Bare Slab Research Articles

Model studies of the Si(111)2 × 1 surface by the pseudofunction method

The recently developed pseudofunction (PSF) slab calculational method is used to study the electronic structure and total energy of the uniformly relaxed, buckling, and Pandey's chain-like reconstruction of the Si(111)2 × 1 surface. It is found Pandey's π bonded chain model is the most favorable by − 0.54 eV surface atom relative to the ideal surface. For the uniformly relaxed case the equilibrium relaxation and the vibrational excitation agree well with generalized valence bond (GVB) calculations. Pandey's chain model yields a surface-resonance band resembling well that of Northrup and Cohen from Γ to J′. An equilibrium surface chain bond length of 2.28 Å is obtained with a bare 6-layer slab. However, an expanded or unstable surface chain is found when the dangling bonds on opposite side surface are saturated with either an H layer or a Cl layer. Thus, results for thin semiconductor slabs may be model-dependent.

Attenuation of long-range surface polaritons in a thin metallic slab with a dielectric coating

Long-wavelength TM electromagnetic modes of a bilayer system consisting of a thin metallic slab in contact with a dielectric slab are analyzed in detail. The theory is applied to the discussion of the attenuation of infrared surface polaritons (SP) guided by a coated thin metallic slab. Both the dependence of SP damping on the SP frequency and on the thickness of each slab is considered. It is shown that, besides an overall increase of SP damping (compared with the damping of SP in a bare metallic slab), at characteristic frequencies of the dielectric overlayer resonant absorption of SP takes place due to conversion of the SP energy into the energy of mechanical vibrations in the dielectric. These effects are most prominent for long-range antisymmetric SP in a thin metallic slab which makes them very suitable as a probe for coatings on metals.

Optimal Flux Distribution in Slab Reactors with Uniform External Source

The problem of optimal flux distribution for maximum power, in bare slab reactors with uniform external source and maximum flux constraint, is solved using optimal control formalism for the case of one group neutron diffusion approximation. A set of optimal solutions, which depend on the magnitude of the external source, the upper and lower limit of the control variable and the maximum flux allowable in the reactor, is obtained. The results corresponding to a critical reactor are included here, as a particular case. A numerical example is used to illustrate the parametric dependence of the solutions.

Optimal flux distribution in slab reactors with uniform external source.

The problem of optimal flux distribution for maximum power, in bare slab reactors with uniform external source and maximum flux constraint, is solved using optimal control for-malism for the case of one group neutron diffusion approximation. A set of optimal solu-tions, which depend on the magnitude of the external source, the upper and lower limit of the control variable and the maximum flux allowable in the reactor, is obtained. The results corresponding to a critical reactor are included here, as a particular case. A numerical example is used to illustrate the parametric dependence of the solutions.

Assessment of impact-sound floor insulation

The fundamental method of calculating sound insulation for various kinds of slab materials is described theoretically, based on the assumptions that there is a well-diffused bending wave field in a floor slab and that the impact-force power spectrum of the tapping machine depends on floor covering and slab materials, while that of the tire is assumed not to depend on these materials. After proving on the basis of many kinds of experimental results that these assumptions do not matter in practical application of the calculating method, the total assessment system that is provided for the purpose of the JIS evaluation indexes is shown. These indexes can be obtained from the two types of impact-sound level, caused by a tire or tapping machine, and the inverse A curve. Using the assessment system, many kinds of practical floor constructions, such as bare concrete slab, floating floor, and timber joist floor, are classified on a matrix of the two L values.

On extrapolated endpoints in the two-group theory of neutron diffusion

The use of an extrapolated-endpoint boundary condition in criticality calculations is discussed from the point of view of two-group neutron-transport theory. The use of a single Milne-problem extrapolated endpoint is justified, from the lowest-order approximation to the transport-theory result, only for certain values of the material properties of a bare multiplying slab.

Computational Experimentation on the Finite Element Method in Bare Slab Criticality Calculations

Based on a self-adjoint form of the one-group neutron transport equation, the finite element method is applied to the computation of the critical halfthickness of a bare slab. Different optional schemes are compared numerically. For a given order of approximation it is shown that accuracy can be improved appreciably by a proper implementation of the nonreentrant boundary condition and by using a varying element size.

