Some properties of the n-dimensional plane symmetric solution

An n-dimensional static plane symmetric solution of Einstein field equation, which is judged as the source of n-dimensional Taub solution, is presented in our previous work. The properties of geodesics of this solution are studied in this Letter. The essence of the source is also investigated. A phantom with dust and photon is suggested as the substance of the source matter.     

The interior field of a magnetized Einstein-Maxwell object

Using the harmonic map ansatz, we reduce the axisymmetric, static Einstein-Maxwell equations coupled with a magnetized perfect fluid to a set of Poisson-like equations. We were able to integrate the Poisson equations in terms of an arbitrary function M = M(ϱ, ζ) and some integration constants. The thermodynamic equation restricts the solutions to only some state equations, but in some cases when the solution exists, the interior solution can be matched with the corresponding exterior one.     

A perturbation solution of the radiative transfer equation in a differentially moving atmosphere

We present a new technique for solving the radiative transfer equation in a differentially moving atmosphere. The method is based on a pertubation of the solution of the transfer problem in a static atmosphere. The perturbation technique may be applied with any method for solving the static atmosphere problem and leads to significant reductions in computer time and storage requirements.The method is flexible and may be used to solve problems involving depth dependence in any of the parameters of the transfer equation.     

Nonlinear and nonlocal transport effects in simple fluids

Correlation function formulae for transport coefficients of 2nd order in arbitrarily dense fluids are derived, using a modified Chapman-Enskog solution of the Liouville equation. Some static correlations are neglected. Approximate evaluation for dilute gases gives essentially the same results as the solution of Boltzmann's equation. As an application higher order transport effects in the critical region are estimated. It is conjectured that they are apparent in sound absorption and the line width of Rayleigh scattering if (T?T_c)/T _c?10^?3.     

Dynamics and stability of chiral fluid

Starting from the linear sigma model with constituent quarks we derive hydrodynamic equations which are coupled to the order-parameter field, e.g. the chiral fluid dynamics. For a static system in thermal equilibrium this model leads to a chiral phase transition which, depending on the choice of the quark-meson coupling constant g, could be a crossover or a first order one. We investigate the stability of the chiral fluid in the static and expanding background by considering the evolution of perturbations with respect to the mean-field solution. In the static background the spectrum of plane-wave perturbations consists of two branches, one corresponding to the sound waves and another to the σ-meson excitations. For large g these two branches cross and the excitation spectrum acquires exponentially growing modes. The stability analysis is also done for the Bjorken-like background solution by explicitly solving the time-dependent differential equation for perturbations in the η space. In this case the growth rate of unstable modes is significantly reduced.     

Analytical static structure factors for the restricted primitive model

The mean static structure for the restricted primitive model formed by m ionic species is presented. Explicit expressions for the partial static structure factors are obtained from the Blum’s solution for the primitive model, which depend on an accumulative parameter, γ, expressed in terms of the Debye length. Additionally, the number-number, number-charge and charge-charge structure factors are provided. An equation to calculate the radial distribution functions which tends to the contact values when r→σ⁺ is also given. Finally, molecular dynamics simulation is performed to assess the accuracy of the theoretical results.     

An elastodynamic solution of finite long orthotropic hollow cylinder under torsion impact

The paper presents an analytical method to solve the elastodynamic problem of a finite-length orthotropic hollow cylinder subjected to a torsion impact often occurring in engineering fields. The elastodynamic solution is composed of a quasi-static solution of homogeneous equation satisfied with the non-homogeneous boundary condition and a dynamic solution of non-homogeneous equation satisfied with homogeneous boundary condition. The quasi-static solution can be obtained by directly solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of a non-homogeneous dynamic equation is obtained by means of a finite Hankel transform to a radial variable r, Laplace transform to a time variable t and finite Fourier transform to an axial variable z. Thus, the elastodynamic solution of the finite length of an orthotropic hollow cylinder subjected to a torsion impact is obtained. On the other hand, a dynamic finite element for the same problem is also carried out by applying the ANSYS finite-element analysis system. Comparing the theoretical solution with finite-element solution, it can be found that two kinds of results obtained by making use of two different solving methods are suitably approached. Therefore, it is further concluded that the methods and computing processes of the theoretical solution are effective and accurate.     

