Our simulations show that dispersion can have a crucial effect on the patterns produced by oblique-incidence ion sputtering. It can lead to the formation of raised and depressed triangular regions traversed by parallel-mode ripples, and these bear a strong resemblance to nanostructures that are commonly observed in experiments. In addition, if dispersion and transverse smoothing are sufficiently strong, highly ordered ripples form. Finally, dispersion can cause the formation of protrusions and depressions that are elongated along the projected beam direction even when there is no transverse instability. This may explain why topographies of this kind form for high angles of ion incidence in cases in which ion-induced mass redistribution is believed to dominate curvature-dependent sputtering.

Plasticity in soft amorphous materials typically involves collective deformation patterns that emerge on intense shearing. The microscopic basis of amorphous plasticity has been commonly established through the notion of “Eshelby”-type events, localized abrupt rearrangements that induce flow in the surrounding material via nonlocal elastic-type interactions. This universal mechanism in flowing disordered solids has been proposed despite their diversity in terms of scales, microscopic constituents, or interactions. Using a numerical particle-based study, we argue that the presence of frictional interactions in granular solids alters the dynamics of flow by nucleating micro shear cracks that continually coalesce to build up system-spanning fracturelike formations on approach to failure. The plastic-to-brittle failure transition is controlled by the degree of frictional resistance which is in essence similar to the role of heterogeneities that separate the abrupt and smooth yielding regimes in glassy structures.

A method is proposed for the calculation of bulk viscosity, ${\mu }_b$, of dilute gases using nonequilibrium molecular dynamics (NEMD) simulations. The method uses measurement of mechanical ($P_{\mathrm{mech}}$) and thermodynamic pressure ($P_{\mathrm{thermo}}$) in a NEMD simulation of an expanding fluid and then relates the bulk viscosity to them by the relation ${\mu }_b=(P_{\mathrm{mech}}-P_{\mathrm{thermo}})/\mathbf{\nabla }·\vec{u}$, where $\mathbf{\nabla }·\vec{u}$ is the controlled rate of expansion of the fluid per unit volume. A special emphasis is given to the fundamental physical understanding of bulk viscosity in this work. The proposed method is demonstrated for the estimation of bulk viscosity of dilute nitrogen gas in the temperature range of 200–800 K. Variation of bulk viscosity with temperature is reported in the above-mentioned temperature range and is found to be in a reasonably good agreement with the data available in the literature. Furthermore, variation of bulk viscosity with pressure and volumetric expansion rate is obtained. A weak linear dependency of bulk viscosity with pressure is observed, which increases with temperature. However, no significant effect of the rate of volumetric expansion is observed until ${10}^8{\mathrm{s}}^{-1}$. Moreover, the effect of the direction of volumetric change (expansion vs. compression) is also demonstrated in this work.

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes and use them to calculate the time evolution of two dynamical quantities for the system, namely, the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times $1\lesssim t\lesssim L^{z_c}$, where $z_c=4-\eta =15/4$ is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the generalized Langevin equation with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.

Avalanches whose sizes and durations are distributed as power laws appear in many contexts, from physics to geophysics and biology. Here we show that there is a hidden peril in thresholding continuous times series—from either empirical or synthetic data—for the identification of avalanches. In particular, we consider two possible alternative definitions of avalanche size used, e.g., in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that (1) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (2) if—as sometimes done in the literature—avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. This problem—that we have detected in some recent works—leads to misinterpretations of the resulting scaling regimes.

The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for non-Markovian systems; therefore, we investigate the thermodynamic uncertainty relation for time-delayed Langevin systems. We prove that the fluctuation of arbitrary dynamical observables is constrained by the Kullback-Leibler divergence between the distributions of the forward path and its reversed counterpart. Specifically, for observables that are antisymmetric under time reversal, the fluctuation is bounded from below by a function of a quantity that can be identified as a generalization of the total entropy production in Markovian systems. We also provide a lower bound for arbitrary observables that are odd under position reversal. The term in this bound reflects the extent to which the position symmetry has been broken in the system and can be positive even in equilibrium. Our results hold for finite observation times and a large class of time-delayed systems because detailed underlying dynamics are not required for the derivation. We numerically verify the derived uncertainty relations using two single time-delay systems and one distributed time-delay system.

