ANGULAR DISTRIBUTION OF NEUTRONS AT THE INTERFACE OF TWO ADJOINING MEDIA

1950 ◽  
Vol 28a (3) ◽  
pp. 303-314 ◽  
Author(s):  
B. Davison
Keyword(s):  
Angular Distribution ◽  
Half Space ◽  
Infinite Number ◽  
Preceding Paper ◽  
The Other ◽  
Isotropic Scattering ◽  
Neutron Density ◽  
Laboratory System ◽  
Scattering Medium ◽  
Milne Problem

Two media separated by a plane interface and each filling an infinite half-space are considered. Neutrons come in infinite number from infinity in one medium and the neutron density vanishes at infinity; in the other medium. Isotropic scattering in the laboratory system of co-ordinates in both media is assumed and all neutrons are assumed to have the same speed. The angular distribution of neutrons emerging from either medium into the other is obtained in terms of the angular distribution of neutrons for the Milne problem, that is, the angular distribution of neutrons emerging from a scattering medium into a vacuum. The latter angular distribution is tabulated in the preceding paper by LeCaine.

THE NEUTRON DENSITY NEAR A PLANE SURFACE IN A CAPTURING MEDIUM

1950 ◽  
Vol 28a (3) ◽  
pp. 242-267 ◽  
Author(s):  
Jeanne LeCaine
Keyword(s):  
Angular Distribution ◽  
Variational Method ◽  
Plane Surface ◽  
Analytical Form ◽  
High Accuracy ◽  
Neutron Density ◽  
Exact Results ◽  
Milne Problem ◽  
Simple Analytical Form

The variational method is applied to the Milne problem with capture, to obtain, for the density and for the angular distribution, expressions which give quite accurate values and which have a relatively simple analytical form. Tables of the density and angular distribution are included. The extrapolation distances determined by the Variational Method agree to high accuracy with the exact values. The angular distribution determined by the Variational Method is shown to be accurate within 0.05% in all cases where exact results are available. Tables are also given for the density and angular distribution in the Milne problem with capture and constant production.

scholarly journals Benchmarking the invariant embedding method against analytical solutions in model transport problems

2006 ◽  
Vol 21 (2) ◽  
pp. 3-13
Author(s):  
Malin Wahlberg ◽  
Imre Pázsit
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Length Distribution ◽  
Infinite Medium ◽  
Scattering Medium ◽  
Embedding Method ◽  
Invariant Embedding ◽  
Invariant Embedding Method ◽  
Transport Problems ◽  
Energy Dependent

The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade) is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.

Implications of occupancy of 2s1/2 state in sd-shell within RMF+BCS approach

2017 ◽  
Vol 26 (11) ◽  
pp. 1750072 ◽  
Author(s):  
G. Saxena ◽  
M. Kumawat ◽  
M. Kaushik ◽  
U. K. Singh ◽  
S. K. Jain ◽  
...  
Keyword(s):  
Mean Field ◽  
The Other ◽  
Magic Numbers ◽  
Neutron Density ◽  
Shell Closure ◽  
Weakly Bound ◽  
Density Profiles ◽  
Relativistic Mean Field ◽  
Structure Formula ◽  
Bubble Structure

We employ the relativistic mean-field plus BCS (RMF+BCS) approach to study the behavior of [Formula: see text]-shell by investigating in detail the single particle energies, and proton and neutron density profiles along with the deformations and radii of even–even nuclei. Emergence of new shell closure, weakly bound structure and most recent phenomenon of bubble structure are reported in the [Formula: see text]-shell. [Formula: see text]C, [Formula: see text]O and [Formula: see text]S are found to have a weakly bound structure due to particle occupancy in 2[Formula: see text] state. On the other hand [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si are found with depleted central density due to the unoccupied 2[Formula: see text] state and hence they are the potential candidates of bubble structure. [Formula: see text]C and [Formula: see text]O emerge as doubly magic with [Formula: see text] in accord with the recent experiments and [Formula: see text]S emerges as a new proton magic nucleus with [Formula: see text]. [Formula: see text] and [Formula: see text] are predicted as magic numbers in doubly magic [Formula: see text]O, [Formula: see text]Ca and [Formula: see text]Si, respectively. These results are found in agreement with the recent experiments and have consistent with the other parameters of RMF and other theories.

