We study the development of intricate, fully nonlinear immiscible interfacial patterns in the suction-driven radial Hele-Shaw problem. The complex-shaped, contracting fluid-fluid interface arises when an initially circular blob of more viscous fluid, surrounded by less viscous one, is drawn into an eccentric point sink. We present sophisticated numerical simulations, based on a diffuse interface model, that capture the most prominent interfacial features revealed by existing experimental studies of the problem. The response of the system to changes in the capillary number is investigated, accurately revealing the occurrence of finger competition phenomena, and correctly describing the velocity behavior of both inward- and outward-pointing fingers. For the large-capillary-number regime, a set of complex interfacial features (finger merging, shielding, and pinch-off) whose experimental realization is still not available, are predicted.

In this Rapid Communication we consider a front of transition between metastable and stable states in a conservative system. Due to the difference of energies between initial and finite states, such transition front can propagate only while radiating energy. A simulation of such a process in a one-dimensional nonlinear lattice shows an essential imbalance between the energy released in each act of transition, and the density of energy of oscillations behind the front. It means that the stationary front propagation must be accompanied by an essentially nonstationary radiative process. We reveal the origin of this phenomenon and show that the characteristics of the front propagation critically depend on boundary conditions. In the framework of a simple model of a bistable system we propose analytic evaluation of all important features of the transition process, such as front velocity, radiation frequency, and oscillation amplitude. All calculated values are in good agreement with numerical simulation data.

In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.

We study a one-dimensional discrete-time non-Markovian random walk with strong memory correlations subjected to pauses. Unlike the Scher-Montroll continuous-time random walk, which can be made Markovian by defining an operational time equal to the random-walk step number, the model we study keeps a record of the entire history of the walk. This new model is closely related to the one proposed recently by Kumar, Harbola, and Lindenberg [Phys. Rev. E 82, 021101 (2010)], with the difference that in our model the stochastic dynamics does not stop even in the extreme limit of subdiffusion. Surprisingly, this small difference leads to large consequences. The main results we report here are exact results showing ultraslow diffusion and a stationary diffusion regime (i.e., localization). Specifically, the equations of motion are solved analytically for the first two moments, allowing the determination of the Hurst exponent. Several anomalous diffusion regimes are apparent, ranging from superdiffusion to subdiffusion, as well as ultraslow and stationary regimes. We present the complete phase diffusion diagram, along with a study of the persistence and the statistics in the regions of interest.

The Sparre-Andersen theorem is a remarkable result in one-dimensional random walk theory concerning the universality of the ubiquitous first-passage-time distribution. It states that the probability distribution ${\rho }_n$ of the number of steps needed for a walker starting at the origin to land on the positive semiaxes does not depend on the details of the distribution for the jumps of the walker, provided this distribution is symmetric and continuous, where in particular ${\rho }_n\sim n^{-3/2}$ for large number of steps $n$. On the other hand, there are many physical situations in which the time spent by the walker in doing one step depends on the length of the step and the interest concentrates on the time needed for a return, not on the number of steps. Here we modify the Sparre-Andersen proof to deal with such cases, in rather general situations in which the time variable correlates with the step variable. As an example we present a natural process in 2D that shows that deviations from normal scaling are present for the first-passage-time distribution on a semiplane.

For a broad class of planar Markov processes, viz. Lévy processes satisfying certain conditions (valid, e.g., in the case of Brownian motion and Lévy flights), we establish an exact, universal formula describing the shape of the convex hull of sample paths. We show indeed that the average number of edges joining paths' points separated by a time lapse $\Delta \tau \in \left[\Delta {\tau }_1,\Delta {\tau }_2\right]$ is equal to $2\text{ln}\left(\Delta {\tau }_2/\Delta {\tau }_1\right)$, regardless of the specific distribution of the process's increments and regardless of its total duration $T$. The formula also exhibits invariance when the time scale is multiplied by any constant. Apart from its theoretical importance, our result provides insights regarding the shape of two-dimensional objects (e.g., polymer chains) modeled by the sample paths of stochastic processes generally more complex than Brownian motion. In particular, for a total time (or parameter) duration $T$, the average number of edges on the convex hull (“cut off” to discard edges joining points separated by a time lapse shorter than some $\Delta \tau <T$) will be given by $2\text{ln}\left(\frac{T}{\Delta \tau }\right)$. Thus it will only grow logarithmically, rather than at some higher pace.

