The director-density coupling theory was formulated with two parameters ($u_1$ and $u_2$) to explain the acousto-optic effect in nematic liquid crystals. The assumption that the director is not able to accompany rapid oscillations of the sound wave, so that it actually couples to the time-averaged interaction, renders it effectively a $u_1$-independent theory. In this paper, we investigate a route in which the time average is postponed to the end of the calculation. This approach allows us to derive measurable quantities that depend on both $u_1$ and $u_2$.

We investigate the migration of glioma cells as a front propagation phenomenon both theoretically (by using both discrete lattice modeling and a continuum approach) and experimentally. For small effective strength of cell-cell adhesion $q$, the front velocity does not depend on $q$. When $q$ exceeds a critical threshold, a fingeringlike front propagation is observed due to cluster formation in the invasive zone. We show that the experiments correspond to the transient regime, before the regime of front propagation is established. We performed an additional experiment on cell migration. A detailed comparison with experimental observations showed that the theory correctly predicts the maximal migration distance but underestimates the migration of the main mass of cells.

The final stages of pinchoff and breakup of dripping droplets of near-inviscid Newtonian fluids are studied experimentally for pure water and ethanol. High-speed imaging and image analysis are used to determine the angle and the minimum neck size of the cone-shaped extrema of the ligaments attached to dripping droplets in the final microseconds before pinchoff. The angle is shown to steadily approach the value of 18.0 $\pm {0.4}^{\circ }$, independently of the initial flow conditions or the type of breakup. The filament thins and necks following a ${\tau }^{2/3}$ law in terms of the time remaining until pinchoff, regardless of the initial conditions. The observed behavior confirms theoretical predictions.

We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, we find that the master stability function shows a discrete rotational symmetry depending on the number of groups. The coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum, which helps to simplify the evaluation of the master stability function. Our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times, multiple coupling functions, but also with multiple kinds of local dynamics in the networks’ nodes. We illustrate our results by calculating stability in the example of delay-coupled semiconductor lasers and in a model for neuronal spiking dynamics.

Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities of its two units by two competing mechanisms: An exponential decrease of the coupling strength is compensated for by an increase due to desynchronized activity. This mechanism prevents the network from reaching a steady state. Numerical simulations of a coupled map lattice show chaotic trajectories of desynchronized units interrupted by pulses of mutually synchronized clusters. These pulses occur on all scales, sometimes extending to the entire network. Clusters of synchronized units can be triggered by a small group of synchronized units.

Flow patterns arising in a vertical differentially heated layer of nonconducting ferromagnetic fluid placed in an external uniform transverse magnetic field are studied experimentally and discussed from the point of view of the perturbation energy balance. A quantitative criterion for detecting the parametric point where the dominant role in generating a flow instability is transferred between the thermogravitational and thermomagnetic mechanisms is suggested, based on the disturbance energy balance analysis. A comprehensive experimental study of various flow patterns is undertaken, and the existence is demonstrated of oblique thermomagnetic waves theoretically predicted by Suslov [Phys. Fluids 20, 084101 (2008)] and superposed onto the stationary magnetoconvective pattern known previously. It is found that the wave number of the detected convection patterns depends sensitively on the temperature difference across the layer and on the applied magnetic field. In unsteady regimes its value varies periodically by a factor of almost 2, indicating the appearance of two different competing wave modes. The wave numbers and spatial orientation of the observed dominant flow patterns are found to be in good agreement with theoretical predictions.

We developed a model for the enhancement of the heat flux by spherical and elongated nanoparticles in sheared laminar flows of nanofluids. Besides the heat flux carried by the nanoparticles, the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect: it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These dynamical effects, which were not included in existing thermal models, are responsible for changing the thermal properties of flowing fluids as compared to quiescent fluids. The proposed model is strongly supported by extensive numerical simulations, demonstrating a potential increase of the heat flux far beyond the Maxwell-Garnett limit for the spherical nanoparticles. The road ahead, which should lead toward robust predictive models of heat flux enhancement, is discussed.

