We study the one-dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost $\left(X_{max}\ge 0\right)$ and leftmost $\left(X_{min}\le 0\right)$ visited sites up to time $t$. At each time step the existing particles in the system either diffuse (with diffusion constant $D$), die (with rate $a$), or split into two particles (with rate $b$). We focus on the regime $b\le a$ where these two extreme values $X_{max}$ and $X_{min}$ are strongly correlated. We show that at large time $t$, the joint probability distribution function (PDF) of the two extreme points becomes stationary $P(X,Y,t\to \infty )\to p(X,Y)$. Our exact results for $p(X,Y)$ demonstrate that the correlation between $X_{max}$ and $X_{min}$ is nonzero, even in the stationary state. From this joint PDF, we compute exactly the stationary PDF $p\left(\zeta \right)$ of the (dimensionless) span $\zeta =(X_{max}-X_{min})/\sqrt{D/b}$, which is the distance between the rightmost and leftmost visited sites. This span distribution is characterized by a linear behavior $p\left(\zeta \right)\sim \frac{1}{2}(1+\Delta )\zeta$ for small spans, with $\Delta =(\frac{a}{b}-1)$. In the critical case $\left(\Delta =0\right)$ this distribution has a nontrivial power law tail $p\left(\zeta \right)\sim 8\pi \sqrt{3}/{\zeta }^3$ for large spans. On the other hand, in the subcritical case $\left(\Delta >0\right)$, we show that the span distribution decays exponentially as $p\left(\zeta \right)\sim (A^2/2)\zeta exp(-\sqrt{\Delta }\zeta )$ for large spans, where $A$ is a nontrivial function of $\Delta$, which we compute exactly. We show that these asymptotic behaviors carry the signatures of the correlation between $X_{max}$ and $X_{min}$. Finally we verify our results via direct Monte Carlo simulations.

We investigate the phase diagram of $S=1$ quantum spin systems with SU(2)-invariant interactions, at low temperatures and in three spatial dimensions. Symmetry breaking and the nature of extremal states can be studied using random loop representations. The latter confirm the occurrence of ferro- and antiferromagnetic transitions and the breaking of SU(3) invariance. And they reveal the peculiar nature of the nematic extremal states which minimize ${\sum }_x{\left(S_x^i\right)}^2$.

Grains inside a vertically vibrated box undergo a transition from a density-inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behavior near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semiperiodic oscillations of the bed of grains, suggests a new interpretation of the transition analogous to a coupled chain of vertically vibrated damped oscillators. Increasing the size of the container shows metastability of convective states, as well as an overall invariant critical behavior close to the transition.

We present experimental results on the propagation of an ultrasonic wave (40 kHz) in liquid foams, as a function of the foam physical and chemical parameters. We have first implemented an original setup, using transducers in a transmission configuration. The foam coarsening was used to vary the bubble size (remaining in the submillimeter range), and we have made foams with various chemical formulations, to investigate the role of the chemicals at the bubble interfaces or in bulk. The results are compared with recently published theoretical works, and good agreements are found. In particular, for all the foams, we have evidenced two asymptotic limits, at small and large bubble size, connected by a nontrivial resonant behavior, associated to an effective negative density. These qualitative features are robust whatever the chemical formulation; we discuss the observed differences between the samples, in relation to the interfacial and bulk viscoelasticity. These results demonstrate the rich and complex acoustic behavior of foams. While the bubble size remain here always smaller than the sound wavelength, it turns out that one must go well beyond mean-field modeling to describe the foam acoustic properties.

Fluids with competing short-range attractions and long-range repulsions mimic dispersions of charge-stabilized colloids that can display equilibrium structures with intermediate-range order (IRO), including particle clusters. Using simulations and analytical theory, we demonstrate how to detect cluster formation in such systems from the static structure factor and elucidate links to macrophase separation in purely attractive reference fluids. We find that clusters emerge when the thermal correlation length encoded in the IRO peak of the structure factor exceeds the characteristic length scale of interparticle repulsions. We also identify qualitative differences between the dynamics of systems that form amorphous versus microcrystalline clusters.

This paper introduces a unifying theory for describing complex behavior for porous materials. The key ingredients are the stored energy in solid-fluid interaction as well as the solid-solid and fluid-fluid interactions. A finite element formulation is employed which naturally accounts for the pore-pore network effects and is easily applicable to most pore geometries such as cellular solids and foams. The interactions, built in at the finite element level, give rise to the mechanical response of the macroscopic material unit. Through numerical studies, we show that there is strong coupling between fluid and solid that induces complex mechanical response, i.e., hysteresis and anisotropy. It is demonstrated that hysteresis arises directly from the fluid-solid coupling. We term this type of hysteresis emergent hysteresis.

