Umbilic defects of strength $s$ $=$ $\pm$1 were induced in a nematic liquid crystal with negative dielectric anisotropy, confined to Hele-Shaw cells with homeotropic boundary conditions, and their annihilation dynamics followed experimentally. The speeds of individual defects of annihilating defect pairs with strengths of equal magnitude and opposite sign were determined as a function of several externally applied parameters, such as cell gap, electric field amplitude, frequency, and temperature. It was shown that annihilating defects do not approach each other at equal speeds, but that a speed anisotropy is observed, with the positive defect moving faster than the negative one. The defects move more slowly as the strength of the applied electric field or the cell gap is increased. The speed anisotropy is found to be essentially constant for varying external conditions which do not change the material properties of the liquid crystal material, i.e., confinement, electric field amplitude, or frequency. Only for applied conditions that change material properties, such as temperature changing viscosity, does the speed anisotropy vary. The annihilation dynamics was also simulated numerically giving good qualitative agreement with the experiments. Using insight gained from the simulations we interpret the defects’ speed in terms of their overlap and the speed asymmetry as arising from backflow effects and anisotropy in the elastic constants.

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. More precisely, we consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations and linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripelike flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripelike flocks. The case that shows the most interesting behavior is the one of preferred perpendicular alignment between different species. There a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species. The system under investigation is confined to two spatial dimensions.

Clinical studies have shown compelling data of elevated biopotential signals recorded noninvasively from the breasts of women with breast cancer. While these data are compelling and show a strong potential for use in the noninvasive early detection of breast cancer, there remains significant knowledge gaps which must be addressed before this technology can be routinely used for breast cancer detection. A diffusion-drift model is developed to study the spatial and temporal characteristics of the biopotential signals of breast tumors taking into account the morphology and cell division stages. The electric signals of the most common tumor types—papillary, compact, and comedo—are also considered. The largest biopotential signal is observed from the compact tumor, while the smallest signal is observed from the papillary type. The results also show an increase in the time duration of the generated biopotential signals when cancer cells start their transitions at different time instants. The spatial and temporal variations of the biopotential signals are correlated with the tumor pattern which can have important implications for breast cancer detection.

In a complex network, random initial attacks or failures can trigger subsequent failures in a cascading manner, which is effectively a phase transition. Recent works have demonstrated that in networks with interdependent links so that the failure of one node causes the immediate failures of all nodes connected to it by such links, both first- and second-order phase transitions can arise. Moreover, there is a crossover between the two types of transitions at a critical system-parameter value. We demonstrate that these phenomena can occur in the more general setting where no interdependent links are present. A heuristic theory is derived to estimate the crossover and phase-transition points, and a remarkable agreement with numerics is obtained.

We report experimental evidence of the propagating capillary solitary waves generated by a localized water surface perturbation. Solitons are formed at the air-water interface with a solid plunger and then propagate with velocities proportional to their amplitudes. The shape of the forward front of such solitons is independent of the plunger shape and is given by the hyperbolic secant profile. We find that the nonlinearity of capillary waves is responsible for a small dispersion in the capillary wave group velocity and the soliton existence. This dispersion can be further reduced by adding minute concentrations of proteins to water.

Motivated by the problem of efficiently separating nanoparticles of different character held in solution, we investigate trajectory deflection and particle trapping in flows of nanoparticle suspensions past patterned surfaces. We consider rigid atomistic particles suspended in a viscous liquid solvent and driven by a pressure gradient through a channel, one side of which has a pattern of alternating stripes which attract or repel the particles. We first consider van der Waals forces alone, where the wall interaction is obtained by summing over semi-infinite slabs of material having a Lennard-Jones interaction with or without an attractive term, yielding a force field with nontrivial three-dimensional spatial variation. This wall interaction can either trap particles on the attractive stripes or deflect the trajectories of mobile particles away from the direction of mean flow. Using molecular dynamics simulations we determine the motion of particles of different sizes in this potential, and observe distinct but modest deflections of several degrees from the direction of the imposed fluid flow. The effects of electrostatic interactions are considered by decorating the particles and walls with opposite charges, resulting in significantly more trapping and larger deflection angles. We use Langevin simulations to treat the motion of larger particles in the van der Waals case, and again observe particle trapping and deflection, although the numerical details of the results differ from the molecular dynamics simulations. In the Langevin case we are furthermore able to obtain bounds on the deflection angle from an analysis of the associated Fokker-Planck equation. We conclude that patterned surfaces deflect particle trajectories to a degree depending on their size, and may be used as a vector chromatography separation technique.

