The hydrodynamics of two oscillating foils in side-by-side configuration is numerically investigated for in-phase and out-of-phase pitching at Reynolds number of 4000 and Strouhal numbers of $\text{St}=0.25\text{–}0.5$. The effects of phase difference (in-phase and out-of-phase) and Strouhal number on symmetric attributes of the wake and unsteady propulsive performance of the foils are studied in detail. At lower Strouhal numbers, there is a quasisteady performance in both thrust generation and power consumption, which coincides with persistence of the wake symmetry. As Strouhal number increases, however, in-phase and out-of-phase pitching display unsteady cycle-averaged behavior with very different wake characteristics. The asymmetric wake of in-phase pitching foils at high Strouhal numbers transitions to a quasisymmetric wake, when an extensive interaction between the two vortex streets is observed in the wake. This coincides with an improvement on the propulsive performance of the foils. In contrast, the symmetric wake of the out-of-phase pitching foils at a high Strouhal number transitions to an asymmetric wake. The adverse effect of this transition is only observed on the propulsive performance of one foil while the other exploits the wake towards a better performance. The collective performance of the the out-of-phase pitching system, however, remains unchanged. There is also a strong correlation between the wake symmetric characteristics and total nonzero side-force production.

Dense plasmas occur in stars, giant planets, and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state-of-the-art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials—core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.

In this paper, it is proposed to improve the quality of a variational description of a closed quantum system by adding fictitious dissipation that reduces the entanglement. The proposal is implemented for a small Bose-Hubbard chain in the mean field regime, which shows chaotic behavior and associated fast growth of quantum fluctuations. For appropriately chosen dissipation, good agreement with the truncated Wigner approximation is found. This shows that, when chaos leads to the breakdown of a variational method, adding fictitious dissipation can be a cure.

We report on Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, and the probability density for the particle spreading is Gaussian like, but the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behavior is not a consequence of either a space- or time-dependent diffusivity, but is induced by external nonthermal noise acting on the particle dwelling in a periodic potential. The existence of the exponential tail in the increment statistics leads to colossal enhancement of diffusion, drastically surpassing the previously researched situation known as “giant” diffusion. This colossal diffusion enhancement crucially impacts a broad spectrum of the first arrival problems, such as diffusion limited reactions governing transport in living cells.

A spin system can be thought of as an information coding system that transfers information of the interaction configuration into information of the equilibrium state of the spin variables. Hence it can be expected that the relations between the interaction configuration and equilibrium states are consistent with the known laws of information theory. We show that Shannon's rate distortion theorem can be used to obtain a universal constraint on neighboring spin correlations for a broad range of Ising spin systems with two-body spin interactions. Remarkably, this constraint gives a bound for the multicritical point in the phase diagram, when a mean-field behavior for the neighboring spin pairs can be expected in the paramagnetic phase.

Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown to emerge as a special case. Most importantly, the hallmark of strong nonlinearity—relaxation oscillations—is shown in quantum mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations are found to occur via two distinct mechanisms in phase space.

The impact of the classical dynamic on the fluctuation properties in the eigenvalue spectrum of nonrelativistic quantum billiards (QBs) are now well understood based on the semiclassical approach which provides an approximation for the fluctuating part ${\rho }^{\mathrm{fluc}}\left(k\right)$ of the spectral density in terms of a trace formula, that is, a sum over classical periodic orbits of its classical counterpart, abbreviated as CB. This connection between the eigenvalue spectrum of a quantum system and the classical periodic orbits is discernible in the Fourier transform of ${\rho }^{\mathrm{fluc}}\left(k\right)$ from eigenwave number $k$ to length, which exhibits peaks at the lengths of the periodic orbits. The uprise of interest in properties of graphene related to their relativistic Dirac spectrum implicated the emergence of intensive studies of relativistic neutrino billiards (NBs), consisting of a spin-1/2 particle governed by the Dirac equation and confined to a bounded planar domain. In distinction to QBs, NBs do not have a well-defined classical limit. Yet comparison of their length spectra showed that for massless spin-1/2 particles those of the NB exhibit peaks at positions corresponding to the lengths of periodic orbits with an even number of reflections at the boundary of the CB associated with the corresponding QB. In order to understand the transition from the relativistic to the nonrelativistic regime, we derive an exact quantization condition for massive NBs and use it to obtain a trace formula. This trace formula provides a direct link between the spectral density of a NB and the classical dynamic of the corresponding QB through the periodic orbits of the associated CB.

