It is generally accepted that a Worthington jet occurs when a droplet impacts onto a liquid pool. However, in this experimental study of the impact of viscous droplets onto a less-viscous liquid pool, we identify another jet besides the Worthington jet, forming a two-jet phenomenon. The two jets, a surface-climbing jet and the Worthington jet, may appear successively during one impact event. By carefully tuning the impact conditions, we find that the two-jet phenomenon is jointly controlled by the droplet-pool viscosity ratio, the droplet Weber number, and the droplet-pool miscibility. The mechanism of the surface-climbing jet is completely different from that of the Worthington jet: the liquid in the pool climbs along the surface of the droplet and forms a liquid layer which converges at the droplet apex and produces the surface-climbing jet. This surface-climbing jet has a very high speed, i.e., an order of magnitude higher than the droplet impact speed. The effects of the impact speed, droplet viscosity, droplet size, and surface tension on the surface-climbing jet are also analyzed. This study not only provides physical insights into the mechanism of droplet and jet dynamics but also will be helpful in the optimization of the droplet impact process in many relevant applications.

We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving boundary problem that is a higher-dimensional analog of Hele-Shaw flow. Here we are concerned with the development of pinch-off singularities characterized by a blowup of the interface curvature and the bubble subsequently breaking up into two; these singularities do not occur in the corresponding two-dimensional Hele-Shaw problem. By applying a numerical scheme based on the level set method, we show that solutions to our problem can undergo pinch-off in various geometries. A similarity analysis suggests that the minimum radius behaves as a power law in time with exponent $\alpha =1/3$ just before and after pinch-off has occurred, regardless of the initial conditions; our numerical results support this prediction. Further, we apply our numerical scheme to simulate the time-dependent development and translation of axially symmetric Saffman-Taylor fingers and Taylor-Saffman bubbles in a cylindrical tube, highlighting key similarities and differences with the well-studied two-dimensional cases.

Single-cycle pulses with multimillion volts per centimeter field strengths and spectra in the terahertz (THz) band have attracted great interest due to their ability to coherently manipulate molecular orientations and electron spins resonantly and nonresonantly. The tremendous progress made in the development of compact and powerful terahertz sources have identified intense laser-thin foil interaction as a potential candidate for high-power broadband terahertz radiation. They are micrometers in size and deliver radially polarized terahertz pulses with millijoule energy and gigawatt peak power. Although several works have been carried out to investigate the terahertz generation process, their origin and angular distribution are still debated. We present here an indisputable study on their spatiotemporal characteristics and elaborate the underlying physical processes via recording the three-dimensional beam profile along with transient dynamics. These results are substructured with the quantitative visualization of the charge particle spectra.

Relativistic laser-solid target interaction is a powerful source of terahertz radiation where broadband terahertz radiation is emitted from the front and rear surfaces of the target. Even though several experimental works have reported the generation of subpicosecond duration gigawatt peak power terahertz pulses from the target rear surface, the underlying physical process behind their origin is still an open question. Here we discuss a numerical model that can accurately reproduce several aspects of the experimental results. The model is based on the charged particle dynamics at the target rear surface and the evolution of the charge separation field. We identify the major contributors that are responsible for broadband terahertz emission from the rear surface of the target.

Microstructure strongly influences flow and transport properties of porous media. Flow and transport simulations within porous media, therefore, requires accurate three-dimensional (3D) models of the pore and solid phase structure. To date, no imaging method can resolve all relevant heterogeneities from the nano- to the centimeter scale within complex heterogeneous materials such as clay, reservoir rocks (e.g., travertine, chalk, $...$), hardened cement paste, and concrete. To reconstruct these porous materials it is thus necessary to merge information from different 2D and potentially 3D imaging methods. One porous media reconstruction methodology that has been around for at least two decades is simulated annealing (SA). However, realizations with SA typically suffer an artificially reduced long-range connectivity, while multiphase reconstructions are not feasible in most cases because of a prohibitive computational burden. To solve these problems we propose a hierarchical multiresolution and multiphase simulated annealing algorithm. To decrease the computational cost of multiphase simulation, our algorithm sequentially simulates one phase after another, in a hierarchical way, which enables handling multimodal distributions and topological relations. Building upon recent work, our algorithm improves long-range connectivity and CPU efficiency by simulating larger particles using a coarser resolution that is subsequently refined compared to standard SA; our proposed extension not only offers the possibility to perform multiphase reconstruction but also allows us (i) to improve binary reconstruction quality, as quantified, e.g., by multiple-point histograms by up to one order of magnitude and (ii) to achieve an overall speed-up. The proposed algorithm is also shown to outperform the direct sampling multiple-point statistics method for the generation of cement paste microstructure with respect to both generation time and quality.

Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: a dimensionless molecular length scale, the Knudsen number $\mathrm{Kn}$, and a dimensionless frequency $\theta$, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi et al., Phys. Rev. E 89, 033305 (2014)], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large $\mathrm{Kn}$ and $\theta$ was examined. In these cases, the LB method exhibits spurious numerical oscillations that cannot be removed through the use of discrete particle velocities drawn from higher-order Gauss-Hermite quadrature. Here, we identify the origin of these spurious effects and formulate a method to minimize their presence. This proposed method splits the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation into two equations: (1) a homogeneous “gain-free equation” that can be solved directly, containing terms responsible for the spurious oscillations; and (2) an inhomogeneous “remainder equation” with homogeneous boundary conditions (i.e., stationary boundaries) that is solved using the conventional LB algorithm. This proposed “splitting method” is validated using published high-accuracy numerical solutions to the linearized Boltzmann BGK equation where excellent agreement is observed.

The elephant random walk (ERW) is a microscopic, one-dimensional, discrete-time, non-Markovian random walk, which can lead to anomalous diffusion due to memory effects. In this study, I propose a multidimensional generalization in which the probability of taking a step in a certain direction depends on the previous steps in other directions. The original model is generalized in a straightforward manner by introducing coefficients that couple the probability of moving in one direction with the previous steps in all directions. I motivate the model by first introducing a two-elephant system and then elucidating it with a specific coupling. With the explicit calculation of the first moments, I show the existence of two newsworthy relative movement behaviors: one in which one elephant follows the other and another in which they go in opposite directions. With the aid of a Fokker-Planck equation, the second moment is evaluated and two superdiffusion regimes appear, not found in other ERWs. Then, I reinterpret the equations as a bidimensional elephant random walk model, and further generalize it to $N$ dimensions. I argue that the introduction of coupling coefficients is a way of extending any one-dimensional ERW to many dimensions.

A metric ($\chi$) is introduced to quantify the relative proportion of particles having a specified number of near neighbors that are characteristic of liquid-phase properties. It can be used as a simple alternative to other methods for the investigation of some aspects of percolation behavior. Values of $\chi$ are obtained from molecular-dynamics simulations spanning the heterogeneous vapor and liquid region and the supercritical phase of the Lennard-Jones fluid. The supercritical phase can be delineated into regions of different structural properties. At different isochoric subcritical conditions, the temperature versus $\chi$ behavior shows evidence of inflections, which are associated with the onset of transitions from the vapor and liquid region to the supercritical phase. The analysis suggests a phenomenological requirement for the critical point in terms of a near-equal proportion of near neighbors with gaslike and liquidlike characteristics.

An alternative way to study the rules of life-like cellular automata is presented. The proposed perspective studies some multifractal and informational properties of Boolean functions behind these rules. Results from this approach challenge the traditional argument about the simplicity of Lifelike rules.

We develop a model to investigate the time evolution of the mean location and variance of a random walker subject to Poisson-distributed collisions at constant rate. The collisions are instantaneous velocity changes where a new value of velocity is generated from a model probability function. The walker is persistent, which means that it moves at constant velocity between collisions. We study three different cases of velocity transition functions and compute the transport properties from the evolution of the variance. We observe that transport can change character over time and that early times show features that, in general, depend on the initial conditions of the walker.

The canonical phase diagram of the Blume-Emery-Griffiths model with infinite-range interactions is known to exhibit a fourth-order critical point at some negative value of the biquadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth-order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth-order critical point is studied in detail revealing some distinct features from the canonical counterpart.

Mean-field diffusive coupling was known to induce the phenomenon of quenching of oscillations even in identical systems, where the standard diffusive coupling (without mean-field) fails to do so [Phys. Rev. E 89, 052912 (2014)]. In particular, the mean-field diffusive coupling facilitates the transition from amplitude to oscillation death states and the onset of a nontrivial amplitude death state via a subcritical pitchfork bifurcation. In this paper, we show that an adaptive coupling using a low-pass filter in both the intrinsic and extrinsic variables in the coupling is capable of inducing the counterintuitive phenomenon of reviving of oscillations from the death states induced by the mean-field coupling. In particular, even a weak filtering of the extrinsic (intrinsic) variable in the mean-field coupling facilitates the onset of revival (quenching) of oscillations, whereas a strong filtering of the extrinsic (intrinsic) variable results in quenching (revival) of oscillations. Our results reveal that the degree of filtering plays a predominant role in determining the effect of filtering in the extrinsic or intrinsic variables, thereby engineering the dynamics as desired. We also extend the analysis to networks of mean-field coupled limit-cycle and chaotic oscillators along with the low-pass filters to illustrate the generic nature of our results. Finally, we demonstrate the observed dynamical transition experimentally to elucidate the robustness of our results despite the presence of inherent parameter fluctuations and noise.

We generalize an algorithm used widely in the configuration model such that power-law degree sequences with the degree exponent $\lambda$ and the number of links per node $K$ controllable independently may be generated. It yields the degree distribution in a different form from that of the static model or under random removal of links while sharing the same $\lambda$ and $K$. With this generalized power-law degree distribution, the critical point $K_c$ for the appearance of the giant component remains zero not only for $\lambda \le 3$ but also for $3<\lambda <{\lambda }_l\simeq 3.81$. This is contrasted with $K_c=0$ only for $\lambda \le 3$ in the static model and under random link removal. The critical exponents and the cluster-size distribution for $\lambda <{\lambda }_l$ are also different from known results. By analyzing the moments and the generating function of the degree distribution and comparison with those of other models, we show that the asymptotic behavior and the degree exponent may not be the only properties of the degree distribution relevant to the critical phenomena but that its whole functional form can be relevant. These results can be useful in designing and assessing the structure and robustness of networked systems.

