Model Calculation of the Giant Magnetoresistance in Multilayers with an Arbitrary Number of Layers

2002 ◽  
pp. 43-57 ◽  
Author(s):  
M. Ye. Zhuravlev ◽  
W. Schepper ◽  
S. Heitmann ◽  
H. O. Lutz ◽  
A. V. Vedyayev ◽  
...  
Keyword(s):  
Model Calculation ◽  
Arbitrary Number ◽  
Giant Magnetoresistance ◽  
Number Of Layers

Effect of the number of layers on determination of spin asymmetries in current-perpendicular-to-plane giant magnetoresistance

2011 ◽  
Vol 98 (4) ◽  
pp. 042503 ◽  
Author(s):  
Tomohiro Taniguchi ◽  
Hiroshi Imamura ◽  
Tomoya M. Nakatani ◽  
Kazuhiro Hono
Keyword(s):  
Giant Magnetoresistance ◽  
Spin Asymmetries ◽  
Number Of Layers ◽  
Current Perpendicular To Plane

scholarly journals Cloaking Using the Anisotropic Multilayer Sphere

Photonics ◽  
2020 ◽  
Vol 7 (3) ◽  
pp. 52 ◽  
Author(s):  
Sidra Batool ◽  
Mehwish Nisar ◽  
Fabrizio Frezza ◽  
Fabio Mangini
Keyword(s):  
Mathematical Model ◽  
Arbitrary Number ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Number Of Layers ◽  
Multilayer Sphere ◽  
Tangential Directions

We studied a Spherically Radially Anisotropic (SRA) multilayer sphere with an arbitrary number of layers. Within each layer permittivity components are different from each other in radial and tangential directions. Under the quasi-static approximation, we developed a more generalized mathematical model that can be used to calculate polarizability of the SRA multilayer sphere with any arbitrary number of layers. Moreover, the functionality of the SRA multilayer sphere as a cloak has been investigated. It has been shown that by choosing a suitable contrast between components of the permittivity, the SRA multilayer sphere can achieve threshold required for invisibility cloaking.

Inversion of borehole normal resistivity logs

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1541-1548 ◽  
Author(s):  
Fang‐Wei Yang ◽  
Stanley H. Ward
Keyword(s):  
Theoretical Model ◽  
Ridge Regression ◽  
Arbitrary Number ◽  
Inverse Method ◽  
Apparent Resistivity ◽  
Random Noise ◽  
High Resistivity ◽  
Number Of Layers ◽  
Boundary Position ◽  
Resistivity Logs

This paper reports on an investigation of the inversion of borehole normal resistivity data via ridge regression. Interpretation is afforded of individual thin beds and of complicated layered structures. A theoretical solution is given for a layered model containing an arbitrary number of layers in the forward problem. Two forward model results for resistive and conductive thin beds indicate that for high‐resistivity contrasts, the departure between true and apparent resistivity may be more important than the effects caused by the variations in borehole diameter and mud resistivity. Four normal resistivity logs were chosen to test the inversion scheme. Two of the logs were theoretical logs with and without random noise added, and the remaining two were field examples. Theoretical model results and field examples indicate that the inverse method can be used to obtain the resistivity for each layer when the boundary position is known, but it also can be used to obtain the thickness and resistivity for each layer simultaneously.

scholarly journals Elément de poutre multicouche avec glissement d’interface

2007 ◽  
pp. 559-581
Author(s):  
Blaise Rebora ◽  
François Frey
Keyword(s):  
Arbitrary Number ◽  
Beam Element ◽  
Large Displacements ◽  
Corotational Formulation ◽  
Geometric Nonlinearities ◽  
Small Strains ◽  
Number Of Layers ◽  
Von Karman ◽  
Interlayer Slip ◽  
Von Kármán

This paper presents a multilayered two node planar beam element, straight or shallow, of Bernoulli type, with an arbitrary number of layers with interlayer slip. Material and geometric nonlinearities are included. Small strains and slips are assumed. Large displacements are dealt with von Karman strain coupled with corotational formulation. No locking appears. Various tests show the capabilities of this element.

scholarly journals A Theory of Vertical Modes in Multilayer Stratified Fluids

2011 ◽  
Vol 41 (9) ◽  
pp. 1694-1707 ◽  
Author(s):  
Kenji Shimizu
Keyword(s):  
Total Energy ◽  
Shallow Water Equations ◽  
Arbitrary Number ◽  
Energy Equation ◽  
Internal Tide ◽  
Stratified Fluids ◽  
Number Of Layers ◽  
Horizontal Variations ◽  
Linear Interactions ◽  
Generation Problem

Abstract A theory of vertical modes in multilayer stratified fluids is proposed. A matrix notation is introduced to generalize the theory to an arbitrary number of layers. The properties of vertical modes including their orthogonality are derived. The linearized shallow-water equations and total energy equation are then decomposed into vertical modal components in the presence of large horizontal variations in bottom elevation and stratification, which induce linear interactions among vertical modes. The theory is applied to the derivation of vertical modes in three-layer stratified fluids and an internal tide generation problem under two-layer stratification. It is shown that the proposed theory correctly approaches the continuous counterpart as the number of layers increases.

Contributions to the statistical theory of adsorption. II

1938 ◽  
Vol 34 (4) ◽  
pp. 587-598 ◽  
Author(s):  
G. P. Dube
Keyword(s):  
Statistical Theory ◽  
Partition Function ◽  
Adsorption Isotherm ◽  
Critical Phenomena ◽  
General Problem ◽  
Arbitrary Number ◽  
Solid Surfaces ◽  
Attractive Force ◽  
Adsorbed Molecules ◽  
Number Of Layers

The adsorption of gaseous molecules in a monolayer on solid surfaces has been studied theoretically by several workers, namely Fowler, Peierls and Wang. They have shown that the adsorption isotherm exhibits critical phenomena if there is assumed to be an attractive force between the neighbouring adsorbed molecules, and this has provided an explanation of the critical condensation phenomena observed in deposition experiments, for example those of Cockcroft on the deposition of cadmium on copper. The actual critical phenomena observed consist in the deposition of many layers which are formed if the first layer has fairly started. It is of interest, therefore, to consider if there are other ways in which critical phenomena can arise than through interactions in the first layer. The general problem of adsorption of an arbitrary number of layers is too complicated to study because of the mathematical difficulty in constructing the partition function. We therefore confine ourselves to the consideration of adsorption in two layers only.

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