We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with an internal energy depot and interactions inspired by the dissipative particle dynamics method, imposing pairwise friction force on the nearest neighbors. We study orientational ordering in a 2D system as a function of energy influx rate and particle density. The model demonstrates a transition into the ordered state on increasing the particle density and increasing the input power. Although both the alignment mechanism and the character of individual motion in our model differ from those in the well-studied Vicsek model, it demonstrates identical statistical properties and phase behavior.

The states of an open quantum system are coupled via the environment of scattering wave functions. The complex coupling coefficients $\omega$ between system and environment arise from the principal value integral and the residuum. At high-level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im$\left(\omega \right)$ and Re$\left(\omega \right)$ influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re$\left(\omega \right)$ in a similar manner as it is well known from discrete states. Im$\left(\omega \right),$ however, leads to width bifurcation and finally (when the system is coupled to one channel, i.e., to one common continuum of scattering wave functions), to a splitting of the system into two parts with different characteristic time scales. The role of observer states is discussed. Physically, the system is stabilized by this splitting since the lifetimes of some states are longer than before, while that of one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wave functions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for $N=2,4,$ and 10 states coupled mostly to one channel.

We investigate nonequilibrium stationary distributions induced by stochastic dichotomous noise in double-well and multiwell models of ion channel gating kinetics. The channel kinetics is analyzed using both overdamped Langevin equations and master equations. With the Langevin equation approach we show a nontrivial focusing effect due to the external stochastic noise, namely, the concentration of the probability distribution in one of the two wells of a double-well system or in one or more of the wells of the multiwell model. In the multiwell system, focusing in the outer wells is shown to be achievable under physiological conditions, while focusing in the central wells has proved possible so far only at very low temperatures. We also discuss the strength of the focusing effect and obtain the conditions necessary for maximal focusing to appear. These conditions cannot be predicted by a simple master equation approach.

The macroscopic cohesion of granular materials made up of sticky particles depends on the particle shapes. We address this issue by performing contact dynamics simulations of 2D packings of nonconvex aggregates. We find that the macroscopic cohesion is strongly dependent on the strain and stress inhomogeneities developing inside the material. The largest cohesion is obtained for nearly homogeneous deformation at the beginning of unconfined axial compression and it evolves linearly with nonconvexity. Interestingly, the aggregates in a sheared packing tend to form more contacts with fewer neighboring aggregates as the degree of nonconvexity increases. We also find that shearing leads either to an isotropic distribution of tensile contacts or to the same privileged direction as that of compressive contacts.

By using molecular-dynamics simulations, we determine the jamming phase diagrams at high densities for a bidisperse mixture of soft spheres that interact according to repulsive power-law pair potentials. We observe that the relaxation time varies nonmonotonically as a function of density at constant temperature. Therefore, the jamming phase diagrams contain multiple reentrant glass transitions if temperature and density are used as control parameters. However, if we consider a new formulation of the jamming phase diagrams where temperature over pressure and pressure are employed as control parameters, no nonmonotonic behavior is observed.

A phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid-crystalline phases in two spatial dimensions. Depending on the model parameters, there is a variety of possible coexistences between two liquid-crystalline phases, including a plastic triangular crystal (PTC). Here, we numerically calculate the profiles for the mean density and for the nematic order tensor across the interface for isotropic-PTC and columnar-PTC (or equivalently smectic-$A$–PTC) phase coexistence. As a general finding, the width of the interface with respect to the nematic order parameter characterizing the orientational order is larger than the width of the mean-density interface. In approaching the interface from the PTC side, at first, the mean density goes down, and then the nematic order parameter follows. The relative shift in the two profiles can be larger than a full lattice constant of the plastic crystal. Finally, we also present numerical results for the dynamic relaxation of an initial order-parameter profile towards its equilibrium interfacial profile. Our predictions for the interfacial profiles can, in principle, be verified in real-space experiments of colloidal dispersions.

Cell membranes provide unique local environments for biological reactions, where the diffusion of biomolecules as well as water molecules plays critical roles. Translational and rotational motions of water molecules near membranes are known to be slower than those in bulk. Using all-atom molecular dynamics simulations of a membrane, we show that the temperature dependence of the water molecular motions on the membrane surface is different from that in bulk. Decreasing temperature enhances the water retardation on the membrane surface, and the lateral motions of water molecules are correlated with the vertical motions. We find that trapping times of water molecules onto membrane surfaces are distributed according to a power-law distribution and that the power-law exponents depend linearly on temperature, suggesting a random energy landscape picture. Moreover, we find that water molecules on the membrane surfaces exhibit subdiffusions in translational motions.

