The response of harmonically trapped Brownian particles to an externally imposed oscillatory shear flow is explored by theory and computer simulation. The special case of a single trapped particle is solved analytically. We present explicit results for the time-dependent density and the velocity distribution. The response of the many-body problem is studied by computer simulations. In particular, we investigate the influence of oscillatory shear flow on the internal modes of the cluster. As a function of the shear oscillation frequency, we find resonant behavior for certain (antisymmetric) normal modes, implying that they can be efficiently excited by oscillatory shear. Our results are verifiable in experiments on dusty plasmas and trapped colloidal dispersions.

We report high-sensitivity and high-temperature resolution experimental data for the temperature dependence of the optical birefringence of a nonpolar monolayer smectogen 4-butyloxyphenyl-$4{}^{\prime }$-decyloxybenzoate $(\overline{10}.\text{O}.\overline{4})$ liquid crystal by using a rotating-analyzer technique. The birefringence data cover nematic and smectic-$A$ phases of the $\overline{10}.\text{O}.\overline{4}$ compound. The birefringence data are used to probe the temperature behavior of the nematic order parameter $S\left(T\right)$ in the vicinity of both the nematic-isotropic $(N-I)$ and the nematic–smectic-$A$ ($N-\text{Sm}A$) transitions. For the $N-I$ transition, from the data sufficiently far away from the smectic-$A$ phase, the average value of the critical exponent $\beta$ describing the limiting behavior of $S\left(T\right)$ is found to be $0.2507\pm 0.0010$, which is in accordance with the so-called tricritical hypothesis, which predicts $\beta =0.25$ and excludes higher theoretical values. The critical behavior of $S\left(T\right)$ at the $N-I$ transition is discussed in detail by comparing our results with the latest reports in the literature and we conclude that by comparing with the previously reported results, the isotropic internal field assumption by the Vuks-Chandrasekhar-Madhusudana model is adequate to extract the critical behavior of $S\left(T\right)$ from the optical birefringence data. We observe that there is no discontinuous behavior in the optical birefringence, signaling the second-order nature of the $N-\text{Sm}A$ transition. The effect of the coupling between the nematic and smectic-$A$ order parameters on the optical birefringence near the $N-\text{Sm}A$ transition is also discussed. In a temperature range of about $4\text{K}$ above and below the $N-\text{Sm}A$ transition, the pretransitional evidence for the $N-\text{Sm}A$ coupling have been detected. From the analysis of the optical birefringence data above and below the $N-\text{Sm}A$ transition by means of various fitting expressions we test the validity of the scaling relation $\lambda =1-\alpha$ between the critical exponent $\lambda$ describing the limiting behavior of the nematic order parameter and the specific heat capacity exponent $\alpha$. We then show that the temperature derivative of the nematic order parameter $S\left(T\right)$ near $T_{NA}$ exhibits the same power-law divergence as the specific heat capacity with an effective critical exponent of $0.2303\pm 0.0035$.

We study how the orientational correlations of DNA confined to nanochannels depend on the channel diameter $D$ by means of Monte Carlo simulations and a mean-field theory. This theory describes DNA conformations in the experimentally relevant regime where the Flory–de Gennes theory does not apply. We show how local correlations determine the dependence of the end-to-end distance of the DNA molecule upon $D$. Tapered nanochannels provide the necessary resolution in $D$ to study experimentally how the extension of confined DNA molecules depends upon $D$. Our experimental and theoretical results are in qualitative agreement.

Cooperation has been recognized as a fundamental driving force in many natural, social, and economic systems. We investigate whether, given a complex-networked system in which agents (nodes) interact with one another according to the rules of evolutionary games and are subject to failure or death, cooperation can prevail and be optimized. We articulate a control scheme to maximize cooperation by introducing a time tolerance, a time duration that sustains an agent even if its payoff falls below a threshold. Strikingly, we find that a significant cooperation cluster can emerge when the time tolerance is approximately uniformly distributed over the network. A heuristic theory is derived to understand the optimization mechanism, which emphasizes the role played by medium-degree nodes. Implications for policy making to prevent or mitigate large-scale cascading breakdown are pointed out.

