When a stream of shampoo is fed onto a pool in one's hand, a jet can leap sideways or rebound from the liquid surface in an intriguing phenomenon known as the Kaye effect. Earlier studies have debated whether non-Newtonian effects are the underlying cause of this phenomenon, making the jet glide on top of a shear-thinning liquid layer, or whether an entrained air layer is responsible. Herein we show unambiguously that the jet slides on a lubricating air layer. We identify this layer by looking through the pool liquid and observing its rupture into fine bubbles. The resulting microbubble sizes suggest this air layer is of submicron thickness. This thickness estimate is also supported by the tangential deceleration of the jet during the rebounding.

In contrast to a soap bubble, an antibubble is a liquid globule surrounded by a thin film of air. The collapse behavior of an antibubble is studied using a high-speed video camera. It is found that the retraction velocity of the thin air film of antibubbles depends on the thickness of the air film, $e$, the surface tension coefficient σ, etc., and varies linearly with ${(\sigma /\rho e)}^{1/2}$, according to theoretical analysis and experimental observations. During the collapse of the antibubble, many tiny bubbles can be formed at the rim of the air film due to the Rayleigh instability. In most cases, a larger bubble will emerge finally, which holds most of the volume of the air film.

We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by $\sqrt{t}$, the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.

We study the thermal phase transitions in the generalized classical $XY$ model on the two-dimensional square lattice using single-cluster Monte Carlo simulations. In particular, we examine the (spin-wave) stiffness (helicity modulus) jump at the transition between the low-temperature algebraic phases and the disordered high-temperature regime. Employing a finite-size scaling ansatz from conformal field theory to estimate the termination of the algebraic phases that does not require knowledge of the critical properties, we provide an unbiased estimate of the stiffness jump. Our results are in full accord with the Berzinskii-Kosterlitz-Thouless scenario, i.e., the jump in the helicity modulus does not depend explicitly on the strength of the nematic coupling, but relates directly to the vorticity of the vortex excitations that drive the phase transition. We comment on previous work on related models, where Berzinskii-Kosterlitz-Thouless transition temperatures were based on scaling assumptions contradicted by our findings.

Recently, an expansion as a power series in $1/d$ has been presented for the specific entropy of a complete dimer covering of a $d$-dimensional hypercubic lattice. This paper extends from 3 to 10 the number of terms known in the series. Likewise, an expansion for the entropy, dependent on the dimer density $p$, of a monomer-dimer system, involving a sum ${\sum }_k{a}_k\left(d\right)p^k$, has been offered recently. We herein extend the number of known expansion coefficients from 6 to 20 for the hypercubic lattices of general dimensionality $d$ and from 6 to 24 for the hypercubic lattices of dimensionalities $d<5$. We show that these extensions can lead to accurate numerical estimates of the $p$-dependent entropy for lattices with dimension $d>2$. The computations of this paper have led us to make the following marvelous conjecture: In the case of the hypercubic lattices, all the expansion coefficients $a_k\left(d\right)$ are positive. This paper results from a simple melding of two disparate research programs: one computing to high orders the Mayer series coefficients of a dimer gas and the other studying the development of entropy from these coefficients. An effort is made to make this paper self-contained by including a review of the earlier works.

We show that directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially periodic and symmetric potential can be reliably controlled by tailoring a biharmonic temporal force, in coherence with the degree-of-symmetry-breaking mechanism. We demonstrate that the effect of finite temperature on the purely deterministic ratchet scenario can be understood as an effective noise-induced change of the potential barrier which is in turn controlled by the degree-of-symmetry-breaking mechanism. Remarkably, we find that the same universal scenario holds for any symmetric periodic potential, while optimal directed ratchet transport occurs when the impulse transmitted (spatial integral over a half period) by the symmetric spatial force is maximum.

We present an experimental model system to study two-dimensional phase transitions. This system is composed of a monolayer of millimetric beads interacting through shor range magnetic dipole-dipole interactions. As the system is athermal, a mechanical agitation is used to produce an erratic motion of the beads. The two-dimensional melting scenario predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory is observed. Each phase (liquid-hexatic-solid) has been highlighted with the use of both static and dynamic order parameters. Translational and orientational order are, respectively, estimated through the pair correlation function $g\left(r\right)$ and both orientational correlation function $g_6\left(r\right)$ and its temporal counterpart $g_6\left(t\right)$. We observe two transitions by tuning the applied magnetic field $H$. First, a loss of translational order without loss of orientational order is observed. This is the signature of the transition from the solid phase to the so-called “hexatic” phase. Finally, the orientational order disappears, leading to a liquidlike structure.

