The correspondence between exotic quantum holonomy, which occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expression of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, is obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher-order EP, which is broken into lower-order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.

In this work we use standard Hamiltonian-system techniques in order to study the dynamics of three vortices with alternating charges in a confined Bose-Einstein condensate. In addition to being motivated by recent experiments, this system offers a natural vehicle for the exploration of the transition of the vortex dynamics from ordered to progressively chaotic behavior. In particular, it possesses two integrals of motion, the energy (which is expressed through the Hamiltonian $H$) and the angular momentum $L$ of the system. By using the integral of the angular momentum, we reduce the system to a 2-degrees-of-freedom one with $L$ as a parameter and reveal the topology of the phase space through the method of Poincaré surfaces of section. We categorize the various motions that appear in the different regions of the sections and we study the major bifurcations that occur to the families of periodic motions of the system. Finally, we correspond the orbits on the surfaces of section to the real space motion of the vortices in the plane.

We investigate the amplitude death phenomenon in a nonautonomous chained network with complicated piecewise nonlinear coupling functions. An analytical criterion for the boundary of the amplitude death region is derived by using the average method. The mechanism of the amplitude death in the nonautonomous networks is very different from that of autonomous systems and rapid dynamic transitions could halt the amplitude death. Numerical verifications are carried out to check jump transitions among different solution branches and further confirm the correctness of the theoretical results.

The motion of an ellipsoidal particle in a viscoelastic liquid subjected to an unconfined shear flow is addressed by numerical simulations. A complex dynamics is found with different transients and long-time regimes depending on the Deborah number $\text{De}$ ($\text{De}$ is the product of the viscoelastic liquid intrinsic time times the applied shear rate). Spiraling orbits toward a log-rolling motion around the vorticity are observed for low Deborah numbers, whereas the particle aligns with its major axis near to the flow direction at high Deborah numbers. The transition from vorticity to flow alignment is characterized by a periodic regime with small amplitude oscillations around orientations progressively shifting from vorticity to flow direction by increasing $\text{De}$. A range of Deborah numbers is detected such that the periodic solution coexists with the flow alignment regime (bistability). A further range of $\text{De}$ is found where flow alignment is attained differently for particles starting far from or next to the shear plane: in the latter case, very long transients are found; hence an effective bistability (metabistability) is predicted to occur in a large time lapse before reaching the fully aligned state. Finally, the computed Deborah number values for flow alignment favorably compare with available experimental data.

A multiblock approach for the passive scalar thermal lattice Boltzmann method (TLBM) with multiple-relaxation-time collision scheme is proposed based on the Chapman-Enskog analysis. The interaction between blocks is executed in the moment space directly and an external force term is considered. Theoretical analysis shows that all the nonequilibrium parts of the nonconserved moments should be rescaled, while the nonequilibrium parts of the conserved moments can be calculated directly. Moreover, a local scheme based on the pseudoparticles for computing heat flux is proposed with no need to calculate temperature gradient based on the finite-difference scheme. In order to validate the multiblock approach and local scheme for computing heat flux, thermal Couette flow with wall injection is simulated and good results are obtained, which show that the adoption of the multiblock approach does not deteriorate the convergence rate of TLBM and the local scheme for computing heat flux has second-order convergence rate. Further application of the present approach is the simulation of natural convection in a square cavity with the Rayleigh number up to ${10}^9$.

We present a theory of turbulent elasticity, a property of drift-wave–zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter ${|\langle v\rangle }^{\prime }|/\Delta {\omega }_k$ is found to be a measure of the degree of Fickian flux-gradient relation breaking, where ${|\langle v\rangle }^{\prime }|$ is the ZF shearing rate and $\Delta {\omega }_k$ is the turbulence decorrelation rate. For ${|\langle v\rangle }^{\prime }|/\Delta {\omega }_k>1$, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ${\Omega }_{\mathrm{ZF}}=\pm {\gamma }_d^{1/2}{\gamma }_{\mathrm{modu}}^{1/2}$, where ${\gamma }_d$ is the ZF friction coefficient and ${\gamma }_{\mathrm{modu}}$ is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.

The asymmetric simple inclusion process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an “inclusion” counterpart of the asymmetric simple exclusion process. In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids—number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by the following: (i) an inverse square-root law of occupation, (ii) a square-root law of fluctuation, and (iii) a Rayleigh law for the distribution of interexit times. The universality of these results is discussed.

