The potential distributions surrounding elongated insulating dust grains being charged by supersonic plasma flows are studied using the particle-in-cell method. The plasma flow introduces an asymmetry in the dust charging. This leads to a complex surface charge distribution on the dust, and to ion focusing in the wake region. We demonstrate that the charge and potential distributions on the dust surface and the wake behind the dust depend on the rod length and dust inclination angle with respect to the flow. The role of the surface charge distribution in the interactions between insulating rods in a plasma is discussed. Our simulations are carried out in two spatial dimensions, treating ions and electrons as individual particles.

The influence of quantum phase transitions on the evolution of excited levels in the critical parameter region is discussed. The analysis is performed for one- and two-dimensional systems with first- and second-order ground-state transitions. Examples include the cusp and nuclear collective Hamiltonians. Applications in systems of higher dimensions are possible.

Selected pseudo-random-number generators are applied to a Monte Carlo study of the two-dimensional square-lattice site percolation model. A generator suitable for high precision calculations is identified from an application specific test of randomness. After extended computation and analysis, an ostensibly reliable value of $p_c=0.59274598\left(4\right)$ is obtained for the percolation threshold.

In this work, the dynamic behavior of the interfaces in both the standard and random driven lattice gas models (DLG and RDLG, respectively) is investigated via numerical Monte Carlo simulations in two dimensions. These models consider a lattice gas of density $\rho =1∕2$ with nearest-neighbor attractive interactions between particles under the influence of an external driven field applied along one fixed direction in the case of the DLG model, and a randomly varying direction in the case of the RDLG model. The systems are also in contact with a reservoir at temperature $T$. Those systems undergo a second-order nonequilibrium phase transition between an ordered state characterized by high-density strips crossing the sample along the driving field, and a quasilattice gas disordered state. For $T\lesssim T_c$, the average interface width of the strips $\left(W\right)$ was measured as a function of the lattice size and the anisotropic shape factor. It was found that the saturation value $W_{\mathit{sat}}^2$ only depends on the lattice size parallel to the external field axis $L_y$ and exhibits two distinct regimes: $W_{\mathit{sat}}^2\propto \ln L_y$ for low temperatures, that crosses over to $W_{\mathit{sat}}^2\propto L_y^{2{\alpha }_I}$ near the critical zone, ${\alpha }_I=1∕2$ being the roughness exponent of the interface. By using the relationship ${\alpha }_I=1∕(1+{\Delta }_I)$, the anisotropic exponent for the interface of the DLG model was estimated, giving ${\Delta }_I\simeq 1$, in agreement with the computed value for anisotropic bulk exponent ${\Delta }_B$ in a recently proposed theoretical approach. At the crossover region between both regimes, we observed indications of bulk criticality. The time evolution of $W$ at $T_c$ was also monitored and shows two growing stages: first one observes that $W\propto \ln t$ for several decades, and in the following times one has $W\propto t^{{\beta }_I}$, where ${\beta }_I$ is the dynamic exponent of the interface width. By using this value we estimated the dynamic critical exponent of the correlation length in the perpendicular direction to the external field, giving $z_{\perp }^I\approx 4$, which is consistent with the dynamic exponent of the bulk critical transition $z_{\perp }^B$ in both theoretical approaches developed for the standard model. A similar scenario was also observed in the RDLG model, suggesting that both models may belong to the same universality class.

Recent advances in the photonics and optics industries have produced great demand for ever more sophisticated optical devices, such as photonic crystals. However, photonic crystals are notoriously difficult to manufacture. Increasingly, therefore, researchers have turned towards naturally occurring photonic structures for inspiration and a wide variety of elaborate techniques have been attempted to copy and harness biological processes to manufacture artificial photonic structures. Here, we describe a simple, direct process for producing an artificial photonic device by using a naturally occurring structure from the wings of the butterfly Papilio blumei as a template and low-temperature atomic layer deposition of $\mathrm{Ti}{\mathrm{O}}_2$ to create a faithful cast of the structure. The optical properties of the organic-inorganic diffraction structures produced are assessed by normal-incidence specular reflectance and found to be well described by multilayer computation method using a two-dimensional photonic crystal model. Depending on the structural integrity of the initially sealed scale, it was found possible not only to replicate the outer but also the inner and more complex surfaces of the structure, each resulting in distinct multicolor optical behavior as revealed by experimental and theoretical data. In this paper, we also explore tailoring the process to design composite skeleton architectures with desired optical properties and integrated multifunctional (mechanical, thermal, optical, fluidic) properties.