The enhancement of tunneling probability in the nearly integrable system is closely examined, focusing on tunneling splittings plotted as a function of the inverse of the Planck's constant. On the basis of the analysis using the absorber which efficiently suppresses the coupling, creating spikes in the plot, we found that the splitting curve should be viewed as the staircase-shaped skeleton accompanied by spikes. We further introduce renormalized integrable Hamiltonians and explore the origin of such a staircase structure by investigating the nature of eigenfunctions closely. It is found that the origin of the staircase structure could trace back to the anomalous structure in tunneling tail which manifests itself in the representation using renormalized action bases. This also explains the reason why the staircase does not appear in the completely integrable system.

We present a spatiotemporal analysis of a statistically stationary rotating-turbulence experiment, aiming to extract a signature of inertial waves and to determine the scales and frequencies at which they can be detected. The analysis uses two-point spatial correlations of the temporal Fourier transform of velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale. We show that this space-time-dependent anisotropy is well described by the dispersion relation of linear inertial waves at large scale, while smaller scales are dominated by the sweeping of the waves by fluid motion at larger scales. This sweeping effect is mostly due to the low-frequency quasi-two-dimensional component of the turbulent flow, a prominent feature of our experiment that is not accounted for by wave-turbulence theory. These results question the relevance of this theory for rotating turbulence at the moderate Rossby numbers accessible in laboratory experiments, which are relevant to most geophysical and astrophysical flows.

The lattice Boltzmann method (LBM) has been widely used to simulate microgaseous flows in recent years. However, it is still a challenging task for LBM to model that kind of microscale flow involving complex geometries, owing to the use of uniform Cartesian lattices in space. In this work, a boundary condition for microflows in the slip regime is developed for LBM in which the shape of a solid wall is well considered. The proposed treatment is a combination of the Maxwellian diffuse reflection scheme and the simple bounce-back method. A portion of each part is determined by the relative position between the boundary node and curved walls, which is the key point that distinguishes this method from some previous schemes where the smooth curved surface was assumed to be zigzag lines. The present curved boundary condition is implemented with the multiple-relaxation-times model and verified for several established cases, including the plane microchannel flow (aligned and inclined), microcylindrical Couette flow, and the flow over an inclined microscale airfoil. The numerical results agree well with those predicted by the direct simulation Monte Carlo method.

For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the amplitude, phase, and inversion of the coupled lasers. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand nonlocal coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions. The existence is linked to a regime of multistability between the synchronous steady state and asynchronous periodic solutions. We show that amplitude-phase coupling, a concept common in different fields, is necessary for the formation of the chimera states.

Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that incorporates power-law dependencies on time and distance from a special point, such as apex of the cone, which are characterized by a single exponent $\eta$. The same exponent is used to describe the number of spatial conformations of long ideal polymer attached to the special point of a repulsive surface of the same geometry and can be used in calculation of entropic forces between such polymers and surfaces. We use the solution of diffusion equation near such surfaces to find the numerical values of $\eta$, as well as to provide some insight into the behavior of ideal polymers near such surfaces.

An analysis of the efficiency and coefficient of performance (COP) for general heat engines and refrigerators with nonisothermal processes is conducted under the trade-off criterion. The specific heat of the working medium has significant impacts on the optimal configurations of heat devices. For cycles with constant specific heat, the bounds of the efficiency and COP are found to be the same as those obtained through the endoreversible Carnot ones. However, they are independent of the cycle time durations. For cycles with nonconstant specific heat, whose dimensionless contact time approaches infinity, the general alternative upper and lower bounds of the efficiency and COP under the trade-off criteria have been proposed under the asymmetric limits. Furthermore, when the dimensionless contact time approaches zero, the endoreversible Carnot model is recovered. In addition, the efficiency and COP bounds of different kinds of actual heat engines and refrigerators have also been analyzed. This paper may provide practical insight for designing and operating actual heat engines and refrigerators.

While monolayer area fraction versus time $\left(A_n\text{−}t\right)$ curves obtained from surface pressure–area $\left(\pi \text{−}A\right)$ isotherms for desorption-dominated (DD) processes in Langmuir monolayers of fatty acids represent continuous loss, those from Brewster angle microscopy (BAM) also show a two-dimensional (2D) coalescence. For nucleation-dominated (ND) processes both techniques suggest competing processes, with BAM showing 2D coalescence alongside multilayer formation. $\pi$ enhances both DD and ND processes with a lower cutoff for ND processes, while temperature has a lower cutoff for DD but negligible effect on ND processes. Hydrocarbon chain length has the strongest effect, causing a crossover from DD to ND dynamics. Imaging ellipsometry of horizontally transferred films onto Si(100) shows Stranski-Krastanov-like growth for ND process in an arachidic acid monolayer resulting in successive stages of monolayer, trilayer, and multilayer islands, ridges from lateral island coalescence, and shallow wavelike structures from ridge coalescence on the film surface. These studies show that lipophilic attraction between hydrocarbon chains is the driving force at all stages of long-term monolayer dynamics.

