This corrects the article DOI: 10.1103/PhysRevE.91.040901.

This corrects the article DOI: 10.1103/PhysRevE.92.033003.

This corrects the article DOI: 10.1103/PhysRevE.90.022142.

This corrects the article DOI: 10.1103/PhysRevE.92.052715.

This corrects the article DOI: 10.1103/PhysRevE.92.043308.

In this Reply we respond to the criticism of Frewer et al. presented in the Comment on "Statistical symmetries of the Lundgren-Monin-Novikov hierarchy" by Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)]. We discuss physical interpretation of the statistical symmetries, and respond to criticism on the violation of the causality principle. We derive the Lundgren-Monin-Novikov equations for a flow with boundaries. Last, we stress that our work addressed the phenomenon of "external intermittency" (separation between laminar and turbulent flow), and not "internal intermittency" (strong fluctuations at small scales).

The article by M. Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)] proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. In this Comment, however, we show that both symmetries are unphysical due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Finally, we criticize the relation between intermittency and global symmetries as it is presented throughout that study.

In a recent paper [M. Cristelli, A. Zaccaria, and L. Pietronero, Phys. Rev. E 85, 066108 (2012)], the authors analyzed the relation between skewness and kurtosis for complex dynamical systems, and they identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the other with 4/3. They concluded that the observed relation is a universal fact in complex dynamical systems. In this Comment, we test the proposed universal relation between skewness and kurtosis with a large number of synthetic data, and we show that in fact it is not a universal relation and originates only due to the small number of data points in the datasets considered. The proposed relation is tested using a family of non-Gaussian distribution known as q-Gaussians. We show that this relation disappears for sufficiently large datasets provided that the fourth moment of the distribution is finite. We find that kurtosis saturates to a single value, which is of course different from the Gaussian case (K=3), as the number of data is increased, and this indicates that the kurtosis will converge to a finite single value if all moments of the distribution up to fourth are finite. The converged kurtosis value for the finite fourth-moment distributions and the number of data points needed to reach this value depend on the deviation of the original distribution from the Gaussian case.

The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called ϕ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the method considered.

In this work, a numerical scheme based on multipoles and Stokeslet is proposed for calculating the radiation force acting on a single rigid sphere in a viscous fluid. First-order velocity and pressure are obtained from the multipole series solution, and the volumetric force in the acoustic streaming is subsequently calculated from the first-order velocity and pressure. The acoustic streaming equations are solved using the Stokeslet method within a finite domain descretized by tetrahedral elements. The boundary conditions for streaming are imposed using the weighted residue method to obtain the unknown coefficients in the multipole series expansion for the second-order velocity potentials. The radiation forces obtained from this multipole-Stokeslet method match well with Doinikov's series solution, for a wide range of the sphere size. Compared to the complicated series solution, the multipole-Stokeslet method can be easily implemented without the evaluation of the semi-infinite integrals.

Many physical systems can be modeled as large sets of domains "glued" together along boundaries-biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth.

Population annealing is an efficient sequential Monte Carlo algorithm for simulating equilibrium states of systems with rough free-energy landscapes. The theory of population annealing is presented, and systematic and statistical errors are discussed. The behavior of the algorithm is studied in the context of large-scale simulations of the three-dimensional Ising spin glass and the performance of the algorithm is compared to parallel tempering. It is found that the two algorithms are similar in efficiency though with different strengths and weaknesses.

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.

We validate the application of our recent orbital-free density functional theory (DFT) approach [Phys. Rev. Lett. 113, 155006 (2014);] for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the computational costs of the method do not increase with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warm dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].