We study a microscopic model for financial markets on complex networks, motivated by the dynamics of agents and their structure of interaction. The model consists of interacting agents (spins) with local ferromagnetic coupling and global antiferromagnetic coupling. In order to incorporate more realistic situations, we also introduce an external field which changes in time. From numerical simulations, we find that the model shows two-phase phenomena. When the local ferromagnetic interaction is balanced with the global antiferromagnetic interaction, the resulting return distribution satisfies a power law having a single peak at zero values of return, which corresponds to the market equilibrium phase. On the other hand, if local ferromagnetic interaction is dominant, then the return distribution becomes double peaked at nonzero values of return, which characterizes the out-of-equilibrium phase. On random networks, the crossover between two phases comes from the competition between two different interactions. However, on scale-free networks, not only the competition between the different interactions but also the heterogeneity of underlying topology causes the two-phase phenomena. Possible relationships between the critical phenomena of spin system and the two-phase phenomena are discussed.

The liquid cone-jet mode can be produced upon stimulation by a coflowing gas sheath. Most applications deal with the jet breakup, leading to either of two droplet generation regimes: Jetting and dripping. The cone-jet flow pattern is explored by direct axisymmetric volume of fluid (VOF) numerical simulation; its evolution is studied as the liquid flow rate is increased around the jetting-dripping transition. As observed in other focused flows such as electrospraying cones upon steady thread emission, the flow displays a strong recirculating pattern within the conical meniscus; it is shown to play a role on the stability of the system, being a precursor to the onset of dripping. Close to the minimum liquid flow rate for steady jetting, the recirculation cell penetrates into the feed tube. Both the jet diameter and the size of the cell are accurately estimated by a simple theoretical model. In addition, the transition from jetting to dripping is numerically analyzed in detail in some illustrative cases, and compared, to good agreement, with a set of experiments.

We have computed the dispersion curves of plate-mode waves propagating in periodic composite structures composed of isotropic aluminum cylinders embedded in an isotropic nickel background. The phononic crystal has a square symmetry and the calculation is based on the plane-wave expansion method. Along $\Gamma X$ or $\Gamma M$ directions, shear-horizontal modes do not couple to the Lamb wave modes which are polarized in the sagittal plane. Whatever the direction of propagation in between $\Gamma X$ and $\Gamma M$, shear-horizontal modes convert to Lamb waves and couple with the flexural and dilatational modes. This phenomenon is demonstrated both through the mode splitting in the lower-order symmetric band structure and through the calculation of all three components of the particle displacements. The phononic case is different from the pure isotropic plate case where shear-horizontal waves decouple from Lamb waves whatever the direction of propagation.

We analyze the intermittent Brownian dynamics (a succession of adsorption and bulk relocation steps) of a test particle over a single strand. We propose an analytic expression of the relocation time distribution at all times. We show that this distribution has a nontrivial heavily tailed statistics at long time with a diverging average relocation time. In order to experimentally probe this first passage statistics, we follow the intermittent Brownian dynamics of water molecules over long and stiff imogolite mineral strands, using a field cycling NMR dispersion technique. Our analytic derivation is found to be in good agreement with experimental data on a large domain of observation. Implications for the efficiency of a search strategy on a single filament are then discussed and the importance of the confinement and/or the finite size effect is emphasized.

Capillary forces have been measured by atomic force microscopy in the plate-sphere setup between gold, borosilicate glass, GeSbTe, titanium, and UV-irradiated amorphous titanium-dioxide surfaces. The force measurements were performed as a function contact time and surface roughness in the range $0.2–15\mathrm{nm}$ rms and relative humidity ranging between 2% and 40%. It is found that even for the lowest attainable relative humidity $(\sim 2\%\pm 1\%)$ very large capillary forces are still present. The latter suggests the persistence of a nanometers-thick adsorbed water layer that acts as a capillary bridge between contacting surfaces. Moreover, we found a significantly different scaling behavior of the force with rms roughness for materials with different hydrophilicity as compared to gold-gold surfaces.

A simple model for competition-induced speciation is presented and analyzed. Logistic growth with nonlocal interaction is studied on regular and random networks, and the large scale structure of the emerging genomic frequencies is examined. The neutrality assumption is violated if the network is random and the competition is nonlocal. Instead, “hubs” in the sequence space are suppressed by the competition more than nodes of a lower degree. Thus speciation is unavoidable for large-scale free networks. The emerging genetic mixture depends strongly on the initial conditions. The frequency of hubs is much greater in a population that evolved from a single nucleation event than in a population that recovered from a catastrophe.

