Search Results (62)

In the present study, abilities of various macroscopic models (Navier–Stokes–Fourier, Burnett, original and regularized Grad’s 13-moment equations) in predicting the nonequilibrium molecular velocity distribution are examined. The results of the local distribution function reconstruction from flow macroparameters for the models considered are compared with each other and with the reference solution. Two different flows are considered: normal shock wave and stationary regular reflection of oblique shock waves. The Direct Simulation Monte Carlo method is used to obtain the reference solution and the flow macroparameters required for the distribution function reconstruction. All models under consideration predict the distribution function in the upstream low-density region rather poorly, with strong oscillations and unphysical negative values (especially regularized Grad’s 13-moment equations). In the high-density downstream region, the shape of the reference distribution is close to equilibrium, and all macroscopic models predict it rather accurately. Full article

The cross-domain reentry unmanned flight vehicle passes through thin atmospheres and dense atmospheres when it comes across atmospheres in the near-space area. For the early transition regime, the classical macroscopic and mesoscopic approaches are either not accurate or computational too expensive. The hybrid macro-/mesoscopic method is proposed for simulating rarefied gas flows past a cross-domain reentry spheroid–cone unmanned flight vehicle in the present study. The R26 moment scheme is applied in the main flow from a macroscopic point of view, and the discrete velocity method (DVM) is used for solving the Boltzmann equation from a mesoscopic point of view. The simulation results show that the hybrid macro-/mesoscopic scheme is well-suited for non-equilibrium rarefied gas flows past a cross-domain reentry unmanned flight vehicle. The results obtained in this study are consistent with benchmark results, with a maximum density error of 9%. The maximum errors of the heat transfer coefficient and pressure coefficient are 2% and 4.6%, respectively. In addition, as the Knudsen number (Kn) becomes larger, the thickness of the shock layer at the head of the flight vehicle becomes thicker, and non-equilibrium effects become more critical for the aircraft. Since the Boltzmann–Shakhov equation has only been solved close to the wall of the spacecraft, the computational cost can be considerably saved. Full article

Thermal relics with masses in the GeV to TeV range remain possible candidates for the Universe’s dark matter (DM). These neutral particles are often assumed to have vanishing electric and magnetic dipole moments so that they do not interact with single real photons, but the anapole moment, a static electromagnetic property whose features are akin to that of a classical toroidal solenoid, can still be non-zero, permitting interactions with single virtual photons. In some models, DM predominantly annihilates into charged standard model particles through a p-wave process mediated by the anapole moment. The anapole moment is also responsible for another interaction of interest. If a DM medium were subjected to an electric current, a DM particle whose anapole moment was aligned with the current would have lower energy than the state with an antialigned anapole moment. Given these interactions, if a collection of initially unpolarized DM particles were subjected to an electric current, then the DM medium would become partially polarized, according to the Boltzmann distribution. In such a polarized medium, DM annihilation into photons, a subdominant s-wave process realizable through higher order interactions, would be somewhat suppressed. If the local electric current existed during a time in which the DM begins to drop out of thermal equilibrium with the rest of the Universe, the suppressed annihilation could lead to a small local excess in the relic DM density relative to a current-free region. This mechanism by which the local DM density can be perturbed is novel. Using effective interactions to model a DM particle’s anapole moment and polarizabilities (responsible for s-wave annihilation into two photons), we compute the changes in the DM density produced by long- and short-lived currents around freeze out. If we employ the most stringent constraints on DM annihilation into two photons, we find that long-lived currents can result in a fractional change in the DM density on the order of ${10}^{-17}$ for DM masses around 100 GeV; for short-lived currents, this fractional change in local DM density is on the order of ${10}^{-23}$ for the same DM mass. Full article

We investigate the performance of estimators of the generalized empirical likelihood and minimum contrast families in the estimation of dynamic stochastic general equilibrium models, with particular attention to the robustness properties under misspecification. From a Monte Carlo experiment, we found that (i) the empirical likelihood estimator—as well as its version with smoothed moment conditions—and Bayesian inference obtained, in that order, the best performances, including misspecification cases; (ii) continuous updating empirical likelihood, minimum Hellinger distance, exponential tilting estimators, and their smoothed versions exhibit intermediate comparative performance; (iii) the performance of exponentially tilted empirical likelihood, exponential tilting Hellinger distance, and their smoothed versions was seriously compromised by atypical estimates; (iv) smoothed and non-smoothed estimators exhibit very similar performances; and (v) the generalized method of moments, especially in the over-identified case, and maximum likelihood estimators performed worse than their competitors. Full article

