2 edition of **equivalence of the isotropic and monodirectional source problems** found in the catalog.

equivalence of the isotropic and monodirectional source problems

H. H. Natsuyama

- 158 Want to read
- 19 Currently reading

Published
**1967**
by Rand Corporation in Santa Monica, Calif
.

Written in English

- Scattering (Physics)

**Edition Notes**

Includes bibliography.

Statement | [by] H.H. Kagiwada and R.E. Kalaba. |

Series | Rand Corporation. Research memorandum -- RM-5295, Research memorandum (Rand Corporation) -- RM-5295.. |

Contributions | Kalaba, Robert E. |

The Physical Object | |
---|---|

Pagination | 8 p. |

ID Numbers | |

Open Library | OL16544238M |

Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with a linear load. The source is modeled as a microlocally isotropic generalized Gaussian random function whose covariance operator is a classical pseudodifferential operator. In considering the failure of isotropic materials, a general theory of failure must involve a minimal number of properties that then apply across all major types of materials from ductile metals to brittle ceramics. Conceptually, the place to begin is with the consideration of the primary physical variable to be used in the construction of the theory, stress, or strain.

Figure Antenna viewing a small thermal source Equation for source antenna temperature can usefully be interpreted as the average brightness temperature of the source T times a coupling coefficient less than unity. A simple B expression for this coupling coefficient results if we define the useful concept of beam solid angle:A so that. Some essential preliminaries introduce the failure-theory problem by considering the different roles assumed by analytical forms that involve parameters as opposed to those that involve properties of the material. The first section of the derivation of the failure theory is entitled “The Organizing Principle”, and therein it is found that only two properties are allowed for the failure.

The isotropic case of course can be reduced even further using plane stress or plane strain assumption where the Z direction is ignored. Similar plane strain and plane stress assumption can also be made for the orthotropic and transversely isotropic materials. In this case they would reduce to . If we replaced the 25 keV photons with 1 megaelectronvolt (MeV) photons having the same broad parallel-beam geometry, the equivalent dose to the ovaries would be within roughly 20% of the ambient dose equivalent, and the plane isotropic source equivalent dose would likely be within 10–15% of the broad beam equivalent dose.

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The Equivalence of the Isotropic and Monodirectional Source Problems. by H. Natsuyama, Robert E. Kalaba. CitationCited by: Printed in Great Britain NOTE THE EQUIVALENCE OF THE ISOTROPIC AND MONODIRECTIONAL SOURCE PROBLEMS H.

KAGIWADA and R. KALABA The Rand Corporation, Main St., Santa Monica, California (Received 18 May ) Abstract-In the problem of multiple scattering in a plane-parallel medium, the solution of the isotropic source problem is shown to give directly the solution of the monodirectional source by: In the problem of multiple scattering in a plane-parallel medium, the solution of the isotropic source problem is show to give directly the solution of the monodirectional source problem.

The basic functions in the monodirectional case, X,Y,J,I,S, and T, can be calculated by a few algebraic operations on a desk calculator from tabulated values Cited by: Let us assume a monoenergetic isotropic point source at (x 0, y 0 z 0), with energy E 0.

Then, only the direction, Ω → 0 of the incident source particle needs to be sampled, in a steady-state problem. The angular probability density function for an isotropic source is.

A linear transversely isotropic medium is fully defined by five elastic constants. For the definition of these constants using the elastic moduli and coefficients of transverse contraction, see Fig.

If we call the axis of symmetry of the medium “z”, the axes “x” and “y” are “equivalent” and they can be defined arbitrarily in the plane spanned by these two by: 2. In solving the equivalent problem with a point unidirectional source, estimates from col- lisions are used and, in accordance with Eq.

(9), the contribution from each collision is. Furthermore, internal and external intensity fields as well as source functions due to vertically inhomogeneous distributions of emitting sources are obtained. The emphasis here is to obtain exact Cauchy problems which are well solved computationally and to present samplings of the extensive numerical results that have been obtained.

where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).

Do not use the linear elastic material definition when the elastic strains may become large; use a hyperelastic model instead. Even in finite-strain problems the elastic strains should still be small.