We fully describe the mechanisms underlying synchronization in starlike networks of phase oscillators. In particular, the routes to synchronization and the critical points for the associated phase transitions are determined analytically. In contrast to the classical Kuramoto theory, we unveil that relaxation rates to each equilibrium state indeed exist and remain invariant under three levels of descriptions corresponding to different geometric implications. The special symmetry in the coupling determines a quasi-Hamiltonian property, which is further unveiled on the basis of singular perturbation theory. Since starlike coupling configurations constitute the building blocks of technological and biological real world networks, our paper paves the way towards the understanding of the functioning of such real world systems in many practical situations.

An efficient flow assignment strategy is of great importance to alleviate traffic congestion on multilayer networks. In this work, by considering the roles of nodes' local structures on the microlevel, and the different transporting speeds of layers in the macrolevel, an effective traffic-flow assignment strategy on multilayer networks is proposed. Both numerical and semianalytical results indicate that our proposed flow assignment strategy can reasonably redistribute the traffic flow of the low-speed layer to the high-speed layer. In particular, preferentially transporting the packets through small-degree nodes on the high-speed layer can enhance the traffic capacity of multilayer networks. We also find that the traffic capacity of multilayer networks can be improved by increasing the network size and the average degree of the high-speed layer. For a given multilayer network, there is a combination of optimal macrolevel parameter and optimal microlevel parameter with which the traffic capacity can be maximized. It is verified that real-world network topology does not invalidate the results. The semianalytical predictions agree with the numerical simulations.

We use a coarse-grained molecular dynamics simulation to investigate the interaction between neutral or charged nanoparticles (NPs) and a vesicle consisting of neutral and negatively charged lipids. We focus on the interaction strengths of hydrophilic and hydrophobic attraction and electrostatic interactions between a lipid molecule and an NP. A neutral NP passes through the lipid membrane when the hydrophobic interaction is sufficiently strong. As the valence of the positively charged NP increases, the membrane permeation speed of the NP is increased compared with the neutral NP and charged lipids are accumulated around the charged NP. A charged NP with a high valence passes through the lipid membrane via a transient channel formed by charged lipids or transportlike endocytosis. These permeation processes can be classified based on analyses of the density correlation function. When the nonelectrostatic interaction parameters are large enough, a negatively charged NP can be adsorbed on the membrane and a neutral lipid-rich region is formed directly below the NP. The NP is spontaneously incorporated into the vesicle under various conditions and the incorporation is mediated by the membrane curvature. We reveal how the NP's behavior depends on the NP valence, size, and the nonelectrostatic interaction parameters.

Granular materials immersed in a fluid are ubiquitous in daily life, industry, and nature. They include food processing, pastes, cosmetics, paints, concretes, cements, muds, wet sands, snows, landslides, and lava flow. They are known to exhibit a rich variety of complex rheological behavior, but the role of a fluid component in such behavior has remained poorly understood due to the nonlocal and many-body nature of hydrodynamic interactions between solid particles mediated by the fluid. We address this fundamental problem by comparing the microrheological response of athermal granular suspensions with and without hydrodynamic interactions to an externally driven probe particle by numerical simulations. We find that the presence of the fluid drastically increases the drag coefficient of the probe particle by more than one order of magnitude near the jamming transition. We reveal that this is a consequence of the nontrivial long-range nature of hydrodynamic interactions, which originates from unlimited cumulative transmission of near-field hydrodynamic interactions due to the incompressibility of both fluid and solid particles. Force chain formation of solid particles is dynamically coupled with hydrodynamic flow, leading to strong spatiotemporal fluctuations of flow pattern and nonlinear rheological response. Our study reveals essential roles of hydrodynamic interactions in complex rheological behavior of dense granular suspensions under an external drive.