In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs), a graph model used to study the structure and dynamics of complex systems embedded in a two-dimensional space. RGGs, $G(n,\ell )$, consist of $n$ vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidian distance is less than or equal to the connection radius $\ell \in [0,\sqrt{2}]$. To evaluate the topological properties of RGGs we chose two well-known topological indices, the Randić index $R\left(G\right)$ and the harmonic index $H\left(G\right)$. We characterize the spectral and eigenvector properties of the corresponding randomly weighted adjacency matrices by the use of random matrix theory measures: the ratio between consecutive eigenvalue spacings, the inverse participation ratios, and the information or Shannon entropies $S\left(G\right)$. First, we review the scaling properties of the averaged measures, topological and spectral, on RGGs. Then we show that (i) the averaged-scaled indices, $〈R\left(G\right)〉$ and $〈H\left(G\right)〉$, are highly correlated with the average number of nonisolated vertices $〈V_{\times }\left(G\right)〉$; and (ii) surprisingly, the averaged-scaled Shannon entropy $〈S\left(G\right)〉$ is also highly correlated with $〈V_{\times }\left(G\right)〉$. Therefore, we suggest that very reliable predictions of eigenvector properties of RGGs could be made by computing topological indices.

Lipid bilayer membranes under biologically relevant conditions are flexible thin laterally fluid films consisting of two unimolecular layers (monolayers) each about 2 nm thick. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape. The classical Helfrich theory considers the membrane as an elastic two-dimensional (2D) film, which has no particular internal structure. However, various local membrane heterogeneities can result in a lipids tilt relative to the membrane surface normal. On the basis of the classical elasticity theory of 3D bodies, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] derived the most general energy functional, taking into account the tilt and lipid monolayer curvature. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)] showed that Hamm and Kozlov's derivation was incomplete because the tilt-curvature coupling term had been missed. However, the energy functional derived by Terzi and Deserno appeared to be unstable, thereby being invalid for applications that require minimizations of the overall energy of deformations. Here, we derive a stable elastic energy functional, showing that the squared gradient of the curvature was missed in both of these works. This change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability. We also consider the influence of the prestress terms on the stability of the energy functional, and we show that it should be considered small and the effective Gaussian curvature should be neglected because of the stability requirements. We further generalize the theory, including the stretching-compressing deformation modes, and we provide the geometrical interpretation of the terms that were previously missed by Hamm and Kozlov. The physical consequences of the new terms are analyzed in the case of a membrane-mediated interaction of two amphipathic peptides located in the same monolayer. We also provide the expression for director fluctuations, comparing it with that obtained by Terzi and Deserno.

This aim of this paper is mainly to investigate the performance of two typical moment closure schemes in gene regulatory master equations of rational rate laws. When the reaction rate is polynomial, the error bounds between the authentic and approximate moments obtained by schemes of Gaussian moment closure and log-normal moment closure are explicitly given. When the reaction rate is not polynomial, it is shown that the two schemes both behave well in the absence of active-inactive state switch, but in the presence of active-inactive state switch the log-normal closure scheme is far superior to the Gaussian closure scheme in capturing the asymptotic ensemble statistics. Moreover, the accuracy of the log-normal closure method is further confirmed by steady-state analytic results and the conditional Gaussian closure method. It is also disclosed that optimal negative feedback exists in suppressing protein noise in the presence of the on-off switch control.

We study a two-dimensional glass-forming system of slightly polydisperse (LJ) particles using molecular dynamics simulations and demonstrate that in the liquid regime (well above the vitrification temperature) this model shows a number of features typical of the glass transition: (i) the relation between compressibility and structure factor $S\left(q\right)$ is strongly violated; (ii) the dynamical structure factor $S(q,t)$ at low $q$ shows a two-step relaxation; (iii) the time-dependent heat capacity $c_v\left(t\right)$ shows a long-time power-law tail. We show that these phenomena can be rationalized with the idea of composition fluctuations and provide a quantitative theory for the effects (i) and (ii). It implies that such effects must be inherent in all polydisperse colloidal models, including binary LJ mixtures.

Surface temperature is among crucial factors which control wear during sliding dry contact. Using computer modeling, we study the possibility to achieve close to zero rate of surface wear during sliding friction of the special type of materials which possess negative thermal expansion. The numerical simulations reveal two wear regimes for materials with negative thermal expansion coefficient as dependent on the applied normal stress level. When the applied stress is lower than that of a critical level, a steady almost zero wear rate and nanorough surface are achieved during friction. Otherwise, wear rate is of the same order of magnitude as for “traditional” materials with positive thermal expansion coefficient. The critical stress value is analyzed depending on the material's mechanical, thermophysical, and surface roughness characteristics.

