The energy minimization problem for two-level dissipative quantum systems

2010 ◽  
Vol 51 (9) ◽  
pp. 092705 ◽  
Author(s):  
B. Bonnard ◽  
O. Cots ◽  
N. Shcherbakova ◽  
D. Sugny
Keyword(s):  
Minimization Problem ◽  
Energy Minimization ◽  
Quantum Systems ◽  
Dissipative Quantum Systems

scholarly journals Gauss-Newton Method for Segmentation assisted Deformable Registration

2014 ◽  
Author(s):  
Miro Jurisic ◽  
Tobias Fechter ◽  
Frida Hauler ◽  
Hugo Furtado ◽  
Ursula Nestle ◽  
...  
Keyword(s):  
Newton Method ◽  
Minimization Problem ◽  
Energy Minimization ◽  
Numerical Experiments ◽  
High Accuracy ◽  
Energy Model ◽  
Deformable Registration ◽  
Data Sets ◽  
Preliminary Study ◽  
Ct Data

In this work, we try to develop a fast converging method for segmentation assisted deformable registration. The segmentation step consists of a piece-wise constant Mumford-Shah energy model while reg- istration is driven by the sum of squared distances of both initial images and segmented mask with a diffusion regularization. In order to solve this energy minimization problem, a second order Gauss-Newton opti- mization method is used. For the numerical experiments we used CT data sets from the EMPIRE10 challenge. In this preliminary study, we show high accuracy of our algorithm.

scholarly journals On optimal cloaking-by-mapping transformations

2022 ◽  
Author(s):  
Yves Capdeboscq ◽  
Michael Vogelius
Keyword(s):  
Minimization Problem ◽  
Strong Evidence ◽  
Energy Minimization ◽  
Final Section ◽  
Outer Boundary ◽  
Finite Size ◽  
Small Hole ◽  
Lower Degree ◽  
Degree Of Anisotropy

Abstract. A central ingredient of cloaking-by-mapping is the diffeomorphisn which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in [4]. In this work, as in [4], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.

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