We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5–119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder.

Emission of energetic protons (maximum energy ∼18 MeV) from the interaction of relativistic intensity laser with a cone-wire target is experimentally measured and numerically simulated with hybrid particle-in-cell code, lsp [D. R. Welch et al., Phys. Plasmas 13, 063105 (2006)]. The protons originate from the wire attached to the cone after the OMEGA EP laser (670 J, 10 ps, 5 × 10${}^{18}$ W/cm${}^2$) deposits its energy inside the cone. These protons are accelerated from the contaminant layer on the wire surface, and are measured in the radial direction, i.e., in a direction transverse to the wire length. Simulations show that the radial electric field, responsible for the proton acceleration, is excited by three factors, viz., (i) transverse momentum of the relativistic fast electrons beam entering into the wire, (ii) scattering of electrons inside the wire, and (iii) refluxing of escaped electrons by “fountain effect” at the end of the wire. The underlying physics of radial electric field and acceleration of protons is discussed.

We present a method for finding the condensate distribution at the nucleation of superconductivity for arbitrary polygons. The method is based on conformal mapping of the analytical solution of the linearized Ginzburg-Landau problem for the disk and uses the superconducting gauge for the magnetic potential proposed earlier. As a demonstration of the method's accuracy, we calculate the distribution of the order parameter in regular polygons and compare the obtained solutions with available numerical results. As an example of an irregular polygon, we consider a deformed hexagon and prove that its calculation with the proposed method requires the same level of computational efforts as the regular ones. Finally, we extend the method over samples with arbitrary smooth boundaries. With this, we have made simulations for an experimental sample. They have shown perfect agreement with experimental data.

The simple nematic mesogen 5CB was doped with milled BaTiO${}_3$ nanoparticles and was investigated with x-ray scattering. Doping with BaTiO${}_3$ nanoparticles of 9 nm in diameter led to the formation of crystallites. These crystallites precipitated and formed a waxlike nanodispersion of 5CB and nanoparticles, which led to intense x-ray scattering signals characteristic of a multilayer structure. Surprisingly, the multilayers possess unusual interlayer spacing, which cannot be explained by simple smectic order of the calamitic molecules.

The Feshbach projection formalism is applied to consider quantum transmission through a tight-binding wire subject to a time-periodic potential. The wire is coupled with two leads via the coupling constant $v_C$. The periodicity of the potential implies an additional temporal dimension that reduces the problem to stationary transmission through an effectively two-dimensional lattice system. The non-Hermitian effective Hamiltonian is formulated. Thist allows us to trace the redistribution of resonance positions and resonance widths with the growth of $v_C$ from the weak-coupling to the strong-coupling regime.

Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically aligned vortices at strong rotation. For a sample with an aspect ratio $\Gamma =D/L=1$ ($D$ is the sample diameter and $L$ is its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for $\Gamma =1/2$, Weiss and Ahlers [J. Fluid Mech. 688, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for $\Gamma =1/2$ and parameters that allow direct comparison with experiment that the spatial organization of the vertically aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and nontrivial difference with the $\Gamma =1$ sample, where the vertically aligned vortices are distributed randomly.

Generating aerosol droplets via the atomization of thin aqueous films with high frequency surface acoustic waves (SAWs) offers several advantages over existing nebulization methods, particularly for pulmonary drug delivery, offering droplet sizes in the 1–5-$\mu$m range ideal for effective pulmonary therapy. Nevertheless, the physics underlying SAW atomization is not well understood, especially in the context of thin liquid film formation and spreading and how this affects the aerosol production. Here, we demonstrate that the film geometry, governed primarily by the applied power and frequency of the SAW, indeed plays a crucial role in the atomization process and, in particular, the size of the atomized droplets. In contrast to the continuous spreading of low surface energy liquids atop similar platforms, high surface energy liquids such as water, in the present case, are found to undergo transient spreading due to the SAW to form a quasisteady film whose height is determined by self-selection of the energy minimum state associated with the acoustic resonance in the film and whose length arises from a competition between acoustic streaming and capillary effects. This is elucidated from a fundamental model for the thin film spreading behavior under SAW excitation, from which we show good agreement between the experimentally measured and theoretically predicted droplet dimension, both of which consistently indicate a linear relationship between the droplet diameter and the mechanical power coupled into the liquid by the SAW (the latter captured by an acoustic Weber number to the two thirds power, and the reciprocal of the SAW frequency).

The Brazil nut effect is the phenomenon in which a large intruder particle immersed in a vertically shaken bed of smaller particles rises to the top, even when it is much denser. The usual practice while describing these experiments has been to use the dimensionless acceleration $\Gamma =a{\omega }^2/g$, where $a$ and $\omega$ are, respectively, the amplitude and the angular frequency of vibration and $g$ is the acceleration due to gravity. Considering a vibrated quasi-two-dimensional bed of mustard seeds, we show here that the peak-to-peak velocity of shaking $v=a\omega$, rather than $\Gamma$, is the relevant parameter in the regime where boundary-driven granular convection is the main driving mechanism. We find that the rise time $\tau$ of an intruder is described by the scaling law $\tau \sim {(v-v_c)}^{-\alpha }$, where $v_c$ is identified as the critical vibration velocity for the onset of convective motion of the mustard seeds. This scaling form holds over a wide range of $(a,\omega )$, diameter, and density of the intruder.

