Remote synchronization (RS) is characterized by the appearance of phase coherence between oscillators that do not directly interact through a structural link in a network but exclusively through other units that are not synchronized or more weakly synchronized with them. This form of phase synchronization was observed initially in starlike motifs and later in random networks. In this paper, we report on an experimental setup for the analysis of RS in networks of Stuart-Landau oscillators and in particular investigate the behavior of tree structures focusing on the path to synchronization, that is, on the analysis of how synchronization emerges as the coupling strength increases from zero. We find that RS occurs in a region wherein further increases of the coupling strength lead to a direct transition to global synchronization but may also be observed in a second region, corresponding to lower coupling values, wherein it first emerges and then disappears, hallmarking a scenario that we denote as fading of remote synchronization. We show that this result is related to the behavior of pairs of remotely synchronized nodes observed in networks with more general topologies. Experiments are corroborated by numerical simulations confirming the major findings and providing further characterization of the phenomenon. We demonstrate that the distribution of natural oscillation frequencies and the parameter uncertainty in the links both play a fundamental role in shaping the behaviors observed.

Morphogen protein gradients play an essential role in the spatial regulation of patterning during embryonic development. The most commonly accepted mechanism of protein gradient formation involves the diffusion and degradation of morphogens from a localized source. Recently, an alternative mechanism has been proposed, which is based on cell-to-cell transport via thin actin-rich cellular extensions known as cytonemes. Very little is currently known about the precise nature of the contacts between cytonemes and their target cells. Important unresolved issues include how cytoneme tips find their targets, how they are stabilized at their contact sites, and how vesicles are transferred to a receiving cell and subsequently internalized. It has been hypothesized that cytonemes find their targets via a random search process based on alternating periods of retraction and growth, perhaps mediated by some chemoattractant. This is an actin-based analog of the search-and-capture model of microtubules of the mitotic spindle searching for cytochrome binding sites (kinetochores) prior to separation of cytochrome pairs. In this paper we develop a search-and-capture model of cytoneme-based morphogenesis, in which nucleating cytonemes from a source cell dynamically grow and shrink along the surface of a one-dimensional array of target cells until making contact with one of the target cells. We analyze the first-passage-time problem for making contact and then use this to explore the formation of morphogen gradients under the mechanism proposed for Wnt in vertebrates. That is, we assume that morphogen is localized at the tip of a growing cytoneme, which is delivered as a “morphogen burst” to a target cell when the cytoneme makes temporary contact with a target cell before subsequently retracting. We show how multiple rounds of search-and-capture, morphogen delivery, cytoneme retraction, and nucleation events lead to the formation of a morphogen gradient. We proceed by formulating the morphogen bursting model as a queuing process, analogous to the study of translational bursting in gene networks. In order to analyze the expected times for cytoneme contact, we introduce an efficient method for solving first-passage-time problems in the presence of sticky boundaries, which exploits some classical concepts from probability theory, namely, stopping times and the strong Markov property. We end the paper by demonstrating how this method simplifies previous analyses of a well-studied problem in cell biology, namely, the search-and-capture model of microtubule-kinetochore attachment. Although the latter is completely unrelated to cytoneme-based morphogenesis from a biological perspective, it shares many of the same mathematical elements.

When a suspension freezes, a compacted particle layer builds up at the solidification front with noticeable implications on the freezing process. In a directional solidification experiment of monodisperse suspensions in thin samples, we evidence a link between the thickness of this layer and the sample depth. We attribute it to an inhomogeneity of particle density that is attested by the evidence of crystallization at the plates and of random close packing far from them. A mechanical model based on the resulting modifications of permeability enables us to relate the layer thickness to this inhomogeneity and to select the distribution of particle density that yields the best fit to our data. This distribution involves an influence length of sample plates of about 11 particle diameters. Altogether, these results clarify the implications of boundaries on suspension freezing. They may be useful to model polydisperse suspensions with large particles playing the role of smooth boundaries with respect to small ones.

