A SQUID (Superconducting QUantum Interference Device) metamaterial on a Lieb lattice with nearest-neighbor coupling supports simultaneously stable dissipative breather families which are generated through a delicate balance of input power and intrinsic losses. Breather multistability is possible due to the peculiar snaking flux amplitude-frequency curve of single dissipative-driven SQUIDs, which for relatively high sinusoidal flux field amplitudes exhibits several stable and unstable solutions in a narrow frequency band around resonance. These breathers are very weakly interacting with each other, while multistability regimes with a different number of simultaneously stable breathers persist for substantial intervals of frequency, flux field amplitude, and coupling coefficients. Moreover, the emergence of chimera states as well as temporally chaotic states exhibiting spatial homogeneity within each sublattice of the Lieb lattice is demonstrated. The latter of the states emerge through an explosive hysteretic transition resembling explosive synchronization that has been reported before for various networks of oscillators.

We develop methods to efficiently reconstruct the topology and line parameters of a power grid from the measurement of nodal variables. We propose two compressed sensing algorithms that minimize the amount of necessary measurement resources by exploiting network sparsity, symmetry of connections, and potential prior knowledge about the connectivity. The algorithms are reciprocal to established state estimation methods, where nodal variables are estimated from few measurements given the network structure. Hence, they enable an advanced grid monitoring where both state and structure of a grid are subject to uncertainties or missing information.

It has long been believed that eukaryotic flagellated swimming cells feel solid boundaries through direct ciliary contact. Specifically, based on observations of behavior of green alga Chlamydomonas reinhardtii it has been reported that it is their “flagella [that] prevent the cell body from touching the surface” [Kantsler et al., Proc. Natl. Acad. Sci. USA 110, 1187 (2013)]. Here, via investigation of a model swimmer whose flow field closely resembles that of C. reinhardtii, we show that the scattering from a wall can be purely hydrodynamic and that no mechanical or flagellar force is needed for sensing and escaping the boundary.

While in principle, classical density functional theory (cDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated fundamental measure theory models. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionals currently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown that all of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstration of power of cDFT to describe crystallization in a highly inhomogeneous system. First, we show that droplets attached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallites are clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodic calculational cell remain stable to lower temperatures and eventually show the same spontaneous localization of the density into “atoms” but in an amorphous structure having many of the structural characteristics of a glass. A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with the fcc structure typical of bulk Lennard-Jones solids. The fcc crystals have lower free energy than the amorphous structures which in turn are more stable than the liquid droplets. It is demonstrated that as the temperature is raised, the free energy differences between the structures decrease until the solid clusters become less stable than the liquid droplets and spontaneously melt. The presence of energy barriers separating the various structures is therefore clearly demonstrated.

At high temperatures, a droplet can rest on a cushion of its vapor (the Leidenfrost effect). Application of an electric field across the vapor gap fundamentally eliminates the Leidenfrost state by attracting liquid towards the surface. This study uses acoustic signature tracking to study electrostatic suppression of the Leidenfrost state on solid and liquid surfaces. It is seen that the liquid-vapor instabilities that characterize suppression on solid surfaces can be detected acoustically. This can be the basis for objective measurements of the threshold voltage and frequency required for suppression. Acoustic analysis provides additional physical insights that would be challenging to obtain with other measurements. On liquid surfaces, the absence of an acoustic signal indicates a different suppression mechanism (instead of instabilities). Acoustic signature tracking can also detect various boiling patterns associated with electrostatically assisted quenching. Overall, this work highlights the benefits of acoustics as a tool to better understand electrostatic suppression of the Leidenfrost state, and the resulting heat transfer enhancement.

We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels $K_{i,j}=i^{\nu }{j}^{\mu }+j^{\nu }{i}^{\mu }$ homogeneous in masses $i$ and $j$ of merging clusters and fragmentation kernels, $F_{ij}=\lambda K_{ij}$, with parameter $\lambda$ quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulation results when $\theta \equiv \nu -\mu <1$. For $\theta =\nu -\mu >1$, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small $\lambda$, they become steady if $\theta$ is close to 2 and $\lambda$ is very small. Simulation results lead to a conjecture that for $\theta <1$ the system has a stable fixed point, corresponding to the steady-state density distribution, while for any $\theta >1$ there exists a critical value ${\lambda }_c$, such that for $\lambda <{\lambda }_c$, the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass.

MaxCal is a variational principle that can be used to infer distributions of paths in the phase space of dynamical systems. It has been successfully applied to different areas of classical physics, in particular statistical mechanics in and out of equilibrium. In this work, guided by the analogy of the formalism of MaxCal with that of the path integral formulation of quantum mechanics, we explore the extension of its applications to the realm of quantum physics, and show how the Lagrangians of both relativistic and nonrelativistic quantum fields can be built from MaxCal, with a suitable set of constraints. Related, the details of the constraints allow us to reinterpret the concept of inertia.