Isotropic, anisotropic, and Orthotropic Materials Materials can be classified as either isotropic or anisotropic. Isotropic materials have the same material properties in all directions, and normal loads create only normal strains. By compari-son, anisotropic materials have different mate-rial properties in all directions at a point in the.

the material’s response to unidirectional stress to provide an overview of mechanical properties without addressing the complexities of multidirectional stress states.

Most of the chapter will restrictitselftosmall-strainbehavior,althoughthelastsectiononstress-straincurveswillpreview materialresponsetononlinear,yieldandfracturebehavioraswell.

It is still possible to use the lead vector concept (e.g., from the example shown in Figure ).The lead vector of the PU dipole is not a vector field; it is the total sensitivity of a lead under ideal (homogeneous, infinite, isotropic) conditions.

However, in real cases, the PU electrodes may be at a large distance from each other on the body surface, and it is less evident that they shall. ¾Generally, a quasi-isotropic laminate made from woven fabric has plies oriented at 0º, 90º +45º and –45º, with at least % of the plies in each of these four directions.

¾Quasi-isotropic properties can also be achieved with 0º, 60º and º oriented unidirectional plies. •Stated more simply, the directivity of a nonisotropic source is equal to the ratio of its radiation intensity in a given direction over that of an isotropic source.

D ˘D(µ,`) ˘ U(µ,`) U0 ˘ 4 U(µ,`) Prad. If the direction is not speciﬁed, the direction of maximum radiation intensity is implied. Dmax ˘D0 ˘ U U0 ˘. Because of the random nature of the problem, the answer can only be in terms of probabilities. We thus deﬁne p(n∆x,m∆t) 1The paper in German was later translated into English in book form: Einstein, A., Investigations on the Theory of Brownian Movement, Dover Publications,pages.

Radiation is the term used to represent the emission or reception of wave front at the antenna, specifying its strength. In any illustration, the sketch drawn to represent the radiation of an antenna is its radiation can simply understand the function and directivity of an antenna by having a look at its radiation pattern.

Six basic ply material properties (E 1, ν 12, G 12, E 3, ν 13, G 13) are necessary input to the woven fabric laminate mechanics (WFLM) analyses as defined can be found by experiment, some easily (E 1, ν 12) and others less r option is to rely on micromechanics for textile composites, a field in which good progress has been made in the last decade.

Mathematics. Within mathematics, isotropy has a few different meanings. Isotropic manifolds A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. Isotropic quadratic form A quadratic form q is said to be isotropic if there is a non-zero vector v such that q(v) = 0; such a v is an isotropic vector or null vector.

TLDR: An isotropic gaussian is one where the covariance matrix is represented by the simplified matrix $\Sigma = \sigma^{2}I$. Some motivations: Consider the traditional gaussian distribution: $$ \mathcal{N}(\mu,\,\Sigma) $$ where $\mu$ is the mean and $\Sigma$ is the covariance matrix.

isotropic materials. Understand the nature of temperature e ects as a source of thermal expansion strains. Quantify the linear elastic stress and strain tensors from experimental strain-gauge measurements.

Quantify the linear elastic stress and strain tensors resulting from special material loading conditions. Linear elasticity and Hooke. A transversely isotropic material is one with physical properties that are symmetric about an axis that is normal to a plane of transverse plane has infinite planes of symmetry and thus, within this plane, the material properties are the same in all directions.

Hence, such materials are also known as "polar anisotropic" materials. Field Equivalence Principle (2) Problem (a) Volume V 1contains antenna Has currents J 1, M 1 Gives rise to fields E 1and H 1 Interested in radiated fields in V 2 Can replace with simpler problem Problem (b) Due to uniqueness, it is equivalent if Tangential E 1and H 1same on surface Created by fictitious currents J s, M s on surface Note: E.The Equivalence of the Isotropic and Monodirectional Source Problems.

Evaluation of Functionals of Solutions of Fredholm Integral Equations with Displacement Kernels. Fitting Functional Equations to Experimental Data. A linear transversely isotropic medium is fully deﬁned by ﬁve elastic constants. For the deﬁnition of these constants using the elastic moduli and coefﬁcients of transverse contraction, see Fig.

If we call the axis of symmetry of the medium “z”, the axes “x”and“y” are “equivalent” and they can be .