Continuous release of gas bubbles in large numbers from a localized source in a liquid column, popularly known as “bubble plumes”, is very relevant in nature and industries. The bubble plumes morphologically consist of a long continuous stem supporting a dispersed head. Through our direct numerical simulations using two-way coupled Euler-Lagrangian framework, we show that a bubble plume rising in a quiescent liquid column develops clusterlike instabilities for the Grashof numbers, $\text{Gr}>145$. For levels $\text{Gr}<100$, the stem is continuous with a small plume head, whereas at high buoyancy ($\text{Gr}>350$), the plume stem shows intermittently passing puffing instabilities in the form of bubble clusters. The clusters are a group of bubbles localized in space with high concentration that travel upward with speed $C_{ph}=0.45U_C$ and are separated by a distance of at least $5L_0$, where $U_C$ is the characteristic velocity and $L_0$ is the characteristic length based on the injection conditions. The bubble rise Reynolds numbers in the steady state for both the plume head and the stem shows $\text{Re}\propto {\text{Gr}}^{0.45\pm 0.03}$, and the proportionality constant is ten times higher in the plume stem than in the plume head. In the plume core, the spatial acceleration due to the bubble motion generates the turbulent production, whereas, at the plume edge, the small-scale fluctuations generate the mean vorticity. At high Gr, the clusters evolve due to the lift forces acting on the bubbles as a result of increase in the mean vorticity. While rising, bubbles entrain the liquid from the surroundings, and we found that the entrainment rate is not as strong as compared to the classical thermal plumes.

Frosting is a multiscale and multiphysics problem, which presents a significant challenge for numerical methods. In this study, a generalized lattice Boltzmann (LB) model is developed to simulate the frosting of humid air at representative elementary volume scale. In this model, three LB equations are introduced to describe the evolution of distribution functions for velocity, temperature, and humidity (i.e., mass fraction of water vapor in the humid air) fields, respectively. The frost layer is regarded as a porous medium, while the humid air is treated as a plain one. This unified LB model can be applied to describe the phase change and transport processes in these two subdomains seamlessly. Through the Chapman-Enskog analysis, the macroscopic equations for the frosting process can be recovered from the present LB model. Benchmark problems in conduction solidification, convection melting and frosting are simulated, and the numerical results match well with analytical or experimental solutions. Finally, this model is applied to simulate frost formation between two parallel plates, and the influences of air velocity, humidity, temperature, and cold wall temperature are evaluated.

Taking advantage of recent single-particle tracking data, we compare the popular standard mean-squared displacement method with a statistical testing hypothesis procedure for three testing statistics and for two particle types: membrane receptors and the G proteins coupled to them. Each method results in different classifications. For this reason, more rigorous statistical tests are analyzed here in detail. The main conclusion is that the statistical testing approaches might provide good results even for short trajectories, but none of the proposed methods is “the best” for all considered examples; in other words, one needs to combine different approaches to get a reliable classification.

