We extend our $2+1$-dimensional discrete growth model [Ódor et al., Phys. Rev. E 79, 021125 (2009)] with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence. By mapping the slopes onto particles, two-dimensional nonequilibrium binary lattice model emerges, in which the (smoothing or roughening) surface diffusion can be described by attracting or repelling motion of oriented dimers. The binary representation allows simulations on very large size and time scales. We provide numerical evidence for Mullins-Herring or molecular-beam epitaxy class scaling of the surface width. The competition of inverse Mullins-Herring diffusion with a smoothing deposition, which corresponds to a Kardar-Parisi-Zhang (KPZ) process, generates different patterns: dots or ripples. We analyze numerically the scaling and wavelength growth behavior in these models. In particular, we confirm by large size simulations that the KPZ type of scaling is stable against the addition of this surface diffusion, hence this is the asymptotic behavior of the Kuramoto-Sivashinsky equation as conjectured by field theory in two dimensions, but has been debated numerically. If very strong, normal surface diffusion is added to a KPZ process, we observe smooth surfaces with logarithmic growth, which can describe the mean-field behavior of the strong-coupling KPZ class. We show that ripple coarsening occurs if parallel surface currents are present, otherwise logarithmic behavior emerges.

We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering, or electron-electron scattering. These sums correspond to “grains” in momentum space. This equation of motion is supposed to involve only a moderate number of dynamical variables and/or exhibit a sufficiently simple structure such that neither its construction nor its analyzation or solution requires substantial numerical effort. To this end we compute, by means of a projection operator technique, a linear(ized) collision term which determines the dynamics of the above grain sums. This collision term results as nonsingular finite-dimensional rate matrix and may thus be inverted regardless of any symmetry of the underlying model. This facilitates calculations of, e.g., transport coefficients, as we demonstrate for a three-dimensional Anderson model featuring weak disorder.

The short-time critical dynamics of propagation of damage in the Ising ferromagnet in two dimensions is studied by means of Monte Carlo simulations. Starting with equilibrium configurations at $T=\infty$ and magnetization $M=0$, an initial damage is created by flipping a small amount of spins in one of the two replicas studied. In this way, the initial damage is proportional to the initial magnetization $M_0$ in one of the configurations upon quenching the system at $T_C$, the Onsager critical temperature of the ferromagnetic-paramagnetic transition. It is found that, at short times, the damage increases with an exponent ${\theta }_D=1.915\left(3\right)$, which is much larger than the exponent $\theta =0.197$ characteristic of the initial increase of the magnetization $M\left(t\right)$. Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic $\left(⟨R^2\left(t\right)⟩\right)$ grows with an exponent $z^{\ast }\approx \eta \approx 1.9$, which is the same, within error bars, as the exponent ${\theta }_D$. However, the survival probability of the epidemics reaches a plateau so that $\delta =0$. On the other hand, by quenching the system to lower temperatures one observes the critical spreading of the damage at $T_D\simeq 0.51T_C$, where all the measured observables exhibit power laws with exponents ${\theta }_D=1.026\left(3\right)$, $\delta =0.133\left(1\right)$, and $z^{\ast }=1.74\left(3\right)$.

The wetting of a phase-separated colloid-polymer mixture in contact with a hard wall is analyzed using free volume theory in a Nakanishi-Fisher-type approach. We present results for the wetting phase diagram for several model approximations. Our analysis is compared with a previous analysis by Aarts et al. [J. Chem. Phys. 120, 1973 (2004)]. We find that there is a crossover from wetting to drying at a threshold value for the colloid-polymer size ratio and that the transitions are close to the critical point and of second order in nature.

Focal adhesions are the anchoring points of cells to surfaces and are responsible for a large number of surface sensing processes. Nanopatterning studies have shown physiological changes in fibroblasts as a result of decreasing density of external binding ligands. The most striking of these changes is a decreased ability to form mature focal adhesions when lateral ligand distances exceed 76 nm. These changes are usually examined in the context of protein signaling and protein interactions. We show a physical explanation based on the balance between the forces acting on individual ligand connections and the reaction kinetics of those ligands. We propose three stability regimes for focal adhesions as a function of ligand spacing and applied stress: a stable regime, an unstable regime in which a large fraction of unbound protein causes adhesion disintegration, and a regime in which the applied force is too high to form an adhesion structure.

