The dynamics of a planar crack propagating within a brittle disordered material is investigated numerically. The fracture front evolution is described as the depinning of an elastic line in a random field of toughness. The relevance of this approach is critically tested through the comparison of the roughness front properties, the statistics of avalanches, and the local crack velocity distribution with experimental results. Our simulations capture the main features of the fracture front evolution as measured experimentally. However, some experimental observations such as the velocity distribution are not consistent with the behavior of an elastic line close to the depinning transition. This discrepancy suggests the presence of another failure mechanism not included in our model of brittle failure.

Materials often fail when subjected to stresses over a prolonged period. The time to failure, also called the lifetime, is known to exhibit large variability of many materials, particularly brittle and quasibrittle materials. For example, a coefficient of variation reaches 100% or even more. Its distribution shape is highly skewed toward zero lifetime, implying a large number of premature failures. This behavior contrasts with that of normal strength, which shows a variation of only 4%–10% and a nearly bell-shaped distribution. The fundamental cause of this large and unique variability of lifetime is not well understood because of the complex interplay between stochastic processes taking place on the molecular level and the hierarchical and disordered structure of the material. We have constructed fiber network models, both regular and random, as a paradigm for general material structures. With such networks, we have performed Monte Carlo simulations of creep failure to establish explicit relationships among fiber characteristics, network structures, system size, and lifetime distribution. We found that fiber characteristics have large, sometimes dominating, influences on the lifetime variability of a network. Among the factors investigated, geometrical disorders of the network were found to be essential to explain the large variability and highly skewed shape of the lifetime distribution. With increasing network size, the distribution asymptotically approaches a double-exponential form. The implication of this result is that, so-called “infant mortality,” which is often predicted by the Weibull approximation of the lifetime distribution, may not exist for a large system.

Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid, and contained in a rigid container, these modes satisfy Poincaré's equation that has the peculiarity of being hyperbolic with boundary conditions. Inertial modes are, therefore, solutions of an ill-posed boundary-value problem. In this paper, we investigate the mathematical side of this problem. We first show that the Poincaré problem can be formulated in the Hilbert space of square-integrable functions, with no hypothesis on the continuity or the differentiability of velocity fields. We observe that with this formulation, the Poincaré operator is bounded and self-adjoint, and as such, its spectrum is the union of the point spectrum (the set of eigenvalues) and the continuous spectrum only. When the fluid volume is an ellipsoid, we show that the inertial modes form a complete base of polynomial velocity fields for the square-integrable velocity fields defined over the ellipsoid and meeting the boundary conditions. If the ellipsoid is axisymmetric, then the base can be identified with the set of Poincaré modes, first obtained by Bryan [Philos. Trans. R. Soc. London 180, 187 (1889)], and completed with the geostrophic modes.

We propose a scheme based on a multidimensional Chebyshev interpolation to approximate smooth functions that depend on more than one variable. The present method generalizes the one dimensional Chebyshev approximation. The multidimensional approach can be used for generating databases like equation of state in the warm and hot dense matter. It is well suited to the present advance of massively parallel supercomputers.

The functional window is an experimentally observed property of the avian compass that refers to its selectivity around the geomagnetic-field strength. We show that the simple radical-pair model, using biologically feasible hyperfine parameters, can qualitatively explain the salient features of the avian compass as observed in behavioral experiments: its functional window, as well as disruption of the compass action by radio-frequency fields of specific frequencies. Further, we show that adjustment of the hyperfine parameters can tune the functional window, suggesting a possible mechanism for its observed adaptation to field variation. While these lend support to the radical-pair model, we find that in its simplest form—or even with minor augmentations—it cannot quantitatively explain the observed width of the functional window. This suggests deeper generalization of the model, possibly in terms of more nuclei or more subtle environmental interaction than has been considered hitherto. Finally, we examine a possible biological purpose for the functional window; even assuming evolutionary benefit from radical-pair magnetoreception, it seems likely that the functional window could be just a corollary thereof, imparting no additional advantage.

We use stochastic rotation dynamics (SRD) to examine the dynamics of the ejection of an initially strongly confined flexible polymer from a spherical capsid with and without hydrodynamics. The results obtained using stochastic rotation dynamics (SRD) are compared to similar Langevin simulations. Inclusion of hydrodynamic modes speeds up the ejection but also allows the part of the polymer outside the capsid to expand closer to equilibrium. This shows as higher values of radius of gyration when hydrodynamics are enabled. By examining the waiting times of individual polymer beads, we find that the waiting time $t_w$ grows with the number of ejected monomers $s$ as a sum of two exponents. When $\approx 63\%$ of the polymer has ejected, the ejection enters the regime of slower dynamics. The functional form of $t_w$ versus $s$ is universal for all ejection processes starting from the same initial monomer densities. Inclusion of hydrodynamics only reduces its magnitude. Consequently, we define a universal scaling function $h$ such that the cumulative waiting time $t=N_{0}h(s/N_0)$ for large $N_0$. Our unprecedentedly precise measurements of force indicate that this form for $t_w\left(s\right)$ originates from the corresponding force toward the pore decreasing superexponentially at the end of the ejection. Our measured $t_w\left(s\right)$ explains the apparent superlinear scaling of the ejection time with the polymer length for short polymers. However, for asymptotically long polymers, $t_w\left(s\right)$ predicts linear scaling.