We present a Monte Carlo study of the geometric properties of Fortuin-Kasteleyn (FK) clusters of the Ising model on square [two-dimensional (2D)] and simple-cubic [three-dimensional (3D)] lattices. The wrapping probability, a dimensionless quantity characterizing the topology of the FK clusters on a torus, is found to suffer from smaller finite-size corrections than the well-known Binder ratio and yields a high-precision critical coupling as $K_c\left(3\mathrm{D}\right)=0.221654631\left(8\right)$. We then study other geometric properties of FK clusters at criticality. It is demonstrated that the distribution of the critical largest-cluster size $C_1$ follows a single-variable function as $P(C_1,L)d{C}_1=\tilde{P}\left(x\right)dx$ with $x\equiv C_1/L^{d_{\mathrm{F}}}$ ($L$ is the linear size), where the fractal dimension $d_{\mathrm{F}}$ is identical to the magnetic exponent. An interesting bimodal feature is observed in distribution $\tilde{P}\left(x\right)$ in three dimensions, and attributed to the different approaching behaviors for $K\to K_c+0^{\pm }$. To characterize the compactness of the FK clusters, we measure their graph distances and determine the shortest-path exponents as $d_{\min }\left(3\mathrm{D}\right)=1.25936\left(12\right)$ and $d_{\min }\left(2\mathrm{D}\right)=1.0940\left(2\right)$. Further, by excluding all the bridges from the occupied bonds, we obtain bridge-free configurations and determine the backbone exponents as $d_{\mathrm{B}}\left(3\mathrm{D}\right)=2.1673\left(15\right)$ and $d_{\mathrm{B}}\left(2\mathrm{D}\right)=1.7321\left(4\right)$. The estimates of the universal wrapping probabilities for the 3D Ising model and of the geometric critical exponents $d_{\min }$ and $d_{\mathrm{B}}$ either improve over the existing results or have not been reported yet. We believe that these numerical results would provide a testing ground in the development of further theoretical treatments of the 3D Ising model.

We investigate in detail the influence of the violation of the strict residual-entropy hierarchy among the neighboring ground states of different orders on the low-temperature behavior of the specific heat capacity in the magnetic frustrated systems in the framework of the exactly solvable antiferromagnetic spin-$1/2$ Ising model with the multisite interaction in the presence of the external magnetic field on the zigzag ladder. The exact expressions for the residual entropies of all ground states of the model are found, and it is shown that when the strength of the multisite interaction is strong enough then the model exhibits a quite interesting specific situation, namely, that there exist neighboring plateau ground states together with the single-point ground state that separates them, such that the magnetization properties of all of them are different but their entropy per site is the same and equal to zero. It is shown that this fact of the violation of the strict residual-entropy hierarchy between neighboring ground states of different orders leads to the reduction of the possible number of peaks that can appear in the low-temperature behavior of the specific heat capacity in the corresponding regions of the model parametric space. In addition, it is also shown that the absence of the strict residual-entropy hierarchy among neighboring ground states of different orders changes qualitatively the behavior of the specific heat capacity as a function of the external magnetic field, namely, that the typical field-induced sharp double-peak structure in the low-temperature behavior of the specific heat capacity, which is directly related to the very existence of the highly macroscopically degenerated single-point ground states, disappears already for relatively large values of the temperature.

A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex function of the total energy, meaning that ensemble equivalence is violated in a negative-temperature regime. The equilibrium properties of the model are then investigated by molecular dynamics simulations: first, the caloric curve is reconstructed for the microcanonical ensemble and compared to the analytical prediction, and a generalized Maxwell-Boltzmann distribution for the momenta is observed; then the nonequivalence between the microcanonical and canonical descriptions is explicitly shown. Moreover, the validity of the Fluctuation-Dissipation Theorem is verified through a numerical study, also at negative temperature and in the region where the two ensembles are nonequivalent.

An array of globally all-to-all coupled FitzHugh-Nagumo–type oscillators is considered. We suggest an adaptive first-order stable filter control feedback technique to stabilize the steady states of the oscillators. The overall system includes separate networks of coupling and control. Therefore, the controller does not depend on the intrinsic parameters of coupling between the oscillators. We have investigated stabilization of the steady states in an array of nonidentical oscillators analytically, numerically, and experimentally.

Most complex social, biological and technological systems can be described by dynamic networks. Reconstructing network structures from measurable data is a fundamental problem in almost all interdisciplinary fields. Network nodes interact with each other and those interactions often have diversely distributed time delays. Accurate reconstruction of any targeted interaction to a node requires measured data of all its neighboring nodes together with information on the time delays of interactions from these neighbors. When networks are large, these data are often not available and time-delay factors are deeply hidden. Here we show that fast-varying noise can be of great help in solving these challenging problems. By computing suitable correlations, we can infer the intensity and time delay of any targeted interaction with the data of two related nodes (driving and driven nodes) only while all other nodes in the network are hidden. This method is analytically derived and fully justified by extensive numerical simulations.

