Finite element Fourier and Abbe transform methods for calculation of Fraunhofer diffraction patterns of geometrically complex apertures

1990 ◽  
Author(s):  
Hal G. Kraus
Keyword(s):  
Finite Element ◽  
Fraunhofer Diffraction ◽  
Transform Methods ◽  
Geometrically Complex ◽  
Diffraction Patterns

scholarly journals EQsimu: a 3-D finite element dynamic earthquake simulator for multicycle dynamics of geometrically complex faults governed by rate- and state-dependent friction

2019 ◽  
Vol 220 (1) ◽  
pp. 598-609 ◽  
Author(s):  
Dunyu Liu ◽  
Benchun Duan ◽  
Bin Luo
Keyword(s):  
Finite Element ◽  
Message Passing Interface ◽  
Fault System ◽  
Second Phase ◽  
Finite Element Code ◽  
Earthquake Cycle ◽  
Hexahedral Elements ◽  
Earthquake Simulator ◽  
State Dependent ◽  
Geometrically Complex

SUMMARY We develop a finite element dynamic earthquake simulator, EQsimu, to model multicycle dynamics of 3-D geometrically complex faults. The fault is governed by rate- and state-dependent friction (RSF). EQsimu integrates an existing finite element code EQdyna for the coseismic dynamic rupture phase and a newly developed finite element code EQquasi for the quasi-static phases of an earthquake cycle, including nucleation, post-seismic and interseismic processes. Both finite element codes are parallelized through Message Passing Interface to improve computational efficiency and capability. EQdyna and EQquasi are coupled through on-fault physical quantities of shear and normal stresses, slip-rates and state variables in RSF. The two-code scheme shows advantages in reconciling the computational challenges from different phases of an earthquake cycle, which include (1) handling time-steps ranging from hundredths of a second to a fraction of a year based on a variable time-stepping scheme, (2) using element size small enough to resolve the cohesive zone at rupture fronts of dynamic ruptures and (3) solving the system of equations built up by millions of hexahedral elements. EQsimu is used to model multicycle dynamics of a 3-D strike-slip fault with a bend. Complex earthquake event patterns spontaneously emerge in the simulation, and the fault demonstrates two phases in its evolution. In the first phase, there are three types of dynamic ruptures: ruptures breaking the whole fault from left to right, ruptures being halted by the bend, and ruptures breaking the whole fault from right to left. As the fault bend experiences more ruptures, the zone of stress heterogeneity near the bend widens and the earthquake sequence enters the second phase showing only repeated ruptures that break the whole fault from left to right. The two-phase behaviours of this bent fault system suggest that a 10° bend may conditionally stop dynamic ruptures at the early stage of a fault system evolution and will eventually not be able to stop ruptures as the fault system evolves. The nucleation patches are close to the velocity strengthening region. Their sizes on the two fault segments are different due to different levels of the normal stress.

Algorithms for the calculation of X-ray diffraction patterns from finite element data

2010 ◽  
Vol 43 (6) ◽  
pp. 1287-1299 ◽  
Author(s):  
E. Wintersberger ◽  
D. Kriegner ◽  
N. Hrauda ◽  
J. Stangl ◽  
G. Bauer
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Point Of View ◽  
X Ray Diffraction ◽  
Displacement Fields ◽  
X Ray ◽  
Si Substrates ◽  
Diffraction Patterns ◽  
Simulation Point ◽  
Ccd Detectors

A set of algorithms is presented for the calculation of X-ray diffraction patterns from strained nanostructures. Their development was triggered by novel developments in the recording of scattered intensity distributions as well as in simulation practice. The increasing use of two-dimensional CCD detectors in X-ray diffraction experiments, with which three-dimensional reciprocal-space maps can be recorded in a reasonably short time, requires efficient simulation programs to compute one-, two- and three-dimensional intensity distributions. From the simulation point of view, the finite element method (FEM) has become the standard tool for calculation of the strain and displacement fields in nanostructures. Therefore, X-ray diffraction simulation programs must be able to handle FEM data properly. The algorithms presented here make use of the deformation fields calculated on a mesh, which are directly imported into the calculation of diffraction patterns. To demonstrate the application of the developed algorithms, they were applied to several examples such as diffraction data from a dislocated quantum dot, from a periodic array of dislocations in a PbSe epilayer grown on a PbTe pseudosubstrate, and from ripple structures at the surface of SiGe layers deposited on miscut Si substrates.

Fraunhofer diffraction patterns of microparticles

1984 ◽  
Vol 52 (6) ◽  
pp. 519-521 ◽  
Author(s):  
F. A. Fischbach ◽  
J. S. Bond
Keyword(s):  
Fraunhofer Diffraction ◽  
Diffraction Patterns
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