The interaction between a planar shock wave and a spherical flame is studied numerically for an ethylene-oxygen-nitrogen gas mixture. Influences of different initial reactive gas mixture gradients on the shock-flame interaction are investigated by using high-resolution computational simulations. The results show that the different reactive gas mixture gradients can greatly affect the flame evolution in shock accelerated flow. A detonation only emerges in the homogenous reactive gas mixture case, but a distinct shock bifurcation can be found in the inhomogeneous cases where the leftward reflected shock wave propagates in a reverse flow with a high transverse velocity gradient in the inhomogeneous cases. Also, the flame volume and heat release rate increase when the distribution of the reactive gas mixture is uniform or with a positive gradient in this paper, but decrease when the distribution of the reactive gas mixture is with a negative gradient, however, the ratio of unburned to burned regions in the flame zone shows just the opposite trends. Furthermore, the factors affecting the vorticity generation are also analyzed. It is found that the compression term has a relatively stronger influence on the vorticity generation in all the three cases except the period before the reflected shock wave impinges on the distorted flame in the homogeneous case, wherein the baroclinic effect dominates the vorticity generation in the flame zone.

The ubiquitous Lévy $\alpha$-stable distributions lack general closed-form expressions in terms of elementary functions—Gaussian and Cauchy cases being notable exceptions. To better understand this 80-year-old conundrum, we study the complex analytic continuation $p_{\alpha }\left(z\right)$, $z\in \mathbb{C}$, of the symmetric Lévy $\alpha$-stable distribution family $p_{\alpha }\left(x\right)$, $x\in \mathbb{R}$, parametrized by $0<\alpha \le 2$. We first extend known but obscure results, and give a new proof that $p_{\alpha }\left(z\right)$ is holomorphic on the entire complex plane for $1<\alpha \le 2$, whereas $p_{\alpha }\left(z\right)$ is not even meromorphic on $\mathbb{C}$ for $0<\alpha <1$. Next, we unveil the complete complex analytic structure of $p_{\alpha }\left(z\right)$ using domain coloring. Finally, motivated by these insights, we argue that there cannot be closed-form expressions in terms of elementary functions for $p_{\alpha }\left(x\right)$ for general $\alpha$.

A systematic analytic treatment of local fluctuations in the regularized Laplacian growth problem is given. The interface dynamics is stabilized by a short-distance cutoff $\hslash$ preventing the cusps production in a finite time. The regularization mechanism results in the violation of the incompressibility condition of the viscous fluid on a microscale in the vicinity of the moving interface, thus producing local fluctuations of pressure. Dissipation of fluctuations with time is described by universal Dyson Brownian motion, which reduces to the complex viscous Burgers equation in the hydrodynamic approximation. Because of the intrinsic instability of the interface dynamics, tiny fluctuations of pressure generate universal complex patterns with well developed fjords and fingers in a long time asymptotic.

A one-parametric stochastic regularized dynamics of the interface in the Hele-Shaw cell is introduced. The short-distance regularization suggested by the aggregation model stabilizes the growth by preventing the formation of cusps at the interface and makes the interface dynamics chaotic. The introduced stochastic growth process generates universal complex patterns with the well-developed fjords of oil separating the fingers of water. In a long time asymptotic, by coupling a conformal field theory to the stochastic growth process, we introduce a set of observables (the martingales), whose expectation values are constant in time. The martingales are closely connected to degenerate representations of the Virasoro algebra and can be written in terms of conformal correlation functions. A direct link between Laplacian growth and conformal Liouville field theory with the central charge $c\ge 25$ is proposed.

DNA replication fidelity is a critical issue in molecular biology. Biochemical experiments have provided key insights on the mechanism of fidelity control by DNA polymerases in the past decades, whereas systematic theoretical studies on this issue began only recently. Because of the underlying difficulties of mathematical treatment, comprehensive surveys on the template-specific replication kinetics are still rare. Here we propose a first-passage approach to address this problem, in particular the positional fidelity, for complicated processes with high-order neighbor effects. Under biologically relevant conditions, we derived approximate analytical expressions of the positional fidelity which show intuitively how some key kinetic pathways are coordinated to guarantee the high fidelity, as well as the high velocity, of the replication processes. It is also shown that the fidelity at any template position is dominantly determined by the nearest-neighbor template sequences, which is consistent with the idea that replication mutations are randomly distributed in the genome.

