Theory of Brillouin cross section for scattering from magnetic multilayers: Second-order magneto-optic effect in Ni/Cu bilayers and trilayers

2001 ◽  
Vol 63 (10) ◽  
Author(s):  
L. Giovannini ◽  
R. Zivieri ◽  
G. Gubbiotti ◽  
G. Carlotti ◽  
L. Pareti ◽  
...  
Keyword(s):  
Cross Section ◽  
Magnetic Multilayers ◽  
Second Order ◽  
Magneto Optic

Second order magneto-optic effects in Brillouin scattering from spin waves in magnetic multilayers

2001 ◽  
Vol 89 (11) ◽  
pp. 6698-6700 ◽  
Author(s):  
L. Giovannini ◽  
R. Zivieri ◽  
F. Nizzoli ◽  
G. Gubbiotti ◽  
G. Carlotti
Keyword(s):  
Brillouin Scattering ◽  
Spin Waves ◽  
Magnetic Multilayers ◽  
Second Order ◽  
Magneto Optic

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Optimal Solutions for Nonhomogeneous Multiply-Connected Torsional Sections

1989 ◽  
Vol 111 (1) ◽  
pp. 87-93 ◽  
Author(s):  
A. Mioduchowski ◽  
M. G. Faulkner ◽  
B. Kim
Keyword(s):  
Numerical Simulation ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Boundary Value ◽  
Optimization Procedure ◽  
Second Order ◽  
External Boundary ◽  
Optimal Solutions ◽  
Torsion Problem ◽  
Multiply Connected

Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.

The calculation of the second order soft and virtual contributions to the Drell-Yan cross section

1989 ◽  
Vol 319 (3) ◽  
pp. 570-622 ◽  
Author(s):  
T. Matsuura ◽  
S.C. van der Marck ◽  
W.L. van Neerven
Keyword(s):  
Cross Section ◽  
Second Order

Differential three-jet cross section in e+e−-annihilation and comparison with second-order predictions of QCD and abelian vector theory

1982 ◽  
Vol 119 (1-3) ◽  
pp. 239-244 ◽  
Author(s):  
W. Bartel ◽  
D. Cords ◽  
G. Dietrich ◽  
P. Dittmann ◽  
R. Eichler ◽  
...  
Keyword(s):  
Cross Section ◽  
Second Order ◽  
Vector Theory

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Second Order Magneto-Optic Effects in Epitaxial FE(110)/MO(110) Bilayers

1995 ◽  
Vol 384 ◽  
Author(s):  
R.M. Osgood ◽  
R.L. White ◽  
B.M. Clemens
Keyword(s):  
Kerr Effect ◽  
Applied Field ◽  
Second Order ◽  
Magneto Optic

ABSTRACTThe signal measured during a Magneto-Optic Kerr Effect (MOKE) experiment is usually assumed to be linear in the magnetization (or the magnitude of the magneto-optic coupling vector Q that is proportional to the magnetization) so that a plot of the magnetization versus applied field can be obtained. We have observed an appreciable contribution from the Q2 term in the magneto-optic response of epitaxial Fe(110)/Mo(110) bilayers. The Q2 term in the magneto-optic response is much larger than that predicted by existing theory. We re-derive and modify the existing theory to fit the Q2 term.

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