Using state-of-the-art first-principles electronic-band-structure calculations alongside density functional theory, we investigated the structural, elastic, electronic, and magnetic properties of LiMnZ₂ (Z = Se, Te) compounds with a trigonal structure. Initially, we determined the equilibrium lattice structure and atomic positions, which aligned well with experimental values. Ferromagnetism was shown to be more favorable than the non-magnetic state. The elastic constants, cohesive energies, and formation energies indicated that the studied compounds were mechanically stable in the experimentally determined trigonal lattice. The analysis of spin-polarized band structures and density of states revealed that both LiMnZ₂ compounds exhibited perfect half-metallic characters. The total spin magnetic moment per formula unit adhered to the Slater–Pauling rule, being exactly 4 μ_Β, mainly concentrated at the Mn atoms due to the strong spin polarization of the Mn d orbitals. We anticipate that our results will prompt further experimental and computational studies for the application of these layered materials in practical devices. Full article

Planar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been growing. Thus, at this moment, in MathSciNet there are 108 articles with the words rigid systems or uniform systems in their titles. Here, we study the dynamics of the planar rigid polynomial differential systems with homogeneous nonlinearities of arbitrary degree. More precisely, we characterize the existence and non-existence of limit cycles in this class of rigid systems, and we determine the local phase portraits of their finite and infinite equilibrium points in the Poincaré disc. Finally, we classify the global phase portraits in the Poincaré disc of the rigid polynomial differential systems of degree two, and of one class of rigid polynomial differential systems with cubic homogeneous nonlinearities that can exhibit one limit cycle. Full article

A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann–Bhatnagar–Gross–Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem. Full article

The quantum Wigner function and non-equilibrium equation for a microscopic particle in one spatial dimension ($1D$) subject to a potential and a heat bath at thermal equilibrium are considered by non-trivially extending a previous analysis. The non-equilibrium equation yields a general hierarchy for suitable non-equilibrium moments. A new non-trivial solution of the hierarchy combining the continued fractions and infinite series thereof is obtained and analyzed. In a short thermal wavelength regime (keeping quantum features adequate for chemical reactions), the hierarchy is approximated by a three-term one. For long times, in turn, the three-term hierarchy is replaced by a Smoluchovski equation. By extending that $1D$ analysis, a new model of the growth (polymerization) of a molecular chain (template or $te$) by binding an individual unit (an atom) and activation by a catalyst is developed in three spatial dimensions ($3D$). The atom, $te$, and catalyst move randomly as solutions in a fluid at rest in thermal equilibrium. Classical statistical mechanics describe the $te$ and catalyst approximately. Atoms and bindings are treated quantum-mechanically. A mixed non-equilibrium quantum–classical Wigner–Liouville function and dynamical equations for the atom and for the $te$ and catalyst, respectively, are employed. By integrating over the degrees of freedom of $te$ and with the catalyst assumed to be near equilibrium, an approximate Smoluchowski equation is obtained for the unit. The mean first passage time (MFPT) for the atom to become bound to the $te$, facilitated by the catalyst, is considered. The resulting MFPT is consistent with the Arrhenius formula for rate constants in chemical reactions. Full article

Tris(hetaryl)substituted phosphines and their chalcogenides are promising polydentate ligands for the design of metal complexes. An experimental and theoretical conformational analysis of tris[2-(4-pyridyl)ethyl]phosphine, tris[2-(2-pyridyl)ethyl]phosphine, and their chalcogenides was carried out by the methods of dipole moments, IR spectroscopy and DFT B3PW91/6-311++G(df,p) calculations. In solution, these compounds exist as an equilibrium of mainly non-eclipsed (synclinal or antiperiplanar) forms with a predominance of a symmetrical conformer having a gauche-orientation of the C_sp3–C_sp3 bonds of pyridylethyl substituents relative to the P=X bond (X = lone pair, O, S, Se) and a gauche-orientation of the pyridyl rings relative to the zigzag ethylene bridges. Regardless of the presence and nature of the chalcogen atom (oxygen, sulfur, or selenium) in the studied molecules with many axes of internal rotation, steric factors—the different position of the nitrogen atoms in the pyridyl rings and the configuration of ethylene bridges—determine the realization and spatial structure of preferred conformers. Full article