The ground state of twist-bend nematic liquid crystals is a heliconical molecular arrangement in which the nematic director precesses uniformly about an axis, making a fixed angle with it. Both precession senses are allowed in the ground state of these phases. When one of the two helicities is prescribed, a single helical nematic phase emerges. A quadratic elastic theory is proposed here for each of these phases which features the same elastic constants as the classical theory of the nematic phase, requiring all of them to be positive. To describe the helix axis, it introduces an extra director field which becomes redundant for ordinary nematics. Putting together helical nematics with opposite helicities, we reconstruct a twist-bend nematic, for which the quadratic elastic energies of the two helical variants are combined in a nonconvex energy. States with minimal energy and opposite helicities may come in contact along an interface belonging to a special family of developable surfaces, including a peculiar cone, which can be constructed through a general method.

We prepared nanocomposites of a nematic liquid crystal and nanofibers of a conducting polymer (polyaniline). All the nanocomposites exhibit a discontinuous surface anchoring transition from planar to homeotropic in the nematic phase on a perfluoropolymer coated surface with a thermal hysteresis ($\approx$$5.3{}^{\circ }$C). We observe a relatively large bistable conductivity and demonstrate a light driven switching of conductivity and dielectric constant in dye doped nanocomposites in the thermal hysteresis (bistable) region. The experimental results have been explained based on the reorientation of the nanofibers driven by the anchoring transition of the nematic liquid crystal. We show a significant enhancement of the bistable temperature range ($\approx$$13{}^{\circ }$C) by an appropriate choice of compound in the binary system.

We present experimental observations on the electrically forced release of spiral waves pinned to unexcitable circular obstacles in the Belosov-Zhabotinsky reaction. When the applied electric current density reaches the necessary current density $J_{\mathrm{unpin}}$, the spiral tip is detached and subsequently drifts away from the obstacle. $J_{\mathrm{unpin}}$ is found to increase with the obstacle diameter $d$. The growth rate Δ$J_{\mathrm{unpin}}$/Δ$d$ is much higher for obstacles larger than the free spiral core compared to that for smaller obstacles. The experimental findings are confirmed by numerical simulations using the Oregonator model. The results imply that it is more difficult to release spiral waves pinned to larger obstacles, especially when the obstacle size exceeds that of the free spiral core.

The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different continuous-wave and nonstationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von Kármán swirling flow between two counterrotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field and a case with self-sustained magnetic fields. Evidence of long-term memory and $1/f$ noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von Kármán flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large-scale magnetic field.

Three-dimensional (3D) porous structures which are usually discretized by voxels can also be discretized by the level-set method (LSM) and flow, reactive transport, and structure evolution can be modeled. The determination of the solid-liquid interface is detailed as well as the discretization of the governing equations. Comparisons between a one-dimensional analytical solution and LSM are conducted for validation. Deposition in 3D reconstructed media is studied under various flow and reaction conditions. The evolution of the structure is explored locally by means of the pore geometry and globally by means of the permeability and the porosity. The difference between the voxel method and LSM is discussed during the investigations.

We discuss the application of complex-plane Gauss-Laguerre quadrature (CGLQ) to efficiently evaluate two-dimensional Fourier integrals arising as the solution to electromagnetic fields radiated by elementary dipole antennas embedded within planar-layered media exhibiting arbitrary material parameters. More specifically, we apply CGLQ to the long-standing problem of rapidly and efficiently evaluating the semi-infinite length “tails” of the Fourier integral path while simultaneously and robustly guaranteeing absolute, exponential convergence of the field solution despite diversity in the doubly anisotropic layer parameters, source type (i.e., electric or equivalent magnetic dipole), source orientation, observed field type (magnetic or electric), (nonzero) frequency, and (nonzero) source-observer separation geometry. The proposed algorithm exhibits robustness despite unique challenges arising for the fast evaluation of such two-dimensional integrals. Herein we develop the mathematical treatment to rigorously evaluate the tail integrals using CGLQ, as well as discuss and address the specific issues posed to the CGLQ method when anisotropic, layered media are present. To empirically demonstrate the CGLQ algorithm's computational efficiency, versatility, and accuracy, we perform a convergence analysis along with two case studies related to modeling of electromagnetic resistivity tools employed in geophysical prospection of layered, anisotropic Earth media and validating the ability of isoimpedance substrates to enhance the radiation performance of planar antennas placed in close proximity to metallic ground planes.