We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular noninvasive control schemes, such as (Pyragas) time-delayed or washout-filtered feedback control, can be overcome for tracking equilibria or forced periodic orbits in experiments. To demonstrate the use of our noninvasive control, we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability, around two saddle-node bifurcations (folds) and a cusp bifurcation.

The effects of time delay and rewiring probability on stochastic resonance and spatiotemporal order in small-world neuronal networks are studied in this paper. Numerical results show that, irrespective of the pacemaker introduced to one single neuron or all neurons of the network, the phenomenon of stochastic resonance occurs. The time delay in the coupling process can either enhance or destroy stochastic resonance on small-world neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of the pacemaker. More importantly, it is found that the small-world topology can significantly affect the stochastic resonance on excitable neuronal networks. For small time delays, increasing the rewiring probability can largely enhance the efficiency of pacemaker-driven stochastic resonance. We argue that the time delay and the rewiring probability both play a key role in determining the ability of the small-world neuronal network to improve the noise-induced outreach of the localized subthreshold pacemaker.

We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics.

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka and SeGall [Phys. Fluids 23, 092103 (2011)]. As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behavior, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wave numbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin and Kondic [Phys. Fluids 22, 052105 (2010)]. Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. In contrast, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

We present experiments and theory for flows of sugar or salt solutions in cylindrical tubes with semipermeable walls (hollow fiber membranes) immersed in water, quantifying the strength of the osmotic driving force in relation to the dimensionless parameters that specify the system. The pumping efficiency of these flows is limited by the presence of “unstirred” concentration boundary layers near the tube walls, and our primary aim is to understand and quantify these layers and their effect on the flow. We measure the outlet flow rate $Q_{\text{out}}$ while varying the inlet flow rate $Q^{*}$, concentration $c^{*}$, and tube length $L$, and map out the dependence of the flow rate gain $\gamma =Q_{\text{out}}/Q^{*}-1$ on these parameters. A theoretical analysis based on (1) the known velocity field for slow flow in cylindrical porous tubes and (2) a parabolic concentration profile allows us to compute analytically how the flow gain depends on the relative magnitude of radial diffusion and advection as well as the ratio of the osmotic velocity to pumping velocity, in very good agreement with experiments and with no adjustable parameters. Our analysis provides criteria that are useful for optimizing osmotic flow processes in, e.g., water purification devices.

We present numerical solutions of the flow in precessing spheres and spherical shells with small ($r_i/r_o=0.1$) inner cores and either stress-free or no-slip inner boundary conditions. For each of these three cases we consider the sequence of bifurcations as the Reynolds number $\text{Re}=r_o^2\Omega /\nu$ is increased up to $\sim$1280, focusing particular attention on bifurcations that break the antipodal symmetry $\mathbf{U}(-\mathbf{r})=-\mathbf{U}\left(\mathbf{r}\right)$. All three cases have steady and time-periodic symmetric solutions at smaller Re, and quasiperiodic asymmetric solutions at larger Re, but the details of the transitions differ, and include also periodic asymmetric and quasiperiodic symmetric solutions in some of the cases.

Understanding large-scale magnetic field growth in turbulent plasmas in the magnetohydrodynamic limit is a goal of magnetic dynamo theory. In particular, assessing how well large-scale helical field growth and saturation in simulations match those predicted by existing theories is important for progress. Using numerical simulations of isotropically forced turbulence without large-scale shear with its implications, we focus on several additional aspects of this comparison: (1) Leading mean-field dynamo theories which break the field into large and small scales predict that large-scale helical field growth rates are determined by the difference between kinetic helicity and current helicity with no dependence on the nonhelical energy in small-scale magnetic fields. Our simulations show that the growth rate of the large-scale field from fully helical forcing is indeed unaffected by the presence or absence of small-scale magnetic fields amplified in a precursor nonhelical dynamo. However, because the precursor nonhelical dynamo in our simulations produced fields that were strongly subequipartition with respect to the kinetic energy, we cannot yet rule out the potential influence of stronger nonhelical small-scale fields. (2) We have identified two features in our simulations which cannot be explained by the most minimalist versions of two-scale mean-field theory: (i) fully helical small-scale forcing produces significant nonhelical large-scale magnetic energy and (ii) the saturation of the large-scale field growth is time delayed with respect to what minimalist theory predicts. We comment on desirable generalizations to the theory in this context and future desired work.

