We derive the energy spectrum in wave-number–frequency space for turbulent flows based on Kraichnan’s idealized random sweeping hypothesis with additional mean flow, which yields the instantaneous energy spectrum multiplied by a Gaussian frequency distribution. The model spectrum has two adjustable parameters, the mean flow velocity and the sweeping velocity, and has the property that the power-law index of the wave-number spectrum translates to the frequency spectrum, invariant for arbitrary choices of the mean velocity and sweeping velocity. The model spectrum incorporates both Taylor’s frozen-in flow approximation and the random sweeping approximation in a natural way and can be used to distinguish between these two effects when applied to real time-resolved multipoint turbulence data. Evaluated in real space, its properties with respect to space-time velocity correlations are discussed, and a comparison to the recently introduced elliptic model is drawn.

We derive a comprehensive statistical model for dispersion of passive or almost passive admixture particles such as fine particulate matter, aerosols, smoke, and fumes in turbulent flow. The model rests on the Markov limit for particle velocity. It is in accordance with the asymptotic structure of turbulence at large Reynolds number as described by Kolmogorov. The model consists of Langevin and diffusion equations in which the damping and diffusivity are expressed by expansions in powers of the reciprocal Kolmogorov constant $C_0$. We derive solutions of $O\left({C_0}^0\right)$ and $O\left({C_0}^{-1}\right)$. We truncate at $O\left({C_0}^{-2}\right)$ which is shown to result in an error of a few percentages in predicted dispersion statistics for representative cases of turbulent flow. We reveal analogies and remarkable differences between the solutions of classical statistical mechanics and those of statistical turbulence.

The motivation for this work is a dramatically improved understanding of the fluid mechanics of drainage processes with applications such as ${\text{CO}}_2$ storage in saline aquifers and water-alternating-gas injection as an enhanced oil recovery method. In this paper we present in situ distributions of wetting and nonwetting fluids obtained during core-scale two-phase immiscible drainage experiments. The ratio of the viscosity of the resident fluid to that of the invading fluid varies across a range of $0.43$ to 150. Saturation distributions observed during dynamic displacement experiments are surprisingly smooth and do not display only one or a few dominant fingers, contrary to the indications of the current literature. The analysis of the saturation distribution using the fractal dimensions of the dynamic three-dimensional saturation distributions suggests that the constitutive relationships for porous media, namely, the relative permeability functions, are history dependent. Accordingly, it is suggested that the nonlinear, unstable flow regime is the regime where efforts to improve physical understanding must be focused.

The existence of a “$-1$” power-law scaling at low wavenumbers in the longitudinal velocity spectrum of wall-bounded turbulence was explained by multiple mechanisms; however, experimental support has not been uniform across laboratory studies. This letter shows that Heisenberg's eddy viscosity approach can provide a theoretical framework that bridges these multiple mechanisms and explains the elusiveness of the “$-1$” power law in some experiments. Novel theoretical outcomes are conjectured about the role of intermittency and very-large scale motions in modifying the $k^{-1}$ scaling.

We calculate the exact solution of the Fokker-Planck equation for the stationary-state probability density of a harmonic oscillator embedded in an electromagnetic field. The magnetic field is assumed to be a constant and the electric field an external stochastic force with the properties of a Gaussian and exponentially correlated noise (Ornstein-Uhlenbeck process). In this work, we first study the problem in the absence of the magnetic field, then we obtain the complete solution and corroborate that the latter reduces to the former when the magnetic field is suppressed.

Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear $k$-mers (also denoted in publications as rigid rods, needles, sticks) on two-dimensional square lattices $L\times L$ with periodic boundary conditions. Percolation phenomena are investigated for anisotropic relaxation random sequential adsorption of linear $k$-mers. Especially, effect of anisotropic placement of the objects on the percolation threshold has been investigated. A detailed study of the behavior of percolation probability $R_L\left(p\right)$ that a lattice of size $L$ percolates at concentration $p$ in dependence on $k$, anisotropy, and lattice size $L$ has been performed. A nonmonotonic size dependence for the percolation threshold has been confirmed in the isotropic case. We propose a fitting formula for percolation threshold, $p_c=a/k^{\alpha }+b{\log }_{10}k+c$, where $a$, $b$, $c$, and $\alpha$ are the fitting parameters depending on anisotropy. We predict that for large $k$-mers ($k⪆1.2\times {10}^4$) isotropically placed at the lattice, percolation cannot occur, even at jamming concentration.

We investigate the propagation and scattering of highly nonlinear waves in granular systems composed of spheres in contact arranged in a square packing, and study how the presence of small and light spherical interstitial defects, also referred to as intruders, affects the wave propagation. The effects of a single defect are investigated experimentally and compared to numerical simulations, showing very good quantitative agreement. Transmitted and scattered waves are formed, whose characteristics depend on the material properties of the defect in relation to the properties of the particles in the lattice. Experiments and numerical simulations reveal that stiffer defects are more efficient at redistributing energy outside the impacted chain and soft defects induce a localization of the energy at the defect. Finally, the effects of the presence of two defects, placed diagonally or aligned in the square packing are also investigated, as well as how their interaction depends on their relative positions.

