne 0.50$) to an uncorrelated one $({\beta }_w\simeq 0.50)$. We also calculate the Hurst exponent $H$ of the corresponding surfaces. At criticality, ${\beta }_w$ and $H$ have values characteristic of correlated growth, distinguishing second- from first-order phase transitions. It has also been shown that the Family-Vicsek relation for the growth exponents also holds for the noise-reduced roughness with an anomalous scaling.

The effect of coupling between the dipole moment and the orientation is explored based on a relaxation equation for the second rank alignment tensor characterizing the molecular order in liquid crystals and a corresponding equation for the electric polarization. The orientational dynamics leads to a time dependence of the electric polarization. We propose a possibility to measure these effects via the resulting magnetic fields of the magnitude $\mid \mathbf{B}\mid \approx {10}^{-9}\mathrm{T}$. Furthermore, the presence of the electric polarization modifies the orientational dynamics as demonstrated in solution phase diagrams.

We employ the distance matrix method to investigate metabasin dynamics in supercooled water. We find that the motion of the system consists in the exploration of a finite region of configuration space (enclosing several distinct local minima), named metabasin, followed by a sharp crossing to a different metabasin. The characteristic time between metabasin transitions is comparable to the structural relaxation time, suggesting that these transitions are relevant for the long-time dynamics. The crossing between metabasins is accompanied by very rapid diffusional jumps of several groups of dynamically correlated particles. These particles form relatively compact clusters and act as cooperative relaxing units responsible for the density relaxation. We find that these mobile particles are often characterized by an average coordination larger than four, i.e., they are located in regions where the tetrahedral hydrogen bond network is distorted.

We report the control of cell migration by external magnetic forces during the early stage of Dictysostelium discoideum morphogenesis. Magnetically labeled aggregating cells respond to the presence of a magnetic field created by a thin magnetic tip: forces as low as $30\mathrm{pN}$ are sufficient to elicit the aggregation of the cells at the extremity of the tip. This induced magnetotaxis is competitive to classical chemotaxis. We therefore underline the interplay between external mechanical forces and morphogenesis. This magnetic assay will open new possibilities in the study of morphogenesis in Dictyostelium.

The effect of initial spin configurations on zero-temperature Glauber spin dynamics in complex networks is investigated. In a system in which the initial spins are defined by centrality measures at the vertices of a network, a variety of nontrivial diffusive behaviors arise, particularly in relation to functional relationships between the initial and final fractions of positive spins, some of which exhibit a critical point. Notably, the majority spin in the initial state is not always dominant in the final state and the phenomena that occur as a result of the dynamics differ according to the initial condition, even for the same network. It is thus concluded that the initial condition of a complex network exerts an influence on spin dynamics that is equally as strong as that exerted by the network structure.

We demonstrate, in the context of implicit-filtering large eddy simulations (LESs) of geostrophic turbulence, that while the attractor of a well-resolved statistically stationary turbulent flow can be reached in a coarsely resolved LES that is forced by the subgrid scale (SGS) terms diagnosed from the well-resolved computation, the attractor is generically unstable: the coarsely resolved LES system forced by the diagnosed SGS eddy terms has multiple attractors. This points to the importance of interpreting the diagnosed SGS forcing terms in a well-resolved computation or experiment from a combined physical-numerical point of view rather than from a purely physical point of view.

We present a computational algorithm which speeds up Green’s tensor nano-optics calculations by means of optimizing the mesh that represents the system we want to investigate. The algorithm automates the process of creating a variable-size mesh that describes an arbitrary nanostructure. The total number of elements of this mesh is smaller than that of a regular mesh representing the same structure, and thus the Green’s tensor calculations can be performed faster. Precision, however, is kept at a similar level than for the regular mesh. Typically, the algorithm yields a mesh that speeds up Green’s tensor calculations by a factor of 4, while giving a maximum error in the field magnitude of about 5%. The speed-up factor makes it very suitable for otherwise lengthy calculations, and the error should be acceptable for most applications.

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena such as jamming. Recently we reported [Phys. Rev. Lett. 95, 118101 (2005)] a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing an interaction parameter $c$, to account for an interesting mechanochemical process. We have been able to extract all the parameters of the model, except $c$, from experimentally measured quantities. In contrast to earlier models of intracellular molecular motor traffic, our model assigns distinct “chemical” (or, conformational) states to each kinesin to account for the hydrolysis of adenosine triphosphate (ATP), the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine, e.g., the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechanochemical process captured by the parameter $c$.

Two types of patterns rigidly rotating within a disk of a weakly excitable medium are studied using the free-boundary approach. The patterns are spots moving along the boundary of the disk and spiral waves rotating around the disk center. The study reveals a selection mechanism that uniquely determines the shape and the angular velocity of these patterns as a function of the medium excitability and the disk radius. These two types of patterns coexist below some critical parameter value, coincide at a bifurcation point, and do not exist above it. The same selection mechanism is applied to describe a limiting case of a spiral wave rotating in an unbounded medium.

Droplets are natural candidates for use as microfluidic reactors, if active control of their formation and transport can be achieved. We show here that localized heating from a laser can block the motion of a water-oil interface, acting as a microfluidic valve for two-phase flows. A theoretical model is developed to explain the forces acting on a drop due to thermocapillary flow, predicting a scaling law that favors miniaturization. Finally, we show how the laser forcing can be applied to sorting drops, thus demonstrating how it may be integrated in complex droplet microfluidic systems.