The effect of an electric field along the longitudinal axis of a nanoscale liquid thread is studied to understand the mechanism of breakup. The Rayleigh instability (commonly known as the Plateau–Rayleigh instability) of a nanosized liquid water thread is investigated by using molecular dynamics simulations. The breakup mechanism of the liquid nanothread is studied by analyzing the temporal evolution of the thread radius. The influence of the temperature of the liquid nanothread and the electric-field strength on the stability and breakup is the major focus of the study. The results show that the axial electric field has a stabilizing effect even at nanoscale. The results from the simulations are in good agreement with the solutions obtained from the dispersion relation developed by Hohman et al. for the liquid thread. The critical electric-field strength necessary to avoid the breakup of the liquid thread is calculated and other effects such as the splaying and whipping instability are also discussed.

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such cases, one compromises and instead seeks nearly maximally predictive features. Here, we derive upper bounds on the rates at which the number and the coding cost of nearly maximally predictive features scale with desired predictive power. The rates are determined by the fractal dimensions of a process' mixed-state distribution. These results, in turn, show how widely used finite-order Markov models can fail as predictors and that mixed-state predictive features can offer a substantial improvement.

Antifreeze proteins (AFPs) are the key biomolecules that protect many species from suffering the extreme conditions. Their unique properties of antifreezing provide the potential of a wide range of applications. Inspired by the present experimental approaches of creating an antifreeze surface by coating AFPs, here we present a two-dimensional random-field lattice Ising model to study the effect of AFPs on heterogeneous ice nucleation. The model shows that both the size and the free-energy effect of individual AFPs and their surface coverage dominate the antifreeze capacity of an AFP-coated surface. The simulation results are consistent with the recent experiments qualitatively, revealing the origin of the surprisingly low antifreeze capacity of an AFP-coated surface when the coverage is not particularly high as shown in experiment. These results will hopefully deepen our understanding of the antifreeze effects and thus be potentially useful for designing novel antifreeze coating materials based on biomolecules.

Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the $XXZ$ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.

We derive the hydrodynamic equations of motion for a fluid of active particles described by underdamped Langevin equations that reduce to the active-Brownian-particle model, in the overdamped limit. The contraction into the hydrodynamic description is performed by locally averaging the particle dynamics with the nonequilibrium many-particle probability density, whose formal expression is found in the physically relevant limit of high friction through a multiple-time-scale analysis. This approach permits us to identify the conditions under which self-propulsion can be subsumed into the fluid stress tensor and thus to define systematically and unambiguously the local pressure of the active fluid.

We have devised an experiment whereby a bistable system is confined away from its deterministic attractors by means of multiplicative noise. Together with previous numerical results, our experimental results validate the hypothesis that the higher the slope of the noise's multiplicative factor, the more it shifts the stationary states.

We study two-dimensional localized patterns in weakly dissipative systems that are driven parametrically. As a generic model for many different physical situations we use a generalized nonlinear Schrödinger equation that contains parametric forcing, damping, and spatial coupling. The latter allows for the existence of localized pattern states, where a finite-amplitude uniform state coexists with an inhomogeneous one. In particular, we study numerically two-dimensional patterns. Increasing the driving forces, first the localized pattern dynamics is regular, becomes chaotic for stronger driving, and finally extends in area to cover almost the whole system. In parallel, the spatial structure of the localized states becomes more and more irregular, ending up as a full spatiotemporal chaotic structure.

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterized by these two features. We study how these properties affect random-walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first-passage time of the process, and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems, such as heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.

The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950–2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.

We theoretically predict the nonlinear elastic responses of polydisperse biopolymer gels to uniaxial compression. We analyze the competition between compressive stiffening due to polymer densification by out-going solvent flow and compressive softening due to continuous polymer buckling. We point out that the polydispersity in polymer lengths can result in an intrinsic, equilibrium mode of nonaffine compression: nonuniform strain but with uniform force distribution, which is found to be more energetically preferable than affine deformation. In this case, the gel softens significantly after the onset of polymer buckling at small compression, but as compression increases, densification-induced stiffening becomes important and a modulus plateau should be observed for a large range of strain. We also relate our results to recent compression experiments on collagen gels and fibrin gels.

Cyclodextrins and cyclodextrins-modified molecules have interesting and appealing properties due to their capacity to host components that are normally insoluble or poorly soluble in water. In this work, we investigate the interaction of a $\beta$-cyclodextrin polymer (poly-$\beta$-CD) with $\lambda$-DNA. The polymers are obtained by the reaction of $\beta$-CD with epichlorohydrin in alkaline conditions. We have used optical tweezers to characterize the changes of the mechanical properties of DNA molecules by increasing the concentration of poly-$\beta$-CD in the sample. The physical chemistry of the interaction is then deduced from these measurements by using a recently developed quenched-disorder statistical model. It is shown that the contour length of the DNA does not change in the whole range of poly-$\beta$-CD concentration $\left(<300\mu \mathrm{M}\right)$. On the other hand, significant alterations were observed in the persistence length that identifies two binding modes corresponding to the clustering of $\sim 2.6$ and $\sim 14$ polymer molecules along the DNA double helix, depending on the polymer concentration. Comparing these results with the ones obtained for monomeric $\beta$-CD, it was observed that the concentration of CD that alters the DNA persistence length is considerably smaller when in the polymeric form. Also, the binding constant of the polymer-DNA interaction is three orders of magnitude higher than the one found for native (monomeric) $\beta$-CD. These results show that the polymerization of the $\beta$-CD strongly increases its binding affinity to the DNA molecule. This property can be wisely used to modulate the binding of cyclodextrins to the DNA double helix.