After drying colloidal particles suspended in a porous medium a concentration gradient appears. Using ${}^1$H MRI we propose a protocol to observe simultaneously the distributions of air, liquid, and colloid through the unsaturated solid porous structure. Thus we show that the above phenomenon comes from a receding-front effect: The elements migrate towards the free surface of the sample and accumulate in the remaining liquid films. Our understanding of the process makes it possible to establish a simple model without diffusion predicting the drying rate and the concentration distribution in time, in excellent agreement with the experimental observations.

The influence of interactions between particle surface and host fluids in electrorheological suspensions is explored. It is observed that dispersions of nanosized particles of titania in octanoid acid exhibit an anomalously large electrorheologic effect when compared with a similar dispersion of micrometric particles or with a more conventional colloidal suspension of silica in silicone oil. The effect is interpreted as originated by the formation of a thin layer of octanoid acid molecules with the surface of the titania solid particle. The experimental data are fitted with the outcomes of a modified version of conductive models existing in the literature. It is suggested that anomalous large electrorheological effect is mainly originated by the increasing of the effective radius of the nanometric particles, which results in an increasing of the effective volume fraction of the dispersed phase. It is also shown that the deformation of the soft shell around the solid particles, induced by Coulombic force, plays a not negligible role. Some hints for tailoring electrorheologic fluids suitable for different applications are proposed.

We propose that a system of colloidal particles interacting with a honeycomb array of optical traps that each contain three wells can be used to realize a fully packed loop model. One of the phases in this system can be mapped to Baxter's three-coloring problem, offering an easily accessible physical realization of this problem. As a function of temperature and interaction strength, we find a series of phases, including long range ordered loop or stripe states, stripes with sliding symmetries, random packed loop states, and disordered states in which the loops break apart. Our geometry could be constructed using ion trap arrays, BEC vortices in optical traps, or magnetic vortices in nanostructured superconductors.

A mixture of nonelongated monomers $A$ and $B$ capable of formation of three kinds of mesogenic dimers $AA$, $BB$, and $AB$ is investigated. We show the possibility of a temperature-induced transition from one nematic phase consisting mostly of dimers $AB$ composed of dissimilar monomers to a different nematic phase consisting mostly of dimers $AA$ and $BB$ composed of similar monomers. The binding energy of dimers $AB$ is supposed to be lower (the binding of monomers $A$ and $B$ is more preferable) than that of dimers $AA$ and $BB$ (the binding of monomers $A$ with each other and monomers $B$ with each other is less preferable). On the contrary, the interactions of dimers $AA$ themselves with each other, dimers $BB$ with each other, and dimers $AA$ with dimers $BB$ are supposed to be stronger (the interaction energy is lower) than those of dimers $AB$ with each other and with dimers $AA$ and $BB$. If inequality of binding energies is stronger than inequality of interactions between various dimers, but the corresponding energy difference is small, the entropy can play a crucial role in the formation of particular dimer kinds and can drive the transitions between two nematic phases. The theoretical prediction is well reproduced experimentally.

Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Cellular nutrient consumption is influenced by both the nutrient uptake kinetics of an individual cell and the cells' spatial arrangement. Large cell clusters or colonies have inhibited growth at the cluster's center due to the shielding of nutrients by the cells closer to the surface. We develop an effective medium theory that predicts a thickness $\ell$ of the outer shell of cells in the cluster that receives enough nutrient to grow. The cells are treated as partially absorbing identical spherical nutrient sinks, and we identify a dimensionless parameter $\nu$ that characterizes the absorption strength of each cell. The parameter $\nu$ can vary over many orders of magnitude among different cell types, ranging from bacteria and yeast to human tissue. The thickness $\ell$ decreases with increasing $\nu$, increasing cell volume fraction $\varphi$, and decreasing ambient nutrient concentration ${\psi }_{\infty }$. The theoretical results are compared with numerical simulations and experiments. In the latter studies, colonies of budding yeast, Saccharomyces cerevisiae, are grown on glucose media and imaged under a confocal microscope. We measure the growth inside the colonies via a fluorescent protein reporter and compare the experimental and theoretical results for the thickness $\ell$.

We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height $h$. For chaotic orbits below the periodic islands, the survival probability for the particles to reach $h$ is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when $h$ reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when $h$ reaches the position of the lowest KAM island.