Fiber bundle models (FBMs) offer a versatile framework for representing transitions from progressive to abrupt failure in disordered material. We report a FBM-based description of mechanical interactions and associated energy bursts during shear deformation of granular materials. For strain-controlled shearing, where elements fail in a sequential order, we present analytical expressions for strain energy release and failure statistics. Results suggest that frequency-magnitude characteristics of fiber failure vary considerably throughout progressive shearing. Predicted failure distributions were in good agreement with experimentally observed shear stress fluctuations and associated bursts of acoustic emissions. Experiments also confirm a delayed release of acoustic emission energy relative to shear stress buildup, as anticipated by the model. Combined with data-rich acoustic emission measurements, the modified FBM offers highly resolved contact-scale insights into granular media dynamics of shearing processes.

Optical diffractometry is proposed as a practical method of quantitatively analyzing the microscopic structural origins of a wide range of highly efficient and linearly polarized optical diffraction grating produced from holographic polymer-dispersed liquid crystal. The structure is organized by a spatially periodical distribution of submicrometer-scale liquid crystal (LC) droplets in a polymer matrix. Six independent Bragg diffraction spectra were obtained at two orthogonal polarization states at temperatures below, at, and above the nematic-to-isotropic phase transition point. These spectra were simultaneously analyzed by employing anisotropic diffraction theory under the restraint of a simple and widely useful structural model constructed on the basis of the previously reported microscopic observations. The refractive indices of spatially periodic LC- and polymer-rich phases were analyzed using Cauchy's equation as a function of optical wavelength. The present diffractometry was demonstrated for a variety of holographic structures, and the structural parameters were discussed such as the filling ratio of LC droplets to polymer matrix, the orientational order in the droplets, and the thermo-optic properties in the LC droplets. Furthermore, the higher order Bragg diffractions were measured and discussed. The proposed method was examined in consistency by comparisons with polarizing optical microscopy and scanning electron microscopy.

We perform a high-order analytical expansion of the epidemiological susceptible-infectious-recovered multivariate master equation and include terms up to and beyond single-particle fluctuations. It is shown that higher order approximations yield qualitatively different results than low-order approximations, which is incident to the influence of additional nonlinear fluctuations. The fluctuations can be related to a meaningful physical parameter, the basic reproductive number, which is shown to dictate the rate of divergence in absolute terms from the ordinary differential equations more so than the total number of persons in the system. In epidemiological terms, the effect of single-particle fluctuations ought to be taken into account as the reproductive number approaches unity.

We study the influence of wetting on capillary condensation for a simple fluid in a square geometry with surface fields, where the reference system is an infinitely long slit. The corner transfer matrix renormalization group method has been extended to study a two-dimensional Ising model confined in an $L\times L$ geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.

This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of paths on a graph and to random walks. Relationships between some of these matrices are derived in the paper. These relationships are inherited by the centrality measures. They include measures based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix, or mean first-passage times of a random walk. As the random walk defining the centrality measure can be arbitrarily chosen, we pay particular attention to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary (diffusive) random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs with varying mixing parameter and are grouped with the use of the agglomerative clustering technique. It is shown that centrality measures defined with the two different random walks cluster into two separate groups. In particular, the group of centrality measures defined by the maximal-entropy random walk does not cluster with any other measures on change of graphs’ parameters, and members of this group produce mutually closer results than members of the group defined by the ordinary random walk.

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two factors can be varied arbitrarily, it is much more difficult to disentangle these two architectural effects in real networks. Here we propose a solution to this problem, by introducing global and local measures of spatial effects that, through a comparison with adequate null models, effectively filter out the spurious contribution of nonspatial constraints. Our filtering allows us to consistently compare different embedded networks or different historical snapshots of the same network. As a challenging application we analyze the World Trade Web, whose topology is known to depend on geographic distances but is also strongly determined by nonspatial constraints (degree sequence or gross domestic product). Remarkably, we are able to detect weak but significant spatial effects both locally and globally in the network, showing that our method succeeds in retrieving spatial information even when nonspatial factors dominate. We finally relate our results to the economic literature on gravity models and trade globalization.

Statistics of the active temperature and passive concentration advected by the one-dimensional stationary compressible turbulence at ${\mathrm{Re}}_{\lambda }=2.56\times {10}^6$ and $M_t=1.0$ is investigated by using direct numerical simulation with all-scale forcing. It is observed that the signal of velocity, as well as the two scalars, is full of small-scale sawtooth structures. The temperature spectrum corresponds to $G\left(k\right)\propto k^{-5/3}$, whereas the concentration spectrum acts as a double power law of $H\left(k\right)\propto k^{-5/3}$ and $H\left(k\right)\propto k^{-7/3}$. The probability distribution functions (PDFs) for the two scalar increments show that both $\delta T$ and $\delta C$ are strongly intermittent at small separation distance $r$ and gradually approach the Gaussian distribution as $r$ increases. Simultaneously, the exponent values of the PDF tails for the large negative scalar gradients are $q_{\theta }=-4.0$ and $q_{\zeta }=-3.0$, respectively. A single power-law region of finite width is identified in the structure function (SF) of $\delta T$; however, in the SF of $\delta C$, there are two regions with the exponents taken as a local minimum and a local maximum. As for the scalings of the two SFs, they are close to the Burgers and Obukhov-Corrsin scalings, respectively. Moreover, the negative filtered flux at large scales and the time-increasing total variance give evidences to the existence of an inverse cascade of the passive concentration, which is induced by the implosive collapse in the Lagrangian trajectories.