Many bacteria rely on active cell appendages, such as type IV pili, to move over substrates and interact with neighboring cells. Here, we study the motion of individual cells and bacterial colonies, mediated by the collective interactions of multiple pili. It was shown experimentally that the substrate motility of Neisseria gonorrhoeae cells can be described as a persistent random walk with a persistence length that exceeds the mean pili length. Moreover, the persistence length increases for a higher number of pili per cell. With the help of a simple, tractable stochastic model, we test whether a tug of war without directional memory can explain the persistent motion of single Neisseria gonorrhoeae cells. While persistent motion of single cells indeed emerges naturally in the model, a tug of war alone is not capable of explaining the motility of microcolonies, which becomes weaker with increasing colony size. We suggest sliding friction between the microcolonies and the substrate as the missing ingredient. While such friction almost does not affect the general mechanism of single cell motility, it has a strong effect on colony motility. We validate the theoretical predictions by using a three-dimensional computational model that includes explicit details of the pili dynamics, force generation, and geometry of cells.

Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width $L$ separated by distances $D_1$ and $D_2$. The stripes interact with the fluid with long-range forces inducing a large finite-size contribution to the surface free energy. We show that this nonextensive free-energy contribution scales with $lnL$ and drives different types of bridging transition corresponding to the merging of liquid drops adsorbed at neighboring wetting stripes when the separation between them is molecularly small. We determine the surface phase diagram and show that this exhibits two triple points, where isolated drops, double drops, and triple drops coexist. For the symmetric case, $D_1=D_2\equiv D$, our results also confirm that the equilibrium droplet configuration always has the symmetry of the substrate corresponding to either three isolated drops when $D$ is large or a single triple drop when $D$ is small; however, symmetry-broken configurations do occur in a metastable part of the phase diagram which lies very close to the equilibrium-bridging phase boundary. Implications for phase transitions on other types of patterned surface are considered.

The Cahn-Hilliard equation (CHE) is widely used in modeling two-phase fluid flows, and it is critical to solve this equation accurately to track the interface between the two phases. In this paper, a high-order lattice Boltzmann equation model is developed for the CHE via the fourth-order Chapman-Enskog expansion. A truncation error analysis is performed, and the leading error term proportional to the Peclet number is identified. The results are further confirmed by the Maxwell iteration. With the inclusion of a correction term for eliminating the main error term, the proposed model is able to recover the CHE up to third order. The proposed model is tested by several benchmark problems. The results show that the present model is capable of tracking the interface with improved accuracy and stability in comparison with the second-order one.

We study complete wetting of solid walls that are patterned by parallel nanogrooves of depth $D$ and width $L$ with a periodicity of $2L$. The wall is formed of a material which interacts with the fluid via a long-range potential and exhibits first-order wetting transition at temperature $T_w$, should the wall be planar. Using a nonlocal density functional theory we show that at a fixed temperature $T>T_w$ the process of complete wetting depends sensitively on two microscopic length scales $L_c^{+}$ and $L_c^{-}$. If the corrugation parameter $L$ is greater than $L_c^{+}$, the process is continuous similar to complete wetting on a planar wall. For $L_c^{-}<L<L_c^{+}$, the complete wetting exhibits first-order depinning transition corresponding to an abrupt unbinding of the liquid-gas interface from the wall. Finally, for $L<L_c^{-}$ the interface remains pinned at the wall even at bulk liquid-gas coexistence. This implies that nanomodification of substrate surfaces can always change their wetting character from hydrophilic into hydrophobic, in direct contrast to the macroscopic Wenzel law. The resulting surface phase diagram reveals a close analogy between the depinning and prewetting transitions including the nature of their critical points.