The statistical properties of the carrier density profile of graphene in the ground state in the presence of particle-particle interaction and random charged impurity in zero gate voltage has been recently obtained by Najafi et al. [Phys. Rev. E 95, 032112 (2017)]. The nonzero chemical potential ($\mu$) in gated graphene has nontrivial effects on electron-hole puddles, since it generates mass in the Dirac action and destroys the scaling behaviors of the effective Thomas-Fermi-Dirac theory. We provide detailed analysis on the resulting spatially inhomogeneous system in the framework of the Thomas-Fermi-Dirac theory for the Gaussian (white noise) disorder potential. We show that the chemical potential in this system as a random surface destroys the self-similarity, and also the charge field is non-Gaussian. We find that the two-body correlation functions are factorized to two terms: a pure function of the chemical potential and a pure function of the distance. The spatial dependence of these correlation functions is double logarithmic, e.g., the two-point density correlation behaves like $D_2(r,\mu )\propto {\mu }^{2}exp\left[-{\left(-a_{D}lnln{r}^{{\beta }_D}\right)}^{{\alpha }_D}\right]$ (${\alpha }_D=1.82$, ${\beta }_D=0.263$, and $a_D=0.955$). The Fourier power spectrum function also behaves like $ln\left[S\left(q\right)\right]=-{\beta }_S^{-a_S}{\left(lnq\right)}^{a_S}+2ln\mu$ ($a_S=3.0\pm 0.1$ and ${\beta }_S=2.08\pm 0.03$) in contrast to the ordinary Gaussian rough surfaces for which $a_S=1$ and ${\beta }_S=\frac{1}{2}{(1+\alpha )}^{-1}$ ($\alpha$ being the roughness exponent). The geometrical properties are, however, similar to the ungated ($\mu =0$) case, with the exponents that are reported in the text.

It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the dynamical features are governed by its nonlinearity. We study quasiperiodic solutions of nonlinear equations of motion of one-dimensional classical chains. Such quasi-periodic solutions correspond to periodic trajectories in the configuration space of the discrete systems, which allows us to define solitons without relying on a continuum theory. Furthermore, we study the dynamics of solitons in inhomogeneous systems by connecting two chains with distinct parameter sets, where transmission or reflection of solitons occurs at the boundary of the two chains.

In radiation pressure ion acceleration (RPA) research, the transverse stability within laser plasma interaction has been a long-standing, crucial problem over the past decades. In this paper, we present a one-dimensional two-fluid theory extended from a recent work Wan et al. Phys. Rev. Lett. 117, 234801 (2016) to clearly clarify the origin of the intrinsic transverse instability in the RPA process. It is demonstrated that the purely growing density fluctuations are more likely induced due to the strong coupling between the fast oscillating electrons and quasistatic ions via the ponderomotive force with spatial variations. The theory contains a full analysis of both electrostatic (ES) and electromagnetic modes and confirms that the ES mode actually dominates the whole RPA process at the early linear stage. By using this theory one can predict the mode structure and growth rate of the transverse instability in terms of a wide range of laser plasma parameters. Two-dimensional particle-in-cell simulations are systematically carried out to verify the theory and formulas in different regimes, and good agreements have been obtained, indicating that the electron-ion coupled instability is the major factor that contributes the transverse breakup of the target in RPA process.

The study on the dynamics of interacting diseases has attracted considerable attention in recent years. This paper proposes a model for two interacting epidemics spreading concurrently on a two-layer network, where both the epidemic thresholds and the dynamics of disease outbreaks are investigated. The analytical expression of the epidemic threshold shows strong coupling between the two interacting epidemics. Moreover, two metrics, the maximum prevalence and the highest spreading speed, are proposed to describe the outbreak process. Theoretical analysis together with extensive simulations illustrate the functions of various factors, including the network topological parameters, percentage of overlapped network links, vulnerable individuals, and the reciprocity of the two diseases. It is found that the seemingly important factor, i.e., the percentage of overlapped links, possesses no effect on the propagation, while the frequently overlooked factor, i.e., the percentage of vulnerable individuals, has significant effects. For the interaction of the two diseases, the recovery state of one disease is more influential than the other in both the mutually enhanced and the mutually impaired situations.

