大气压下自由燃烧弧的温度场和速度场的数值模拟

采用标准SIMPLE算法，并作了一些修正，给出了具体的计算步骤和流程图，将其应用于磁流体动力学(MHD)方程进行数值求解．得到了轴对称情况下，自由燃烧弧的温度场和速度场的分布，并和实验结果进行了比较。分析了不同辐射模型对温度场的影响，发现辐射导致电弧温度降低，但不同的辐射模型对于电弧的温度影响不大。     

Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion

General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of orientation parameters and also to shed light on the important issue of using the eigenvalue analysis in the study of MBS stability. The validity of using the eigenvalue analysis based on the linearization of the nonlinear equations of motion in the study of the stability of railroad vehicle systems, which have known critical speeds, is examined. It is shown that such an eigenvalue analysis can lead to wrong conclusions regarding the stability of nonlinear systems.     

Analytical methods of solution of the relaxational equations

The master equations system for rotational, vibrational and chemical kinetics in nonuniform gas flows with the sources is studied. Two approximate analytical methods of its solution for the arbitrary rate constants are developed for the case of the smooth distributions. The first method is based on the introduction of slow variables to the discrete equations. The second one uses WKB solution for diffusion approximation in Fokker-Planck form. The particular cases of harmonic and weakly anharmonic oscillators relaxation are examined.     

Elastic response of an orthogonally reinforced plate

This paper develops a three-dimensional fully elastic analytical model of a solid plate that has two sets of embedded, equally spaced stiffeners that are orthogonal to each other. The dynamics of the solid plate are based on the Navier–Cauchy equations of motion of an elastic body. This equation is solved with unknown wave propagation coefficients at two locations, one solution for the volume above the stiffeners and the second solution for the volume below the stiffeners. The forces that the stiffeners exert on the solid body are derived using beam and bar equations of motion. Stress and continuity equations are then written at the boundaries and these include the stiffener forces acting on the solid. A two-dimensional orthognalization procedure is developed and this produces an infinite number of double indexed algebraic equations. These are all written together as a global system matrix. This matrix can be truncated and solved resulting in a solution to the wave propagation coefficients which allows the systems displacements to be determined. The model is verified by comparison to thin plate theory and finite element analysis. An example problem is formulated. Convergence of the series solution is discussed. The frequency limitations of the model are examined.     

Quantum Cosmology in the Bruns–Dicke Theory and its Stability

The Bruns–Dicke theory with a scalar field related to the quantum spinor matter is discussed [1]. The quantum Friedmann cosmology is studied. A solution to the equations of motion describing the quantum Friedmann Universe is examined for stability for the case of a flat model of the Universe. A different exact analytical solution to these equations is derived.     

Hydromagnetic flow of a variable viscosity nanofluid in a rotating permeable channel with hall effects

The flow, heat and mass transfer of water-based nanofluid are examined between two horizontal parallel plates in a rotating system. The effects of Brownian motion, thermophoresis, viscosity and Hall current parameters are considered. The governing partial differential equations are reduced to ordinary differential equations that are then solved numerically using the Runge–Kutta–Fehlberg method. Validation of numerical solution is achieved with an exact solution of primary velocity and found to be in good agreement. Results show that both surfaces experience opposite behavior regarding skin friction, Nusselt and Sherwood numbers in both primary and secondary flows. These physical quantities depend upon dimensionless parameters and numbers.     

Finslerian Extension of Schwarzschild Metric

Continuing [1], the concept of the static and spherically symmetric gravitational field is examined in the context of the fibered Finslerian approach. The approximate analysis of the associated field equations is elaborated in a systematic manner, expanding the equations with respect to the lowvelocity parameters and in the post-Newtonian way. An exact solution which has the meaning of direct extension of the Schwarzschild metric for the Finslerian case has been found assuming that fibres are of constant curvatures.     

Eigenmodes of an anisotropic dielectric spherical body

Quasi-TE and quasi-TM oscillations of an anisotropic spherical body immersed in an isotropic medium are studied. An investigation of the set of Maxwell’s equations within the spherical body shows that it reduces to two coupled differential equations, which are analyzed theoretically for small values of the anisotropy parameter. An approximate solution to these differential equations is obtained. A dispersion relation determining the frequencies of the resonant oscillations is derived for the boundary conditions imposed on the surface of the spherical body. The effect of anisotropy on the spectral characteristics of the resonant oscillations is examined.     

Relation Between Shape Equations for Axisymmetric vesicles

In deriving the shape equation for axisymmetric vesicles from the Helfrich free energy the variation must be taken with respect to the contour. It is pointed out that the widely used Helfiich shape equation and the other one given by Peterson were derived by improper variations, hence both equations need to be examined. The validity of the two equations is discussed based on analysis of their relation revealed by two derived first integrals. A newly found exact solution for the general shape equation is studied and the relation of this exact solution of spherical topology with that of the Helfrich shape equation is discussed.     