A system of smooth “frozen” Janus-type disks is studied. Such disks cannot rotate and are divided by their diameter into two sides of different inelasticities. Taking as a reference a system of colored elastic disks, we find differences in the behavior of the collisions once the anisotropy is included. A homogeneous state, akin to the homogeneous cooling state of granular gases, is seen to arise and the singular behavior of both the collisions and the precollisional correlations are highlighted.

We study the stroboscopic dynamics of a spin-$S$ object subjected to $\delta$-function kicks in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed in the large spin limit, $S\to \infty$. On evolving such a map for large kicking strength and time period, the phase space appears to be chaotic; interestingly, however, the geodesic distance increases linearly with the stroboscopic time implying that the Lyapunov exponent is zero. We derive the Sutherland invariant for the underlying SO(3) matrix governing the dynamics of classical spin variables and study the orbits for weak kicking strength. For the quantum dynamics, we observe that although the phase coherence of a state is retained throughout the time evolution, the fluctuations in the mean values of the spin operators exhibit fractality which is also present in the Floquet eigenstates. Interestingly, the presence of an interaction with another spin results in an ergodic dynamics leading to infinite temperature thermalization.

We propose a model of magnetic friction and investigate the relation between the frictional force and the relative velocity of surfaces in the steady state. The model comprises two square lattices adjacent to each other, the upper of which is subjected to an external force, and the magnetic interaction acts as a kind of potential barrier that prevents the upper lattice from moving. We consider two surface types for the upper lattice: smooth and rough. The behavior of this model is classified into two domains, which we refer to as domains I and II. In domain II, the external force is dominant compared with other forces, whereas in domain I, the velocity of the lattice is suppressed by the magnetic interaction and obeys the Dieterich-Ruina law. This characteristic property can be observed regardless of whether the surface is smooth or rough.

We consider the effect of small independent local noise on a network of quadratic integrate-and-fire neurons, globally coupled via synaptic pulses of finite width. The Fokker-Planck equation for a network of infinite size is reduced to a low-dimensional system of ordinary differential equations using the recently proposed perturbation theory based on circular cumulants. A bifurcation analysis of the reduced equations is performed, and areas in the parameter space, where the noise causes macroscopic oscillations of the network, are determined. The validity of the reduced equations is verified by comparing their solutions with “exact” solutions of the Fokker-Planck equation, as well as with the results of direct simulation of stochastic microscopic dynamics of a finite-size network.

To understand how a complex system is organized and functions, researchers often identify communities in the system's network of interactions. Because it is practically impossible to explore all solutions to guarantee the best one, many community-detection algorithms rely on multiple stochastic searches. But for a given combination of network and stochastic algorithms, how many searches are sufficient to find a solution that is good enough? The standard approach is to pick a reasonably large number of searches and select the network partition with the highest quality or derive a consensus solution based on all network partitions. However, if different partitions have similar qualities such that the solution landscape is degenerate, the single best partition may miss relevant information, and a consensus solution may blur complementary communities. Here we address this degeneracy problem with coarse-grained descriptions of the solution landscape. We cluster network partitions based on their similarity and suggest an approach to determine the minimum number of searches required to describe the solution landscape adequately. To make good use of all partitions, we also propose different ways to explore the solution landscape, including a significance clustering procedure. We test these approaches on synthetic networks and a real-world network using two contrasting community-detection algorithms: The algorithm that can identify more general structures requires more searches, and networks with clearer community structures require fewer searches. We also find that exploring the coarse-grained solution landscape can reveal complementary solutions and enable more reliable community detection.

Cell constriction is a decisive step for division in many cells. However, its physical pathway remains poorly understood, calling for a quantitative analysis of the forces required in different cytokinetic scenarios. Using a model cell composed by a flexible membrane (actin cortex and cell membrane) that encloses the cytoplasm, we study the mechanical conditions necessary for stable symmetric constriction under radial equatorial forces using analytical and numerical methods. We deduce that stable symmetric constriction requires positive effective spontaneous curvature, while spontaneous constriction requires a spontaneous curvature higher than the characteristic inverse cell size. Surface tension reduction (for example by actin cortex growth and membrane trafficking) increases the stability and spontaneity of cellular constriction. A reduction of external pressure also increases stability and spontaneity. Cells with prolate lobes (elongated cells) require lower stabilization forces than oblate-shaped cells (discocytes). We also show that the stability and spontaneity of symmetric constriction increase as constriction progresses. Our quantitative results settle the physical requirements for stable cytokinesis, defining a quantitative framework to analyze the mechanical role of the different constriction machinery and cytokinetic pathways found in real cells, so contributing to a deeper quantitative understanding of the physical mechanism of the cell division process.

The effects of quenched disorder on a single and many active run-and-tumble particles are studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to nondisordered systems.