Pancreatic islets, controlling glucose homeostasis, consist of $\alpha$, $\beta$, and $\delta$ cells. It has been observed that $\alpha$ and $\beta$ cells generate out-of-phase synchronization in the release of glucagon and insulin, counter-regulatory hormones for increasing and decreasing glucose levels, while $\beta$ and $\delta$ cells produce in-phase synchronization in the release of the insulin and somatostatin. Pieces of interactions between the islet cells have been observed for a long time, although their physiological role as a whole has not been explored yet. We model the synchronized hormone pulses of islets with coupled phase oscillators that incorporate the observed cellular interactions. The integrated model shows that the interaction from $\beta$ to $\delta$ cells, of which sign is a subject of controversy, should be positive to reproduce the in-phase synchronization between $\beta$ and $\delta$ cells. The model also suggests that $\delta$ cells help the islet system flexibly respond to changes of glucose environment.

Although the capillary spreading of a drop on a dry substrate is well studied, understanding and describing the physical mechanisms that govern the dynamics remain challenging. Here we study the dynamics of spreading of partially wetting nanodroplets by combining molecular dynamics simulations and continuum phase field simulations. The phase field simulations account for all the relevant hydrodynamics, i.e., capillarity, inertia, and viscous stresses. By coordinated continuum and molecular dynamics simulations, the macroscopic model parameters are extracted. For a Lennard-Jones fluid spreading on a planar surface, the liquid slip at the solid substrate is found to be significant, in fact crucial for the motion of the contact line. Evaluation of the different contributions to the energy transfer shows that the liquid slip generates dissipation of the same order as the bulk viscous dissipation or the energy transfer to kinetic energy. We also study the dynamics of spreading on a substrate with a periodic nanostructure. Here it is found that a nanostructure with a length scale commensurate with molecular size completely inhibits the liquid slip. The dynamic spreading is thus about 30% slower on a nanostructured surface compared to one that is atomically smooth.

Dynamical systems analysis is performed for reacting flows stabilized behind four symmetric bluff bodies to determine the effects of shape on the nature of flame stability, acoustic coupling, and vortex shedding. The task requires separation of regular, repeatable aspects of the flow from experimental noise and highly irregular, nonrepeatable small-scale structures caused primarily by viscous-mediated energy cascading. The experimental systems are invariant under a reflection, and symmetric vortex shedding is observed throughout the parameter range. As the equivalence ratio—and, hence, acoustic coupling—is reduced, a symmetry-breaking transition to von Karman vortices is initiated. Combining principal-components analysis with a symmetry-based filtering, we construct bifurcation diagrams for the onset and growth of von Karman vortices. We also compute Lyapunov exponents for each flame holder to help quantify the transitions. Furthermore, we outline changes in the phase-space orbits that accompany the onset of von Karman vortex shedding and compute unstable periodic orbits (UPOs) embedded in the complex flows prior to and following the bifurcation. For each flame holder, we find a single UPO in flows without von Karman vortices and a pair of UPOs in flows with von Karman vortices. These periodic orbits organize the dynamics of the flow and can be used to reduce or control flow irregularities. By subtracting them from the overall flow, we are able to deduce the nature of irregular facets of the flows.

The behavior of a compound drop, comprising two concentric fluid spheres, in a uniform electric field is studied analytically. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field strength and fluid inertia. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the globule, in terms of the direction of the external flow (pole-to-equator vs equator-to-pole) and the number of vortices (single-vortex vs double vortices) in the shell, and that the senses of the net electric shear stresses at the surfaces of the inner and the outer drops and their relative importance are the key parameters in setting these patterns. A circulation map is constructed, which is used to infer about the likelihood of the flow patterns and transition from one pattern to another for representative fluid systems. For small distortion from the spherical shape, the deformations of the inner and the outer drops are found using normal stress balances at the corresponding surfaces. It is shown that there will be four possible modes for the deformation of the compound drop, which are determined by the net normal electric and hydrodynamic stresses at the pertinent surfaces. The dynamic responses of the inner and the outer drops for representative fluid systems are studied using a deformation map, which characterizes the possibilities of the deformation modes and transition from one mode to another as a function of the fluid properties.

