Three-dimensional semiflexible polymer networks are the structural building blocks of various biological and structural materials. Previous studies have primarily used two-dimensional models for understanding the behavior of these networks. In this paper, we develop a three-dimensional nonaffinity measure capable of providing direct comparison with continuum level homogenized quantities, i.e., strain field. The proposed nonaffinity measure is capable of capturing possible anisotropic microstructures of the filamentous networks. This strain-based nonaffinity measure is used to probe the mechanical behavior at different length scales and investigate the effects of network mechanical and microstructural properties. Specifically, it is found that although all nonaffinity measure components have a power-law variation with the probing length scale, the degree of nonaffinity decreases with increasing the length scale of observation. Furthermore, the amount of nonaffinity is a function of network fiber density, bending stiffness of the constituent filaments, and the network architecture. Finally, it is found that the two power-law scaling regimes previously reported for two-dimensional systems do not appear in three-dimensional networks. Also, unlike two-dimensional models, the exponent of the power-law relation depends weakly on the density of the three-dimensional networks.

Transition to defect-mediated turbulence in the ribbon patterns observed in a viscoelastic Taylor-Couette flow is investigated when the rotation rate of the inner cylinder is increased while the outer cylinder is fixed. In four polymer solutions with different values of the elasticity number, the defects appear just above the onset of the ribbon pattern and trigger the appearance of disordered oscillations when the rotation rate is increased. The flow structure around the defects is determined and the statistical properties of these defects are analyzed in the framework of the complex Ginzburg-Landau equation.

We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in flux would suggest. Nonlocality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling.

Molecular precursors, ultrathin films that precede spreading droplets, are still far from being understood, despite intensive study. The inherent microscopic length scales make small-scale experimental techniques and molecular simulation ideal methods to study this phenomenon. Previous work on molecular precursors using nanoscale droplets, however, consistently suffers from incorrect measurement of the dimensions of the precursor film. An alternative method to accurately characterize the precursor film is presented here. In contrast to previous measures, this method (i) allows for easy detection and characterization of precursors and (ii) yields wetting dynamics that agree with experimental observations. Finally, we briefly comment on previous studies whose conclusions may merit reconsideration in light of the present work.

We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional three-body system with periodic boundary conditions. We demonstrate that such a three-body system may be reduced isomorphically to a spatially periodic system of a single particle experiencing a two-dimensional potential on a rhombic plane. For the case of both Coulombic and gravitational versions, exact expressions of the Hamiltonian have been derived in rhombic coordinates. We simulate the phase-space evolution through an event-driven algorithm that utilizes analytic solutions to the equations of motion. The simulation results show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. While there is no evidence of global chaos in either the Coulombic or the gravitational system, the former exhibits a transition from a completely nonchaotic phase space at low energies to a mixed behavior. Gradual yet striking transitions from mild to intense chaos are indicated with changing energy, a behavior that differentiates the spatially periodic systems studied in this Rapid Communication from the well-understood free-boundary versions of the three-body problem. Our treatment of the three-body systems opens avenues for analysis of the dynamical properties exhibited by spatially periodic versions of various classes of systems studied in plasma and gravitational physics as well as in cosmology.

We disclose the origin of anisotropic percolation perimeters in terms of the stochastic Loewner evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multilayered and directed percolation clusters at criticality are the scaling limits of the Loewner evolution of an anomalous Brownian motion, being superdiffusive and subdiffusive, respectively. The connection between anomalous diffusion and fractal anisotropy is further tested by using long-range power-law correlated time series (fractional Brownian motion) as the driving functions in the evolution process. The fact that the resulting traces are distinctively anisotropic corroborates our hypothesis. Under the conceptual framework of SLE, our study therefore reveals different perspectives for mathematical and physical interpretations of non-Markovian processes in terms of anisotropic paths at criticality and vice versa.

A skewness of the probability for instantaneous current fluctuations, in a nonequilibrium steady state, is observed experimentally in a dusty plasma. This skewness is attributed to the spatial asymmetry, which is imminent to the nonequilibrium systems due to the external hydrodynamic gradient. Using the modern framework of the large deviation theory, we extend the Onsager-Machlup ansatz for equilibrium fluctuations to systems with a preferred spatial direction, and provide a modulated Gaussian probability distribution, which is tested by simulations. This probability distribution is also of potential interest for other statistical disciplines. Connections with the principles of statistical mechanics, due to Boltzmann and Gibbs, are discussed as well.

Two-dimensional (2D) multifractal detrended fluctuation analysis (MF-DFA) has been used to study monofractality and multifractality on 2D surfaces, but when it is used to calculate the generalized Hurst exponent in a fixed time scale, the presence of crossovers can bias the outcome. To solve this problem, multiscale multifractal analysis (MMA) was recent employed in a one-dimensional case. MMA produces a Hurst surface $h(q,s)$ that provides a spectrum of local scaling exponents at different scale ranges such that the positions of the crossovers can be located. We apply this MMA method to a 2D surface and identify factors that influence the results. We generate several synthesized surfaces and find that crossovers are consistently present, which means that their fractal properties differ at different scales. We apply MMA to the surfaces, and the results allow us to observe these differences and accurately estimate the generalized Hurst exponents. We then study eight natural texture images and two real-world images and find (i) that the moving window length (WL) and the slide length (SL) are the key parameters in the MMA method, that the WL more strongly influences the Hurst surface than the SL, and that the combination of $\mathrm{WL}=4$ and $\mathrm{SL}=4$ is optimal for a 2D image; (ii) that the robustness of $h(2,s)$ to four common noises is high at large scales but variable at small scales; and (iii) that the long-term correlations in the images weaken as the intensity of Gaussian noise and salt and pepper noise is increased. Our findings greatly improve the performance of the MMA method on 2D surfaces.