Generation of petawatt-class pulses with a nearly single-cycle duration or with a strongly asymmetric longitudinal profile using a thin plasma layer are investigated via particle-in-cell simulations and the analytical flying mirror model. It is shown that the transmitted pulses having a duration as short as about 4 fs (1.2 laser cycles) or one-cycle front (tail) asymmetric pulses with peak intensity of about ${10}^{21}\mathrm{W}/{\mathrm{cm}}^2$ can be produced by optimizing system parameters. Here, a new effect is found for the shaping of linearly polarized laser pulses, owing to which the peak amplitude of the transmitted pulse becomes larger than that of the incoming pulse, and intense harmonics are generated. Characteristics of the transmitting window are then studied for different parameters of laser pulse and plasma layer. For a circular polarization, it is shown that the flying mirror model developed for shaping laser pulses with ultrathin foils can be successfully applied to plasma layers having a thickness of about the laser wavelength, which allows the shape of the transmitted pulse to be analytically predicted.

A variational framework is developed to examine the equilibrium states of a semiflexible polymer that is constrained to lie on a fixed surface. As an application the confinement of a closed polymer loop of fixed length $2\pi R$ within a spherical cavity of smaller radius, $R_0$, is considered. It is shown that an infinite number of distinct periodic completely attached equilibrium states exist, labeled by two integers: $n=2,3,4,\cdots$ and $p=1,2,3,\cdots$, the number of periods of the polar and azimuthal angles, respectively. Small loops oscillate about a geodesic circle: $n=2$, $p=1$ is the stable ground state; states with higher $n$ exhibit instabilities. If $R\ge 2R_0$ new states appear as oscillations about a doubly covered geodesic circle; the state $n=3,p=2$ replaces the twofold as the ground state in a finite band of values of $R$. With increasing $R$, loop states make a transition from oscillatory and orbital behavior on crossing the poles, returning to oscillation upon collapse to a multiple cover of a geodesic circle (signaled, respectively, by an increase in $p$ and an increase in $n$). The force transmitted to the surface does not increase monotonically with loop size, but does asymptotically. It behaves discontinuously where $n$ changes. The contribution to energy from geodesic curvature is bounded. In large loops, the energy becomes dominated by a state independent contribution proportional to the loop size; the energy gap between the ground state and excited states disappears.

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrödinger equations with the attractive self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction. These mixed modes are of a “symbiotic” type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA and are unstable.

The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions: one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this paper, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional force is included in the recovered momentum equation. The additional force has the following features. First, it is proportional to the macroscopic velocity. Second, it is zero in every single-phase region but is nonzero in the interface. Therefore it can be interpreted as an interfacial force. To investigate the effects of the additional interfacial force, numerical simulations are carried out for the problem of Rayleigh-Taylor instability, droplet splashing on a thin liquid film, and the evolution of a falling droplet under gravity. Numerical results demonstrate that, with the increase of the velocity or the Reynolds number, the additional interfacial force will gradually have an important influence on the interface and affect the numerical accuracy.

Complex systems are characterized by a huge number of degrees of freedom often interacting in a nonlinear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently, techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This paper develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession, approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem, this paper solves important problems concerning the applicability and the accuracy of estimated parameters.

