Many fibers in biomaterials such as tendon, elastin, or silk feature a nonlinear stiffening behavior of the stress-strain relationship, where the rigidity of the material increases severely as the material is being stretched. Here we show that such nonlinear stiffening is beneficial for a fiber's ability to withstand cracks, leading to a flaw tolerant state in which stress concentrations around cracks are diminished. Our findings, established by molecular mechanics and the derivation of a theoretical scaling law, explain experimentally observed fiber sizes in a range of biomaterials and point to the importance of nonlinear stiffening to enhance their fracture properties. Our study suggests that nonlinear stiffening provides a mechanism by which nanoscale mechanical properties can be scaled up, providing a means towards bioinspired fibrous material and structural design.

The synchronization of biological activity with the alternation of day and night (circadian rhythm) is performed in the brain by a group of neurons, constituting the suprachiasmatic nucleus (SCN). The SCN is divided into two subgroups of oscillating cells: the ventrolateral (VL) neurons, which are exposed to light (photic signal), and the dorsomedial (DM) neurons, which are coupled to the VL cells. When the coupling between these neurons is strong enough, the system synchronizes with the photic period. Upon increasing the cell coupling, the entrainment of the DM cells has been recently shown to occur via a very sharp (jumping) transition when the period of the photic input is larger than the intrinsic period of the cells. Here, we characterize this transition with a simple realistic model. We show that two bifurcations possibly lead to the disappearance of the endogenous mode. Using a mean-field model, we show that the jumping transition results from a supercritical Hopf-like bifurcation. This finding implies that both the period and strength of the stimulating photic signal, and the relative fraction of cells in the VL and DM compartments, are crucial in determining the synchronization of the system.

The structure of the system consisting of an aspirating pipette and an aspirated vesicle is investigated with fixed total vesicle volume, total vesicle surface area, and aspirated volume fraction, based on the bending-energy model. Through an energetic consideration, the usage of an aspirated volume fraction can be converted to the aspirating pressure for the determination of a phase diagram; the procedure identifies a first-order transition, between a weakly aspirated state and the strongly aspirated state, as the pressure increases. The physical properties of the system are obtained from minimization of the bending energy by an implementation of the simulated annealing Monte Carlo procedure, which searches for a minimum in a multivariable space. An analysis of the hysteresis effects indicates that the experimentally observed aspirating and releasing critical pressures are related to the location of the spinodal points.

We analyze the dynamics of structural transitions between normal right-handed B form and unusual left-handed Z form for a linear DNA molecule. The dynamics under the external torque in physiological buffer is modeled by a Langevin equation, with the potential term given by the authors previously [Phys. Rev. E 84, 021926 (2011)]. With this model, we first simulate the relaxation processes around B-form structure after sudden changes of the external torques, where slow relaxation $\sim t^{-1/2}$ as a function of the elapsed time $t$ is observed. Then, the dynamics of structural transition from Z form to B form is computed under various external torque strength. For small external torques, the transition proceeds via nucleation and the growth, while for higher torques, Z-form structure becomes unstable, and the transition mechanism is switched to a spinodal-like process. These numerical results are qualitatively understood by simple phenomenological arguments.

In a recent paper, Phys. Rev. E 81, 041137 (2010), the author attempts to derive ten necessary conditions for the stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been obtained solely from the first and second laws of thermodynamics. The Onsager reciprocity relations have not been invoked, and the author's results are supposed to be valid independent of the choice of the boundary conditions. In the present Comment, in agreement with the general theory established by Glansdorff-Prigogine in 1954 and 1970, we show that there is no variational principle expressing the necessary conditions for the stability of dissipative systems involving convective effects when the system is out of the Onsager region. In particular, we prove that the basic equations constituting the starting point of the analysis of the author, attempting to derive ten necessary conditions for the stability involving magnetohydrodynamical effects, are incorrect and in contradiction with the laws of the thermodynamics of irreversible processes.

In their Comment on Phys. Rev E 81, 041137 (2010), a paper that focused on the necessary conditions for the stability of dissipative fluids and plasmas, the authors claim that the basic equations of the paper are in contradiction with the laws of thermodynamics of irreversible processes [Sonnino, Tlidi, and Evslin, preceding paper, Phys. Rev. E 86, 043101 (2012)]. Here, we show that one of the basic equations of the Comment is just a particular case of the results of the criticized paper. As for two further tenets of the Comment, counterexamples are found in the literature and are discussed here.

