Modern large engineered network systems normally work in cooperation and incorporate dependencies between their components for purposes of efficiency and regulation. Such dependencies may become a major risk since they can cause small-scale failures to propagate throughout the system. Thus, the dependent nodes could be a natural target for malicious attacks that aim to exploit these vulnerabilities. Here we consider a type of targeted attack that is based on the dependencies between the networks. We study strategies of attacks that range from dependency-first to dependency-last, where a fraction $1-p$ of the nodes with dependency links, or nodes without dependency links, respectively, are initially attacked. We systematically analyze, both analytically and numerically, the percolation transition of partially interdependent networks, where a fraction $q$ of the nodes in each network are dependent on nodes in the other network. We find that for a broad range of dependency strength $q$, the “dependency-first” attack strategy is actually less effective, in terms of lower critical percolation threshold $p_c$, compared with random attacks of the same size. In contrast, the “dependency-last” attack strategy is more effective, i.e., higher $p_c$, compared with a random attack. This effect is explained by exploring the dynamics of the cascading failures initiated by dependency-based attacks. We show that while “dependency-first” strategy increases the short-term impact of the initial attack, in the long term the cascade slows down compared with the case of random attacks and vice versa for “dependency-last.” Our results demonstrate that the effectiveness of attack strategies over a system of interdependent networks should be evaluated not only by the immediate impact but mainly by the accumulated damage during the process of cascading failures. This highlights the importance of understanding the dynamics of avalanches that may occur due to different scenarios of failures in order to design resilient critical infrastructures.

We discuss the design of interlayer edges in a multiplex network, under a limited budget, with the goal of improving its overall performance. We analyze the following three problems separately; first, we maximize the smallest nonzero eigenvalue, also known as the algebraic connectivity; second, we minimize the largest eigenvalue, also known as the spectral radius; and finally, we minimize the spectral width. Maximizing the algebraic connectivity requires identical weights on the interlayer edges for budgets less than a threshold value. However, for larger budgets, the optimal weights are generally nonuniform. The dual formulation transforms the problem into a graph realization (embedding) problem that allows us to give a fuller picture. Namely, before the threshold budget, the optimal realization is one-dimensional with nodes in the same layer embedded to a single point, while beyond the threshold, the optimal embeddings generally unfold into spaces with dimension bounded by the multiplicity of the algebraic connectivity. Finally, for extremely large budgets the embeddings again revert to lower dimensions. Minimizing the largest eigenvalue is driven by the spectral radius of the individual networks and its corresponding eigenvector. Before a threshold, the total budget is distributed among interlayer edges corresponding to the nodal lines of this eigenvector, and the optimal largest eigenvalue of the Laplacian remains constant. For larger budgets, the weight distribution tends to be almost uniform. In the dual picture, the optimal graph embedding is one-dimensional and nonhomogeneous at first, with the nodes corresponding to the layer with the largest spectral radius distributed on a line according to its eigenvector, while the other layer is embedded at the origin. Beyond this threshold, the optimal embedding expands to be multidimensional, and for larger values of the budget, the two layers fill the embedding space. Finally, we show how these two problems are connected to minimizing the spectral width.

We used inelastic x-ray scattering to gain insight into the complex terahertz dynamics of a diluted Au-nanoparticle suspension in glycerol. We observe that, albeit sparse, Au nanoparticles leave clear signatures on the dynamic response of the system, the main one being an additional mode propagating at the nanoparticle-glycerol interface. A Bayesian inferential analysis of the line shape reveals that such a mode, at variance with conventional acoustic modes, keeps a hydrodynamiclike behavior well beyond the continuous limit and down to subnanometer distances.

We present a detailed study of the kinetic cluster growth process during gelation of weakly attractive colloidal particles by means of experiments on critical Casimir attractive colloidal systems, simulations, and analytical theory. In the experiments and simulations, we follow the mean coordination number of the particles during the growth of clusters to identify an attractive-strength independent cluster evolution as a function of mean coordination number. We relate this cluster evolution to the kinetic attachment and detachment rates of particles and particle clusters. We find that single-particle detachment dominates in the relevant weak attractive-strength regime, while association rates are almost independent of the cluster size. Using the limit of single-particle dissociation and size-independent association rates, we solve the master kinetic equation of cluster growth analytically to predict power-law cluster mass distributions with exponents $-3/2$ and $-5/2$ before and after gelation, respectively, which are consistent with the experimental and simulation data. These results suggest that the observed critical Casimir-induced gelation is a second-order nonequilibrium phase transition (with broken detailed balance). Consistent with this scenario, the size of the largest cluster is observed to diverge with power-law exponent according to three-dimensional percolation on approaching the critical mean coordination number.