We present the first-order self-energy correction to the linear response coefficients of polaronic systems within the truncated phase space approach developed by the present authors. Due to the system-bath coupling, the external perturbation induces a retarded internal field which dynamically screens the external force. Whereas the effect on the mobility is of second order, dynamical properties such as the effective mass and the optical absorption are modified in first order. The Fröhlich polaron is used to illustrate the results.

We study the energy minimization for a particle in a quadratic well in the presence of short-ranged heavy-tailed disorder, as a toy model for an elastic manifold. The discrete model is shown to be described in the scaling limit by a continuum Poisson process model which captures the three universality classes. This model is solved in general, and we give, in the present case (Frechet class), detailed results for the distribution of the minimum energy and position, and the distribution of the sizes of the shocks (i.e., switches in the ground state) which arise as the position of the well is varied. All these distributions are found to exhibit heavy tails with modified exponents. These results lead to an “exotic regime” in Burgers turbulence decaying from a heavy-tailed initial condition.

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law $D^{-1/2}$ with the dimension $D$ of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

A method is introduced to simulate jamming of polyhedral grains under controlled stress that incorporates global degrees of freedom through the metric tensor of a periodic cell containing grains. Jamming under hydrostatic (isotropic) stress and athermal conditions leads to a precise definition of the ideal jamming point at zero shear stress. The structures of tetrahedra jammed hydrostatically exhibit less translational order and lower jamming-point density than previously described maximally random jammed hard tetrahedra. Under the same conditions, cubes jam with negligible nematic order. Grains with octahedral symmetry having $s>0.5$ (where $s$ interpolates from octahedra [$s=0$] to cubes [$s=1$]) jam with an abundance of face-face contacts in the absence of nematic order. For sufficiently large face-face contact number, percolating clusters form that span the entire simulation box. The response of hydrostatically jammed tetrahedra and cubes to shear-stress perturbation is also demonstrated with the variable-cell method.

We study the effect of a neutral particle on the ionic flow through a nanopore using a basic uniform field theory and the coupled Poisson-Nernst-Planck and Navier-Stokes (PNP-NS) equations. We consider hourglass and cylindrical pore profiles and examine how the difference in pore shape changes the position dependence of the current change due to the particle. Good quantitative agreement between both calculations is seen, though we find that the simple theory is unable to correctly capture the change in the access resistance of the pore if a particle is placed at the pore entrance. Finally, we examine the spatial variations in the solutions of the PNP-NS equations, finding that the electro-osmotic flow through the pore is completely disrupted for sufficiently large particles.

Hair cells conduct auditory transduction in vertebrates. In lower vertebrates such as frogs and turtles, due to the active mechanism in hair cells, hair bundles (stereocilia) can be spontaneously oscillating or quiescent. Recently an amplitude death phenomenon has been proposed [K.-H. Ahn, J. R. Soc. Interface, 10, 20130525 (2013)] as a mechanism for auditory transduction in frog hair-cell bundles, where sudden cessation of the oscillations arises due to the coupling between nonidentical hair bundles. The gating of the ion channel is intrinsically stochastic due to the stochastic nature of the configuration change of the channel. The strength of the noise due to the channel gating can be comparable to the thermal Brownian noise of hair bundles. Thus, we perform stochastic simulations of the elastically coupled hair bundles. In spite of stray noisy fluctuations due to its stochastic dynamics, our simulation shows the transition from collective oscillation to amplitude death as interbundle coupling strength increases. In its stochastic dynamics, the formation of the amplitude death state of coupled hair bundles can be seen as a sudden suppression of the displacement fluctuation of the hair bundles as the coupling strength increases. The enhancement of the signal-to-noise ratio through the amplitude death phenomenon is clearly seen in the stochastic dynamics. Our numerical results demonstrate that the multiple number of transduction channels per hair bundle is an important factor to the amplitude death phenomenon, because the phenomenon may disappear for a small number of transduction channels due to strong gating noise.