We analyze the dynamics of rotary biomotors within a simple nanoelectromechanical model, consisting of a stator part and a ring-shaped rotor having 12 proton-binding sites. This model is closely related to the membrane-embedded ${\mathrm{F}}_0$ motor of adenosine triphosphate (ATP) synthase, which converts the energy of the transmembrane electrochemical gradient of protons into mechanical motion of the rotor. It is shown that the Coulomb coupling between the negative charge of the empty rotor site and the positive stator charge, located near the periplasmic proton-conducting channel (proton source), plays a dominant role in the torque-generating process. When approaching the source outlet, the rotor site has a proton energy level higher than the energy level of the site, located near the cytoplasmic channel (proton drain). In the first stage of this torque-generating process, the energy of the electrochemical potential is converted into potential energy of the proton-binding sites on the rotor. Afterwards, the tangential component of the Coulomb force produces a mechanical torque. We demonstrate that, at low temperatures, the loaded motor works in the shuttling regime where the energy of the electrochemical potential is consumed without producing any unidirectional rotation. The motor switches to the torque-generating regime at high temperatures, when the Brownian ratchet mechanism turns on. In the presence of a significant external torque, created by ATP hydrolysis, the system operates as a proton pump, which translocates protons against the transmembrane potential gradient. Here we focus on the ${\mathrm{F}}_0$ motor, even though our analysis is applicable to the bacterial flagellar motor.

The primary Bjerknes force is responsible for the quick translational motion of radially oscillating bubbles in a sound field. The problem is classical in the case of small-amplitude oscillations, for which an analytical expression of the force can be easily obtained, and predicts attraction of sub-resonant bubbles by pressure antinodes. But for high-amplitude sound fields the bubbles undergo large-amplitude nonlinear oscillations, so that no analytical expression for the force is available in this case. The bubble dynamics is approximated on physical grounds, following the method of Hilgenfeldt et al. [J. Fluid Mech. 365, 171 (1998)], but carefully accounting for surface tension. The analytical expression of the maximum radius of the bubble is recovered, the time of maximum expansion is noticeably refined, and an estimation of the collapse time is found. An analytical expression for the time-varying bubble volume is deduced, and the Bjerknes force is obtained in closed form. The result is valid for any shape of the sound field, including purely standing or purely traveling waves, and is ready to use in a theoretical model of bubble cloud evolution. In addition, the well-known sign inversion of the Bjerknes force for large standing waves is recovered and the inversion threshold in the parameter space is obtained analytically. The results are in good agreement with numerical simulations and allow a quantitative assessment of the effects of physical parameters. It is found that either reduction of the surface tension or increase in the static pressure should produce a widening of the bubble-free region near high-amplitude pressure antinodes.

The design of perfect electromagnetic cloaks is usually based on the coordinate transformation method. However, for cloaks with arbitrary shapes, it is difficult to express analytically such coordinate transformation. Thus, we have to resort to numerical methods to design approximate cloaks. In this paper, we propose a numerical method of designing cloaks with arbitrary shapes. According to this method, spatial compressions are treated as homeomorphous mappings and described in numerical forms. The corresponding coordinate transformations are therefore expressed numerically. As an application of this method, we deduced the discrete constitutive parameters of a two-dimensional polygon cloak, and verified the results by numerical simulations. This method can be also used in cases with acoustic waves and matter waves.

DNA is a common extracellular matrix component of bacterial biofilms. We find that bacteria can spontaneously order in a matrix of aligned concentrated DNA, in which rod-shaped cells of Pseudomonas aeruginosa follow the orientation of extended DNA chains. The alignment of bacteria is ensured by elasticity and liquid crystalline properties of the DNA matrix. These findings show how behavior of planktonic bacteria may be modified in extracellular polymeric substances of biofilms and illustrate the potential of using complex fluids to manipulate embedded nanosized and microsized active particles.

The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents $\delta =0.16\left(2\right)$, $\beta =0.28\left(2\right)$, and $z=1.58$ are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that the PCPD falls in the same universality class as DP.