We study a discrete stochastic linear metapopulation model to understand the effect of risk spreading by dispersion. We calculate analytically the stable distribution of populations in different habitats. The simultaneous distribution of populations in habitats has a complicated self-similar structure, but the population in each habitat follows a log-normal distribution. A class of discrete stochastic matrix models was mostly dealt with numerically. Our analytical predictions are robust in the wide range of parameters. Qualitative predictions of the current results should hold in the case of multiple habitats. We thus conclude that environmental stochasticity always promotes dispersal.

We study the variability of passive scalar diffusion via the statistics of stochastic particle dispersion in a chaotic flow. We find that at intermediate times when the statistics of individual trajectories start to exhibit scaling-law behaviors, scalar variance over the entire domain exhibits multimodal structure. We demarcate the domain based on Lagrangian coherent structures and find that the conditional statistics exhibit strong unimodal behavior, indicating coherence of effective diffusion among each Lagrangian partition of the flow.

Motion in a one-dimensional (1-D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row. Due to their hydrodynamic interactions, the spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longitudinal and transverse waves is described.

We present a systematic, multiscale, fully detailed numerical modeling for dynamics of fluid flow and ion transport covering Ohmic, limiting, and overlimiting current regimes in conductance of ion-selective membrane. By numerically solving the Poisson-Nernst-Planck-Navier-Stokes equations, it is demonstrated that the electroconvective instability, arising from the electric field acting upon the extended space charge layer, and the induced strong vortical fluid flow are the dominant factors of the overlimiting current in the planar membrane system. More importantly, at the transition between the limiting and the overlimiting current regimes, hysteresis of electric current is identified. The hysteresis demonstrates the important role of the electroconvective flow in enhancing of current in electrolyte systems with ion-selective membrane.

Melting of a two-dimensional plasma crystal occurring due to a mode-coupling instability is studied using particle tracking and particle image velocimetry techniques. By combining these techniques, it is possible to identify the location of a propagating melting front and find a characteristic scale length for the temperature gradient across the front. It is found that the measurements of heat transport are consistent with a simple two-dimensional model allowing us to estimate the thermal diffusivity. The measured values for the thermal diffusivity are consistent with previously measured values.

In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large deviations approach to show that, in contrast, different states can exchange stability as system size is varied in a driven, bistable reaction-diffusion system. This striking effect is related to a shift from a spatially uniform to a nonuniform transition state and should generically be possible in a wide range of nonequilibrium physical and biological systems.

Excitability is observed in a variety of natural systems, such as neuronal dynamics, cardiovascular tissues, or climate dynamics. The stochastic FitzHugh-Nagumo model is a prominent example representing an excitable system. To validate the practical use of a model, the first step is to estimate model parameters from experimental data. This is not an easy task because of the inherent nonlinearity necessary to produce the excitable dynamics, and because the two coordinates of the model are moving on different time scales. Here we propose a Bayesian framework for parameter estimation, which can handle multidimensional nonlinear diffusions with large time scale separation. The estimation method is illustrated on simulated data.

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximate limit solutions found originally in unrelated fields, first in [L. Turban, J. Phys. A 25, 127 (1992)] and later in [P. L. Krapivsky and S. Redner, Am. J. Phys. 64, 546 (1996)].

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time $\alpha$ decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction $\phi$, temperature $T$, and aspect ratio $\alpha$. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of $\alpha$, onto a universal scaling function ${\mathcal{F}}_{\pm }\left(\right|\phi -{\phi }_0|,T,\alpha )$, which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions. ${\mathcal{F}}_{\pm }$ for both the translational and rotational DOF are characterized by the $\alpha$-dependent scaling exponents $\mu$ and $\delta$ and packing fraction ${\phi }_0\left(\alpha \right)$ that signals the crossover in the scaling form ${\mathcal{F}}_{\pm }$ from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility of structural relaxation at ${\phi }_0$, $m\left({\phi }_0\right)$, decreases monotonically with increasing aspect ratio for both ellipses and dimers. For $\alpha >{\alpha }_p$, where ${\alpha }_p$ is the location of the peak in the packing fraction ${\phi }_J$ at jamming onset, the rotational DOF are strongly coupled to the translational DOF, and the dynamic scaling exponents and ${\phi }_0$ are similar for the rotational and translational DOF. For $1<\alpha <{\alpha }_p$, the translational DOF become frozen at higher temperatures than the rotational DOF, and ${\phi }_0$ for the rotational degrees of freedom increases above ${\phi }_J$. Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. Thus, zero-temperature contact counting arguments do not apply to structural relaxation of dense liquids of anisotropic particles near the glass transition.