Optimal Control of Steady State Neutron Flux Distribution in Slab Reactors

The algorithm is presented for seeking optimal control of the steady state neutron flux distribution making use of Pontryagin's Maximum Principle, for a one group model of the bare slab reactor as well as for a two group model of the reflected slab reactor, both of which are homogeneous except for the control material. The performance criterion to be minimized is the spatial square integral error between the thermal flux distribution and the desired flux shape, and the control variable is the cross section of the absorbing material. A numerical example is given for the bare reactor where the desired shape is assumed to be uniformly flat. The non-linear nature of the problem imparts a complex aspect to the algorithm concerning the steepest descent method, as indicated by the numerical example. The results show that, as the bounds of the control variable are relaxed, the number of switchings is increased and a better performance criterion is obtained but this is accompanied by a higher hot spot factor.

Solution of the Initial-Value Neutron-Transport Problem for a Slab with Infinite Reflectors

The initial-value transport problem of monoenergetic neutrons migrating in a thin slab surrounded by infinitely thick reflectors is solved for isotropic scattering by using the normal-mode expansion technique of Case. The results obtained indicate that the reflector may give rise to a branch-cut integral term typical of a semi-infinite medium while the central slab may contribute a summation over discrete residue terms. Exact expressions are obtained for these discrete time eigenvalues, and sample numerical results are presented showing the behavior of real time eigenvalues as a function of the material properties of the slab and reflector. In the limit of purely absorbing reflectors or a bare slab, the present solution has the properties which have been previously reported by others who used the approach of Lehner and Wing.

Solution of the linear transport equation by finite fourier transforms

A new method to solve the energy-independent transport equation in a bare slab by finite Fourier transforms is developed. For thin slabs or slabs of moderate thickness the neutron scalar flux, the transmission, the reflection, and the absorption coefficients are shown to have simple forms not previously known. The method is essentially simpler than existing solutions for the slab problem for obtaining numerical answers or approximate analytical solutions. While solutions for isotropic and anisotropic scattering with a particular scattering function are given, the method is well suited for a general type of scattering function.

Transport Solution of the One-Speed Slab Albedo Problem

Case's method of normal mode expansion is applied to the slab albedo problem (the problem of finding the angular density in a bare slab with monodirectional neutrons incident upon one face). The problem is reduced to determining expansion coefficients which are shown to depend upon the solution of two nonhomogeneous Fredholm integral equations. Using Neumann iteration to solve for the coefficients, explicit solutions are obtained for the angular density, scalar density, and net current in zero and first order approximations. (auth)

Orthogonal Polynomial Angular Expansion of the Boltzmann Equation

The angular dependence of the solution of the monoenergetic Boltzmann equation in slab geometry with isotropic scattering is expanded classically in the set of Jacobi polynomials which are orthogonal in the interval −1 to +1 with respect to the weight function w(μ) = (1 − μ)α (1 + μ)β. The low order solution obtained by retaining only the first two terms in the expansion is investigated in detail. In this low order it is shown that a proper choice of α and β leads to the exact asymptotic transport eigenvalue. With this choice of α and β a significant improvement in the linear extrapolation distance and the critical size of a bare slab over the usual (P − 1) diffusion theory is obtained. However, it is shown that, in general, the truncated set of classical Jacobi equations does not conserve neutrons. A modification in the truncation procedure is made in order to obtain neutron conservation while retaining the advantages of the Jacobi expansion. The choices α = β = -½ and α = β = −1 are discussed in some detail and shown to have advantages over the corresponding Legendre (α = β = 0) expansion.

Green's Function for a Bare Slab with Anisotropic Scattering

The Green's function problem for a bare slab with anisotropic neutron scattering is developed. The one-velocity Boltzmann equation for plane symmetry, with the assumption that the scattering function can be expanded into a finite series of Legendre polynomials, is used in the derivation. (C.E.S.)

Measurement of Impact Sound Transmission Through Floors

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