Mesoscopic hydrodynamic equations are solved to investigate coarsening dynamics of two interacting nanodroplets on chemically patterned substrates. The effects of different parameters such as the surface chemical pattern, the slip length, the profile of the disjoining pressure, the size of the droplets, and the contact angles on the coarsening are studied. Our results reveal that the presence of a chemical heterogeneity can enhance or weaken the coarsening dynamics depending on the pattern type and positions of the droplets on the substrate. Also increasing the contact angles to values larger than a critical value may qualitatively change the coarsening process, and the profile of the disjoining pressure and the slippage can appreciably modify the coarsening rate.

In order to identify the basic conditions for thermal rectification we investigate a simple model with nonuniform, graded mass distribution. The existence of thermal rectification is theoretically predicted and numerically confirmed, suggesting that thermal rectification is a typical occurrence in graded systems, which are likely to be natural candidates for the actual fabrication of thermal diodes. In view of practical implications, the dependence of rectification on the asymmetry and system's size is studied.

The conditions necessary for the formation of a monolayer and a bilayer of a mutated form (P499C) of human cytochrome P450 reductase on a Au(110)/electrolyte interface have been determined using a quartz crystal microbalance with dissipation, atomic force microscopy, and reflection anisotropy spectroscopy (RAS). The molecules adsorb through a Au-S linkage and, for the monolayer, adopt an ordered structure on the Au(110) substrate in which the optical axes of the dipoles contributing to the RAS signal are aligned roughly along the optical axes of the Au(110) substrate. Differences between the absorption spectrum of the molecules in a solution and the RAS profile of the adsorbed monolayer are attributed to surface order in the orientation of dipoles that contribute in the low energy region of the spectrum, a roughly vertical orientation on the surface of the long axes of the isoalloxazine rings and the lack of any preferred orientation in the molecular structure of the dipoles in the aromatic amino acids. Our studies establish an important proof of principle for immobilizing large biological macromolecules to gold surfaces. This opens up detailed studies of the dynamics of biological macromolecules by RAS, which have general applications in studies of biological redox chemistry that are coupled to protein dynamics.

In this paper, based on the regular Korteweg–de Vries (KdV) system, we study negative-order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs, conservation laws, and explicit multisoliton and multikink wave solutions thorough bilinear Bäcklund transformations. The NKdV equations studied in our paper are differential and actually derived from the first member in the negative-order KdV hierarchy. The NKdV equations are not only gauge equivalent to the Camassa-Holm equation through reciprocal transformations but also closely related to the Ermakov-Pinney systems and the Kupershmidt deformation. The bi-Hamiltonian structures and a Darboux transformation of the NKdV equations are constructed with the aid of trace identity and their Lax pairs, respectively. The single and double kink wave and bell soliton solutions are given in an explicit formula through the Darboux transformation. The one-kink wave solution is expressed in the form of $\tanh$ while the one-bell soliton is in the form of $\mathrm{sech}$, and both forms are very standard. The collisions of two-kink wave and two-bell soliton solutions are analyzed in detail, and this singular interaction differs from the regular KdV equation. Multidimensional binary Bell polynomials are employed to find bilinear formulation and Bäcklund transformations, which produce $N$-soliton solutions. A direct and unifying scheme is proposed for explicitly building up quasiperiodic wave solutions of the NKdV equations. Furthermore, the relations between quasiperiodic wave solutions and soliton solutions are clearly described. Finally, we show the quasiperiodic wave solution convergent to the soliton solution under some limit conditions.

We report an anchoring transition of a liquid crystal under the influence of an electric field ($E$ field) in the vicinity of a first-order anchoring transition (ATr) temperature showing bistable homeotropic ($H$) and planar ($P$) states. By means of polarizing microscopy combined with retardation and switching and dielectric measurements, three important observations were made: (1) The anchoring transition from $H$ to $P$ driven by an $E$ field is first order with a threshold $E$-field strength, which decreases with increasing temperature; (2) the thickness of the $H$ layer that is to be converted to the $P$ orientation increases toward ATr temperature $T_{\mathrm{ATr}}$; and (3) the temperature dependence of both parameters is well described by a power law.