Ordered crack patterns contain plentiful physical mechanisms and are useful for technological applications such as lithography, template, and biomimicry. Here we report on ordered multiple ring-shaped cracks induced by indentation in metal films on soft elastic polydimethylsiloxane (PDMS) substrates. It is shown that the indentation triggers the deformation of PDMS substrate and generates a radial tensile stress in the film, leading to the formation of ring-shaped cracks with a nearly uniform spacing. The morphological characteristics and evolution behaviors of the multiple ring-shaped cracks are revealed by optical microscopy, atomic force microscopy, and scanning electron microscopy. Their formation mechanisms are discussed by theoretical analysis based on the fracture mechanics. The report in this work can promote better understanding of the indentation-induced stress anisotropy and mode competition in rigid-film–soft-substrate systems and provide a facile strategy to control the crack patterns by simple mechanical loading.

We present a systematic numerical investigation concerning the combined effects of sliding friction and particle shape (i.e., angularity) parameters on the shear strength and microstructure of granular packings. Sliding friction at contacts varied from 0 (frictionless particles) to 0.7, and the particles were irregular polygons with an increasing number of sides, ranging from triangles to disks. We find that the effect of local friction on shear strength follows the same trend for all shapes. Strength first increases with local friction and then saturates at a shape-dependent value. In contrast, the effect of angularity varies, depending on the level of sliding friction. For low friction values (i.e., under 0.3), the strength first increases with angularity and then declines for the most angular shapes. For high friction values, strength systematically increases with angularity. At the microscale, we focus on the connectivity and texture of the contact and force networks. In general terms, increasing local friction causes these networks to be less connected and more anisotropic. In contrast, increasing particle angularity may change the network topology in different directions, directly affecting the macroscopic shear strength. These analyses and data constitute a first step toward understanding the joint effect of local variables such as friction and grain shape on the macroscopic rheology of granular systems.

The homogenization approach to wave propagation through saturated porous media is extended in order to include the compressibility of the interstitial fluid and the existence of several connected pore components which may or not percolate. The necessary theoretical developments are summarized and the Christoffel equation whose solutions provide the wave velocities is presented. Some analytical developments are proposed for isotropic media. Finally, a systematic application to a synthetic porous medium illustrates the methodology and its results.

We investigate the sedimentation of initially packed paramagnetic particles in the presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle-induced magnetic interactions are significantly smaller compared to the gravitational acceleration, we do observe a measurable reduction of the decompaction rate as the amplitude of the applied magnetic field is increased. While induced magnetic dipole-dipole interactions between particles can be either attractive or repulsive depending on the particles relative alignment, our observations reveal an effective overall enhancement of the cohesion of the initial pack of particles due to the induced interactions, very likely promoting internal chain forces in the initial pack of particles. The influence of the magnetic field on the particles once they disperse after being decompacted is, however, found to remain marginal.

We focus on the self-propelled motion of an oil droplet within an aqueous phase or an aqueous droplet within an oil phase, which originates from an interfacial chemical reaction of surfactant. The droplet motion has been explained by mathematical models, which require the assumption that the chemical reaction increases the interfacial tension. However, several experimental reports have demonstrated self-propelled motion with the chemical reaction decreasing the interfacial tension. Our motivation is to construct an improved mathematical model, which explains these experimental observations. In this process, we consider the concentrations of the reactant and product on the interface and of the reactant in the bulk. Our numerical calculations indicate that the droplet potentially moves in the cases of both an increase and a decrease in the interfacial tension. In addition, the reaction rate and size dependencies of the droplet speed observed in experiments were well reproduced using our model. These results indicate the potential of our model as a universal one for droplet motion.

We report the results of simulations of rigid colloidal helices suspended in a shear flow, using dissipative particle dynamics for a coarse-grained representation of the suspending fluid, as well as deterministic trajectories of non-Brownian helices calculated from the resistance tensor derived under the slender-body approximation. The shear flow produces nonuniform rotation of the helices, similarly to other high aspect ratio particles, such that more elongated helices spend more time aligned with the fluid velocity. We introduce a geometric effective aspect ratio calculated directly from the helix geometry and a dynamical effective aspect ratio derived from the trajectories of the particles and find that the two effective aspect ratios are approximately equal over the entire parameter range tested. We also describe observed transient deflections of the helical axis into the vorticity direction that can occur when the helix is rotating through the gradient direction and that depend on the rotation of the helix about its axis.

Nonlinear dispersion relation for the finite-amplitude dust acoustic modes is obtained taking into account resonant particle trapping in the wave. The kinetic model predicts a frequency shift scaling $\propto \sqrt{\varphi }$ relative to the linear dispersion relation with $\varphi$ being the wave amplitude of the electrostatic potential. The species contributions to the nonlinear frequency shift have opposite sign: positive for trapped electrons and ions and negative for particles. It is shown that the relative importance of these contributions depends on the electron-to-ion or particle temperature ratio, particle charge, and Havnes parameter. In typical complex plasma experiments, the kinetic frequency shift is dominated by the positive ion contribution. As a result, the nonlinear modification of the dispersion relation affects the wave dispersion properties and may provide the acoustic-like behavior to the wave number domain $k{\lambda }_{Di}\sim 1$.

