We investigate two types of chimera states, patterns consisting of coexisting spatially separated domains with coherent and incoherent dynamics, in ring networks of Stuart-Landau oscillators with symmetry-breaking coupling, under the influence of noise. Amplitude chimeras are characterized by temporally periodic dynamics throughout the whole network, but spatially incoherent behavior with respect to the amplitudes in a part of the system; they are long-living transients. Chimera death states generalize chimeras to stationary inhomogeneous patterns (oscillation death), which combine spatially coherent and incoherent domains. We analyze the impact of random perturbations, addressing the question of robustness of chimera states in the presence of white noise. We further consider the effect of symmetries applied to random initial conditions.

We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter, such as an applied perpendicular or parallel magnetic fields, are considered in the general case of partial openness. These expressions are then used to obtain the ensemble-averaged density of maxima, a measure recently suggested to contain invaluable information concerning the correlation widths of chaotic systems. The correlation width is then calculated for the case of energy variation, and a significant deviation from the Weisskopf estimate is found in the case of two terminals. The results are extended to more than two terminals. All of our results are analytical. The use of these results in other fields, such as nuclei, where the system can only be studied through a variation of the energy, is then discussed.

The mean size of exponentially dividing Escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time, and individual growth rate are only starting to be characterized. Recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables. Here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times. We found that scaling relations based on the means collapse both size and doubling-time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means. Our data on these joint fluctuations highlight the importance of cell individuality: Single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the “division hazard rate function,” which defines the probability rate of dividing as a function of measurable parameters. This “model free” approach gives a rationale for the universal body-size distributions observed in microbial ecosystems across many microbial species, presumably dividing with multiple mechanisms. Additionally, our experiments show a crossover between fast and slow growth in the relation between individual-cell growth rate and division time, which can be understood in terms of different regimes of genome replication control.

Lipid bilayers are a model system for studying the properties of cell membranes. For lipid bilayers of a single lipid component, there is a phase transition from a fluid phase to a gel phase as the temperature is decreased. The dynamic behavior of lipids in the gel phase is interesting: some models show dynamic heterogeneity with a large disparity in timescales between fast and slow molecules, and a spatial segregation of the slow molecules. In this paper we study the dynamics of coarse-grained models of lipid bilayers using the dry Martini, Lennard-Jones Martini, polarizable Martini, and BMW models. All four models show similar dynamical behaviors in the gel phase although the transition temperature is model-dependent. We find that the primary mode of transport in the gel phase is a hopping of the lipid molecules. Hopping is seen in both the translational and rotational dynamics, which are correlated, i.e., the lipid molecules display a swing-like motion in the gel phase.

We study the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape. First, the average particle velocity is found as a function of the driving velocity and the wavelength of the optical potential energy landscape. The relationship between average particle velocity and driving velocity is found to be well described by a theoretical model treating the landscape as sinusoidal, but only at small trap spacings. At larger trap spacings, a nonsinusoidal model for the landscape must be used. Subsequently, the critical velocity required for a particle to move across the landscape is determined as a function of the wavelength of the landscape. Finally, the velocity of a particle driven at a velocity far exceeding the critical driving velocity is examined. Both of these results are again well described by the two theoretical routes for small and large trap spacings, respectively. Brownian motion is found to have a significant effect on the critical driving velocity but a negligible effect when the driving velocity is high.

Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (${\mathrm{CO}}_2$ + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the ${\mathrm{CO}}_2$ + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of ${\mathrm{CO}}_2$ the smaller the surface tension and the easier the drop deforms.

We present a strong relationship between the microstructural characteristics of, and the fluid velocity fields confined to, three-dimensional random porous materials. The relationship is revealed through simultaneously extracting correlation functions ${\mathcal{R}}_{uu}\left(r\right)$ of the spatial (Eulerian) velocity fields and microstructural two-point correlation functions ${\mathcal{S}}_2\left(r\right)$ of the random porous heterogeneous materials. This demonstrates that the effective physical transport properties depend on the characteristics of complex pore structure owing to the relationship between ${\mathcal{R}}_{uu}\left(r\right)$ and ${\mathcal{S}}_2\left(r\right)$ revealed in this study. Further, the mean excess plot was used to investigate the right tail of the streamwise velocity component that was found to obey light-tail distributions. Based on the mean excess plot, a generalized Pareto distribution can be used to approximate the positive streamwise velocity distribution.

