The observation of von Kármán type vortices during the impact of water droplets onto a pool of water is reported. Shadowgraph imaging and laser-sheet visualization are used to document these events. The appearance of these vortices occurs within theoretically predicted regions in a Reynolds-splash number parameter space. In addition, and also in agreement with theoretical predictions, smooth splashing, with vortices absent, is found for smaller Reynolds number.

We consider Erd$\ddot{\mathrm{o}}$s-Rényi–type networks embedded in one-dimensional ($d_e=1$) and two-dimensional ($d_e=2$) Euclidean space with the link-length distribution $p\left(r\right)\sim r^{-\delta }$. The dimension $d$ of these networks, as a function of $\delta$, has been studied earlier and has been shown to depend on $\delta$. Here we consider diffusion, annihilation, and chemical reaction processes on these spatially constrained networks and show that their dynamics is controlled by the dimension $d$ of the system. We study, as a function of the exponent $\delta$ and the embedding dimension $d_e$, the average distance $\langle r\rangle \sim t^{1/d_w}$ a random walker has traveled after $t$ time steps as well as the probability of the random walker's return to the origin $P_0\left(t\right)$. From these quantities we determine the network dimension $d$ and the dimension $d_w$ of the random walk as a function of $\delta$. We find that the fraction $d/d_w$ governs the number of survivors as a function of time $t$ in the annihilation process ($A+A\to 0$) and in the chemical reaction process ($A+B\to 0$), showing that the relations derived for ordered and disordered lattices with short-range links remain valid also in the case of complex embedded networks with long-range links.

For many real-world networks only a small “sampled” version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN component(s) of directed networks, a description of the effects of BFS sampling on other topological properties is all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure and the number and structure of strongly connected components in sampled networks. In addition, at a low sampling coverage (i.e., less than 40$\%$), the values of average degree, variance of out-degree, degree autocorrelation, and link reciprocity are overestimated by 30$\%$ or more in BFS-sampled networks and only attain values within 10$\%$ of the corresponding values in the complete networks when sampling coverage is in excess of 65$\%$. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.

Pore-scale flow simulations were conducted to investigate the permeability tensor of anisotropic porous media constructed using the Voronoi tessellation method. This construction method enabled the introduction of anisotropy to the media at the particle level in a random and yet controllable way. Simulations were carried out for media with different degrees of anisotropy through varying the mean aspect ratio of grain particles. The simulation results were then analyzed using the Kozeny-Carman (KC) model. The KC model describes the permeability of the anisotropic media in a tensor form with the anisotropy represented by different tortuosities along the three principal directions. The tortuosity tensor was found to be a complex function of the particle morphology, which is yet to be fully determined. However, the results presented have established the starting point for further theoretical development to formulate such a function and to build closed-form analytical permeability models for anisotropic porous media based on first principles.

The propagation speed $V_c$ of the streamwise velocity fluctuations $u^{\prime }$ in turbulent channel flows is calculated using direct numerical simulation (DNS) data at four Mach numbers ($M=0$, $0.8$, $2.0$, and $3.0$). The profiles of $V_c$ are shown to display remarkable similarity at different $M$. Quantitative models are developed based on a statistical structure called Velocity-Vorticity Correlation Structure (VVCS), defined as the vorticity region most correlated to velocity fluctuations at a fixed location. Good agreement with DNS-measured propagation velocities is obtained throughout the channel and for all $M$. The result confirms earlier speculation that the near-wall propagation is due to an advection by coherent vortex structures, and validates the concept of the VVCS.

In this paper we present a model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use a Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles, which are modeled by stochastic processes correlated in time. We are able to reproduce the ballistic regime in the mean square displacement of single particles and the transition to a normal diffusion regime for long times. For the dispersion of particle pairs we find a $t^2$ dependence of the mean square separation at short times and a $t$ dependence for long ones. For intermediate times indications for a Richardson $t^3$ law are observed in certain situations. Finally, the influence of inertia of real particles on the dispersion is investigated.

We consider a Brownian particle that is confined in a two-dimensional enclosure and driven by a combination of input signals. It has been shown that the logic gates can be formed by considering the state of the particle experiencing an entropic barrier as the output signal. For a consistent logical output, it is necessary to optimize the strength of the noise driving the particle for a given system size. The variation of the logical output behavior exhibits a turnover at an optimal value of system size parameter, implying a size resonance condition in entropic transport. The role of a transverse bias field used to tune the transport between the entropy dominated regime and the energy dominated regime is elucidated.

We study reaction-diffusion processes with concentration-dependent diffusivity. First, the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes is determined. We then consider two natural inhomogeneous realizations. The two-species annihilation process is investigated in the situation when the reactants are initially separated, namely each species occupies a half space. In particular, we establish the growth law of the width of the reaction zone. The single-species annihilation process is studied in the situation when the spatially localized source drives the system toward the nonequilibrium steady state. Finally, we investigate a dissolution process with a localized source of diffusing atoms which react with the initially present immobile atoms forming immobile molecules.

A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of a magnetic particle chain in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chain which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of magnetic dipole moments and extended forms of the Oseen-Burgers tensor to account for both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a good description of the particle dynamics. Only a small error of deviation is observed when benchmarking the numerical scheme against a more computationally intensive method, the direct simulation method. The numerical results are compared with experiments and the simulated rotational dynamics correspond well with those obtained from video-microscopy experiments qualitatively and quantitatively. In addition, a dimensionless number ($R_T$) is derived as the sole control parameter for the rotational bead chain dynamics. Numerically and experimentally, $R_T\approx$ 1 is the boundary between rigid “rod” and dynamic “breaking and reformation” behaviors.