Complex plasmas are interesting systems as the charged dust can self-assemble into different types of ordered structures. To understand the mechanisms which govern the transitions from one type of structure to another, it is necessary to know both the dust charge and the confining electric fields within the environment, parameters which are difficult to measure independently. As dust is usually confined in a plasma sheath where the ions stream from the bulk plasma to the negative lower electrode, the problem is further complicated by the ion wake field, which develops downstream of the dust grains in a flowing plasma. The differences in local ion density caused by the wake field change the equilibrium dust charge and shielding distance of the dust grains, and thus affect the interaction between grains. Here we use a molecular dynamics simulation of ion flow past dust grains to investigate the interaction between the dust particles and ions. We consider a long vertical chain of particles confined within a glass box placed on the lower electrode of a Gaseous Electronics Conference rf reference cell. We apply the model iteratively to self-consistently determine the dust charge, electric field, and ion density along the length of the chain as well as the ion flow speed. Simulation results indicate that the ion flow speed within the box is subsonic.

Echolocating bats locate a target by sonar. The performance of this system is related to the shape of the binaural conformation in bats. From numerical predictions, it was found that in a central frequency band, the orientation of a strong sidelobe is shifted nearly linearly in the vertical direction. Inspired by this, the authors built an accurate wide-scope elevation estimation system by constructing a pair of erect artificial pinnae and realized simultaneous elevation and azimuth estimation by constructing a pair of orthogonal pinnae. By demonstrating the simplicity of spatial target echolocation, the authors showed that only two independent single-output neural networks were needed for either elevation or azimuth estimation. This method could be applied to imitate any other mammal species with similar pinna directivity patterns to facilitate and improve an artificial echolocation system.

Using a computer simulation, we have studied the random sequential adsorption of stiff linear $k$-mers onto a square lattice. Each such particle occupies $k$ adjacent lattice sites. During deposition, the two mutually perpendicular orientations of the particles are equiprobable, hence, a macroscopically isotropic monolayer is formed. However, this monolayer is locally anisotropic, since the deposited particles tend to form domains of particles with the same orientation. Using the “excluded area” concept, we have classified lattice sites into several types and examined how the fraction of each type of lattice site varies as the number of deposited particles increases. The behaviors of these quantities have allowed us to identify the following stages of domain formation: (i) the emergence of domain seeds, (ii) the filling of domains, and (iii) densification of the domains.

An alternative design of the measurement capacitor for high-pressure studies of complex liquids or soft matter systems is presented. Subsequently, results for the precritical anomaly of dielectric constant in 1-nitropropane–octane critical mixture are reported. First, the pressure dependence of the critical consolute temperature $T_C$ up to $P=0.55\mathrm{GPa}$ was determined and portrayed using the derivative-based analysis. Second, temperature and pressure evolutions of dielectric constant on approaching the critical consolute point at ($T_C=304.1\mathrm{K}$ and $P_C=403\mathrm{MPa}$) were studied. They revealed that the pretransitional anomaly $\varepsilon \left(P\to P_C\right)$ is notably more pronounced than for $\varepsilon \left(T\to T_C\right)$. For both paths, the static domain extends even to as low frequency as $f=100\mathrm{Hz}$, whereas for tests under atmospheric pressure, they require at least $f=100\mathrm{kHz}$. The discussion of the impact of correction-to-scaling terms, including the unique case of the pressure paths, is also presented.

A general hierarchical structure is developed for phase-field lattice-Boltzmann simulations with dissimilar time scales. The number of the grid levels can be artificially selected in a reasonable range, which can enhance the time marching step by two to three orders of magnitude in comparison with explicit methods. Constructed on a massively parallel platform, the mesh distribution is dynamically adjusted according to a gradient criterion. The developed high performance computing scheme is applied to simulate the coupled thermosolutal dendrite evolution. Numerical tests indicate that the computing efficiency can be further improved by two to three orders of magnitude, which makes numerical simulation of fully coupled thermosolutal dendrite growth viable for alloys with Lewis number $\sim {10}^4$. The domain size which equivalently consists of billions of uniform meshes is handled to simulate multidendrite evolution. Results show that the domain temperature becomes extremely uneven due to the release of latent heat, which causes a significant difference from isothermal solidification. A simple analytical model is proposed to predict the relation between growth velocity and Lewis number, and the growth morphologies of both equiaxed and directional multiple dendrites are discussed. The combination of the hierarchical mesh structure and the phase-field lattice-Boltzmann method provides an efficiency-driven approach to solve the coupled thermosolutal microstructure evolution.

We study the effect of stress inhomogeneity on the behavior of fluid-driven fracture development in weakly consolidated granular systems. Using numerical models we investigate the change in fracture growth rate and fracture pattern structure in unconsolidated granular packs (also referred to as soft-sands) as a function of the change in the confining stresses applied to the system. Soft-sands do not usually behave like brittle, linear elastic materials, and as a consequence, poroelastic models are often not applicable to describe their behavior. By making a distinction between “cohesive” and “compressive” grain-grain contact forces depending on their magnitude, we propose an expression that describes the fluid opening pressure as a function of the mean value and the standard deviation of the “compressive stress” distribution. We also show that the standard deviation of this distribution can be related with the extent to which fracture “branches” reach into the material.

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.