Recent experiments [P. Brunet, J. Eggers, and R. D. Deegan, Phys. Rev. Lett. 99, 144501 (2007)] have shown that a liquid droplet on an inclined plane can be made to move uphill by sufficiently strong, vertical oscillations. In order to investigate this counterintuitive phenomenon we use a model in which liquid inertia and viscosity are assumed negligible so that the motion of the droplet is dominated by the applied acceleration due to the oscillation of the plate, gravity, and surface tension. We explain how the leading order motion of the droplet can be separated into a spreading mode and a swaying mode. For a linear contact line law, the maximum rise velocity occurs when these modes are in phase. We show that, both with and without contact angle hysteresis, the droplet can climb uphill and also that, for certain contact line laws, the motion of the droplet can produce footprints similar to experimental results. We show that if the two modes are out of phase when there is no contact angle hysteresis, the inclusion of hysteresis can force them into phase. This in turn increases the rise velocity of the droplet and can, in some cases, cause a sliding droplet to climb.

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.

In the study of networked systems such as biological, technological, and social networks the available data are often uncertain. Rather than knowing the structure of a network exactly, we know the connections between nodes only with a certain probability. In this paper we develop methods for the analysis of such uncertain data, focusing particularly on the problem of community detection. We give a principled maximum-likelihood method for inferring community structure and demonstrate how the results can be used to make improved estimates of the true structure of the network. Using computer-generated benchmark networks we demonstrate that our methods are able to reconstruct known communities more accurately than previous approaches based on data thresholding. We also give an example application to the detection of communities in a protein-protein interaction network.

From nonlinear models and direct numerical simulations we report on several findings of relevance to the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories. The incompressible, direct numerical simulations (DNSs) were performed in two (2D) and three dimensions (3D), and at a range of density ratios of the fluid combinations (characterized by the Atwood number). We investigated several acceleration histories, including acceleration profiles of the general form $g\left(t\right)\sim t^n$, with $n\ge 0$ and acceleration histories reminiscent of the linear electric motor experiments. For the 2D flow, results from numerical simulations compare well with a 2D potential flow model and solutions to a drag-buoyancy model reported as part of this work. When the simulations are extended to three dimensions, bubble and spike growth rates are in agreement with the so-called level 2 and level 3 models of Mikaelian [K. O. Mikaelian, Phys. Rev. E 79, 065303(R) (2009)], and with corresponding 3D drag-buoyancy model solutions derived in this article. Our generalization of the RT problem to study variable $g\left(t\right)$ affords us the opportunity to investigate the appropriate scaling for bubble and spike amplitudes under these conditions. We consider two candidates, the displacement $Z$ and width $s^2$, but find the appropriate scaling is dependent on the density ratios between the fluids—at low density ratios, bubble and spike amplitudes are explained by both $s^2$ and $Z$, while at large density differences the displacement collapses the spike data. Finally, for all the acceleration profiles studied here, spikes enter a free-fall regime at lower Atwood numbers than predicted by all the models.

Modulated rotating waves (MRW), bifurcated from the thermal-Rossby waves that arise at the onset of convection of a fluid contained in a rotating spherical shell, and their stability, are studied. For this purpose, Newton-Krylov continuation techniques are applied. Nonslip boundary conditions, an Ekman number $E={10}^{-4}$, and a low Prandtl number fluid $\text{Pr}=0.1$ in a moderately thick shell of radius ratio $\eta =0.35$, differentially heated, are considered. The MRW are obtained as periodic orbits by rewriting the equations of motion in the rotating frame of reference where the rotating waves become steady states. Newton-Krylov continuation allows us to obtain unstable MRW that cannot be found by using only time integrations, and identify regions of multistability. For instance, unstable MRW without any azimuthal symmetry have been computed. It is shown how they become stable in a small Rayleigh-number interval, in which two branches of traveling waves are also stable. The study of the stability of the MRW helps to locate and classify the large sequence of bifurcations, which takes place in the range analyzed. In particular, tertiary Hopf bifurcations giving rise to three-frequency stable solutions are accurately determined.

We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flat liquid metallic film on a solid substrate. These fluctuations are represented by a stochastic noise term added to the deterministic equation for the film thickness within the long-wave approximation. Unlike the case of polymeric films, we find that this noise, while remaining white in time, must be colored in space, at least in some regimes. The corresponding noise term is characterized by a nonzero correlation length, ${\ell }_c$, which, combined with the size of the system, leads to a dimensionless parameter $\beta$ that accounts for the relative importance of the spatial correlation $\left(\beta \sim {\ell }_c^{-1}\right)$. We perform the linear stability analysis (LSA) of the film both with and without the noise term and find that for ${\ell }_c$ larger than some critical value (depending on the system size), the wavelength of the peak of the spectrum is larger than that corresponding to the deterministic case, while for smaller ${\ell }_c$ this peak corresponds to smaller wavelength than the latter. Interestingly, whatever the value of ${\ell }_c$, the peak always approaches the deterministic one for larger times. We compare LSA results with the numerical simulations of the complete nonlinear problem and find a good agreement in the power spectra for early times at different values of $\beta$. For late times, we find that the stochastic LSA predicts well the position of the dominant wavelength, showing that nonlinear interactions do not modify the trends of the early linear stages. Finally, we fit the theoretical spectra to experimental data from a nanometric laser-melted copper film and find that at later times, the adjustment requires smaller values of $\beta$ (larger space correlations).