The generalized traveling wave method (GTWM) is applied to the nonlinear Schrödinger (NLS) equation with general perturbations in order to obtain the equations of motion for an ansatz with six collective coordinates, namely the soliton position, the amplitude, the inverse of the soliton width, the velocity, the chirp, and the phase. The advantage of the new ansatz is that it yields three pairs of canonically conjugated coordinates and momenta that all are well-behaved. The new ansatz is applied to model the dynamics of a soliton in a dispersion-shifted optical fiber described by the generalized NLS, including dissipation, higher-order dispersion, Raman scattering, and self-steepening perturbations. It is shown that the GTWM is equivalent to the modified method of moments, which considers the time variation of the norm, the first and the second moment of the norm, the momentum, the first moment of the momentum, and the energy for the perturbed NLS equation.

We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found. We argue how these transients are caused and can be understood by a hierarchy of block decompositions of the quasiperiodic lattice. A comparison to the cases of periodic and fully randomized lattices is performed.

Existing continuum descriptions of discrete adhesive birth-death-movement processes provide accurate predictions of the average discrete behavior for limited parameter regimes. Here we present an alternative continuum description in terms of the dynamics of groups of contiguous occupied and vacant lattice sites. Our method provides more accurate predictions, is valid in parameter regimes that could not be described by previous continuum descriptions, and provides information about the spatial clustering of occupied sites. Furthermore, we present a simple analytic approximation of the spatial clustering of occupied sites at late time, when the system reaches its steady-state configuration.

The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of topological volume, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analyses put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.

Despite over a century of characterization efforts, liquid-liquid critical point compositions are difficult to identify with good accuracy. Reported values vary up to 10% for even well-studied systems. Here, a technique is presented for high-precision determination of the critical composition of a partially miscible binary liquid system. Ninety-degree laser light-scattering intensities from single-phase samples are analyzed using an equation derived from nonclassical power laws and the pseudospinodal approximation. Results are reported for four liquid-liquid systems (aniline + hexane, isobutyric acid + water, methanol + cyclohexane, and methanol + carbon disulfide). Compared to other methods, the ${90}^{\circ }$ light-scattering approach has a strong dependence on composition near the critical point, is less affected by temperature fluctuations, and is insensitive to the presence of trace impurities in the samples. Critical compositions found with ${90}^{\circ }$ light scattering are precise to the parts-per-thousand level and show long-term reproducibility.

Film boiling on a horizontal surface is a typical example of the Rayleigh-Taylor instability. During the film boiling, phase changes take place at the interface, and thus heat and mass transfer must be taken into consideration in the stability analysis. Moreover, since the vapor layer is not quite thick, a viscous flow must be analyzed. Existing studies assumed equal kinematic viscosities of two fluids, and/or considered thin viscous fluids. The purpose of this study is to derive the analytical dispersion relation of the Rayleigh-Taylor instability for more general conditions. The two fluids have different properties. The thickness of the vapor layer is finite, but the liquid layer is thick enough to be nearly semi-infinite in view of perturbation. Initially, the vapor is in equilibrium with the liquid at the interface, and the direction of heat transfer is from the vapor side to the liquid side. In this case, the phase change has a stabilizing effect on the growth rate of the interface. When the vapor layer is thin, there is a coupled effect of the vapor viscosity, phase change, and vapor thickness on the critical wave number. For the other limit of a thick vapor, both the liquid and vapor viscosities influence the critical wave number. Finally, the most unstable wavelength is investigated. When the vapor layer is thin, the most unstable wavelength is not affected by phase change. When the vapor layer is thick, however, it increases with the increasing rate of phase change.

The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.

The drag anisotropy of slender filaments is a critical physical property allowing swimming in low-Reynolds number flows, and without it linear translation is impossible. Here we show that, in contrast, net rotation can occur under isotropic drag. We first demonstrate this result formally by considering the consequences of the force- and torque-free conditions on swimming bodies and we then illustrate it with two examples (a simple swimmers made of three rods and a model bacterium with two helical flagellar filaments). Our results highlight the different role of hydrodynamic forces in generating translational versus rotational propulsion.

We study the nonequilibrium steady states that emerge when two interacting three-dimensional Potts blocks slide on each other. As at equilibrium the Potts model exhibits different types of phase transitions for different numbers $q$ of spin states, we consider the following three cases: $q=2$ (i.e., the Ising case), $q=3$, and $q=9$, which at equilibrium yield, respectively, a second-order phase transition, a weak first-order transition, and a strong first-order transition. In our study we focus on the anisotropic character of the steady states that result from the relative motion and discuss the change in finite-size signatures when changing the number $q$ of spin states.

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

Numerical simulations of self-gravitating systems are generally based on $N$-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we perform one-dimensional Vlasov simulations of a long-standing cosmological problem, namely, the fractal properties of an expanding Einstein–de Sitter universe in Newtonian gravity. The $N$-body results are confirmed for high-density regions and extended to regions of low matter density, where the $N$-body approach usually fails.

Using the non-linear optimal velocity models as an example, we show that there exists an emergent intrinsic scale that characterizes the interaction strength between multiple clusters appearing in the solutions of such models. The interaction characterizes the dynamics of the localized quasisoliton structures given by the time derivative of the headways, and the intrinsic scale is analogous to the “charge” of the quasisolitons, leading to non-trivial cluster statistics from the random perturbations to the initial steady states of uniform headways. The cluster statistics depend both on the quasisoliton charge and the density of the traffic. The intrinsic scale is also related to an emergent quantity that gives the extremum headways in the cluster formation, as well as the coexistence curve separating the absolute stable phase from the metastable phase. The relationship is qualitatively universal for general optimal velocity models.