This Rapid Communication identifies the physical mechanism for the quench of turbulent resistivity in two-dimensional magnetohydrodynamics. Without an imposed, ordered magnetic field, a multiscale, blob-and-barrier structure of magnetic potential forms spontaneously. Magnetic energy is concentrated in thin, linear barriers, located at the interstices between blobs. The barriers quench the transport and kinematic decay of magnetic energy. The local transport bifurcation underlying barrier formation is linked to the inverse cascade of $\langle A^2\rangle$ and negative resistivity, which induce local bistability. For small-scale forcing, spontaneous layering of the magnetic potential occurs, with barriers located at the interstices between layers. This structure is effectively a magnetic staircase.

Thermal metamaterials based on core-shell structures have aroused wide research interest, e.g., in thermal cloaks. However, almost all the relevant studies only discuss linear materials whose thermal conductivities are temperature-independent constants. Nonlinear materials (whose thermal conductivities depend on temperatures) have seldom been touched; however, they are important in practical applications. This situation largely results from the lack of a general theoretical framework for handling such nonlinear problems. Here we study the nonlinear responses of thermal metamaterials with a core-shell structure in two or three dimensions. By calculating the effective thermal conductivity, we derive the nonlinear modulation of a nonlinear core. Furthermore, we reveal two thermal coupling conditions, under which this nonlinear modulation can be efficiently manipulated. In particular, we reveal the phenomenon of nonlinearity enhancement. Then this theory helps us to design a kind of intelligent thermal transparency devices, which can respond to the direction of thermal fields. The theoretical results and finite-element simulations agree well with each other. This work not only offers a different mechanism to achieve nonlinearity modulation and enhancement in thermotics, but also suggests potential applications in thermal management, including illusion.

We investigate the evolution of a target qubit caused by its multiple random collisions with $N$-qubit clusters. Depending on the cluster state, the evolution of the target qubit may correspond to its effective interaction with a thermal bath, a coherent (laser) drive, or a squeezed bath. In cases where the target qubit relaxes to a thermal state, its dynamics can exhibit a quantum advantage, whereby the target-qubit temperature can be scaled up proportionally to $N^2$ and the thermalization time can be shortened by a similar factor, provided the appropriate coherence in the cluster is prepared by nonthermal means. We dub these effects quantum superthermalization because of the analogies to superradiance. Experimental realizations of these effects are suggested.

We study the effects of distinct types of quenched disorder in the contact process with a competitive dynamics on bipartite sublattices. In the model, the particle creation depends on its first and second neighbors and the extinction increases according to the local density. The clean (without disorder) model exhibits three phases: inactive (absorbing), active symmetric, and active asymmetric, where the latter exhibits distinct sublattice densities. These phases are separated by continuous transitions; the phase diagram is reentrant. By performing mean-field analysis and Monte Carlo simulations we show that symmetric disorder destroys the sublattice ordering and therefore the active asymmetric phase is not present. On the other hand, for asymmetric disorder (each sublattice presenting a distinct dilution rate) the phase transition occurs between the absorbing and the active asymmetric phases. The universality class of this transition is governed by the less-disordered sublattice. Finally, our results suggest that random-field disorder destroys the phase transition if it breaks the symmetry between two active states.

During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (“spin”) variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative models are often preferred to handle correlated binary data. One popular alternative, especially in life sciences, is the Cox distribution (or the closely related dichotomized Gaussian distribution and log-normal Cox point process), where the spins are generated independently conditioned on the drawing of a latent variable with a multivariate normal distribution. This article explores the conditions for a principled replacement of the Ising distribution by a Cox distribution. It shows that the Ising distribution itself can be treated as a latent variable model, and it explores when this latent variable has a quasi-normal distribution. A variational approach to this question reveals a formal link with classic mean-field methods, especially Opper and Winther's adaptive TAP approximation. This link is confirmed by weak coupling (Plefka) expansions of the different approximations and then by numerical tests. Overall, this study suggests that an Ising distribution can be replaced by a Cox distribution in practical applications, precisely when its parameters lie in the “mean-field domain.”