We propose a computational framework for the self-consistent dynamics of a microsphere system driven by a pulsed acoustic field in an ideal fluid. Our framework combines a molecular dynamics integrator describing the dynamics of the microsphere system with a time-dependent integral equation solver for the acoustic field that makes use of fields represented as surface expansions in spherical harmonic basis functions. The presented approach allows us to describe the interparticle interaction induced by the field as well as the dynamics of trapping in counter-propagating acoustic pulses. The integral equation formulation leads to equations of motion for the microspheres describing the effect of nondissipative drag forces. We show (1) that the field-induced interactions between the microspheres give rise to effective dipolar interactions, with effective dipoles defined by their velocities and (2) that the dominant effect of an ultrasound pulse through a cloud of microspheres gives rise mainly to a translation of the system, though we also observe both expansion and contraction of the cloud determined by the initial system geometry.

A wideband equivalent circuit is proposed for the accurate analysis of scattering from a set of stacked slit gratings illuminated by a plane wave with transverse magnetic or electric polarization that impinges normally or obliquely along one of the principal planes of the structure. The slit gratings are printed on dielectric slabs of arbitrary thickness, including the case of closely spaced gratings that interact by higher-order modes. A $\mathrm{\Pi }$-circuit topology is obtained for a pair of coupled arrays, with fully analytical expressions for all the circuit elements. This equivalent $\mathrm{\Pi }$ circuit is employed as the basis to derive the equivalent circuit of finite stacks with any given number of gratings. Analytical expressions for the Brillouin diagram and the Bloch impedance are also obtained for infinite periodic stacks.

Driven diffusive systems have provided simple models for nonequilibrium systems with nontrivial structures. Steady-state behavior of these systems with constant boundary conditions have been studied extensively. Comparatively less work has been carried out on the responses of these systems to time-dependent parameters. We report the modifications to the probability density function of a two-particle exclusion model in response to a periodically changing perturbation to its boundary conditions. The changes in the shape of the distribution as a function of the frequency of the perturbation contains considerable structure. A dynamical phase transition in which the system response changes abruptly as a function of perturbation frequency was observed. We interpret this structure to be a consequence of the existence of a typical time scale associated with the dynamics of density shock profiles within the system.

We present and analyze a minimal exactly solved model that exhibits a mixed-order phase transition known in the literature as the Thouless effect. Such hybrid transitions do not fit into the modest classification of thermodynamic transitions and, as such, they used to be overlooked or incorrectly identified in the past. The recent series of observations of such transitions in many diverse systems suggest that a new taxonomy of phase transitions is needed. The spin model we present due to its simplicity and possible experimental designs could bring us to this goal. We find the Hamiltonian of the model from which partition function is easily calculated. Thermodynamic properties of the model, i.e., discontinuous magnetization and diverging susceptibility, are discussed. Finally, its generalizations and further research directions are proposed.

This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call “ratchet flow.” A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.

Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of these systems, which include rich linear and nonlinear elasticity. Existing computational approaches have focused on both lattice-based and off-lattice networks obtained from the random placement of rods. It is not obvious, a priori, whether the two architectures have fundamentally similar or different mechanics. If they are different, it is not clear which of these represents a better model for biological networks. Here, we show that both approaches are essentially equivalent for the same network connectivity, provided the networks are subisostatic with respect to central force interactions. Moreover, for a given subisostatic connectivity, we even find that lattice-based networks in both two and three dimensions exhibit nearly identical nonlinear elastic response. We provide a description of the linear mechanics for both architectures in terms of a scaling function. We also show that the nonlinear regime is dominated by fiber bending and that stiffening originates from the stabilization of subisostatic networks by stress. We propose a generalized relation for this regime in terms of the self-generated normal stresses that develop under deformation. Different network architectures have different susceptibilities to the normal stress but essentially exhibit the same nonlinear mechanics. Such a stiffening mechanism has been shown to successfully capture the nonlinear mechanics of collagen networks.