The current partially ionized plasmas models for xenon show substantial differences since the description of pressure and thermal ionization region becomes a formidable task, prompting the need for an improved understanding of dense xenon plasmas behavior at above 100 GPa. We performed double-shock compression experiments on dense xenon to determine accurately the Hugoniot up to 172 GPa using a time-resolved optical radiation method. The planar strong shock wave was produced using a flyer plate impactor accelerated up to ∼6 km/s with a two-stage light-gas gun. The time-resolved optical radiation histories were acquired by using a multiwavelength channel optical transience radiance pyrometer. Shock velocity was measured and mass velocity was determined by the impedance-matching methods. The experimental equation of state of dense xenon plasmas are compared with the self-consistent fluid variational calculations of dense xenon in the region of partial ionization over a wide range of pressures and temperatures.

Multiparticle collision dynamics (MPCD) is a particle-based fluid simulation technique that is becoming increasingly popular for mesoscale fluid modeling. However, some confusion and conflicting results persist in literature regarding several important methodological details, in particular the enforcement of the no-slip condition and thermostatting in forced flow. These issues persist in simple flows past stationary boundaries, which we exclusively focus on here. We discuss the parametrization of MPCD fluids and its consequences for fluid-solid boundaries in great detail, and show that the method of virtual particles proposed by Lamura et al. and adopted by many others is required only for parameter choices that lead to viscosities dominated by collisional contributions. We test several implementations of the virtual particle method and discuss how to completely eliminate slip at stationary boundaries. We also show that stochastic boundary reflection rules are inherently problematic for forced flow and suggest a possible remedy. Finally, we discuss the most robust way to achieve forced flow and evaluate several thermostatting methods in the process. All discussion is limited to solid objects that do not move as a result of collisions with MPCD particles (i.e., walls). However, the results can be extended to solutes that experience forces and torques due to interactions with MPCD particles (e.g., colloids). The detailed analysis presented for this simple case provides the level of rigor and accuracy to the MPCD method required for the study of more complex systems.

We study group chase and escape with some fast chasers. In our model chasers look for the nearest target and move to one of the nearest sites in order to catch the target. On the other hand, targets try to escape from the nearest chaser. When a chaser catches a target, the target is removed from the system and the number of targets decreases. The lifetime of targets, at which all targets caught, decreases as $t^{\alpha }$ with increasing the number of chasers. When there are no fast chasers and the total number of chasers is small, the exponent $\alpha$ is large. When the total number of chasers is large, $\alpha$ becomes small. There is an optimal number of chasers to minimize the cost used in order to catch all targets. However, when we add a few fast chasers, the region with the large $\alpha$ vanishes. The optimal number of chasers vanishes, and the cost monotonically increases with increasing the number of chasers.

A dielectric measurement method has been proposed to apply to the study of the microstructure of electrorheological (ER) fluids. To test our measurement method the dielectric permittivity increment caused by pair and chain formation was measured in dilute Brownian ER fluids composed of silicone oil and nanosized silica particles. The critical values of the electric field required to induce structure formation were experimentally determined from the electric field dependence of the measured permittivity increment. From the electric field induced time evolution of the relative permittivity of ER fluids, the characteristic times of the pair and chain formation were calculated. Our experimental results for the time constants are in good agreement with the corresponding theoretical data obtained from the Eyring theory.

The deterministic Landau-Lifshitz-Gilbert equation has been used to investigate the nonlinear dynamics of magnetization and the specific power loss in magnetic nanoparticles with uniaxial anisotropy driven by a rotating magnetic field, generalizing the results obtained for the isotropic case found by P. F. de Châtel, I. Nándori, J. Hakl, S. Mészáros, and K. Vad [J. Phys. Condens. Matter 21, 124202 (2009)]. As opposed to many applications of magnetization reversal in single-domain ferromagnetic particles, where losses must be minimized, in this paper, we study the mechanisms of dissipation used in cancer therapy by hyperthermia, which requires the enhancement of energy losses. We show that for circularly polarized field, the energy loss per cycle is decreased by the anisotropy compared to the isotropic case when only dynamical effects are taken into account. Thus, in this case, in the low-frequency limit, a better heating efficiency can be achieved for isotropic nanoparticles. The possible role of thermal fluctuations is also discussed. Results obtained are compared to experimental data.

The denaturation transition of circular DNA is studied within a Poland-Scheraga-type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant $\kappa$ associated with the overtwisting energy for any given loop entropy exponent $c$. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for $c\le 2$. For $c>2$ and $\kappa =0$ we find that the model exhibits a first-order transition. The transition becomes of higher order for any $\kappa >0$. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent $c$.