In the last few decades many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological, and historical processes. In the present paper we suggest a model of the Nazi Germany invasion of Poland, France, and the USSR based on kinetic theory. We simulate this process with the Cauchy boundary problem for two-element kinetic equations. The solution of the problem is given in the form of a traveling wave. The propagation velocity of a front line depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the front-line velocities agree with the historical data.

In this paper we present a unified shell model for stably stratified and convective turbulence. Numerical simulation of this model for stably stratified flow shows Bolgiano-Obukhbov scaling in which the kinetic energy spectrum varies as $k^{-11/5}$. The shell model of convective turbulence yields Kolmogorov's spectrum. These results are consistent with the energy flux and energy feed due to buoyancy, and are in good agreement with direct numerical simulations of Kumar et al. [Phys. Rev. E 90, 023016 (2014)].

We investigate experimentally the sweeping of a nonwetting fluid by a wetting one in a quasi-two-dimensional porous medium consisting of random obstacles. We focus primarily on the resulting phase distributions and the residual nonwetting phase saturation as a function of the normalized wetting fluid flow rate—the capillary number Ca—at steady state. The wetting liquid is then flowing in the medium partially saturated by immobile nonwetting liquid blobs. The decrease of the nonwetting saturation is an irreversible process that depends strongly on flow history and more specifically on the highest value of Ca reached in the past. At lower Ca values, when capillary forces are dominant, the residual steady state saturation depends significantly on the initial phase configuration. However, at higher Ca, the saturation becomes independent of the history and thus follows a master curve that converges to an asymptotic residual value. Blob sizes range over four orders of magnitude in our experimental domain, following a probability distribution function $P$ that scales with the blob size $s$ as $P\left(s\right)\propto s^{-2}$ for blob sizes larger than the typical pore size. It also exhibits a maximum size cutoff $s_{\max }$, that decreases as $s_{\max }\propto {\text{Ca}}^{-1}$. To determine the flow properties, we have measured the pressure drop $\left(B\right)$ versus the flow rate (Ca). In the ranges of low and high Ca values, the relationship between Ca and $B$ is found to be linear, following Darcy's law $\left(B\propto \text{Ca}\right)$. In the intermediate regime, the progressive mobilization of blobs leads to a nonlinear dependence $B\propto {\text{Ca}}^{0.65}$, due to an increase of the available flow paths.

In this paper we describe the physical processes that lead to the generation of giant electromagnetic pulses (GEMPs) at powerful laser facilities. Our study is based on experimental measurements of both the charging of a solid target irradiated by an ultra-short, ultra-intense laser and the detection of the electromagnetic emission in the GHz domain. An unambiguous correlation between the neutralization current in the target holder and the electromagnetic emission shows that the source of the GEMP is the remaining positive charge inside the target after the escape of fast electrons accelerated by the ultra-intense laser. A simple model for calculating this charge in the thick target case is presented. From this model and knowing the geometry of the target holder, it becomes possible to estimate the intensity and the dominant frequencies of the GEMP at any facility.

A simple setup for the generation of ultra-intense quasistatic magnetic fields, based on the generation of electron currents with a predefined geometry in a curved snail (or ‘escargot’) target, is proposed and analyzed. Particle-in-cell simulations and qualitative estimates show that gigagauss scale magnetic fields may be obtained with existent laser facilities. The described mechanism of the strong magnetic field generation may be useful in a wide range of applications, from laboratory astrophysics to magnetized inertial confinement fusion schemes.

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square ${\left[0,1\right]}^2.$ The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths $a$ and $b=1/a$, and the radius $r$ used to connect the nodes. When $a=1$ we recover the RGG, and when $a\to \infty$ the very elongated rectangle generated resembles a one-dimensional RGG. We obtain here analytical expressions for the average degree, degree distribution, connectivity, average path length, and clustering coefficient for RRG. These results provide evidence that show that most of these properties depend on the connection radius and the side length of the rectangle, usually in a monotonic way. The clustering coefficient, however, increases when the square is transformed into a slightly elongated rectangle, and after this maximum it decays with the increase of the elongation of the rectangle. We support all our findings by computational simulations that show the goodness of the theoretical models proposed for RRGs.

The quantum ergodic conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a $\delta$ function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple observables, in agreement with Shnirelman's theorem, but this putative Wigner function violates several important requirements. Consequently, we transfer the conjecture to the Fourier transform of the Wigner function, that is, the chord function. We show that all the relevant consequences of the usual conjecture require only information contained within a small (Planck) volume around the origin of the phase space of chords: translations in ordinary phase space. Loci of complete orthogonality between a given eigenstate and its nearby translation are quite elusive for the Wigner function, but our local conjecture stipulates that their pattern should be universal for ergodic eigenstates of the same Hamiltonian lying within a classically narrow energy range. Our findings are supported by numerical evidence in a Hamiltonian exhibiting soft chaos. Heavily scarred eigenstates are remarkable counter-examples of the ergodic universal pattern.