The thermodynamic curvature scalar $R$ for the Lennard-Jones system is evaluated in phase space, including vapor, liquid, and solid state. We paid special attention to the investigation of $R$ along vapor-liquid, liquid-solid, and vapor-solid equilibria. Because $R$ is a measure of interaction strength, we traced out the line $R=0$ dividing the phase space into regions with effectively attractive ($R<0$) or repulsive ($R>0$) interactions. Furthermore, we analyzed the dependence of $R$ on the strength of attraction applying a perturbation ansatz proposed by Weeks-Chandler-Anderson. Our results show clearly a transition from $R>0$ (for poorly repulsive interaction) to $R<0$ when loading attraction in the intermolecular potential.

We report results of the splay ($K_{11}$) and bend ($K_{33}$) elastic constants and the effective flexoelectric coefficient of three bent-core liquid crystals belonging to a homologous series of 4-cyanoresorcinol bisbenzoates with varying chain lengths. Based on the results of x-ray scattering studies, one of the three compounds with a shorter chain length (C4) has few, if any, clusters present in its nematic phase and behaves quite normally, whereas the others two with longer chain lengths (C6 and C7) show the presence of cybotactic nematic phase with smectic C type clusters. These grow in size with a reduction in temperature. $K_{33}$ is found to be the least for C7, whereas it is weakly dependent on temperature. $K_{33}$ is somewhat higher for C4 and C6 and is almost independent of temperature. $K_{11}$ for C6 and C7 is higher by 20$\%$ to 50$\%$ than C4 depending on the temperature. $K_{11}$ increases linearly with a reduction in temperature for the three compounds. For C6 $K_{11}>K_{33}$ by a factor up to ∼2 depending on the temperature, for C4 it is greater by a factor up to 1.3, and for C7 it is greater by a factor of ∼2.5. These results suggest that the clusters do not have any effect on $K_{11}$. The magnitude of the effective flexoelectric coefficient $e=\left(\right|e_1-e_3\left|\right)$ is measured by creating a uniform lying helix (ULH) configuration in a planar cell. By doping the bent-core system with a small wt$\%$ of a chiral dopant, the ULH is obtained by cooling planar cells to the cholesteric phase under weak electric field. The effective flexoelectric coefficient is greater for the bent-core systems than for calamatics but it is much lower than would otherwise have been expected for such systems. $|e_1-e_3|$ for C4 > C6 ≈ C7 is greater by 20$\%$ to 25$\%$ than C6 and C7 at the same reduced temperature. These differences in the effective flexoelectric coefficient can easily arise from a difference in the chain lengths among the members of the series but if the presence of clusters were to have an influence on $|e_1-e_3|$, then these would reduce it, contrary to the expectations for the bent-core systems.

We study the centrifugal fingering instabilities that occur in rotating Hele-Shaw cells containing two different fluids. A weakly nonlinear analysis of the problem is performed, considering that the surface tension between the rotating fluids changes with the local curvature of the interface. It is shown that the coupling between the contact angle and the variable interfacial tension permits the control of the interface disturbances. As a result, linear perturbations and nonlinear finger competition phenomena can be properly controlled and suppressed.

A buoyancy-driven hydrodynamic instability appearing when an aqueous acid solution of HCl overlies a denser alkaline aqueous solution of NaOH in a vertically oriented Hele-Shaw cell is studied both experimentally and theoretically. The peculiarity of this reactive convection pattern is its asymmetry with regard to the initial contact line between the two solutions as convective plumes develop in the acidic solution only. We investigate here by a linear stability analysis (LSA) of a reaction-diffusion-convection model of a simple $A+B\to C$ reaction the relative role of solutal versus thermal effects in the origin and location of this instability. We show that heat effects are much weaker than concentration-related ones such that the heat of reaction only plays a minor role on the dynamics. Computation of density profiles and of the stability analysis eigenfunctions confirm that the convective motions result from a diffusive layer convection mechanism whereby a locally unstable density stratification develops in the upper acidic layer because of the difference in the diffusion coefficients of the chemical species. The growth rate and wavelength of the pattern are determined experimentally as a function of the Brinkman parameter of the problem and compare favorably with the theoretical predictions of both LSA and nonlinear simulations.