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Global modeling aims to build mathematical models of concise description. Polynomial Model Search (PoMoS) and Global Modeling (GloMo) are two complementary algorithms (freely downloadable at the following address: http://www.cesbio.ups-tlse.fr/us/pomos_et_glomo.html) designed for the modeling of observed dynamical systems based on a small set of time series. Models considered in these algorithms are based on ordinary differential equations built on a polynomial formulation. More specifically, PoMoS aims at finding polynomial formulations from a given set of 1 to $N$ time series, whereas GloMo is designed for single time series and aims to identify the parameters for a selected structure. GloMo also provides basic features to visualize integrated trajectories and to characterize their structure when it is simple enough: One allows for drawing the first return map for a chosen Poincaré section in the reconstructed space; another one computes the Lyapunov exponent along the trajectory. In the present paper, global modeling from single time series is considered. A description of the algorithms is given and three examples are provided. The first example is based on the three variables of the Rössler attractor. The second one comes from an experimental analysis of the copper electrodissolution in phosphoric acid for which a less parsimonious global model was obtained in a previous study. The third example is an exploratory case and concerns the cycle of rainfed wheat under semiarid climatic conditions as observed through a vegetation index derived from a spatial sensor.

The intrinsic viscosities for prolate and oblate spheroidal suspensions in a dilute Newtonian fluid are studied using a three-dimensional lattice Boltzmann method. Through directly calculated viscous dissipation, the minimum and maximum intrinsic viscosities and the period of the tumbling state all agree well with the analytical solution for particles with different aspect ratios. This numerical test verifies the analysis on maximum and minimum intrinsic viscosities. Different behavior patterns of transient intrinsic viscosity in a period are analyzed in detail. A phase lag between the transient intrinsic viscosity and the orientation of the particle at finite Reynolds number (Re) is found and attributed to fluid and particle inertia. At lower Re, the phase lag increases with Re. There exists a critical Reynolds number ${\text{Re}}_a$ at which the phase lag begins to decrease with Re. The ${\text{Re}}_a$ depends on the aspect ratio of the particle. We found that both the intrinsic viscosity and the period change linearly with Re when $\text{Re}<{\text{Re}}_a$ (low-Re regime) and nonlinearly when $\text{Re}>{\text{Re}}_a$ (high-Re regime). In the high-Re regime, the dependence of the period on Re is consistent with a scaling law, and the dependence of the intrinsic viscosity on Re is well described by second-degree polynomial fits.

We outline a rigorous method which can be used to solve the many-body Schrödinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the geometry of the electronic system as well as the polarization of the quantized electromagnetic field are explicitly taken into account. We accomplish this by performing repeated truncations of many-body spaces in order to keep the size of the many particle basis on a manageable level. The electron-electron and electron-photon interactions are treated in a nonperturbative manner using “exact numerical diagonalization.” Our results demonstrate that including the diamagnetic term in the photon-electron interaction Hamiltonian drastically improves numerical convergence. Additionally, convergence with respect to the number of photon states in the joint photon-electron Fock space basis is fast. However, the convergence with respect to the number of electronic states is slow and is the main bottleneck in calculations.

This Reply addresses two issues raised in the Comment [Phys. Rev. E 84, 068701 (2011)] by Karlin, Succi, and Chikatamarla (KSC): (1) A lattice Boltzmann (LB) model, which is claimed to have an $H$ theorem, is not qualified to be called an entropic lattice Boltzmann equation (ELBE); and (2) the real ELBE with a variable relaxation time performs exceedingly well, as exhibited by their simulations of decaying “Kida vortex” flow in a three-dimensional periodic cube free of no-slip boundary. The first issue is a semantic one. We note that it was Karlin, Succi, and others who “prove the $H$ theorem for lattice Bhatnagar-Gross-Krook models,” which is the model we called ELBE in our original study to distinguish it from the usual lattice BGK model without the $H$ theorem. Regardless of how this model is named, it does not affect the results and conclusions of our study in any way. Second, the focus of our original study is to quantify the errors of various LB models near no-slip boundaries. Hence, KSC's example, which is free of no-slip boundaries, is not relevant to our study. The results in our original paper are valid and its conclusions remain unchallenged. On the other hand, KSC's assertion that their real ELBE “provides a reliable subgrid simulation” of turbulence is not substantiated.

