Second-Order Shape Derivative for Hyperbolic PDEs

2018 ◽  
pp. 64-73
Author(s):  
J. Cagnol ◽  
J.-P. Zolésio
2013 ◽  
Vol 37 (12-13) ◽  
pp. 7095-7127 ◽  
Author(s):  
Hassan Yousefi ◽  
Asadollah Noorzad ◽  
Jamshid Farjoodi

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Jerico B. Bacani ◽  
Julius Fergy T. Rabago

The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary value problems, separately. The paper focused on solving the second-order shape derivative of the objective functional using the velocity method with nonautonomous velocity fields. This work confirms the classical results of Delfour and Zolésio in relating shape derivatives of functionals using velocity method and perturbation of identity technique.


2021 ◽  
Vol 14 (2) ◽  
pp. 645-688
Author(s):  
Guozhi Dong ◽  
Michael Hintermueller ◽  
Ye Zhang
Keyword(s):  

Author(s):  
W. L. Bell

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.


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