The six-vertex model on a square lattice is “exactly solvable” because an exact formula for the free energy can be obtained by the Bethe ansatz. However, exact formulas for the correlations of local bulk observables, such as the orientation of the arrow at a given edge, are, in general, not available. In this Rapid Communication, we consider the isotropic “zero-field” six-vertex model at small $\Delta$. We derive the long-distance asymptotic formula of arrow-arrow correlations, which display power law decays with one anomalous exponent. Our method is based on an interacting fermion representation of the six-vertex model and does not use any information obtained from the exact solution.

In previous papers analytical expressions were derived and validated for the packing fraction of bimodal hard spheres with small size ratio, applicable to ordered (crystalline) [H. J. H. Brouwers, Phys. Rev. E 76, 041304 (2007);H. J. H. Brouwers, Phys. Rev. E 78, 011303 (2008)] and disordered (random) packings [H. J. H. Brouwers, Phys. Rev. E 87, 032202 (2013)]. In the present paper the underlying statistical approach, based on counting the occurrences of uneven pairs, i.e., the fraction of contacts between unequal spheres, is applied to trimodal discretely sized spheres. The packing of such ternary packings can be described by the same type of closed-form equation as the bimodal case. This equation contains the mean volume of the spheres and of the elementary cluster formed by these spheres; for crystalline arrangements this corresponds to the unit cell volume. The obtained compact analytical expression is compared with empirical packing data concerning random close packing of spheres, taken from the literature, comprising ternary binomial and geometric packings; good agreement is obtained. The presented approach is generalized to ordered and disordered packings of multimodal mixes.

For a significant number of viruses a structural transition of the protein container that encapsulates the viral genome forms an important part of the life cycle and is a prerequisite for the particle becoming infectious. Despite many recent efforts the mechanism of this process is still not fully understood, and a complete characterization of the expansion pathways is still lacking. We present here a coarse-grained model that captures the essential features of the expansion process and allows us to investigate the conditions under which a viral capsid becomes unstable. Based on this model we demonstrate that the structural transitions in icosahedral viral capsids are likely to occur through a low-symmetry cascade of local expansion events spreading in a wavelike manner over the capsid surface.

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [Phys. Rev. Lett. 110, 028701 (2013)], some of the authors proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.

We investigate the effectiveness of a Global time-delay autosynchronization control scheme aimed at stabilizing traveling wave solutions of the cubic-quintic Ginzburg-Landau equation in the Benjamin-Feir-Newell unstable regime. Numerical simulations show that a global control can be efficient and also can create other patterns such as spatiotemporal intermittency regimes, standing waves, or uniform oscillations.

We report 3% conversion efficiency of laser energy into Kr $K$-shell ($\approx 13$ keV) radiation, consistent with theoretical predictions. This is $\approx 10\times$ greater than previous work. The emission was produced from a 4.1-mm-diameter, 4-mm-tall gas pipe target filled with 1.2 or 1.5 atm of Kr gas. 160 of the National Ignition Facility laser beams deposited $\approx 700$ kJ of 3$\omega$ light into the target in an $\approx 140$ TW, 5.0-ns-duration square pulse. The Dante diagnostics measured $\approx 5$ TW into 4$\pi$ solid angle of $\ge 12$ keV x rays for $\approx 4$ ns, which includes both continuum emission and flux in the Kr He${}_{\alpha }$ line at 13 keV.

A slider is pulled by means of a flexible link on a flat solid surface which exhibits anisotropic frictional properties. The resulting trajectory of the slider is assessed experimentally. First, we check that the experimental results are in excellent agreement with a theoretical description of the problem based on an expression of the frictional forces. Second, we point out that the trajectory of the slider can be recovered by the use of a “maximum of energy release rate” criterion which is generally used to predict the path of a fracture even if the validity of the principle is difficult to verify in the latter complex systems.

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.

A death of oscillation is reported in a network of coupled synchronized oscillators in the presence of additional repulsive coupling. The repulsive link evolves as an averaging effect of mutual interaction between two neighboring oscillators due to a local fault and the number of repulsive links grows in time when the death scenario emerges. Analytical condition for oscillation death is derived for two coupled Landau-Stuart systems. Numerical results also confirm oscillation death in chaotic systems such as a Sprott system and the Rössler oscillator. We explore the effect in large networks of globally coupled oscillators and find that the number of repulsive links is always fewer than the size of the network.

Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases, such as a generalization of Wigner crystals at low particle densities and stripe phases at densities between $\rho =1/3$ and $1/2$. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterized at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.

We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a “logical” resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.