We study by using Monte Carlo simulations the hysteresis in unzipping and rezipping of a double stranded DNA (dsDNA) by pulling its strands in opposite directions in the fixed force ensemble. The force is increased at a constant rate from an initial value $g_0$ to some maximum value $g_m$ that lies above the phase boundary and then decreased back again to $g_0$. We observed hysteresis during a complete cycle of unzipping and rezipping. We obtained probability distributions of work performed over a cycle of unzipping and rezipping for various pulling rates. The mean of the distribution is found to be close (the difference being within $10\%$, except for very fast pulling) to the area of the hysteresis loop. We extract the equilibrium force versus separation isotherm by using the work theorem on repeated nonequilibrium force measurements. Our method is capable of reproducing the equilibrium and the nonequilibrium force-separation isotherms for the spontaneous rezipping of dsDNA.

Intermittent dust acoustic wave turbulence self-excited by downward ion flow in dissipative dusty plasma is experimentally observed and investigated. The power spectra of the temporal dust density fluctuation show distinct bumps in the low-frequency regime and power-law scaling in the high-frequency regime. The structure-function analysis demonstrates the multifractal dynamics of the wave turbulence. Decreasing dissipation by decreasing neutral pressure leads to a more turbulent state with a less distinct low-frequency bump in the power spectrum, more stretched non-Gaussian tails in the histogram of the wave-height increment at a small time interval $\tau$, and a higher degree of multifractality. The loss of long time memory with increasing $\tau$ for a more turbulent state causes a change from the distribution with stretched non-Gaussian tails to Gaussian with increasing $\tau$.

We propose a method to obtain an approximate closed form expression for the Madelung energy (ME) of Yukawa lattices. Such a method is applied for lattices of different topologies and dimensions. The obtained Madelung energies have a satisfactory accuracy for all ranges of the screening parameter $\kappa$ of the Yukawa potential, and it becomes exact in the asymptotic limits $\kappa \to 0$ and $\kappa \to +\infty$. For instance, for the triangular lattice, the maximum relative error of the ME given by the method is about 0.0047. Also, satisfactory results are obtained for the one-component plasma limit. The Madelung constants of the two-dimensional hexagonal BN and square NaCl and the three-dimensional cubic NaCl crystals are estimated with a relative error of 0.004, 0.006, and 0.03, respectively. Finally, different ways to improve the method are presented and discussed.

Stable fluid filaments with diameters of several micrometers and slenderness ratios well above 1000 are unique objects formed by some liquid crystalline phases of bent-core mesogens. We present a technique to determine filament tensions from their deflection under defined loads. A strong temperature dependence is observed, with a minimum near the clearing temperature. Both the nonlinear relation between filament tension and diameter and the substantial increase of the tension with lower temperatures indicate contributions of volume terms, in addition to surface capillary forces. We discuss a model that relates these bulk terms to elastic forces, originating from the undulated smectic layer structure. This model can explain the origin of the filament stability.

We explore the mechanism behind the ambiguous nonlinear mechanical response of biopolymer networks and cells. Our theoretical analysis is based on the inelastic glassy wormlike chain model (iGWLC), which accounts for simultaneous softening and stiffening in terms of two antagonistic mechanisms: viscoelastic stress stiffening caused by polymer stretching, and inelastic fluidization caused by bond breaking. On this basis, we derive a set of simple schematic constitutive equations that faithfully reproduce the rich inelastic phenomenology of biopolymer networks and cells.

Focusing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the Lévy-Itô nature of the noise in the thermal conductance. For white noises, we prove that the Lévy-Itô composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a nonequilibrium linearly coupled chain, which signals the independence of mechanical and thermodynamical properties. In contrast, for the nonlinearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. The vast majority of the literature on the subject deals with affine normalization. We argue that more general normalizations are natural from a mathematical and physical point of view and work them out. The problem is approached using the language of renormalization-group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.

The linear noise approximation (LNA) offers a simple means by which one can study intrinsic noise in monostable biochemical networks. Using simple physical arguments, we have recently introduced the slow-scale LNA (ssLNA), which is a reduced version of the LNA under conditions of timescale separation. In this paper we present the first rigorous derivation of the ssLNA using the projection operator technique and show that the ssLNA follows uniquely from the standard LNA under the same conditions of timescale separation as those required for the deterministic quasi-steady-state approximation. We also show that the large molecule number limit of several common stochastic model reduction techniques under timescale separation conditions constitutes a special case of the ssLNA.

We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase.

The confining pressure $P$ is perhaps the most important parameter controlling the properties of granular matter. Strongly compressed granular media are, in many respects, simple solids in which elastic perturbations travel as ordinary phonons. However, the speed of sound in granular aggregates continuously decreases as the confining pressure decreases, completely vanishing at the jamming-unjamming transition. This anomalous behavior suggests that the transport of energy at low pressures should not be dominated by phonons. In this work we use simulations and theory to show how the response of granular systems becomes increasingly nonlinear as pressure decreases. In the low-pressure regime the elastic energy is found to be mainly transported through nonlinear waves and shocks. We numerically characterize the propagation speed, shape, and stability of these shocks and model the dependence of the shock speed on pressure and impact intensity by a simple analytical approach.

We report that the pressure coefficient of the glass transition temperature, $d{T}_g$/$dp$, which is commonly used to determine the pressure sensitivity of the glass transition temperature $T_g$, can be predicted in the thermodynamic scaling regime. We show that the equation derived from the isochronal condition combined with the well-known scaling, $T{V}^{\gamma }$ $=$ const, predicts successfully values of $d{T}_g$/$dp$ for a variety of glass-forming systems, including van der Waals liquids, polymers, and ionic liquids.