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the specific variable speed rule used does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.

I formulate a dynamical model for microtubules interacting with a catastrophe-inducing boundary. In this model microtubules are either waiting to be nucleated, actively growing or shrinking, or stalled at the boundary. I first determine the steady-state occupation of these various states and the resultant length distribution. Next, I formulate the problem of the mean first-passage time to reach the boundary in terms of an appropriate set of splitting probabilities and conditional mean first-passage times and solve explicitly for these quantities using a differential equation approach. As an application, I revisit a recently proposed search-and-capture model for the interaction between microtubules and target chromosomes [M. Gopalakrishnan and B. S. Govindan, Bull. Math. Biol. 73, 2483 (2011)]. I show how my approach leads to a direct and compact solution of this problem.

We explore the nonequilibrium dynamics of noninteracting classical particles in a one-dimensional driven superlattice which is composed of domains exposed to different time-dependent forces. It is shown how the combination of directed transport and conversion processes from diffusive to ballistic motion causes strong correlations between velocity and phase for particles passing through a superlattice. A detailed understanding of the underlying mechanism allows us to tune the resulting velocity distributions at distinguished points in the superlattice by means of local variations of the applied driving force. As an intriguing application we present a scheme how initially diffusive particles can be transformed into a monoenergetic pulsed particle beam whose parameters such as its energy can be varied.

We consider the modulational instability (MI) of Bose-Einstein condensate (BEC) described by a modified Gross-Pitaevskii (GP) equation with higher-order nonlinearity both analytically and numerically. A new explicit time-dependent criterion for exciting the MI is obtained. It is shown that the higher-order term can either suppress or enhance the MI, which is interesting for control of the system${}^{,}$ instability. Importantly, we predict that with the help of the higher-order nonlinearity, the MI can also take place in a BEC with repulsively contact interactions. The analytical results are confirmed by direct numerical simulations.

The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration, and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the coefficients of an $\epsilon$ expansion. By rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices.

We investigated the validity of fluctuation-dissipation relations in the nonequilibrium stationary state of fluidized granular media under gravity by two independent approaches, based on theory and numerical simulations. A phenomenological Langevin-type theory describing the fluctuation of center of mass height, which was originally constructed for a one-dimensional granular gas on a vibrating bottom plate, was generalized to any dimensionality, even for the case in which the vibrating bottom plate is replaced by a thermal wall. The theory predicts a fluctuation-dissipation relation known to be satisfied at equilibrium, with a modification that replaces the equilibrium temperature by an effective temperature defined by the center of mass kinetic energy. To test the validity of the fluctuation-dissipation relation, we performed extensive and accurate event-driven molecular dynamics simulations for the model system with a thermal wall at the bottom. The power spectrum and response function of the center of mass height were measured and closely compared with theoretical predictions. It is shown that the fluctuation-dissipation relation for the granular system is satisfied, especially in the high-frequency (short time) region, for a wide range of system parameters. Finally, we describe the relationship between systematic deviations in the low-frequency (long time) region and the time scales of the driven granular system.

Synthetic biomolecular spiders with “legs” made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site. The spider's legs hop to nearest-neighbor sites with the constraint that the distance between any two legs cannot exceed a maximal span. We establish analytic results for bipedal spiders, and investigate multileg spiders numerically. In experimental realizations legs usually convert substrates into products (visited sites). The binding of legs to products is weaker, so the hopping rate from the substrates is smaller. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a counterintuitive behavior—the more spiders are slowed down on unvisited sites, the more motile they become.

We develop a general method to detect hidden nodes in complex networks, using only time series from nodes that are accessible to external observation. Our method is based on compressive sensing and we formulate a general framework encompassing continuous- and discrete-time and the evolutionary-game type of dynamical systems as well. For concrete demonstration, we present an example of detecting hidden nodes from an experimental social network. Our paradigm for detecting hidden nodes is expected to find applications in a variety of fields where identifying hidden or black-boxed objects based on a limited amount of data is of interest.