The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schrödinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

An influence of a high-voltage ($3–17$ kV) 20 ns pulse on a weakly-ionized low-pressure ($0.1–10$ Pa) capacitively coupled radiofrequency (RF) argon plasma is studied experimentally. The plasma evolution after pulse exhibits two characteristic regimes: a bright flash, occurring within 100 ns after the pulse (when the discharge emission increases by 2–3 orders of magnitude over the steady-state level), and a dark phase, lasting a few hundreds $\mu$s (when the intensity of the discharge emission drops significantly below the steady-state level). The electron density increases during the flash and remains very large at the dark phase. 1D3V particle-in-cell simulations qualitatively reproduce both regimes and allow for detailed analysis of the underlying mechanisms. It is found that the high-voltage nanosecond pulse is capable of removing a significant fraction of plasma electrons out of the discharge gap, and that the flash is the result of the excitation of gas atoms, triggered by residual electrons accelerated in the electric field of immobile bulk ions. The secondary emission from the electrodes due to vacuum UV radiation plays an important role at this stage. High-density plasma generated during the flash provides efficient screening of the RF field (which sustains the steady-state plasma). This leads to the electron cooling and, hence, onset of the dark phase.

A study of anisotropic heat transport in reversed shear (nonmonotonic $q$-profile) magnetic fields is presented. The approach is based on a recently proposed Lagrangian-Green's function method that allows an efficient and accurate integration of the parallel (i.e., along the magnetic field) heat transport equation. The magnetic field lines are described by a nontwist Hamiltonian system, known to exhibit separatrix reconnection and robust shearless ($dq/dr=0$) transport barriers. The changes in the magnetic field topology due to separatrix reconnection lead to bifurcations in the equilibrium temperature distribution. For perturbations of moderate amplitudes, magnetic chaos is restricted to bands flanking the shearless region. As a result, the temperature flattens in the chaotic bands and develops a very sharp radial gradient at the shearless region. For perturbations with larger amplitude, shearless Cantori (i.e., critical magnetic surfaces located at the minimum of the $q$ profile) give rise to anomalous temperature relaxation involving widely different time scales. The first stage consists of the relatively fast flattening of the radial temperature profile in the chaotic bands with negligible flux across the shearless region that, for practical purposes, on a short time scale acts as an effective transport barrier despite the lack of magnetic flux surfaces. In the long-time scale, heat starts to flow across the shearless region, albeit at a comparatively low rate. The transport of a narrow temperature pulse centered at the reversed shear region exhibits weak self-similar scaling with non-Gaussian scaling functions indicating that transport at this scale cannot be modeled as a diffusive process with a constant diffusivity. Evidence of nonlocal effective radial transport is provided by the existence of regions with nonzero heat flux and zero temperature gradient. Parametric flux-gradient plots exhibit multivalued loops that question the applicability of the Fourier-Fick's prescription even in the presence of a finite pinch velocity.

The interplay between traffic dynamics and epidemic spreading on complex networks has received increasing attention in recent years. However, the control of traffic-driven epidemic spreading remains to be a challenging problem. In this Brief Report, we propose a method to suppress traffic-driven epidemic outbreak by properly removing some edges in a network. We find that the epidemic threshold can be enhanced by the targeted cutting of links among large-degree nodes or edges with the largest algorithmic betweenness. In contrast, the epidemic threshold will be reduced by the random edge removal. These findings are robust with respect to traffic-flow conditions, network structures, and routing strategies. Moreover, we find that the shutdown of targeted edges can effectively release traffic load passing through large-degree nodes, rendering a relatively low probability of infection to these nodes.

Based on conventional Ito or Stratonovich interpretation, zero-mean multiplicative noise can induce shifts of attractors or even changes of topology to a deterministic dynamics. Such phenomena usually introduce additional complications in analysis of these systems. We employ in this paper a new stochastic interpretation leading to a straightforward consequence: The steady state distribution is Boltzmann-Gibbs type with a potential function severing as a Lyapunov function for the deterministic dynamics. It implies that an attractor corresponds to the local extremum of the distribution function and the probability is equally distributed right on an attractor. We consider a prototype of nonequilibrium processes, noisy limit cycle dynamics. Exact results are obtained for a class of limit cycles, including a van der Pol type oscillator. These results provide a new angle for understanding processes without detailed balance and can be verified by experiments.

The Langevin description of Brownian motion in inhomogeneous suspensions is here revisited. Inhomogeneous suspensions are characterized by a position-dependent friction coefficient, which can significantly influence the dynamics of the suspended particles. Outstanding examples are suspensions in confinement or in the presence of a temperature gradient. The Langevin approach in inhomogeneous systems encounters a fundamental difficulty related to the interpretation of the multiplicative noise induced by the position-dependent friction. We show that the so-called Ito-Stratonovich dilemma is originated by the violation of the macroscopic force balance condition in the traditional procedure of eliminating the fast variables. Repairing this deficit, we rederive the extended overdamped Langevin equation directly from the infradamped Langevin equation. This is without invoking the Fokker-Planck formalism, such that the self-completeness of the Langevin framework is restored. Furthermore, we derive the generalized forms of the drift-force relation and the Smoluchowski equation for inhomogeneous suspensions in a straightforward manner.