The synchronization behavior of networked chaotic oscillators with periodic coupling is investigated. It is observed in simulations that the network synchronizability could be significantly influenced by tuning the coupling frequency, even making the network alternating between the synchronous and nonsynchronous states. Using the master stability function method, we conduct a detailed analysis of the influence of coupling frequency on network synchronizability and find that the network synchronizability is maximized at some characteristic frequencies comparable to the intrinsic frequency of the local dynamics. Moreover, it is found that as the amplitude of the coupling increases, the characteristic frequencies are gradually decreased. Using the finite-time Lyapunov exponent technique, we investigate further the mechanism for the maximized synchronizability and find that at the characteristic frequencies the power spectrum of the finite-time Lyapunov exponent is abruptly changed from the localized to broad distributions. When this feature is absent or not prominent, the network synchronizability is less influenced by the periodic coupling. Our study shows the efficiency of finite-time Lyapunov exponent in exploring the synchronization behavior of temporally coupled oscillators and sheds lights on the interplay between the system dynamics and structure in general temporal networks.

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B. subtilis 168 and E. coli ATCC 25922 under conditions leading to compact colonies in the classically alleged Eden regime, where individual motility is suppressed. Non-KPZ scaling is indeed observed for all accessible times, KPZ asymptotics being ruled out for our experiments due to the monotonic increase of front branching with time. Simulations of an effective model suggest the occurrence of transient nonuniversal scaling due to diffusive morphological instabilities, agreeing with expectations from detailed models of the relevant biological reaction-diffusion processes.

We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress $\sigma$ while being deformed with strain rate $\dot{\epsilon }$, the microscopic structural relaxation time ${\tau }_{\mathrm{str}}$ is given by the universal relation $\sigma /G_{\infty }\dot{\epsilon }$ with $G_{\infty }$ a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxation time and ${\tau }_{\mathrm{str}}$ is in fact further reduced even though $\sigma$ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

We show how a weak force $f$ enables intruder motion through dense granular materials subject to external mechanical excitations, in the present case, stepwise shearing. A force acts on a Teflon disk in a two-dimensional system of photoelastic disks. This force is much smaller than the smallest force needed to move the disk without any external excitation. In a cycle, the material plus intruder are sheared quasistatically from $\gamma =0$ to ${\gamma }_{\text{max}}$, and then backwards to $\gamma =0$. During various cycle phases, fragile and jammed states form. Net intruder motion $\delta$ occurs during fragile periods generated by shear reversals. $\delta$ per cycle, e.g., the quasistatic rate $c$, is constant, linearly dependent on ${\gamma }_{\text{max}}$ and $f$. It vanishes as $c\propto {({\varphi }_c-\varphi )}^a$, with $a\simeq 3$ and ${\varphi }_c\simeq {\varphi }_J$, reflecting the stiffening of granular systems under shear [J. Ren, J. A. Dijksman, and R. P. Behringer, Phys. Rev. Lett. 110, 018302 (2013)] as $\varphi \to {\varphi }_J$. The intruder motion induces large-scale grain circulation. In the intruder frame, this motion is a granular analog to fluid flow past a cylinder, where $f$ is the drag force exerted by the flow.

Many real-world systems can be modeled as interconnected multilayer networks, namely, a set of networks interacting with each other. Here, we present a perturbative approach to study the properties of a general class of interconnected networks as internetwork interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore, we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked systems, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems.

The Crow-Kimura model is commonly used in the modeling of genetic evolution in the presence of mutations and associated selection pressures. We consider a modified version of the Crow-Kimura model, in which population sizes are not fixed and Allee saturation effects are present. We demonstrate the evolutionary dynamics in this system through an analytical approach, examining both symmetric and single-peak fitness landscape cases. Especially interesting are the dynamics of the populations near extinction. A special version of the model with saturation and degradation on the single-peak fitness landscape is investigated as a candidate of the Allee effect in evolution, revealing reduction tendencies of excessively large populations, and extinction tendencies for small populations. The analytical solutions for these dynamics are presented with accuracy $\mathcal{O}(1/N)$, where $N$ is the number of nucleotides in the genome.

Large portions of the endoplasmic reticulum (ER) in eukaryotic cells are organized as dynamic networks whose segments are connected by three-way junctions. Here we show that ER junctions move subdiffusively with signatures of fractional Brownian motion and a strong dependence on the cytoskeleton's integrity: The time-averaged mean square displacement scales as ${\langle r^2\left(\tau \right)\rangle }_t\sim {\tau }^{\alpha }$ with $\alpha \approx 0.5$ in untreated cells and $\alpha \approx 0.3$ when disrupting microtubules, with successive steps being anticorrelated in both cases. We explain our observations by considering ER junctions to move like monomers in (semi)flexible polymer segments immersed in a viscoelastic environment. We also report that ER networks have a nontrivial fractal dimension $d_f\approx 1.6$ on mesoscopic scales and we provide evidence that the organelle's dynamics is governed by fractons.

Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We thus identify a generic feature of anisotropic active particles in three dimensions.