Preconditioned characteristic boundary conditions for solution of the preconditioned Euler equations at low Mach number flows

Preconditioned characteristic boundary conditions (BCs) are implemented at artificial boundaries for the solution of the two- and three-dimensional preconditioned Euler equations at low Mach number flows. The preconditioned compatibility equations and the corresponding characteristic variables (or the Riemann invariants) based on the characteristic forms of preconditioned Euler equations are mathematically derived for three preconditioners proposed by Eriksson, Choi and Merkle, and Turkel. A cell-centered finite volume Roe’s method is used for the discretization of the preconditioned system of equations on unstructured meshes. The accuracy and performance of the preconditioned characteristic BCs applied at artificial boundaries are evaluated in comparison with the non-preconditioned characteristic BCs and the simplified BCs in computing steady low Mach number flows. The two-dimensional flow over the NACA0012 airfoil and three-dimensional flow over the hemispherical headform are computed and the results are obtained for different conditions and compared with the available numerical and experimental data. The sensitivity of the solution to the size of computational domain and the variation of the angle of attack for each type of BCs is also examined. Indications are that the preconditioned characteristic BCs implemented in the preconditioned system of Euler equations greatly enhance the convergence rate of the solution of low Mach number flows compared to the other two types of BCs.     

Gauge independence and chiral symmetry breaking in a strong magnetic field

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of the truncated Schwinger-Dyson equations evaluated on the fermion mass shell, is manifestly gauge independent.     

Spherically Symmetric Static Solutions of the Einstein Equations with Elastic Matter Source

The Einstein equations for a spherically symmetric static distribution of elastic matter are examined. The existence of regular solutions near the center is proven under a fairly mild hypothesis on the constitutive equation. These solutions are uniquely determined by the choice of central pressure and constitutive equation. It is also shown for a Hookean elastic material that these solutions can be integrated outward till the radial pressure vanishes, thus one can join an exterior Schwarzschild metric to obtain a maximal solution of the Einstein equations.     

Analytical solutions of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles

A two-stream Maxwellian distribution function with two unknown parameters corresponding to the mean velocity and the shear stress is used to obtained an approximate analytic solution of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles. For small magnetic field, solutions are presented for the four moments equations and the Maxwell's equations. The dynamical behaviour of the electron and ion gas is examined.     

Some physical properties of neutrino-gravitational fields

A new solution of the Einstein-neutrino field equations is given. This solution is of Plebanski class [4n]₃ and describes a beam of neutrinos propagating along straight geodesies but possessing an inherent angular momentum density. Another previously known solution is also examined, and using some calculations given by Bonnor it is concluded that a uniform beam of neutrinos is gravitationally stable and that two such beams radiating in the same sense do not interact.     

Quantum-hydrodynamic approach to the problem of electron exchange between atomic particles and nanosystems

The application of quantum-hydrodynamic methods for solving the problem of electron exchange between atomic particles and solid surfaces, and nanosystems has been examined. The derivation of a system of equations that is alternative to the nonstationary Schrödinger equation is given to describe the dynamics of electronic processes with variable charge and current densities. A comparison of results of solving the nonstationary Schrödinger equation and the quantum-hydrodynamic system of equations shows that both approaches give a good coincidence. The numerical solution to the system of quantum-hydrodynamic equations has a number of advantages, because it does not lead to oscillations at the boundary of the computational mesh and nor to the problem of exponential growth in numerical complexity for many-electron systems.     

The multipole expansion far from an isolated source

The static field equations of general relativity are examined as deviations from a Schwarzschild solution in isotropic form. The multipole expansion is recovered with hypergeometric radial dependence.     

Acoustic wave propagation in a binary mixture of inviscid fluids

Linearized equations governing the thermo-mechanical behaviour of a binary mixture of inviscid fluids are derived. Restrictions which are sufficient for the equations to have a unique solution are imposed on some of the material constants. The propagation of plane harmonic waves of small amplitude in the mixture is examined and the inequalities are shown to ensure a physically reasonable response. As an application of the theory properties of acoustic waves in a binary mixture of ideal gases are evaluated numerically.     

A novel pressure–velocity formulation and solution method for fluid–structure interaction problems

In the standard approach for simulating fluid–structure interaction problems the solution of the set of equations for solids provides the three displacement components while the solution of equations for fluids provides the three velocity components and pressure. In the present paper a novel reformulation of the elastodynamic equations for Hookean solids is proposed so that they contain the same unknowns as the Navier–Stokes equations, namely velocities and pressure. A separate equation for pressure correction is derived from the constitutive equation of the solid material. The system of equations for both media is discretised using the same method (finite volume on collocated grids) and the same iterative technique (SIMPLE algorithm) is employed for the pressure–velocity coupling. With this approach, the continuity of the velocity field at the interface is automatically satisfied. A special pressure correction procedure that enforces the compatibility of stresses at the interface is also developed. The new method is employed for the prediction of pressure wave propagation in an elastic tube. Computations were carried out with different meshes and time steps and compared with available analytic solutions as well as with numerical results obtained using the Flügge equations that describe the deformation of thin shells. For all cases examined the method showed very good performance.     

Energy radiation by an arbitrary axisymme tricsystem

The Bondi/Van der Burg/Metzner solution of the Einstein field equations for an arbitrary axisymmetric system is examined. Expressions for the energy and momentum of the system are obtained by tetrad formalism.     

Equation of state of a supercritical fluid based on the Ornstein-Zernike equation

A numerical modeling of the thermodynamic properties of a fluid is performed using the method of integral equations. The predictions are compared with the results of MC and MD simulations. The problem of stability of the numerical solution is examined. The methods for correcting the correlation functions and for estimating their uncertainties are proposed.