The propulsion velocity of active colloids that asymmetrically catalyze a chemical reaction is probed experimentally as a function of their sizes. It is found that over the experimentally accessible range, the velocity decays as a function of size, with a rate that is compatible with an inverse size dependence. A diffusion-reaction model for the concentrations of the fuel and waste molecules that takes into account a two-step process for the asymmetric catalytic activity on the surface of the colloid is shown to predict a similar behavior for colloids at the large size limit, with a saturation for smaller sizes.

We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk relaxation to localization in a single state. At low temperatures, both models exhibit scaling behavior. We discuss the growing length and time scales associated with amorphous order, and the fraction of pinned spins required to localize the system in a single state. These results, obtained for finite dimensional interacting models, provide a theoretical scenario for the effect of random pinning that differs qualitatively from previous approaches based either on mean-field, mode-coupling, or renormalization group treatments.

Numerous experiments have indicated that the fracture front (in three dimensions) and crack lines (in two dimensions) in disordered solids and rocklike materials is rough. It has been argued that the roughness exponent $\zeta$ is universal. Using extensive simulations of a two-dimensional model, we provide strong evidence that if extended correlations and anisotropy—two features that are prevalent in many materials—are incorporated in the models that are used in the numerical simulation of crack propagation, then $\zeta$ will vary considerably with the extent of the correlations and anisotropy. The results are consistent with recent experiments that also indicate deviations of $\zeta$ from its supposedly universal value, as well as with the data from rock samples.

We consider a multistate contact process (CP) in which new particles are created with probabilities that depend on the fitness of the parent particle and with mutations that occur at the time of creation. The fitness is determined by the Kauffman $NK$ model. Using Monte Carlo simulations, we show that such an evolutional CP exhibits critical behaviors that differ from the basic CP. In addition, we present numerical results suggesting that the fitness averaged over surviving particles exhibits a maximum value at the critical point.

The cumulant expansion is used to estimate generalized Lyapunov exponents of the random-frequency harmonic oscillator. Three stochastic processes are considered: Gaussian white noise, Ornstein-Uhlenbeck, and Poisson shot noise. In some cases, nontrivial numerical difficulties arise. These are mostly solved by implementing an appropriate importance-sampling Monte Carlo scheme. We analyze the relation between random-frequency oscillators and many-particle systems with pairwise interactions like the Lennard-Jones gas.

Granular oscillation in an unequally two-compartmentalized system is investigated experimentally, yielding two time periods: ${\tau }^{LS}$ represents the time period for particles moving from the large to the small compartment, and ${\tau }^{SL}$ is the time needed for movement in a reverse direction. We construct the phase diagram for the unequal system, discovering that there exist two different granular oscillation states. In the GOI state, ${\tau }^{LS}>{\tau }^{SL}$ is observed, and $({\tau }^{LS}-{\tau }^{SL})$ increases as the difference between the two compartment widths is enlarged. In contrast, ${\tau }^{LS}<{\tau }^{SL}$ is found in the GOII state, where the total number of particles is considerably lower than that in the GOI state. A flux model, accompanied by a proposed generalized granular temperature, is adopted to quantitatively calculate the observed time periods for both granular oscillation states. We find that the proposed temperature in each compartment is crucial in discriminating ${\tau }^{LS}$ from ${\tau }^{SL}$, and this is supported by the molecular dynamics analysis of mean kinetic energy of particles in a single compartment.

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

Kink sites play a critical role in crystal growth. The incorporation of a growth unit into a kink site (1) maintains the free energy of the edge constant and (2) creates another site with the same properties. These properties allow growth through successive incorporation events to proceed in a self-sustaining manner such that the equilibrium spacing between kinks is maintained on average. Traditionally the distributions of kink sites have been determined using a single-site model whereby the probabilities of encountering a kink site adjacent to an edge and encountering a disturbance along an edge are assumed equivalent. In this paper, we develop multisite models that determine the probabilities of encountering kink sites; with the requirement that they obey both properties necessary for growth through successive self-sustaining incorporation events. The probabilities determined using the multisite models diverge significantly from the single-site model for edges with intermolecular interactions $\lesssim 6k_{b}T$ between successive molecules. The implications of these findings for the development of predictive crystal shape models and experimental analysis are discussed.