Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture joints. From this model, it was revealed that the number of hierarchies ($N$) can be used to tailor and to amplify mechanical properties nonlinearly and with high sensitivity over a wide range of values (orders of magnitude) for a given volume and weight. Additionally, increasing hierarchy was found to result in mechanical interlocking of higher-order teeth, which creates additional load resistance capability, thereby preventing catastrophic failure in major teeth and providing flaw tolerance. Hence, this paper shows that the diversity of hierarchical and fractal-like interfaces and joints found in nature have definitive functional consequences and is an effective geometric-structural strategy to achieve different properties with limited material options in nature when other structural geometries and parameters are biologically challenging or inaccessible. This paper also indicates the use of hierarchy as a design strategy to increase design space and provides predictive capabilities to guide the mechanical design of synthetic flaw-tolerant bioinspired interfaces and joints.

We investigate the influence of dry friction on an asymmetric, granular piston of mass $M$, composed of two materials, undergoing inelastic collisions with bath particles of mass $m$. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the friction strength. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio $M/m$, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution.

A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of generic one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems, but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling work on particle coalescence, and induces an unexpected coupling between the convolution and the rate of facet loss. As a generic framework, the theory concisely illustrates how the universal processes of facet removal and neighbor merger are moderated by the system-specific mean-field velocity describing average rates of length change. For a simple, example facet dynamics associated with the directional solidification of a binary alloy, agreement between the predicted scaling state and that observed after direct numerical simulation of 40 000 000 facets is reasonable given the limiting assumption of noncorrelation between neighbors; relaxing this assumption is a clear path forward toward improved quantitative agreement with data in the future.

We consider the propagation of energy along a protein chain in the Davydov approximation. We study the fully discrete Davydov equations including the anharmonic corrections in the hydrogen bond potential and find approximate variational solutions. We show analytically that for the harmonic interaction of the hydrogen bonds of the Davydov model the waves travel with velocities less than half the sound velocity for the relevant biological parameters. We find, for weak nonlinearity of the hydrogen bonds, two branches of soliton solutions. The first one gives a new type of strongly stable cusped discrete supersonic soliton. The second branch captures the main component of a more complicated breather solution compared to the one studied by Gaididei et al. and reproduces the Davydov soliton of the continuum limit. These results show the possibility of coherent protein chain deformation due to the anharmonicity of the hydrogen bond interactions. These supersonic waves are shown to provide a viable mechanism for energy transport in spite of the temperature influence in the soliton lifetime.

An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte Carlo method to sample the space of possible weights during inner rounds and an analytic approach to convey the extracted information from one outer round to the next one. The results show that the protocol under attack fails to synchronize faster than an eavesdropper using this algorithm.

The collective dynamics of ensembles of chemically powered sphere dimer motors is investigated. Sphere dimers are self-propelled nanomotors built from linked catalytic and noncatalytic spheres. They consume fuel in the environment and utilize the resulting self-generated concentration gradients to produce directed motion along their internuclear axes. In collections of such motors, the individual motors interact through forces that arise from concentration gradients, hydrodynamic coupling, and direct intermolecular forces. Under nonequilibrium conditions it is found that the sphere dimer motors self-assemble into transient aggregates with distinctive structural correlations and exhibit swarming where the aggregates propagate through the system. The mean square displacement of a dimer motor in the ensemble displays short-time ballistic and long-time diffusive regimes and, for ensembles containing many motors, an increasingly prominent intermediate regime. The self-diffusion coefficient of a motor in a many-motor system behaves differently from that of an isolated motor, and the decay of orientational correlations is a nonmonotonic function of the number of motors. The results presented here illustrate the phenomena to be expected in applications, such as cargo transport, where many motors may act in consort.

We present a modeling approach that enables numerical simulations of a boiling Van der Waals fluid based on the diffuse interface description. A boundary condition is implemented that allows in and out flux of mass at constant external pressure. In addition, a boundary condition for controlled wetting properties of the boiling surface is also proposed. We present isothermal verification cases for each element of our modeling approach. By using these two boundary conditions we are able to numerically access a system that contains the essential physics of the boiling process at microscopic scales. Evolution of bubbles under film boiling and nucleate boiling conditions are observed by varying boiling surface wettability. We observe flow patters around the three-phase contact line where the phase change is greatest. For a hydrophilic boiling surface, a complex flow pattern consistent with vapor recoil theory is observed.

The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric field driving ion flow so that some of them can become unstable. This instability is expected to naturally occur in presheaths of gas discharges at sufficiently small pressures and thus affect sheaths and discharge structures.

We study the percolation transition of the geometrical clusters in the square-lattice LCCC model [a kinetic opinion exchange model introduced by Lallouache, Chakrabarti, Chakraborti, and Chakrabarti, Phys. Rev. E 82, 056112 (2010)] with the change in conviction and influencing parameter. The cluster is comprised of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion ($\Omega$). The transition point is different from that obtained for the transition of the order parameter (average opinion value) found by Lallouache et al. Although the transition point varies with the change in the threshold value of the opinion, the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size, the cluster size distribution, and the Binder cumulant remain the same. The exponents are also independent of the values of conviction and influencing parameters, indicating the robustness of this transition. The exponents do not match any other known percolation exponents (e.g., the static Ising, dynamic Ising, and standard percolation). This means that the LCCC model belongs to a separate universality class.