The effect of the heat capacity of the liquid phase on the heat of fusion liquidus equation of compound semiconductors

We have critically examined the assumptions involved in the derivation of Vieland's widely used heat of fusion liquidus equation for binary compounds and conclude that the thermodynamic form of this equation ignores the relative partial molar heat capacity of the liquid solution. Taking into account this quantity, we obtain the generalized heat of fusion equation which is exact and show its complete equivalence to its alternative, the heat of formation equation. The generalized result provides a correction term to Vieland's equation which can be expressed as a function of the activity coefficients at the compound composition. Applying the correction term to the activity coefficients derived for a number of useful solution models, we find that the regular solution form of Vieland's equation is exact, as shown previously, if α (interchange energy) is a constant or a linear function of temperature. But when α is expanded as an nth order polynomial in temperature (simple solution), Vieland's equation is inexact for n ? 2. In addition, it is demonstrated that for a regular associated solution and for Darken's quadratic representation, Vieland's thermodynamic equation is exact only with certain restrictions, while for a quasi-chemical solution it is invalid.     

Paraxial imaging electron optics and its spatial-temporal aberrations for a bi-electrode concentric spherical system with electrostatic focusing

The paraxial solutions play an important role in studying electron optical imaging system and its spatial-temporal aberrations, as was discussed in previous paper [1], but investigation of a bi-electrode concentric spherical system with electrostatic focusing directly from paraxial electron ray equation and paraxial electron motion equation has not been done before. In this paper, we shall use the paraxial equations to study the spatial-temporal trajectories and their aberrations for a bi-electrode concentric spherical system with electrostatic focusing.In the present paper, start from the paraxial ray equation and paraxial motion equation, the paraxial spatial-temporal trajectory of moving electron emitted from the photocathode has been solved for a bi-electrode concentric spherical system with electrostatic focusing. The paraxial static and dynamic electron optics, as well as the paraxial spatial-temporal aberrations in this system are then discussed, the general regularity of imaging in paraxial optical system has been explored. The paraxial spatial aberrations, as well as the paraxial temporal aberrations with different orders, have been defined and deduced, that are classified by the order of (?_z/?_ac)^1/2 and (?_T/?_ac)^1/2. Thus we get same conclusions about paraxial spatial and temporal aberrations as we have given in the previous paper and it completely shows that the paraxial spatial-temporal aberrations can be investigated directly from the paraxial ray equation and paraxial motion equation.     

Conformal anisotropic relativistic charged fluid spheres with a linear equation of state

We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner–Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p _⊥ to be proportional to the radial pressure p _r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.     

Critical value computation for H∞-Riccati difference equations

In designing finite horizon discrete time H_∞ controllers, the associated H_∞-Riccati difference equations must be solved. But the Riccati equation has a non-negative solution only when γ⁻² is small enough. So it is important to get the upper bound of the parameter, i.e., the critical value that ensures the existence of the solution to the Riccati equation. The solution sequence of the Riccati difference equation can be constructed by the conjoined basis of an associated linear Hamiltonian difference system. Based on this expression and the Hamiltonian difference system eigenvalue theorems, the equivalence between the critical value and the first order eigenvalue of the linear Hamiltonian difference system is presented. Since the critical value is also shown to be the fundamental eigenvalue of a generalized Rayleigh quotient, an extended form of Wittrick-Williams algorithm is presented to search this value.     

Conformal Structures of Static Vacuum Data

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null infinity obstructs the development of a smooth conformal structure at null infinity. For the solution-jets arising from time reflection symmetric data to extend smoothly to the critical sets it is necessary that the Cotton tensor of the initial three-metric h satisfies a certain conformally invariant condition (*) at space-like infinity, it is sufficient that h be asymptotically static at space-like infinity. The purpose of this article is to characterize the gap between these conditions. We show that with the class of metrics which satisfy condition (*) on the Cotton tensor and a certain non-degeneracy requirement is associated a one-form κ with conformally invariant differential dκ. We provide two criteria. If h is real analytic, κ is closed, and one of its integrals satisfies a certain equation then h is conformal to static data near space-like infinity. If h is smooth, κ is asymptotically closed, and one of its integrals satisfies a certain equation asymptotically then h is asymptotically conformal to static data at space-like infinity.     

Monte carlo simulation of a nucleon interacting with a neutral scalar boson field

A recently proposed Monte Carlo algorithm to solve a Schrödinger equation expressed in Fock-space representation, suitable for the case of hamiltonians describing problems in one-dimensional discrete momentum space, is now extended to the one-, two- and three-dimensional continuous k-spaces. This extension is tested by employing it for an analytically solvable hamiltonian. For this purpose the ‘static source’ limit of the hamiltonian corresponding to the interaction between a nucleon and a neutral, scalar boson field is simulated. The results of the Monte Carlo procedure reproduce very well the exact solution.     