We investigate erosion patterns observed in a horizontal granular bed resulting from seepage of water motivated by observation of beach rills and channel growth in larger scale land forms. Our experimental apparatus consists of a wide rectangular box filled with glass beads with a narrow opening in one of the side walls from which eroded grains can exit. Quantitative data on the shape of the pattern and erosion dynamics are obtained with a laser-aided topography technique. We show that the spatial distribution of the source of groundwater can significantly impact the shape of observed patterns. An elongated channel is observed to grow upstream when groundwater is injected at a boundary adjacent to a reservoir held at constant height. An amphitheater (semicircular) shape is observed when uniform rainfall infiltrates the granular bed to maintain a water table. Bifurcations are observed as the channels grow in response to the groundwater. We further find that the channels grow by discrete avalanches as the height of the granular bed is increased above the capillary rise, causing the deeper channels to have rougher fronts. The spatiotemporal distribution of avalanches increase with bed height when partial saturation of the bed leads to cohesion between grains. However, the overall shape of the channels is observed to remain unaffected indicating that seepage erosion is robust to perturbation of the erosion front.

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor $S_b(q,t)$ and the susceptibility ${\chi }_b\left(t\right)$ to detect the spatial correlations of configuration changes. Here ${\chi }_b\left(t\right)$ attains a maximum at $t=t_b^{\max }$ as a function of time $t$, where the fraction of the particles with broken bonds ${\phi }_b\left(t\right)$ is about $1/2$. In the four-point scheme, treating the structure factor $S_4(q,t)$ and the susceptibility ${\chi }_4\left(t\right)$, we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of ${\chi }_4\left(t\right)$ is attained at $t=t_4^{\max }$, where these two contributions become of the same order. As a result, $t_4^{\max }$ is considerably shorter than $t_b^{\max }$.

We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces either by an in-phase bending or an antiphase squeezing mode. The bending mode has a long-wave nature, and is present even at a vanishingly small destabilizing field. In contrast, the squeezing mode has finite wave-number characteristics and originates only beyond a threshold strength of the electric field. This is in contrast to the instabilities of the viscous films with multiple interfaces where both modes are found to possess long-wave characteristics. The elastic film is unstable by bending mode when the stabilizing forces due to the in-plane curvature and the elastic stiffness are strong and the destabilizing electric field is relatively weak. In comparison, as the electric field increases, a subdominant squeezing mode can also appear beyond a threshold destabilizing field. A dominant squeezing mode is observed when the destabilizing field is significantly strong and the elastic films are relatively softer with lower elastic modulus. In the absence of liquid layers, a free elastic film is also found to be unstable by long-wave bending and finite wave-number squeezing modes. The LSA asymptotically recovers the results obtained by the previous formulations where the membrane bending elasticity is approximately incorporated as a correction term in the normal stress boundary condition. Interestingly, the presence of a very weak stabilizing influence due to a smaller interfacial tension at the elastic-viscous interfaces opens up the possibility of fabricating submicron patterns exploiting the instabilities of a trilayer.

We investigate theoretically, with the aid of numerical calculations based on a Landau–de Gennes theory, how two cubic cholesteric blue phases of a chiral liquid crystal, BP I and BP II, are stabilized when a guest component, such as a polymer network, is introduced and replace energetically costly defect regions. We show that the temperature range of stable BP I is significantly widened by the guest component, while the stability of BP II is only modestly enhanced.

We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a three-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its “pure” population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable “mixed” fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a nonzero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.

We introduce a minimal model of population range expansion in which the phenotypes of individuals present no selective advantage and differ only in their diffusion rate. We show that such neutral phenotypic variability (i.e., that does not modify the growth rate) alone can yield phenotype segregation at the front edge, even in absence of genetic noise, and significantly impact the dynamical properties of the expansion wave. We present an exact asymptotic traveling wave solution and show analytically that phenotype segregation accelerates the front propagation. The results are compatible with field observations such as invasions of cane toads in Australia or bush crickets in Britain.