Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems but have not been fully explored in high-dimensional networks. Here we study large networks consisting of randomly coupled rate units. We identify a type of bifurcation in which a continuous part of the eigenvalue spectrum of the linear stability matrix crosses the instability line at nonzero frequency. This bifurcation occurs when the interactions are delayed and partially antisymmetric and leads to a heterogeneous oscillatory state in which oscillations are apparent in the activity of individual units but not on the population-average level.

We describe the phenomenon of localization in the epidemic susceptible-infective-susceptible model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp localization transition; instead there is a smooth crossover from localized to delocalized states as we approach the epidemic threshold from below. Analyzing these long-lasting local outbreaks for a random regular graph with a hub, we show how this localization can be detected from the shape of the distribution of the number of infective nodes.

We employ two tight-binding (TB) approaches to systematically study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of $N$ monomers (base pairs): (I) at the base-pair level, using the onsite energies of base pairs and the hopping integrals between successive base pairs, i.e., a wire model and (II) at the single-base level, using the onsite energies of the bases and the hopping integrals between neighboring bases, i.e., an extended ladder model since we also include diagonal hoppings. We solve a system of $M$ (matrix dimension) coupled equations [(I) $M=N$, (II) $M=2N]$ for the time-independent problem, and a system of $M$ coupled first order differential equations for the time-dependent problem. We perform a comparative study of stationary and time-dependent aspects of the two TB variants, using realistic sets of parameters. The studied properties include HOMO and LUMO eigenspectra, occupation probabilities, density of states and HOMO-LUMO gaps as well as mean over time probabilities to find the carrier at each site [(I) base pair or (II) base], Fourier spectra, which reflect the frequency content of charge transfer, and pure mean transfer rates from a certain site to another. The two TB approaches give coherent, complementary aspects of electronic properties and charge transfer in B-DNA monomer polymers and dimer polymers.

This work clarifies the notion of correlated and cooperative motions appearing during the α-relaxation process through the role of the molecular weight of the constitutive units and of the interchain dipolar interactions. By studying amorphous copolymers of poly(ethylene-co-vinyl acetate) with different vinyl acetate contents, we show that the correlated motions are not sensitive to the interchain dipolar interactions, in contrast to the cooperative motions, which increase with a strengthening of the intermolecular interactions for this sample family. Concerning the influence of the molecular weight $m_0$, the notion of “correlated motions” seems to be equivalent to the notion of “cooperative motions” only for low $m_0$ systems.

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $\varphi$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)]. By taking an $L^{\infty }$ norm of the energy of the full binary system, designated as $E_{\infty }$, we have shown that ${\int }_0^t{E}_{\infty }\left(\tau \right)d\tau$ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with ${128}^3$ to ${512}^3$ collocation points and over the duration of our DNSs confirm that $E_{\infty }$ remains bounded as far as our computations allow.

When a colloidal sessile droplet dries on a substrate, the particles suspended in it usually deposit in a ringlike pattern. This phenomenon is commonly referred to as the “coffee-ring” effect. One paradigm for why this occurs is as a consequence of the solutes being transported towards the pinned contact line by the flow inside the drop, which is induced by surface evaporation. From this perspective, the role of the liquid-gas interface in shaping the deposition pattern is somewhat minimized. Here, we propose an alternative mechanism for the coffee-ring deposition. It is based on the bulk flow within the drop transporting particles to the interface where they are captured by the receding free surface and subsequently transported along the interface until they are deposited near the contact line. That the interface captures the solutes as the evaporation proceeds is supported by a Lagrangian tracing of particles advected by the flow field within the droplet. We model the interfacial adsorption and transport of particles as a one-dimensional advection-generation process in toroidal coordinates and show that the theory reproduces ring-shaped depositions. Using this model, deposition patterns on both hydrophilic and hydrophobic surfaces are examined in which the evaporation is modeled as being either diffusive or uniform over the surface.