A string-like self-dual solution of Yang-Mills theory

We attempt to obtain Nielsen-Olesen strings in pure Yang-Mills theory without Higgs scalars. This is inspired by recent work interpreting the Prasad-Sommerfield monopole as a static self-dual Yang-Mills solution in which A₄^a plays the role of the Higgs field. In similar fashion, we make A₃^aA₄^a serve as the two required isovector fields in an ansatz independent of x₃ and x₄. The condition of self-duality results in a single Painlevé equation of the third kind (or equivalently, a radial sinh-Gordon equation in 2 + 0 dimensions), the solution of which determines A_μ^a. We make use of the extensive analysis of the former equation carried out by Wu, McCoy and collaborators in the context of the scaling limit of the two-dimensional Ising model. Their simplest solution yields a flux value of ?2π/e just as in the Nielsen-Olesen model and flux is quantized in multiples of this unit. The string tension (action per unit time per unit distance) diverges as r^?2 (In r)^?2 as r → 0 for the same Wu-McCoy solution.     

A new sphaleron in the Weinberg-Salam theory?

The same topological argument that previously gave a sphaleronS (i.e. a static, but unstable, classical solution) suggests the existence of another sphaleronS ^* in the Weinberg-Salam theory. There appear to be two alternatives: eitherS ^* is just a superposition of twoS's infinitely far apart, or it is a truly new axisymmetric solution, probably with a single core. We propose an ansatz for a newS ^*. The resulting equations of motion can be solved asymptotically, but it is not clear if a general solution is possible.     

Neue Lösungsformen der Boltzmann-Gleichung für monoenergetischen Neutronentransport in kugelförmiger Geometrie

In Chapter I thesingular solution of the Boltzmann equation for neutron transport in spherical geometry will be derived. The calculation will be performed in two steps. First, a partial differential equation (7) with an assumed density (6) on its right hand side will be solved. But the partial solution found in this way will generally not yield the assumed density. Therefore on has to add a suitable solution of the homogeneous differential equation (10). This addition leads to an equation of compatibility which turns out to be a Sonine integral equation (12). The second step of the calculation is the solution of this integral equation. The total solution of the Boltzmann equation will be written down in two different representations, (15) and (31), but its uniqueness has been proved. The main singularity at the center of the sphere is proportional to l/(?√1 μ²). A term log ? does not appear, but a term proportional to log [(1+μ)/(1?μ)] does which, however, loses its importance at the center of the sphere ?=0 in comparison with the main singularity. A characteristic equation needs not occur in this mathematical procedure; it may or may not be introduced. Therefore no hint at the spectrum of the Boltzmann operator in spherical geometry will be given. In Chapter II it will be shown that there exists a remarkably short integral representation of theregular solution (38) which satisfies from the first all requirements, if the validity of the characteristic equation (3) is supposed. But there are also regular solutions, given by the difference of two singular solutions, which need not satisfy a characteristic equation. In Chapter III both kinds of regular solutions in spherical geometry are given assuperpositions of solutions in plane geometry which belong to the discrete or to the continuous spectrum of the Boltzmann operator. The regular solutions are identical with the corresponding well-known series of spherical harmonics, where the supposition of a characteristic equation needs also not necessarily be made for exact solutions in the infinite space. A preliminary discussion of this problem is given in the introduction.     

Diffusion approximations for the scattering of resonance-line photons: Interior and boundary layer solutions

Resonance-line scattering in static low density media with large optical thickness has a diffusive behavior in both space and frequency because photons belonging to the Lorentzian wings of the line may be scattered almost monochromatically a very large number of times. This diffusive behavior holds on frequency scales and spatial scales, χ_c and τ_c, much larger than the scales associated with one elementary scattering of a wing-photon.A method developed for diffusion approximations in neutron transport theory, suitably generalized to handle diffusion in frequency space, is applied to the case of conservative scattering in a bounded medium with interior sources and zero incoming radiation. The method is to separate the line radiation field into an interior part and a boundary layer part which goes to zero in the interior. Each part is expanded in terms of a small parameter ?, which is the ratio of the mean free-path at frequency χ_c to the characteristic spatial scale τ_c.It is shown that the leading term in the interior asymptotic expansion is isotropic, zero on the boundary, and obeys a space and frequency diffusion equation. In the boundary-layer expansion, the leading term is of order ? and is a solution to a monochromatic transfer equation in a semi-infinite, plane-parallel medium. The emergent radiation field is shown to be of order ? and proportional to the gradient of the interior solution at the boundary. Its angular dependence, in the case of isotropic scattering in the atom frame, is given by the Ambartsoumian H-function. A comparison is presented between numerical solutions of the full transfer equation and asymptotic solutions. Non-conservative scattering and time-dependent problems are briefly discussed.