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.

Simulation of the Organization of Heteroepitaxial Monolayer Islands Under Anisotropic Conditions

2004 ◽  
Vol 854 ◽  
Author(s):  
Gajendra Pandey ◽  
Robert V. Kukta
Keyword(s):  
Point Defects ◽  
Surface Stress ◽  
Lattice Mismatch ◽  
Finite Size ◽  
Source Model ◽  
Crystalline Material ◽  
Elastic Fields ◽  
High Anisotropy ◽  
Degree Of Anisotropy ◽  
Hexagonal Arrays

ABSTRACTThis paper addresses the effect of anisotropy on the organization of epitaxial islands deposited on a substrate. Focus is on in-plane anisotropies in surface stress and lattice mismatch between the film and substrate materials. Starting from a configuration where island sizes and position are random, evolution towards equilibrium through mass transport via condensation/evaporation is simulated. The effect of the degree of anisotropy is investigated. An efficient numerical method is obtained by reducing a model of square monolayer islands of finite size to point defects that interact through their elastic fields. Models for both the kinetics and energetics of the system are obtained by this reduction. It is found that the point source model is accurate for island separations larger than about 3 times the width of an island. Under isotropic conditions islands tend to form into hexagonal arrays, and as there is no preferred orientation of these arrays, defects analogous to grain boundaries in a crystalline material tend to arise. With anisotropy islands tend to align in particular directions. This is found to enhance organization in cases of modest anisotropy and cause islands to form into zigzagged lines in cases of high anisotropy.

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 What Does the Evidence Tell Us about ‘Thinking and Working Politically’ in Development Assistance?

2019 ◽  
Vol 7 (2) ◽  
pp. 155-168 ◽  
Author(s):  
Niheer Dasandi ◽  
Ed Laws ◽  
Heather Marquette ◽  
Mark Robinson
Keyword(s):  
Strong Evidence ◽  
Critical Review ◽  
Final Section ◽  
Political Process ◽  
Development Assistance ◽  
Evidence Base ◽  
Aid Effectiveness ◽  
The Core ◽  
Success Stories ◽  
High Standards

This article provides a critical review of the evidence on ‘thinking and working politically’ (TWP) in development. Scholars and practitioners have increasingly recognised that development is a fundamentally political process, and there are concerted efforts underway to develop more politically-informed and adaptive ways of thinking and working in providing development assistance. However, while there are interesting and engaging case studies in the emerging, largely practitioner-based literature, these do not yet constitute a strong evidence base that shows these efforts can be clearly linked to more effective aid programming. Much of the evidence used so far to support these approaches is anecdotal, does not meet high standards for a robust body of evidence, is not comparative and draws on a small number of self-selected, relatively well-known success stories written primarily by programme insiders. The article discusses the factors identified in the TWP literature that are said to enable politically-informed programmes to increase aid effectiveness. It then looks at the state of the evidence on TWP in three areas: political context, sector, and organisation. The aim is to show where research efforts have been targeted so far and to provide guidance on where the field might focus next. In the final section, the article outlines some ways of testing the core assumptions of the TWP agenda more thoroughly, to provide a clearer sense of the contribution it can make to aid effectiveness.

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.

Some magnetic properties of metals I. General introduction, and properties of large systems of electrons

1952 ◽  
Vol 211 (1107) ◽  
pp. 500-516 ◽  
Keyword(s):  
Thermodynamic Potential ◽  
Final Section ◽  
Finite Size ◽  
Magnetic Behaviour ◽  
General Introduction ◽  
Field Independent ◽  
Explicit Formulae ◽  
Large Systems ◽  
Limiting Case ◽  
Degeneracy Parameter

A general introduction surveying the problems to be examined in a series of papers is followed by a detailed treatment of the magnetic behaviour of a large system of electrons. The Schrödinger equation is solved on the assumption that the system is unbounded, and the modifications caused by the finite size of the system are then determined for the limiting case in which the system is much larger than the electronic orbits. An expression is then obtained for the density of states, and the free energy of the system found assuming that k T < E 0 , where E 0 is the degeneracy parameter. The magnetic susceptibility, thermodynamic potential and specific heat are discussed for the two cases N constant and E 0 constant. Explicit formulae are given for the temperature-dependence of the field-independent term in the susceptibility. In the final section the corrections due to electron spin are introduced.

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