We study the dynamics of dipolar gas in deep lattices described by a nonlocal nonlinear discrete Gross-Pitaevskii equation. The stabilities and the propagation properties of traveling plane waves in the system with defects are discussed in detail. For a clean lattice, both energetic and dynamical stabilities of the traveling plane waves are studied. It is shown that the system with attractive local interaction can preserve the stabilities, i.e., the dipoles can stabilize the gas because of repulsive nonlocal dipole-dipole interactions. For a lattice with defects, within a two-mode approximation, the propagation properties of traveling plane waves in the system map onto a nonrigid pendulum Hamiltonian with quasimomentum-dependent nonlinearity (induced by the nonlocal interactions). Competition between defects, quasimomentum of the gas, and nonlocal interactions determines the propagation properties of the traveling plane waves. Critical conditions for crossing from a superfluid regime with propagation preserved to a normal regime with defect-induced damping are obtained analytically and confirmed numerically. In particular, the critical conditions for supporting the superfluidity strongly depend on the defect type and the quasimomentum of the plane waves. The nonlocal interaction can significantly enhance the superfluidity of the system.

Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of $\alpha$, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime $\alpha \in [0.6,0.95]$ where it is known that only one giant component, denoted ${\mathrm{C}}_1$, initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime ${\mathrm{C}}_1$ stops growing and eventually a second giant component, denoted ${\mathrm{C}}_2$, emerges in a continuous percolation transition. The delay between the emergence of ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ and their asymptotic sizes both depend on the value of $\alpha$ and we establish by several techniques that there exists a bifurcation point ${\alpha }_c=0.763\pm 0.002$. For $\alpha \in [0.6,{\alpha }_c)$, ${\mathrm{C}}_1$ stops growing the instant it emerges and the delay between the emergence of ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ decreases with increasing $\alpha$. For $\alpha \in ({\alpha }_c,0.95]$, in contrast, ${\mathrm{C}}_1$ continues growing into the supercritical regime and the delay between the emergence of ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ increases with increasing $\alpha$. As we show, ${\alpha }_c$ marks the minimal delay possible between the emergence of ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ (i.e., the smallest edge density for which ${\mathrm{C}}_2$ can exist). We also establish many features of the continuous percolation of ${\mathrm{C}}_2$ including scaling exponents and relations.

We develop a reduced complexity model for three-dimensional sand dunes, based on a simplified description of the longitudinal and lateral sand transport. The spatiotemporal evolution of a dune migrating over a nonerodible bed under unidirectional wind is reduced to the dynamics of its crest line, providing a simple framework for the investigation of three-dimensional dunes, such as barchan and transverse dunes. Within this model, we derive analytical solutions for barchan dunes and investigate the stability of a rectilinear transverse dune against lateral fluctuations. We show, in particular, that the latter is unstable only if the lateral transport on the dune slip face prevails over that on the upwind face. We also predict the wavelength and the characteristic time that control the subsequent evolution of an unstable transverse dune into a wavy ridge and the ultimate fragmentation into barchan dunes.

Recent theoretical and experimental studies suggested the large-amplitude angular jump mechanism of the reorientational motions of water molecules. In this paper, we study the correlation effects of such angular jump motions, which are important for understanding a number of biological processes involving the motions of water molecules, by using molecular dynamics simulations. The results show that large-angular jump motions of a water molecule can enhance the successive jump motions of the same water molecule and the surrounding water molecules. Such a correlation can extend up to a distance of two water layers and is propagated through the perturbations to the local hydrogen bond networks. A detailed molecular picture of the correlation propagation is shown based on the molecular simulations.

We calculate an analytical expression for the terrace-width distribution $P\left(s\right)$ for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions $q$ on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

We develop a Landau theory for bend flexoelectricity in liquid crystals of bent-core molecules. In the nematic phase of the model, the bend flexoelectric coefficient increases as we reduce the temperature toward the nematic to polar phase transition. At this critical point, there is a second-order transition from high-temperature uniform nematic phase to low-temperature nonuniform polar phase composed of twist-bend or splay-bend deformations. To test the predictions of Landau theory, we perform Monte Carlo simulations to find the director and polarization configurations as functions of temperature, applied electric field, and interaction parameters.