The public goods game is a powerful metaphor for exploring the maintenance of social cooperative behavior in a group of interactional selfish players. Here we study the emergence of cooperation in the public goods games with diverse contributions in finite populations. The theory of stochastic process is innovatively adopted to investigate the evolutionary dynamics of the public goods games involving a diversity of contributions. In the limit of rare mutations, the general stationary distribution of this stochastic process can be analytically approximated by means of diffusion theory. Moreover, we demonstrate that increasing the diversity of contributions greatly reduces the probability of finding the population in a homogeneous state full of defectors. This increase also raises the expectation of the total contribution in the entire population and thus promotes social cooperation. Furthermore, by investigating the evolutionary dynamics of optional public goods games with diverse contributions, we find that nonparticipation can assist players who contribute more in resisting invasion and taking over individuals who contribute less. In addition, numerical simulations are performed to confirm our analytical results. Our results may provide insight into the effect of diverse contributions on cooperative behaviors in the real world.

Obstacle-anchored vortices can be terminated by the application of high-frequency wave trains in excitable media. We theoretically derived the dependency between the obstacle radius and the maximum unpinning period through reinterpretation of the well-known eikonal equation. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for improving the stimulation protocol of implantable cardiac pacemakers.

Young’s equation, describing an interfacial equilibrium condition of a liquid droplet on a smooth solid surface, raises issues concerning the existence of a sine term which has not yet been resolved theoretically and continues to be discussed to the present day. From a thermodynamics viewpoint, the equilibrium condition arises by minimizing the total free energy of the system while intensive parameters are kept constant. In the derivation, variations in the virtual work in both horizontal and vertical directions of the droplet on the smooth solid are considered. From a hydrodynamics viewpoint, there is a momentum jump condition at the gas-liquid interface that is derived based on a mechanical balance. Using standard mathematical procedures such as Stokes’ theorem and differential geometry, a test volume is considered across the interface between two continuous phases from which the jump condition is derived. In the present paper, Young’s equation is revisited from the point of view of the momentum jump condition at the two-phase interface and a modified Young’s equation is derived. The analytical solution derived from the modified Young’s equation is then used to compare theory with experimental data. The line tension and contact angle for a lens droplet are also discussed on the basis of this model.

Wavelet-based bispectral analysis has been applied in various physical and engineering fields in recent years, but discussion of its significance testing, which distinguishes statistically meaningful results from those due to random noise, has been scarce and incomplete in the literature. Previously derived significance levels for wavelet bicoherence were either preliminary or based on numerical simulations of a limited sample size. The present study reviewed relevant previous works analytically identified the sampling distribution of the estimated wavelet bicoherence and derived expressions for its significance levels for any given probability value. Its application in analyzing a turbulent shear flow around a bluff body was demonstrated in detail. The significance testing developed here helped to identify significant quadratic couplings among a triad of scales in a separated turbulent shear layer over very short time intervals. The results obtained here can be applied to a wide variety of research topics for detecting nonlinearity in physical systems.

A self-consistent dusty plasma fluid model has been extended to incorporate all the noble gases as the carrier gas. An analysis of void closure in complex plasma composed of these gases over a wide range of experimental parameters is presented. Driving potential-pressure maps are constructed, which show the range in parameter space where isotropic void-free dust crystals can be expected, where a void is to be expected and where the discharge is expected to extinguish.

Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, $\beta$. This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant quantum Monte Carlo which scales linearly in $\beta$, with a quadratic term that comes in to play for the number of time slices larger than hundred, and demonstrate that the sign problem is identical to HF.

The optical properties of a metal film perforated with coaxial elliptical hole arrays have been investigated experimentally and a simple analysis model that qualitatively explains the experimental results has been presented. In our structure, two localized excitations, i.e., the short- and long-axis localized surface-plasmon modes of the elliptical nanoparticles or nanoholes can be excited, which couples, respectively, with the surface-plasmon polariton modes and causes different optical response. As a consequence, the transmission features can be manipulated by the polarization state of the incident light.

We report a combined x-ray photon correlation spectroscopy and rheometry study of moderately concentrated suspensions of silica colloids that form a gel on cooling. During gel formation, the suspensions acquire a shear modulus that increases with time, while the thermal motion of the colloids becomes localized over an increasingly restricted range. The nanometer-scale localization length characterizing this motion obeys an exact relationship with the shear modulus predicted theoretically from mode coupling calculations [K. S. Schweizer and G. Yatsenko, J. Chem. Phys. 127, 164505 (2007)]. This scaling thus demonstrates a direct quantitative connection between the microscopic dynamics and macroscopic rheology. It further indicates the importance of local structure over longer-range correlations in dictating the dynamical and mechanical properties of such gels.

Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption is taken into account within Gibbsian approximation. Binary clusters are treated by means of statistical-mechanical considerations: tracing out the molecular degrees of freedom of the more volatile component, we obtain a coarse-grained system described in terms of the single-component mean-field kinetic nucleation theory [V. I. Kalikmanov, J. Chem. Phys. 124, 124505 (2006)], allowing an adequate treatment of clusters of arbitrary size. The model opens a route toward studying binary nucleation in complex systems with nanosized critical clusters.

Here we examine a lattice-gas model that has been extended to include collective shear moves and friction interactions between particles. A shearlike field is applied by periodically translating entire subsections of the lattice with respect to one another, as opposed to biasing the individual movements of particles. Friction is introduced by forming a network of temporary bonds between particles that prevent particles from moving along with the flow. The extent of the network is controlled by the sticking parameter, $P_{\text{stk}}$. We find that there are two distinct phases in the model: an isotropic phase that exhibits only small fluctuations in local density, and a striped phase that features one or more large clusters of particles that span the system. We examine the transition between these two phases using the radial distribution function. By introducing a measure of viscosity, we examine the relationship between the viscosity and shear rate for many different densities and values of $P_{\text{stk}}$, and pursue an analogy to colloidal shear-thickening systems.

We present a detailed study of a dilute suspension of carbon nanotubes (CNTs) in a pentylcyanobiphenyl (5CB) liquid crystal (LC) by probing the dielectric properties as a function of applied ac voltage and frequency. In principle, to minimize the elastic distortion in the nematic matrix, the monodispersed CNTs follow the nematic director without disturbing the director field significantly. A strong anchoring energy due to $\pi \text{−}\pi$ electron stacking between LC-CNT molecules results in an increase in the dielectric anisotropy for the hybrid system, indicating a significant enhancement in the orientational order parameter. The frequency-dependent dielectric anisotropy for the composite system reveals the intrinsic frequency response of the LC-CNT anchoring mechanism. As a matter of consequence, the extracted value of splay elastic constant suggests that LC-CNT anchoring has an impact on the structural modification of the hybrid $\text{LC}+\text{CNT}$ system. This strong anchoring energy stabilizes local pseudonematic domains, giving rise to a nonzero dielectric anisotropy in the isotropic phase that also shows an intrinsic frequency response.

Bacterial outer membrane porins (Omp) that have robust $\beta$-barrel structures, show potential applications for nanomedicine devices in synthetic membranes and single molecule detection biosensors. Here, we explore the conformational dynamics of a set of 22 outer membrane porins, classified into five major groups: general porins, specific porins, transport Omps, poreless Omps and composed pores. Normal mode analysis, based on mechanical vibration theory and elastic network model, is performed to study the fluctuations of residues of aforementioned porins around their equilibrium positions. We find that a simple modification in this model considering weak interaction between protein and membrane, dramatically enhance the stability of results and improve the correlation coefficient between computational output and experimental results.

It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores, both with and without an external potential applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear $IV$ curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the $C$-terminal tails causes cations to be pumped across the microtubule wall and propagate in both directions down the microtubule through the lumen, returning to the bulk solution through its open ends. This effect is demonstrated to add directly to the longitudinal current through the lumen resulting from an external voltage source applied across the two ends of the microtubule. The predicted persistent currents directed through the microtubule wall and along the lumen could be significant in directing the dissipation of weak, endogenous potential gradients toward one end of the microtubule within the cellular environment.

It has been shown that, in models of excitable clusters of voltage-gated sodium channels, the spontaneous rate of action potential and signal encoding ability exhibit multiple peaks at different cluster sizes due to an entropy effect in small system. In this paper, we show that similar results can be found in excitable cluster of ligand-gated calcium channels. Furthermore, we demonstrate that the periodicity of spontaneous ${\text{Ca}}^{2+}$ spikes elicited by the cluster reveals multiple maxima at small discrete cluster sizes.

The stability of two semiconductor lasers that are spatially separated by a passive resonator is analyzed using the composite-cavity mode approach. We study the nonlinear interactions of three composite-cavity modes and identify regions of in-phase and out-of-phase laser locking in the parameter plane of the transmission coefficients of the coupling mirrors and the laser length difference. Bifurcation analysis shows that the structure of the locking regions strongly depends on (i) the length of the passive resonator and (ii) the amount of amplitude-phase coupling of the laser field. Specifically, we find a single locking region when the passive resonator and the lasers have comparable lengths and up to three separate locking regions when the passive resonator is much shorter than the lasers. Furthermore, we use the recently developed 0–1 test for chaos to uncover intricate regions of chaotic dynamics that shrink in size and eventually disappear as the passive resonator length becomes comparable to the laser length.