The rotation of rigid bodies and oscillation of flexible structures under turbulence are described and characterized in the spectral domain. Laboratory experiments combined with theory are used to unravel and explain the characteristic power-law decay of the spectrum of rotation and oscillation of simple structures. It is shown that the energy-containing eddies and inertial subrange of the incoming velocity spectrum strongly modulate the unsteady motions of structures. The spectra of the rotation and oscillation of the structures exhibit distinctive power-law decays $f^{+2}$ and $f^{-5/3-2}$ in the comparatively low- and high-frequency regions. The range of these regions depends on the phenomenon triggering the motions, i.e., thrust or vortex-induced motions.

The direct transition to overlimiting current bypassing the stage of limiting currents is considered for imperfect membranes. Instability of the quiescent steady-state one-dimensional solution, which is the result of a balance of diffusion and electromigration, is investigated on the basis of the full Nernst-Planck-Poisson-Stokes system and a simplified quasielectroneutral system. A three-layer geometry, electrolyte-porous membrane-electrolyte, is considered. The usual assumption of a constant electrochemical potential along the membrane surface is removed from consideration. The effect of bulk and surface effects on the instability and transition to the overlimiting currents is evaluated for a different membrane selectivity. It becomes clear that for sufficiently small fixed charge concentration (large ion concentration in the electrolyte), the monotonic instability is replaced by an oscillatory one. The dependence of instability on the membrane porosity is found to be weak.

An estimator for the dynamical temperature in an arbitrary ensemble is derived in the framework of the conjugate variables theorem. We prove directly that its average indeed gives the inverse temperature and that it is independent of the ensemble. We test this estimator numerically by a simulation of the two-dimensional $XY$ model in the canonical ensemble. As this model is critical in the whole region of temperatures below the Berezinski-Kosterlitz-Thouless critical temperature $T_{\text{BKT}}$, we use a generalization of Wolff's unicluster algorithm. The numerical results allow us to confirm the robustness of the analytical expression for the microscopic estimator of the temperature. This microscopic estimator has also the advantage that it gives a direct measure of the thermalization process and can be used to compute absolute errors associated with statistical fluctuations. In consequence, this estimator allows for a direct, absolute, and stringent test of the ergodicity of the underlying Markov process, which encodes the algorithm used in a numerical simulation.

We examine the correlations between rings in random network glasses in two dimensions as a function of their separation. Initially, we use the topological separation (measured by the number of intervening rings), but this leads to pseudo-long-range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring. This effect is associated with the noncircular nature of the shells. It is, therefore, necessary to use the geometrical distance between ring centers. Hence we find a generalization of the Aboav-Weaire law out to larger distances, with the correlations between rings decaying away when two rings are more than about three rings apart.

The theory of rotational diffusion of particles of various symmetry embedded in a liquid crystal host, essential to interpret a variety of spectroscopic observables, has been available for some time, but only for the case of rigid molecules. Here we generalize the treatment and present a theory to describe the rotational diffusion of shape-changing particles dispersed in nematic liquid crystals. The interaction of the particles with the environment is modeled by an effective field potential, while the particles are allowed to assume an arbitrary discrete number of shapes. The transition between shapes is modeled by a Markovian process which is combined with rotational diffusion. Our model is applied to the simple case of a particle that can exchange between three shapes: a rod, a disk, and a sphere. We consider in detail the effect of shape transitions in some selected correlation functions which are relevant for experiments.