In fundamental-measure theories the bulk excess free-energy density of a hard-sphere fluid mixture is assumed to depend on the partial number densities $\left\{{\rho }_i\right\}$ only through the four scaled-particle-theory variables $\left\{{\xi }_{\alpha }\right\}$, i.e., $\Phi \left(\left\{{\rho }_i\right\}\right)\to \Phi \left(\left\{{\xi }_{\alpha }\right\}\right)$. By imposing consistency conditions, it is proven here that such a dependence must necessarily have the form $\Phi \left(\left\{{\xi }_{\alpha }\right\}\right)=-{\xi }_0\ln (1-{\xi }_3)+\Psi \left(y\right){\xi }_1{\xi }_2/(1-{\xi }_3)$, where $y\equiv {\xi }_2^2/12\pi {\xi }_1(1-{\xi }_3)$ is a scaled variable and $\Psi \left(y\right)$ is an arbitrary dimensionless scaling function which can be determined from the free-energy density of the one-component system. Extension to the inhomogeneous case is achieved by standard replacements of the variables $\left\{{\xi }_{\alpha }\right\}$ by the fundamental-measure (scalar, vector, and tensor) weighted densities $\left\{n_{\alpha }\left(\mathbf{r}\right)\right\}$. Comparison with computer simulations shows the superiority of this bulk free energy over the White Bear one.

We investigate the dissipative loss in the $\pm J$ Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the whole range of the bond randomness as a function of the sweep rate by means of frustration-preserving hard-spin mean-field theory. Data collapse within the entirety of the spin-glass phase driven adiabatically (i.e., infinitely slow field variation) is found, revealing a power-law scaling of the hysteresis area as a function of the antiferromagnetic bond fraction and the temperature. Two dynamic regimes separated by a threshold frequency ${\omega }_c$ characterize the dependence on the sweep rate of the oscillating field. For $\omega <{\omega }_c$, the hysteresis area is equal to its value in the adiabatic limit $\omega =0$, while for $\omega >{\omega }_c$ it increases with the frequency through another randomness-dependent power law.

We study the rotational diffusion of aging Laponite suspensions for a wide range of concentrations using depolarized dynamic light scattering. The measured orientational correlation functions undergo an ergodic to nonergodic transition that is characterized by a concentration-dependent ergodicity-breaking time. We find that the relaxation times associated with rotational degree of freedom as a function of waiting time, when scaled with their ergodicity-breaking time, collapse on two distinct master curves. These master curves are similar to those previously found for the translational dynamics; the two different classes of behavior were attributed to colloidal gels and glasses. Therefore, the aging dynamics of rotational degree of freedom provides another signature of the distinct dynamical behavior of colloidal gels and glasses.

Nanoparticle catalysts dispersed on high-surface-area electronic support materials are used in a wide range of applications. Nano-sized particles afford a high active surface area per unit volume of an electrocatalytic medium. However, the gain in active surface area for desired surface reactions is offset in part by enhanced rates of degradation processes that cause losses in catalyst mass, catalyst surface area, and electrocatalytic activity. A dynamic model of surface-area-loss phenomena based on the theories of Lifshitz and Slyozov [J. Phys. Chem. Solids 19, 35 (1961)], Wagner [Z. Elektrochem. 65, 581 (1961)], and Smoluchowski [Z. Phys. Chem. 92, 129 (1917)] is presented. A population balance equation in particle space accounts for nanoparticle dissolution, redeposition, and coagulation. It relates kinetic rates of these processes to the evolution of the particle-size distribution and its moments. Our analysis of the temporal dynamics of the number density, mean radii, surface area, and mass moments focuses on the important case of reaction-limited Ostwald ripening. Transient solutions reveal unique scaling relationships between the moments of the evolving distribution. Diagnostic criteria established from the scaling relationships are applied to previously published experimental degradation data for supported nanoparticle catalysts in polymer electrolyte fuel cells.