Reciprocity is firmly established as an important mechanism that promotes cooperation. An efficient information exchange is likewise important, especially on structured populations, where interactions between players are limited. Motivated by these two facts, we explore the role of facilitators in social dilemmas on networks. Facilitators are here mirrors to their neighbors—they cooperate with cooperators and defect with defectors—but they do not participate in the exchange of strategies. As such, in addition to introducing direct reciprocity, they also obstruct information exchange. In well-mixed populations, facilitators favor the replacement and invasion of defection by cooperation as long as their number exceeds a critical value. In structured populations, on the other hand, there exists a delicate balance between the benefits of reciprocity and the deterioration of information exchange. Extensive Monte Carlo simulations of social dilemmas on various interaction networks reveal that there exists an optimal interplay between reciprocity and information exchange, which sets in only when a small number of facilitators occupy the main hubs of the scale-free network. The drawbacks of missing cooperative hubs are more than compensated for by reciprocity and, at the same time, the compromised information exchange is routed via the auxiliary hubs with only marginal losses in effectivity. These results indicate that it is not always optimal for the main hubs to become leaders of the masses, but rather to exploit their highly connected state to promote tit-for-tat-like behavior.

When an equilibrium state of a physical or biological system suffers a loss of stability (e.g., via a bifurcation), it may be both possible and desirable to stabilize the equilibrium via closed-loop feedback control. Significant effort has been devoted towards using such control to prevent oscillatory or chaotic behavior in dynamical systems, both continuous-time and discrete-time. Regarding control in discrete-time systems, most prior attempts to stabilize unstable equilibria require that the system be perturbed once during each time step. However, there are examples of systems for which this is neither feasible nor possible. In this paper, we analyze a restricted feedback control method for discrete-time systems (restricted in the sense that the controller's perturbations may be applied only in every other time step). We apply our theoretical analysis to a specific example from cardiac electrophysiology in which this sort of restricted feedback control is especially relevant. The example is a useful test case for the theory, and one for which an experimental setup is rather straightforward.

We measure the decay rates of magnetic field modes in a turbulent flow of liquid sodium below the dynamo threshold. We observe that turbulent fluctuations induce energy transfers between modes with different symmetries (dipolar and quadrupolar). Using symmetry properties, we show how to measure the decay rate of each mode without being restricted to the one with the smallest damping rate. We observe that the respective values of the decay rates of these modes depend on the shape of the propellers driving the flow. Dynamical regimes, including field reversals, are observed only when the modes are both nearly marginal. This is in line with a recently proposed model.

We analyze electro-osmotic flow about a dielectric solid of zero surface charge, using the prototypic configurations of a spherical particle and an infinite circular cylinder. We assume that the ratio $\delta$ of Debye width to particle size is asymptotically small, and consider the flow engendered by the application of a uniform electric field; the control parameter is $E$—the voltage drop on the particle (normalized by the thermal scale) associated with this field. For moderate fields, $E=O\left(1\right)$, the induced $\zeta$ potential scales as the product of the applied-field magnitude and the Debye width; being small compared with the thermal voltage, its resolution requires addressing one higher asymptotic order than that resolved in the comparable analysis of electrophoresis of charged particles. For strong fields, $E=O\left({\delta }^{-1}\right)$, the $\zeta$ potential becomes comparable to the thermal voltage, depending nonlinearly on $\delta$ and $E$. We obtain a uniform approximation for the $\zeta$-potential distribution, valid for both moderate and strong fields; it holds even under intense fields, $E\gg {\delta }^{-1}$, where it scales as $log\left|E\right|$. The induced-flow magnitude therefore undergoes a transition from an $E^2$ dependence at moderate fields to an essentially linear variation with $\left|E\right|$ at intense fields. Remarkably, surface conduction is negligible as long as $E\ll {\delta }^{-2}$: the $\zeta$ potential, albeit induced, remains mild even under intense fields. Thus, unlike the related problem of induced-charge flow about a perfect conductor, the theoretical velocity predictions in the present problem may actually be experimentally realized.

Wave dispersion relations in the strongly coupled liquid phase of a two-dimensional system of dust grains interacting via both Yukawa and dipole interactions are investigated. The model system comprises a layer of charged superparamagnetic grains in a plasma in an external, uniform magnetic field $\mathbf{B}$ whose magnitude and direction can be varied. Because the induced magnetic dipole moments of the grains lie along $\mathbf{B}$, the interaction between the grains becomes anisotropic as $\mathbf{B}$ is tilted with respect to the layer. The theoretical approach uses a reformulated quasilocalized charge approximation that can treat dipole interactions, combined with molecular dynamics simulations. The mode dispersion relations are found to depend on the relative strengths of the Yukawa and dipole interactions and the direction of wave propagation in the plane.

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.