We study a concerted propagation of a fast crack with the process zone where a rearrangement of the solid structure takes place. The latter is treated as a second-order local phase transformation. We demonstrate that the propagation of such a zone gives rise to a nonlinear frictionlike force exerted on the crack tip, resisting its propagation. Depending on the temperature, it produces three regimes of crack motion, which differ in the behavior of the crack tip process zone: (i) always existing, (ii) only emerging at a high crack speed, and (iii) flickering. We show that the latter regime exhibits crack velocity jumps.

We derive the von Kármán–Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic “four-fifths” law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges.

We present in detail the recently introduced entropic lattice Boltzmann model for compressible flows [N. Frapolli et al., Phys. Rev. E 92, 061301(R) (2015)]. The model is capable of simulating a wide range of laminar and turbulent flows, from thermal and weakly compressible flows to transonic and supersonic flows. The theory behind the construction of the model is laid out and its thermohydrodynamic limit is discussed. Based on this theory and the hydrodynamic limit thereof, we also construct the boundary conditions necessary for the simulation of solid walls. We present the inlet and outlet boundary conditions as well as no-slip and free-slip boundary conditions. Details necessary for the implementation of the compressible lattice Boltzmann model are also reported. Finally, simulations of compressible flows are presented, including two-dimensional supersonic and transonic flows around a diamond and a NACA airfoil, the simulation of the Schardin problem, and the three-dimensional simulation of the supersonic flow around a conical geometry.

While originally discovered in the context of the Gaussian unitary ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters, the profile develops a rarefaction wave while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam type anharmonic chain, we will demonstrate that the time-integrated current has a deterministic contribution, linear in time $t$, and fluctuations of size $t^{1/3}$ with a Tracy-Widom distributed random amplitude.

We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling $J>0$ in the armchair direction and ferromagnetic interaction $J^{\prime }<0$ in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio $Q_2$ and spin stiffness $\rho$ in two directions for various coupling ratios $\alpha =J^{\prime }/J$ under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point ${\alpha }_c=-0.93$. Through the finite-size scaling analysis on $Q_2, {\rho }_x$, and ${\rho }_y$, we determined the critical exponent related to the correlation length $\nu$ to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing $\alpha$. A phase diagram in the coupling ratio $\alpha \text{-magnetic}$ field $h$ plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat $C\left(T\right)$ for different $\alpha$'s intersects precisely at one point, similar to that of liquid ${}^3\mathrm{He}$ under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of $Q_2, \rho$, and $C\left(T\right)$ are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by the analysis of particular physical systems and do not necessarily apply to general situations. The central concepts in this paper—the swatch and the cloth—provide a description of the local topology of a cell complex that is general (any physical system that can be represented as a cell complex is admissible) and complete (any statistical question about the local topology can be answered from the cloth). Furthermore, this approach allows a distance to be defined that measures the similarity of the local topology of two cell complexes. The distance is used to identify a steady state of a model grain boundary network, quantify the approach to this steady state, and show that the steady state is independent of the initial conditions. The same distance is then employed to show that the long-term properties in simulations of a specific model of a dislocation network do not depend on the implementation of dislocation intersections.

The type of malicious attack inflicting on networks greatly influences their stability under ordinary percolation in which a node fails when it becomes disconnected from the giant component. Here we study its generalization, $k$-core percolation, in which a node fails when it loses connection to a threshold $k$ number of neighbors. We study and compare analytically and by numerical simulations of $k$-core percolation the stability of networks under random attacks (RA), localized attacks (LA) and targeted attacks (TA), respectively. By mapping a network under LA or TA into an equivalent network under RA, we find that in both single and interdependent networks, TA exerts the greatest damage to the core structure of a network. We also find that for Erdős-Rényi (ER) networks, LA and RA exert equal damage to the core structure, whereas for scale-free (SF) networks, LA exerts much more damage than RA does to the core structure.

Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.

The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing-free dividing surface. We show here that it is possible to define such optimal dividing surface in systems with non-Markovian friction. However, a more direct approach to rate calculation is based on invariant manifolds and avoids the use of a dividing surface altogether, Using that method we obtain an explicit expression for the rate of crossing an anharmonic potential barrier. The excellent performance of our method is illustrated with an application to a realistic model for $\mathrm{LiNC}\rightleftharpoons \mathrm{LiCN}$ isomerization.

We describe a kind of self-propelling motion of bacteria based on the cooperative action of rotating flagella on the surface of bacteria. Describing the ensemble of rotating flagella in the framework of the hydrodynamics with spin, the reciprocal theorem of Stokesian hydrodynamics is generalized accordingly. The velocity of the self-propulsion is expressed in terms of the characteristics of the vector field of flagella orientation and it is shown that the unusually high velocities of Thiovulum majus bacteria may be explained by the cooperative action of the rotating flagella. The expressions obtained enable us to estimate the torque created by the rotary motors of the bacterium and show quantitative agreement with the existing experimental data.

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Turbulent mixing induced by Rayleigh-Taylor (RT) instability occurs ubiquitously in many natural phenomena and engineering applications. As the simplest and primary descriptor of the mixing process, the evolution of mixing width of the mixing zone plays a notable role in the flows. The flows generally involve complex varying acceleration histories and widely varying density ratios, two dominant factors affecting the evolution of mixing width. However, no satisfactory theory for predicting the evolution has yet been established. Here a theory determining the evolution of mixing width in general RT flows is established to reproduce, first, all of the documented experiments conducted for diverse (i.e., constant, impulsive, oscillating, decreasing, increasing, and complex) acceleration histories and all density ratios. The theory is established in terms of the conservation principle, with special consideration given to the asymmetry of the volume-averaged density fields occurring in actual flows. The results reveal the sensitivity or insensitivity of the evolution of a mixing front of a neighboring light or heavy fluid to the degree of asymmetry and thus explain the distinct evolutions in two experiments with the same configurations.

The grayscale lattice Boltzmann (LB) model has been recently developed to model single-phase fluid flow through heterogeneous porous media. Flow is allowed in each voxel but the degree of flow depends on that voxel's resistivity to fluid motion. Here we extend the grayscale LB model to multiphase, immiscible flow. The new model is outlined and then applied to a number of test cases, which show good agreement with theory. This method is subsequently used to model the important case where each voxel may have a different resistance to each particular fluid that is passing through it. Finally, the method is applied to model fluid flow through real porous media to demonstrate its capability. Both the capillary and viscous flow regimes are recovered in these simulations.

In the recent paper by Teles et al. [Phys. Rev. E 92, 020101 (2015)], it was suggested that the inversed temperature profiles in various astrophysical objects—ranging from the solar corona to the interstellar molecular clouds—can be explained by the specific features of relaxation in the long-range interacting systems. Here, we show that this mechanism can really work in the self-gravitating interstellar gaseous clouds; but it is irrelevant in the solar (and stellar) coronas where stratification of density is produced by the external gravitational field.

We present evidence that the mechanism proposed in Teles et al. [Phys. Rev. E 92, 020101 (2015)], referred to as the TGDC mechanism, does apply to a model with repulsive mean-field interactions where it produces temperature inversion in a state whose inhomogeneity is due to an external field. Such evidence contradicts the core statement of the Comment. We also discuss a related issue, concerning the possible application of the TGDC mechanism to the solar corona.

The earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the earth's core is believed to be between buoyancy, Coriolis, and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different from the corresponding solutions in which the field is weak.

Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment. We use the method to study the common fluctuation relations and prove that they are satisfied.