The orientationally dependent elastic energy and hydrodynamic behavior of colloidal disks with homeotropic surface anchoring suspended in the nematic liquid crystal 4-cyano-4${}^{\prime }$-pentylbiphenyl (5CB) have been investigated. In the absence of external torques, the disks align with the normal of the disk face $\widehat{a}$ parallel to the nematic director $\widehat{n}$. When a magnetic field is applied, the disks rotate $\widehat{a}$ by an angle $\theta$ so that the magnetic torque and the elastic torque caused by distortion of the nematic director field are balanced. Over a broad range of angles, the elastic torque increases linearly with $\theta$ in quantitative agreement with a theoretical prediction based on an electrostatic analogy. When the disks are rotated to angles $\theta >\frac{\pi }{2}$, the resulting large elastic distortion makes the disk orientation unstable, and the director undergoes a topological transition in which $\theta \pi -\theta$. In the transition, a defect loop is shed from the disk surface, and the disks spin so that $\widehat{a}$ sweeps through $\pi$ radians as the loop collapses back onto the disk. Additional measurements of the angular relaxation of disks to $\theta =0$ following removal of the external torque show a quasi-exponential time dependence from which an effective drag viscosity for the nematic can be extracted. The scaling of the angular time dependence with disk radius and observations of disks rotating about $\widehat{a}$ indicate that the disk motion affects the director field at surprisingly modest Ericksen numbers.

The splay and bend elastic constants of the bent-core oxadiazole material [C5-Ph-ODBP-Ph-OC12] have been investigated as a function of temperature across the nematic phase. The bend constant $K_{33}$ is found to take values of ∼3.0 pN and to be almost temperature independent, whereas, the splay constant $K_{11}$ increases monotonically from ∼3.5 pN close to the isotropic phase transition to values of ∼9 pN deep in the nematic phase. No pretransitional divergence is observed in either $K_{11}$ or $K_{33}$ at temperatures approaching the underlying phase. This behavior of the elastic constants is distinct from that observed in rodlike liquid crystal systems but appears to share characteristics with the few other bent-core nematic systems studied to date. We discuss the interdependence of the elastic constants, the birefringence, and the order parameter to allow a comparison of the observed behavior with theory. We show that calculations of the elastic constants via molecular-field theory and atomistic modeling are in excellent qualitative as well as good quantitative (within 2 pN) agreement with the measurements across the temperature range, offering a deeper understanding of the elasticity in bent-core nematic materials than has been, hitherto, available.

We present a series of nonequilibrium molecular dynamics simulations, investigating the rupture mechanisms in glassy polymer films confined between two solid surfaces. Such systems provide a useful model for the strong nonlinear reinforcement of rubber by colloidal filler particles. Depending on the degree of confinement three qualitatively different rupture modes have been found, which originate from the interplay of internal (polymer-polymer) and external (polymer-wall) interactions. In very thin films we observe the formation and stretching of many single-chain bridges between the confining surfaces. Progressing to thicker samples we observe fewer bridges, consisting of bundled polymer chains, and eventually just one large bridge in thick specimens. The yield stress and the elongational modulus of the polymer films have been calculated from the stress-strain curves at various temperatures and confinements and their behavior has been analyzed in terms of polymer-polymer and polymer-surface interaction energies. The thinnest films (5 monomer diameters) are always glassy in our simulations, while the others display a glass transition temperature around 0.50–0.55 (in units ${\varepsilon }_0/k_{\text{B}}$ of the Lennard-Jones interaction energy), depending on their thickness. This range of values, which has been determined using both the nonequilibrium tensile simulations and equilibrium diffusion data, agrees with the transition temperature previously found by shear simulations [Baljon and Robbins, Science 271, 482 (1996)].

The flow of electromagnetic wave energy through a chain of coupled cavities is considered. The cavities are assumed to be of sufficiently irregular shape that their eigenmodes are described by random matrix theory. The cavities are coupled by electrically short single mode transmission lines. Approximate expressions for the power coupled into successive cavities are derived, and the predictions are compared with Monte Carlo simulations. The analytic formulas separate into a product of factors. Consequently, the distribution of power in the last cavity of a very long chain approaches lognormal. For lossless cavities, signatures of Anderson localization, similar to those of the conductances of quantum wires, are observed.