The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the coevolving charged particles. The equilibrium statistical mechanics solution of the model is worked out analytically, both in the canonical and the microcanonical ensembles. The competition between the two modes is shown to yield ensemble inequivalence, at variance with the standard scenario where just one wave is allowed to develop. As a consequence, both temperature jumps and negative specific heat can show up in the microcanonical ensemble. The relevance of these findings for both plasma physics and free electron laser applications is discussed.

We studied the efficiency of two different schemes for a magnetically driven quantum heat engine, by considering as the “working substance” a single nonrelativistic particle trapped in a cylindrical potential well, in the presence of an external magnetic field. The first scheme is a cycle, composed of two adiabatic and two isoenergetic reversible trajectories in configuration space. The trajectories are driven by a quasistatic modulation of the external magnetic-field intensity. The second scheme is a variant of the former, where the isoenergetic trajectories are replaced by isothermal ones, along which the system is in contact with macroscopic thermostats. This second scheme constitutes a quantum analog of the classical Carnot cycle.

We provide a general formula of quantum transfer that includes the nonadiabatic effect under periodic environmental modulation by using full counting statistics in Hilbert-Schmidt space. Applying the formula to an anharmonic junction model that interacts with two bosonic environments within the Markovian approximation, we find that the quantum transfer is divided into the adiabatic (dynamical and geometrical phases) and nonadiabatic contributions. This extension shows the dependence of quantum transfer on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequency of spectral density. We show that the nonadiabatic contribution represents the reminiscent effect of past modulation including the transition from the initial condition of the anharmonic junction to a steady state determined by the very beginning of the modulation. This enables us to tune the frequency range of modulation, whereby we can obtain the quantum flux corresponding to the geometrical phase by setting the initial condition of the anharmonic junction.

This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of two to three layers of densely packed spheres. The Shields function is 0.065 which is just above the sediment entrainment threshold to give a bed-load regime. The applied methodology is a combination of three technologies, i.e., the direct numerical simulation of turbulent flow; the combined finite-discrete element modeling of the deformation, movement, and collision of the particles; and the immersed boundary method for the fluid-solid interaction. It is shown that the presence of entrained particles significantly modifies the flow profiles of velocity, turbulent intensities, and shear stresses in the vicinity of a rough bed. The quasi-streamwise-aligned streaky structures are not observed in the near-wall region and the particles scatter on the rough bed owing to their large size. However, in the outer flow region, the turbulent coherent structures recover due to the weakening rough-bed effects and particle interferences. First- and second-order statistical features of particle translational and angular velocities, together with sediment concentration and volumetric flux density profiles, are presented. Several key parameters of the particle saltation trajectory are calculated and agree closely with published experimental data. Time histories of the hydrodynamic forces exerted upon a typical saltating particle, together with those of the particle's coordinates and velocities, are presented. A strong correlation is shown between the abruptly decreasing streamwise velocity and increasing vertical velocity at collision which indicates that the continuous saltation of large-grain-size particles is controlled by collision parameters such as particle incident angle, local bed packing arrangement, and particle density, etc.

The convective stability thresholds and nonlinear spatiotemporal evolution of convective rolls in a plane horizontal layer subject to steady gravity and high-frequency transversal vibration are numerically investigated considering a laterally periodic convective cell with rigid, impermeable horizontal boundaries. Simulations are performed for parameters adapted to laboratory experiments with an ethanol-water mixture with negative Soret coupling between temperature and concentration gradients. The characteristics of the wave and steady patterns are investigated depending on heat and vibration intensities. The weakly nonlinear traveling wave and modulated traveling wave are found as stable solutions within certain domains of parameters. Temporal Fourier decomposition is used together with other diagnostic tools to analyze the complex bifurcation and spatiotemporal properties that are caused by the interplay of the high-frequency vibrations, Soret induced gradients, and mixing of the fluid.