Cooperative self-assembly is a ubiquitous phenomenon found in natural systems which is used for designing nanostructured materials with new functional features. Its origin and mechanisms, leading to improved functionality of the assembly, have attracted much attention from researchers in many branches of science and engineering. These complex structures often come with hyperbolic geometry; however, the relation between the hyperbolicity and their spectral and dynamical properties remains unclear. Using the model of aggregation of simplexes introduced by Šuvakov et al. [Sci. Rep. 8, 1987 (2018)], here we study topological and spectral properties of a large class of self-assembled structures or nanonetworks consisting of monodisperse building blocks (cliques of size $n=3,4,5,6$) which self-assemble via sharing the geometrical shapes of a lower order. The size of the shared substructure is tuned by varying the chemical affinity $\nu$ such that for significant positive $\nu$ sharing the largest face is the most probable, while for $\nu <0$, attaching via a single node dominates. Our results reveal that, while the parameter of hyperbolicity remains ${\delta }_{max}=1$ across the assemblies, their structure and spectral dimension $d_s$ vary with the size of cliques $n$ and the affinity when $\nu \ge 0$. In this range, we find that $d_s>4$ can be reached for $n\ge 5$ and sufficiently large $\nu$. For the aggregates of triangles and tetrahedra, the spectral dimension remains in the range $d_s\in [2,4)$, as well as for the higher cliques at vanishing affinity. On the other end, for $\nu <0$, we find $d_s\eqsim 1.57$ independently on $n$. Moreover, the spectral distribution of the normalized Laplacian eigenvalues has a characteristic shape with peaks and a pronounced minimum, representing the hierarchical architecture of the simplicial complexes. These findings show how the structures compatible with complex dynamical properties can be assembled by controlling the higher-order connectivity among the building blocks.

Using grand-canonical Monte Carlo simulations, we investigate the phase diagram of hard rods of length $L$ with additional contact (sticky) attractions on square and cubic lattices. The phase diagram shows a competition between gas-liquid and ordering transitions (which are of demixing type on the square lattice for $L\ge 7$ and of nematic type on the cubic lattice for $L\ge 5$). On the square lattice, increasing attractions initially lead to a stabilization of the isotropic phase. On the cubic lattice, the nematic transition remains of weak first order upon increasing the attractions. In the vicinity of the gas-liquid transition, the coexistence gap of the nematic transition quickly widens. These features are different from nematic transitions in the continuum.

This work analyzes the porosity effects on laminar flow and drag reduction of Newtonian fluids flowing over and through permeable surfaces. A fully developed laminar flow in a channel partially replaced with a porous material is considered. The analytical solutions for the velocity and shear stress are given and examined to identify the influence of the porosity on the flow. The scaling laws in the porous media are determined using asymptotic analysis in the limit of infinitely small permeability. Direct numerical simulations are performed and the transport equation for the kinetic energy is examined to establish the dependency of the porosity on the flow. We found that the impact of the porosity depends on the permeability. For high permeability, the higher porosity induces the increase of driving force and accelerates the flow while it decelerates the flow for low permeability by causing stronger viscous drag of the porous medium.

We investigate numerically the flow of an electrically conducting fluid in a rapidly rotating spherical shell where the inner boundary spins slightly faster than the outer one. The magnetic field evolves self-consistently from an initial dipolar configuration of weak amplitude, and a toroidal field is produced by winding this poloidal field through the internal differential rotation. First, we characterize the axisymmetric field solutions obtained at long times when the Lorentz force is negligible and the flow follows the steady, purely hydrodynamical solution. We then examine the stability of these solutions, focusing on the regime of large magnetic Reynolds numbers where the field is dominantly toroidal. When the ratio of the azimuthal Alfvén frequency to the rotation frequency exceeds a certain value, a nonaxisymmetric instability develops. We show that the instability properties are compatible with those expected for the magnetorotational instability. Finally, we compare the instability properties with predictions obtained from a local linear stability analysis. The linear analysis agrees well with the numerical simulation results, except in a number of cases where the discrepancies are attributed to shearing effects on the unstable modes.