Analytic method for the solution of the one-group, integral transport equation for a homogeneous sphere

1978 ◽  
Vol 56 (6) ◽  
pp. 648-655
Author(s):  
Michael S. Milgram
Keyword(s):  
Transport Equation ◽  
Diffusion Theory ◽  
Analytic Method ◽  
Matrix Eigenvalue Problem ◽  
Homogeneous Sphere ◽  
Analytic Approximations ◽  
The Matrix ◽  
The One ◽  
Integral Transport ◽  
Taylor’S Series

The one-group integral transport equation for the spatial distribution of the flux density in a homogeneous critical sphere is reduced to a standard matrix eigenvalue problem, and the matrices are small. The elements of the matrix are simple functions, the eigenvalues correspond to critical values of the number of secondaries/collision, and the eigenvectors represent the coefficients of the Taylor's series of the flux expanded about the centre of the sphere. Analytic approximations and numerical results are cited and the connection with classical diffusion theory is developed.

Preparation of Electron Transparent Metal-Matrix Composites

1968 ◽  
Vol 26 ◽  
pp. 334-335 ◽  
Author(s):  
M. R. Pinnel ◽  
A. Lawley
Keyword(s):  
Stainless Steel ◽  
Load Transfer ◽  
Volume Fraction ◽  
Steel Wire ◽  
Initial Step ◽  
Interfacial Region ◽  
Matrix Composites ◽  
Specific Test ◽  
The Matrix ◽  
The One

Numerous phenomenological descriptions of the mechanical behavior of composite materials have been developed. There is now an urgent need to study and interpret deformation behavior, load transfer, and strain distribution, in terms of micromechanisms at the atomic level. One approach is to characterize dislocation substructure resulting from specific test conditions by the various techniques of transmission electron microscopy. The present paper describes a technique for the preparation of electron transparent composites of aluminum-stainless steel, such that examination of the matrix-fiber (wire), or interfacial region is possible. Dislocation substructures are currently under examination following tensile, compressive, and creep loading. The technique complements and extends the one other study in this area by Hancock.The composite examined was hot-pressed (argon atmosphere) 99.99% aluminum reinforced with 15% volume fraction stainless steel wire (0.006″ dia.).Foils were prepared so that the stainless steel wires run longitudinally in the plane of the specimen i.e. the electron beam is perpendicular to the axes of the wires. The initial step involves cutting slices ∼0.040″ in thickness on a diamond slitting wheel.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals Exenatide Microspheres for Monthly Controlled-Release Aided by Magnesium Hydroxide

Pharmaceutics ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 816
Author(s):  
Yuxuan Ge ◽  
Zhenhua Hu ◽  
Jili Chen ◽  
Yujie Qin ◽  
Fei Wu ◽  
...  
Keyword(s):  
Controlled Release ◽  
Dosage Form ◽  
Continuous Phase ◽  
Plga Microspheres ◽  
Receptor Agonists ◽  
Monkey Model ◽  
The Matrix ◽  
Glass Membrane ◽  
The One ◽  
Long Acting

GLP-1 receptor agonists are a class of diabetes medicines offering self-regulating glycemic efficacy and may best be administrated in long-acting forms. Among GLP-1 receptor agonists, exenatide is the one requiring the least dose so that controlled-release poly(d, l-lactic-co-glycolic acid) (PLGA) microspheres may best achieve this purpose. Based on this consideration, the present study extended the injection interval of exenatide microspheres from one week of the current dosage form to four weeks by simply blending Mg(OH)2 powder within the matrix of PLGA microspheres. Mg(OH)2 served as the diffusion channel creator in the earlier stage of the controlled-release period and the decelerator of the self-catalyzed degradation of PLGA (by the formed lactic and glycolic acids) in the later stage due to its pH-responsive solubility. As a result, exenatide gradually diffused from the microspheres through Mg(OH)2-created diffusion channels before degradation of the PLGA matrix, followed by a mild release due to Mg(OH)2-buffered degradation of the polymer skeleton. In addition, an extruding–settling process comprising squeezing the PLGA solution through a porous glass membrane and sedimentation-aided solidification of the PLGA droplets was used to prepare the microspheres to ensure narrow size distribution and 95% encapsulation efficiency in an aqueous continuous phase. A pharmacokinetic study using rhesus monkey model confirmed the above formulation design by showing a steady blood concentration profile of exenatide with reduced CMAX and dosage form index. Mg·(OH)2

Human Rights as Land Rights in the Pacific

1993 ◽  
Vol 6 (1) ◽  
pp. 61-80 ◽  
Author(s):  
John D'Arcy May
Keyword(s):  
Human Rights ◽  
Case Studies ◽  
Papua New Guinea ◽  
Land Rights ◽  
Human Community ◽  
The Earth ◽  
The Pacific ◽  
West Papua ◽  
The Matrix ◽  
The One

Do human rights in their conventional, Western understanding really meet the needs of Pacific peoples? This article argues that land rights are a better clue to those needs. In Aboriginal Australia, Fiji, West Papua and Papua New Guinea, case studies show that people's relationship to land is religious and implicitly theological. The article therefore suggests that rights to land need to be supplemented by rights of the land extending to the earth as the home of the one human community and nature as the matrix of all life.

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