We present a study of a phase-transition-driven separation in microemulsions of nanosized lyotropic inverse micelles and thermotropic liquid crystal pentylcyanobiphenyl (5CB) with 5%, 8%, and 15% micelle concentration. Using deuteron nuclear magnetic resonance (DNMR) microimaging in combination with conventional microscopy as well as ac calorimetry, we demonstrate a phase separation scenario in which micelles are expelled from the nematic phase during the $\mathrm{I}\text{−}\mathrm{N}$ conversion. Due to a difference in density the micelle-rich isotropiclike phase spatially separates from the micelle-free nematic phase. A relatively sharp interface, formed between the two phases, can be controllably shifted by temperature-induced conversion between the phases. Once expelled, micelles do not remix into the nematic phase, whereas in the isotropic state their remixing takes place over several days. Temperature dependence of the linewidth of isotropic spectral component has been analyzed in terms of molecular reorientations mediated by translational displacements, assuming isotropically distributed directors of nanosized nematic domains. With our results, the existence of the proposed transparent nematic state cannot be completely ruled out. However, if present, the nematic order in such a phase must be extremely low.

In many biological systems, biological variability (i.e., systematic differences between the system components) can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In principle, the distribution of single-element properties should thus allow predicting features of such patterns. For a mathematical model of a paradigmatic and well-studied pattern formation process, spiral waves of cAMP signaling in colonies of the slime mold Dictyostelium discoideum, we explore this possibility and observe a pronounced anticorrelation between spiral waves and cell properties (namely, the firing rate) and particularly a clustering of spiral wave tips in regions devoid of spontaneously firing (pacemaker) cells. Furthermore, we observe local inhomogeneities in the distribution of spiral chiralities, again induced by the pacemaker distribution. We show that these findings can be explained by a simple geometrical model of spiral wave generation.

Sensory systems pass information about an animal’s environment to higher nervous system units through sequences of action potentials. When these action potentials have essentially equivalent wave forms, all information is contained in the interspike intervals (ISIs) of the spike sequence. How do neural circuits recognize and read these ISI sequences? We address this issue of temporal sequence learning by a neuronal system utilizing spike timing dependent plasticity (STDP). We present a general architecture of neural circuitry that can perform the task of ISI recognition. The essential ingredients of this neural circuit, which we refer to as “interspike interval recognition unit” (IRU) are (i) a spike selection unit, the function of which is to selectively distribute input spikes to downstream IRU circuitry; (ii) a time-delay unit that can be tuned by STDP; and (iii) a detection unit, which is the output of the IRU and a spike from which indicates successful ISI recognition by the IRU. We present two distinct configurations for the time-delay circuit within the IRU using excitatory and inhibitory synapses, respectively, to produce a delayed output spike at time $t_0+\tau \left(R\right)$ in response to the input spike received at time $t_0$. $R$ is the tunable parameter of the time-delay circuit that controls the timing of the delayed output spike. We discuss the forms of STDP rules for excitatory and inhibitory synapses, respectively, that allow for modulation of $R$ for the IRU to perform its task of ISI recognition. We then present two specific implementations for the IRU circuitry, derived from the general architecture that can both learn the ISIs of a training sequence and then recognize the same ISI sequence when it is presented on subsequent occasions.

Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects have, however, proved to be sensitive to the details of the underlying topology and dynamics. Here we introduce a minimal population structure that is described by two distinct hierarchical levels of interaction, similar to the structured metapopulation concept of ecology and island models in population genetics. We believe this model is able to identify effects of spatial structure that do not depend on the details of the topology. While effects depending on such details clearly lie outside the scope of our approach, we expect that those we are able to reproduce should be generally applicable to a wide range of models. We derive the dynamics governing the evolution of a system starting from fundamental individual level stochastic processes through two successive mean-field approximations. In our model of population structure the topology of interactions is described by only two parameters: the effective population size at the local scale and the relative strength of local dynamics to global mixing. We demonstrate, for example, the existence of a continuous transition leading to the dominance of cooperation in populations with hierarchical levels of unstructured mixing as the benefit to cost ratio becomes smaller then the local population size. Applying our model of spatial structure to the repeated prisoner’s dilemma we uncover a counterintuitive mechanism by which the constant influx of defectors sustains cooperation. Further exploring the phase space of the repeated prisoner’s dilemma and also of the “rock-paper-scissor” game we find indications of rich structure and are able to reproduce several effects observed in other models with explicit spatial embedding, such as the maintenance of biodiversity and the emergence of global oscillations.