Turbulence with inverse energy cascade and its transport properties are investigated experimentally in a flow associated with a westward propagating jet. Turbulence and the jet were produced by an electromagnetic force in a rotating tank filled with an electrolytic saline solution. The parabolic free surface emulated the topographic $\beta$ effect which evoked the zonation. The spectral and transport flow characteristics were highly anisotropic. Turbulence is diagnosed by exploring the analogy between vertical and horizontal turbulent overturns in, respectively, stably stratified and quasigeostrophic flows which gives rise to a method of potential vorticity (PV) monotonizing. The anisotropization of transport properties of the flow is investigated using the finite scale Lyapunov exponent technique. After initial exponential particle separation, radial (meridional in geophysical and planetary applications) diffusion attains a short-ranged Richardson regime which transitions to the Taylor (scale-independent diffusivity) one. The azimuthal (zonal) diffusion exhibits a double-plateau structure which attains a superdiffusive regime on large scales. The transition to the Taylor regime for the radial diffusion takes place at a scale of turbulence anisotropization. The radial eddy diffusivity in both regimes as well as the transition scale are all determined by the rate of the inverse energy cascade, $\epsilon$, that can be diagnosed by the PV monotonizing. Conversely, $\epsilon$ can be deduced from the scale of the Richardson-Taylor regime transition in the radial eddy diffusivity which, thus, provides an additional tool of diagnosing anisotropic macroturbulence with inverse energy cascade.

The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of $\sim 15$ MeV passing through a WDP of beryllium with an electronic density around the solid value $n_e\approx 3\times {10}^{23}{\mathrm{cm}}^{-3}$ and with temperature around $\sim 40$ eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.

We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.

Work fluctuation and total entropy production play crucial roles in small thermodynamic systems subject to large thermal fluctuations. We investigate a trade-off relation between them in a nonequilibrium situation in which a system starts from an arbitrary nonequilibrium state. We apply a variational method to study this problem and find a stationary solution against variations over protocols that describe the time dependence of the Hamiltonian of the system. Using the stationary solution, we find the minimum of the total entropy production for a given amount of work fluctuation. An explicit protocol that achieves this is constructed from an adiabatic process followed by a quasistatic process. The obtained results suggest how one can control the nonequilibrium dynamics of the system while suppressing its work fluctuation and total entropy production.

In a recent study about chaos synchronization in complex networks [Nat. Commun. 5, 4079 (2014)], it is shown that a stable synchronous cluster may coexist with vast asynchronous nodes, resembling the phenomenon of a chimera state observed in a regular network of coupled periodic oscillators. Although of practical significance, this new type of state, namely, the isolated-desynchronization state, is hardly observed in practice due to its strict requirements on the network topology. Here, by the strategy of pinning coupling, we propose an effective method for inducing isolated-desynchronization states in symmetric networks of coupled chaotic oscillators. Theoretical analysis based on eigenvalue analysis shows that, by pinning a group of symmetric nodes in the network, there exists a critical pinning strength beyond which the group of pinned nodes can completely be synchronized while the unpinned nodes remain asynchronous. The feasibility and efficiency of the control method are verified by numerical simulations of both artificial and real-world complex networks with the numerical results in good agreement with the theoretical predictions.

Growing living cultures of Escherichia coli bacteria are investigated using real-time in situ rheology and rheoimaging measurements. In the early stages of growth (lag phase) and when subjected to a constant stationary shear, the viscosity slowly increases with the cell's population. As the bacteria reach the exponential phase of growth, the viscosity increases rapidly, with sudden and temporary abrupt decreases and recoveries. At a certain stage, corresponding grossly to the late phase of growth, when the population stabilizes, the viscosity also keeps its maximum constant value, with drops and recoveries, for a long period of time. This complex rheological behavior, which is observed to be shear strain dependent, is a consequence of two coupled effects: the cell density continuous increase and its changing interacting properties. Particular attention is given to the late phase of growth of E. coli populations under shear. Rheoimaging measurements reveal, near the static plate, a rotational motion of E. coli aggregates, collectively tumbling and flowing in the shear direction. This behavior is interpreted in the light of a simple theoretical approach based on simple rigid body mechanics.

For many organisms, the number of sensory neurons is largely determined during development, before strong environmental cues are present. This is despite the fact that environments can fluctuate drastically both from generation to generation and within an organism's lifetime. How can organisms get by by hard coding the number of sensory neurons? We approach this question using rate-distortion theory. A combination of simulation and theory suggests that when environments are large, the rate-distortion function—a proxy for material costs, timing delays, and energy requirements—depends only on coarse-grained environmental statistics that are expected to change on evolutionary, rather than ontogenetic, time scales.