Rayleigh–Taylor (RT) instability is a basic fluid interface instability that widely exists in nature and in the engineering field. To investigate the impact of the initial inclined interface on compressible RT instability, the two-component discrete Boltzmann method is employed. Both the thermodynamic non-equilibrium (TNE) and hydrodynamic non-equilibrium (HNE) effects are studied. It can be found that the global average density gradient in the horizontal direction, the non-organized energy fluxes, the global average non-equilibrium intensity and the proportion of the non-equilibrium region first increase and then reduce with time. However, the global average density gradient in the vertical direction and the non-organized moment fluxes first descend, then rise, and finally descend. Furthermore, the global average density gradient, the typical TNE intensity and the proportion of non-equilibrium region increase with increasing angle of the initial inclined interface. Physically, there are three competitive mechanisms: (1) As the perturbed interface elongates, the contact area between the two fluids expands, which results in an increasing gradient of macroscopic physical quantities and leads to a strengthening of the TNE effects. (2) Under the influence of viscosity, the perturbation pressure waves on both sides of the material interface decrease with time, which makes the gradient of the macroscopic physical quantity decrease, resulting in a weakening of the TNE strength. (3) Due to dissipation and/or mutual penetration of the two fluids, the gradient of macroscopic physical quantities gradually diminishes, resulting in a decrease in the intensity of the TNE. Full article

Rare-earth-free permanent magnets with the L1₀ phase are actively researched for their potential as a future class of magnetic materials, capable of operating at higher temperatures and in challenging corrosion environments such as renewable energy applications. Among these classes, MnGa shows potential, being cost effective and having interesting magnetic properties. A MnGa magnetic alloy, with composition Mn_73.6Ga_26.4 in atomic percent, was produced via the out-of-equilibrium method, and its structural and magnetic properties were assessed using X-ray diffraction (XRD), transmission electron microscopy (TEM), selected area electron diffraction (SAED) and extended magnetic characterization. We show that the MnGa alloy submitted to thermal annealing in optimal conditions exhibits a two-phase microstructure, where small nanocrystals of tetragonal L1₀/D0₂₂ magnetic phase are embedded within a D0₁₉ MnGa matrix of a non-collinear antiferromagnetic nature. These co-existing, magnetically different phases produce an optimal set of promising magnetic properties, larger than the values reported in the literature for single-phase MnGa alloys and thin films. Such large values are explained by the exchange coupling between competing non-collinear magnetic sublattices of the D0₁₉ MnGa with the net moment of the small magnetic nanocrystals of tetragonal symmetry. Full article

Grid refinement is used to reduce computing costs while maintaining the precision of fluid simulation. In the lattice Boltzmann method (LBM), grid refinement often uses interpolated values. Here, we developed a method in which interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaled the nonequilibrium part of the populations, thereby developing a recalibration procedure that allows for the transfer of information between different LBM stencils in the simulation domain. Then, we built a nonuniform lattice that uses stencils with different shapes on the transition. The resulting procedure was verified by performing benchmarks with the 2D Poisselle flow and the advected vortex. It is suggested that grids with adaptive geometry can be built with the proposed method. Full article

Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath ($hb$), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution $W_{eq}$ generates orthogonal (Hermite) polynomials $H_n$ in momenta. Suitable moments $W_n$ of W (using the $H_n$’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the $W_n$’s yield irreversibly approach to equilibrium. The approach is extended (without $hb$) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ${\varphi }^4$ field theory (without $hb$). The extension to one non-relativistic quantum particle (with $hb$) employs the non-equilibrium Wigner function ($W_Q$): difficulties related to non-positivity of $W_Q$ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ${\varphi }^4$ field theory (a meson gas off-equilibrium, without $hb$), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ${\varphi }^4$ theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ${\varphi }^4$ one, yielding an approach to equilibrium. Full article

Entropy density behavior poses many problems when we study non-equilibrium situations. In particular, the local equilibrium hypothesis (LEH) has played a very important role and is taken for granted in non-equilibrium problems, no matter how extreme they are. In this paper we would like to calculate the Boltzmann entropy balance equation for a plane shock wave and show its performance for Grad’s 13-moment approximation and the Navier–Stokes–Fourier equations. In fact, we calculate the correction for the LEH in Grad’s case and discuss its properties. Full article

The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole–wall collision, and Rayleigh–Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole–wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh–Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS. Full article