Orthonormal basis of wavelets with customizable frequency bands

2016 ◽  
Vol 14 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Frequency Domain ◽  
Infinite Number ◽  
Orthonormal Basis ◽  
The Other ◽  
Just Intonation ◽  
Frequency Bands ◽  
Orthonormal Bases ◽  
Major Scale ◽  
Dilation Factor ◽  
New Type

We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.

Determination of Stresses in Cemented Lap Joints

1953 ◽  
Vol 20 (3) ◽  
pp. 355-364
Author(s):  
R. W. Cornell
Keyword(s):  
Differential Equations ◽  
Infinite Number ◽  
Lap Joints ◽  
The Other ◽  
Complete Analysis ◽  
Stress Distributions ◽  
Lap Joint ◽  
Analogy Method ◽  
Set Up

Abstract A variation and extension of Goland and Reissner’s (1) method of approach is presented for determining the stresses in cemented lap joints by assuming that the two lap-joint plates act like simple beams and the more elastic cement layer is an infinite number of shear and tension springs. Differential equations are set up which describe the transfer of the load in one beam through the springs to the other beam. From the solution of these differential equations a fairly complete analysis of the stresses in the lap joint is obtained. The spring-beam analogy method is applied to a particular type of lap joint, and an analysis of the stresses at the discontinuity, stress distributions, and the effects of variables on these stresses are presented. In order to check the analytical results, they are compared to photoelastic and brittle lacquer experimental results. The spring-beam analogy solution was found to give a fairly accurate presentation of the stresses in the lap joint investigated and should be useful in analyzing other cemented lap-joint structures.

Vibration of an Infinitely Extending Plate Resting on an Elastic Foundation

1963 ◽  
Vol 30 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Kazuyosi Ono
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
The Other ◽  
Damped Oscillation

Free vibrations and forced vibrations of an infinitely extending plate resting on an elastic foundation and carrying a mass are solved. Then the amplitudes of the free vibrations produced by an impulse applied to the mass on the plate are determined, and it is found that two kinds of vibration are produced in the plate: One is a free vibration and the other is a special vibration, which consists of an infinite number of free vibrations and resembles a damped oscillation.

scholarly journals Tribo-electricity and friction. III.—Solid elements and textiles

1928 ◽  
Vol 118 (779) ◽  
pp. 108-113 ◽  
Keyword(s):  
General Practice ◽  
Filter Paper ◽  
Reliable Method ◽  
Preceding Paper ◽  
Systematic Investigation ◽  
The Other ◽  
Textile Material ◽  
Distilled Water ◽  
Initial Surface

1. No systematic investigation on this subject has yet been attempted. The efforts made to group these materials in a series according to the charges generated when they are rubbed two at a time are of uncertain value because of (1) impurities of substance and surface, (2) indeterminate initial surface strains. Moreover, the general practice has been to rub the solids when held, one in each hand. A more reliable method is to mount the bodies in a mechanism which ensures that the same parts of them come into contact at each fresh stroke. In the present research, the elements, mostly metals, are those specified in the preceding paper. The textiles are made and cleansed as described in an earlier paper. Silk, cotton and linen in our experience behave reliably when fully cleaned. The other great textile material, wool, is more oily and cannot be readily cleansed; so is less trustworthy. We therefore at present confine ourselves to one animal and one vegetable textile, choosing the pure samples of silk and cotton specified in the above paper. Also filter paper, another convenient fabric, is used after being boiled in several lots of distilled water. As the silk and cotton are treated with boiling chloroform, we tried exhausting the filter paper in this solvent to see if such treatment affected the cellulose in any way; but no effect on the properties of the paper could be found.

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