We analyze the finite-temperature phase diagram of ultrathin magnetic films by introducing a mean-field theory, valid in the low-anisotropy regime, i.e., close to the spin reorientation transition. The theoretical results are compared with Monte Carlo simulations carried out on a microscopic Heisenberg model. Connections between the finite-temperature behavior and the ground-state properties of the system are established. Several properties of the stripe pattern, such as the presence of canted states, the stripe width variation phenomenon, and the associated magnetization profiles, are also analyzed.

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to subdiffusion ($D=0$). A question arises whether such a transition happens in higher dimensions. Numerically $D$ can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a recent expectation that is based on a renormalization-group analysis, we deduce that $D$ is finite, suggest an “effective-range-hopping” procedure to evaluate it, and contrast the results with the linear estimate. The same approach is useful in the analysis of networks that are described by quasi-one-dimensional sparse banded matrices.

The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. A modern duality analysis fashion with real-space renormalization is found to be available for estimating the location of the critical points with a wide range of the randomness parameter. As a simple test bed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which is known as a skillful technique to protect the quantum state.

The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a two-dimensional model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied the amplitude and the correlation length. The chain model is based on a bead-spring approach, enriched with a global Lennard-Jones potential and angular interactions. We show that spatial correlations in the noise inhibit the chain geometry dynamics, enhancing the preservation of the polymer shape. This is supported by the analysis of correlation functions of both the module length and angles between neighboring modules, which have been measured for the noise amplitude ranging over three orders of magnitude. Moreover, we have observed the correlation length dependent bead motion synchronization and the spontaneous polymer unfolding, resulting from an interplay between chain potentials and the spatially structured noise.

We study crystallization of chiral crystals from achiral molecules using a master equation based on a simple reaction model. Although there is no chiral symmetry breaking in the reaction model, random fluctuations drive the system to a homochiral state. The time necessary for the appearance of the homochiral state is proportional to the total number of molecules in the system. This behavior is described by a diffusion equation in a size space with a position-dependent diffusion coefficient. We also study the effect of chiral impurities, which affect the crystal growth. Depending on the type of impurities, the chiral symmetry breaking occurs either deterministically or with the help of random fluctuations.

Microorganisms like bacteria can sense concentrations of chemoattractants in their medium very accurately. They achieve this through interaction between the receptors on their cell surfaces and chemoattractant molecules (like sugar). Physical processes like diffusion set some limits on the accuracy of detection, which was discussed by Berg and Purcell in the late seventies. We re-examine their work in order to assess what insight it may offer for making efficient, practical biosensors. We model the functioning of a typical biosensor as a reaction-diffusion process in a confined geometry. Using available data first we characterize the system by estimating the kinetic constants for the binding and unbinding reactions between the chemoattractants and the receptors. Then we compute the binding flux for this system, which Berg and Purcell had discussed. Unlike in microorganisms where the interval between successive measurements determines the efficiency of the nutrient searching process, it turns out that biosensors depend on long time properties like signal saturation time, which we study in detail. We also develop a mean field description of the kinetics of the system.

We investigate the majority-vote model with two states ($-1,+1$) and a noise parameter $q$ on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter $q$. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction $p$ of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio $\gamma /\nu$, $\beta /\nu$, and $1/\nu$ for several values of rewiring probability $p$. The critical noise $q_c$ and $U^{*}$ were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.

We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by Lévy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary probability distribution, the occupation probability, the mean first passage time, and the average time to reach a node on the network. We found that the long-range navigation using the Lévy random walk strategy, compared with the normal random walk strategy, is more efficient at reducing the time to cover the network. The dynamical effect of using the Lévy walk strategy is to transform a large-world network into a small world. Our exact results provide a general framework that connects two important fields: Lévy navigation strategies and dynamics on complex networks.

Analytical solutions for the shape of both hanging and sitting droplets under the effects of gravity and surface tension are presented. The modeling also includes the action of molecular forces arising between the liquid and the substrate, which are responsible for the formation of a stable nanometric film in the region close to the droplet contact line. The shape of the droplet is completely described by an analytical solution that also accounts for the pancake-shaped droplets as a limiting case. We find expressions that relate microscopic and nanoscopic aspects, such as the strengths of the molecular forces and the thickness of the nanometric film, to macroscopic quantities, such as the cross-sectional area and the width of the droplet. We study the effect of gravity on the contact angle and find that for small droplets the contact angle follows a power law with the droplet's size. For sitting droplets we find that the there is an upper limit for the value of the gravity.

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from $d=2$ to the upper critical dimension $d=6$. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in the full ensemble of loops with negative weight, i.e., nontrivial (system spanning) loops as well as topologically trivial (“small”) loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize—using this extensive and exhaustive numerical study—the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations, we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.