It has been alleged in several papers that the so-called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate the accuracy of the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in $L_2$ norm to the DCTRWs than the telegraph equation. We conclude, therefore, that first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.

In this paper spatial dynamics of the Beddington-DeAngelis predator-prey model is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. In Turing space, we found that this model has coexistence of $H_0$ hexagon patterns and stripe patterns, $H_{\pi }$ hexagon patterns, and $H_0$ hexagon patterns. To better describe the real ecosystem, we consider the ecosystem as an open system and take the environmental noise into account. It is found that noise can decrease the number of the patterns and make the patterns more regular. What is more, noise can induce two kinds of typical pattern transitions. One is from the $H_{\pi }$ hexagon patterns to the regular stripe patterns, and the other is from the coexistence of $H_0$ hexagon patterns and stripe patterns to the regular stripe patterns. The obtained results enrich the finding in the Beddington-DeAngelis predator-prey model well.

Drop impacts on solid and liquid surfaces exhibit complex dynamics due to the competition of inertial, viscous, and capillary forces. After impact, a liquid lamella develops and expands radially, and under certain conditions, the outer rim breaks up into an irregular arrangement of filaments and secondary droplets. We show experimentally that the lamella expansion and subsequent breakup of the outer rim can be controlled by length scales that are of comparable dimension to the impacting drop diameter. Under identical impact parameters (i.e., fluid properties and impact velocity) we observe unique splashing dynamics by varying the target cross-sectional geometry. These behaviors include (i) geometrically shaped lamellae and (ii) a transition in splashing stability, from regular to irregular splashing. We propose that regular splashes are controlled by the azimuthal perturbations imposed by the target cross-sectional geometry and that irregular splashes are governed by the fastest-growing unstable Plateau-Rayleigh mode.

The standard theory of field-line random walk is based on the description of turbulence in the wave number space. The latter description takes into account the details of turbulence at small scales. Such details, however, are not important in the theory of random walking magnetic field lines. In the present paper we therefore use simple decorrelation models to estimate the field-line diffusion coefficient. Previous results are recovered as special limits. It is shown that a full analytical description is possible and that the only parameter controlling the field-line diffusion coefficient is the Kubo number.

We present the implementation of the Blaizot-Méndez-Wschebor approximation scheme of the nonperturbative renormalization group we present in detail, which allows for the computation of the full-momentum dependence of correlation functions. We discuss its significance and its relation with other schemes, in particular, the derivative expansion. Quantitative results are presented for the test ground of scalar $O\left(N\right)$ theories. Besides critical exponents, which are zero-momentum quantities, we compute the two-point function at criticality in the whole momentum range in three dimensions and, in the high-temperature phase, the universal structure factor. In all cases, we find very good agreement with the best existing results.

A system of interacting vortices under overdamped motion, which has been commonly used in the literature to model flux-front penetration in disordered type-II superconductors, was recently related to a nonlinear Fokker-Planck equation, characteristic of nonextensive statistical mechanics, through an analysis of its stationary state. Herein, this connection is extended by means of a thorough analysis of the time evolution of this system. Numerical data from molecular-dynamics simulations are presented for both position and velocity probability distributions $P(x,t)$ and $P(v_x,t)$, respectively; both distributions are well fitted by similar $q$-Gaussian distributions, with the same index $q=0$, for all times considered. Particularly, the evolution of the system occurs in such a way that $P(x,t)$ presents a time behavior for its width, normalization, and second moment, in full agreement with the analytic solution of the nonlinear Fokker-Planck equation. The present results provide further evidence that this system is deeply associated with nonextensive statistical mechanics.

Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.

An analytical solution for the out-of-equilibrium quasistationary states of the paradigmatic Hamiltonian mean field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a specific class of initial condition, the so called (single-level) water-bag type. In this paper a step forward is taken by considering an arbitrary number of overlapping water bags. The theory is benchmarked to direct microcanonical simulations performed for the case of a two-level water-bag. The comparison is shown to return an excellent agreement.

We investigate the onset of irreversibility in a dense granular medium subjected to cyclic shear in a split-bottom geometry. To probe the micro- and mesoscale, we image bead trajectories in three dimensions throughout a series of shear strain oscillations. Although beads lose and regain contact with neighbors during a cycle, the global topology of the contact network exhibits reversible properties for low oscillation amplitudes. With increasing reversal amplitude, a transition to an irreversible diffusive regime occurs.

We examine the branch structure of radial diffusion-limited aggregation (DLA) clusters for evidence of multifractality. The lacunarity of DLA clusters is measured and the generalized dimensions $D\left(q\right)$ of their mass distribution is estimated using the sandbox method. We find that the global $n$-fold symmetry of the aggregates can induce anomalous scaling behavior into these measurements. However, negating the effects of this symmetry, standard scaling is recovered.