In this paper, the nonlinear interaction between kinetic instabilities driven by multiple ion beams and magnetized electrons is investigated. Electron diffusion across magnetic field lines is enhanced by the coupling of plasma instabilities. A two-dimensional collisionless particle-in-cell simulation is performed accounting for singly and doubly charged ions in a cross-field configuration. Consistent with prior linear kinetic theory analysis and observations from coherent Thomson scattering experiments, the present simulations identify an ion-ion two-stream instability due to multiply charged ions (flowing in the direction parallel to the applied electric field) which coexists with the electron cyclotron drift instability (propagating perpendicular to the applied electric field and parallel to the $E\times B$ drift). Small-scale fluctuations due to the coupling of these naturally driven kinetic modes are found to be a mechanism that can enhance cross-field electron transport and contribute to the broadening of the ion velocity distribution functions.

In this paper, we demonstrate that the lattice Boltzmann method can be successfully adopted to investigate the dynamics of epidemics. Numerical simulations prove the excellent accuracy properties of the approach, which recovers the solution of the popular SIR model. Because spatial effects are naturally accounted for in the lattice Boltzmann formulation, the present scheme appears to be more competitive than traditional solution procedures. Interestingly, it allows us to simulate scenarios characterized by selective lockdown configurations.

We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is studied to quantify the channel diversity and to assess a specific system's performance. System-specific features such as unstirred field components give rise to nontrivial interchannel correlations and need to be properly accounted for in modeling based on random matrix theory. To address this challenge, we propose a two-step hybrid approach. Based on an ensemble of experimentally measured scattering matrices for different random metasurface configurations, we first learn a system-specific pair of coupling matrix and unstirred contribution to the Hamiltonian, and then add an appropriately weighted stirred contribution. We verify that our method is capable of reproducing the experimentally found distribution of the effective rank with good accuracy. The approach can also be applied to other wave phenomena in complex media.

We investigate the transport properties of an anharmonic oscillator, modeled by a single-site Bose-Hubbard model, coupled to two different thermal baths using the numerically exact thermofield based chain-mapping matrix product states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the nonequilibrium dynamics of strongly interacting system irrespective of the system-bath coupling against the global master equation approach in Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site interactions, temperature bias as well as the system-bath couplings on the steady-state transport properties. Last, we also show evidence of non-Markovian dynamics by studying the nonmonotonicity of the time evolution of the trace distance between two different initial states.

Nanoscale pattern formation on the surface of a solid that is bombarded with a broad ion beam is studied for angles of ion incidence, $\theta$, just above the threshold angle for ripple formation, ${\theta }_c$. We carry out a systematic expansion in powers of the small parameter $\epsilon \equiv {(\theta -{\theta }_c)}^{1/2}$ and retain all terms up to a given order in $\epsilon$. In the case of two diametrically opposed, obliquely incident beams, the equation of motion close to threshold and at sufficiently long times is rigorously shown to be a particular version of the anisotropic Kuramoto-Sivashinsky equation. We also determine the long-time, near-threshold scaling behavior of the rippled surface's wavelength, amplitude, and transverse correlation length for this case. When the surface is bombarded with a single obliquely incident beam, linear dispersion plays a crucial role close to threshold and dramatically alters the behavior: highly ordered ripples can emerge at sufficiently long times and solitons can propagate over the solid surface. A generalized crater function formalism that rests on a firm mathematical footing is developed and is used in our derivations of the equations of motion for the single and dual beam cases.

Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known divergences in the Landau–de Gennes formulation. Our results agree with the asymptotic results of Dzyaloshinskii for the Frank-Oseen energy far from the defect core, but reveal biaxial order at intermediate distances from the core, crossing over to uniaxial but axisymmetric configurations as the core is approached. The elastic terms considered in our energy allow for the separate control of surface tension, anchoring, and elasticity contrast, and are used to analyze recent results for lyotropic chromonic liquid crystals. The latter display unusually large defect cores (on the order of tens of microns) which can be used for a quantitative comparison with the theory. Both $\pm 1/2$ disclination configurations are well reproduced by our calculations. Elastic anisotropy is also shown to lead to qualitative changes in the disclination polarization, a quantity that is proportional to the active stress in models of active matter.

The gradient-based optimization method for deep machine learning models suffers from gradient vanishing and exploding problems, particularly when the computational graph becomes deep. In this work, we propose the tangent-space gradient optimization (TSGO) for probabilistic models to keep the gradients from vanishing or exploding. The central idea is to guarantee the orthogonality between variational parameters and gradients. The optimization is then implemented by rotating the parameter vector towards the direction of gradient. We explain and test TSGO in tensor network (TN) machine learning, where TN describes the joint probability distribution as a normalized state $\left|\psi \right.〉$ in Hilbert space. We show that the gradient can be restricted in tangent space of $\langle \psi |\psi \rangle =1$ hypersphere. Instead of additional adaptive methods to control the learning rate $\eta$ in deep learning, the learning rate of TSGO is naturally determined by rotation angle $\theta$ as $\eta =tan\theta$. Our numerical results reveal better convergence of TSGO in comparison to the off-the-shelf Adam.