scholarly journals Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball

2009 ◽  
Vol 27 ◽  
pp. 311-321 ◽  
Author(s):  
Carlos Conca ◽  
Rajesh Mahadevan ◽  
Leon Sanz
2014 ◽  
Vol 26 (03) ◽  
pp. 1450005 ◽  
Author(s):  
Daniel Grieser

A plasmon of a bounded domain Ω ⊂ ℝn is a non-trivial bounded harmonic function on ℝn\∂Ω which is continuous at ∂Ω and whose exterior and interior normal derivatives at ∂Ω have a constant ratio. We call this ratio a plasmonic eigenvalue of Ω. Plasmons arise in the description of electromagnetic waves hitting a metallic particle Ω. We investigate these eigenvalues and prove that they form a sequence of numbers converging to one. Also, we prove regularity of plasmons, derive a variational characterization, and prove a second-order perturbation formula. The problem can be reformulated in terms of Dirichlet–Neumann operators, and as a side result, we derive a formula for the shape derivative of these operators.


2008 ◽  
Vol 60 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Carlos Conca ◽  
Rajesh Mahadevan ◽  
León Sanz
Keyword(s):  

2020 ◽  
Vol 268 (8) ◽  
pp. 4102-4118 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro

2010 ◽  
Vol 22 (9) ◽  
pp. 092104 ◽  
Author(s):  
Anne Bagué ◽  
Daniel Fuster ◽  
Stéphane Popinet ◽  
Ruben Scardovelli ◽  
Stéphane Zaleski

1991 ◽  
Vol 24 (7) ◽  
pp. 73-80 ◽  
Author(s):  
M. Maciejewski

The paper presents procedure, results and conclusions drawn from laboratory studies of nitrification and denitrification chambers of two-phase biological reactors with recirculation system, for a designed wastewater treatment plant of 270 000 m3/day capacity, for the city of Gdańsk. On the 1:17 physical model, observations of stream lines and measurements of the velocity field in some characteristic regions have been performed. The measurements have been carried out for 14 different configurations of the reactor operation, depending on the aerator turbines, mammoth rotors and prototypical mixers with horizontal axle and with guide-ring. Based on these studies, and having introduced some structural innovations aimed at improving flow uniformity around aerators and rotors, a variant optimal from the point-of-view of hydraulic properties and energy consumption has been proposed for realization. Moreover, using results of some other investigations performed on a structure in technical scale, conclusions concerning the following questions have been presented: I/ the importance of uniform velocity distribution in the reactor for final effeot of operation of the wastewater treatment plant, II/ relationships between velocity, discharge and hydraulic efficiency of the wastewater treatment plant chambers, III/ the influence of geometry of chambers and of recirculation on the efficiency of the purification process. The paper includes drawings, figures and short descriptions of the following experimental techniques used in the investigations: the method of varying temperature field, the colorimetric method, the conductometric method and the method using a current micrometer. A video film on the study is available.


Author(s):  
K. P. Staudhammer ◽  
L. E. Murr

The effect of shock loading on a variety of steels has been reviewed recently by Leslie. It is generally observed that significant changes in microstructure and microhardness are produced by explosive shock deformation. While the effect of shock loading on austenitic, ferritic, martensitic, and pearlitic structures has been investigated, there have been no systematic studies of the shock-loading of microduplex structures.In the current investigation, the shock-loading response of millrolled and heat-treated Uniloy 326 (thickness 60 mil) having a residual grain size of 1 to 2μ before shock loading was studied. Uniloy 326 is a two phase (microduplex) alloy consisting of 30% austenite (γ) in a ferrite (α) matrix; with the composition.3% Ti, 1% Mn, .6% Si,.05% C, 6% Ni, 26% Cr, balance Fe.


Author(s):  
P.P.K. Smith

Grains of pigeonite, a calcium-poor silicate mineral of the pyroxene group, from the Whin Sill dolerite have been ion-thinned and examined by TEM. The pigeonite is strongly zoned chemically from the composition Wo8En64FS28 in the core to Wo13En34FS53 at the rim. Two phase transformations have occurred during the cooling of this pigeonite:- exsolution of augite, a more calcic pyroxene, and inversion of the pigeonite from the high- temperature C face-centred form to the low-temperature primitive form, with the formation of antiphase boundaries (APB's). Different sequences of these exsolution and inversion reactions, together with different nucleation mechanisms of the augite, have created three distinct microstructures depending on the position in the grain.In the core of the grains small platelets of augite about 0.02μm thick have farmed parallel to the (001) plane (Fig. 1). These are thought to have exsolved by homogeneous nucleation. Subsequently the inversion of the pigeonite has led to the creation of APB's.


Author(s):  
Naresh N. Thadhani ◽  
Thad Vreeland ◽  
Thomas J. Ahrens

A spherically-shaped, microcrystalline Ni-Ti alloy powder having fairly nonhomogeneous particle size distribution and chemical composition was consolidated with shock input energy of 316 kJ/kg. In the process of consolidation, shock energy is preferentially input at particle surfaces, resulting in melting of near-surface material and interparticle welding. The Ni-Ti powder particles were 2-60 μm in diameter (Fig. 1). About 30-40% of the powder particles were Ni-65wt% and balance were Ni-45wt%Ti (estimated by EMPA).Upon shock compaction, the two phase Ni-Ti powder particles were bonded together by the interparticle melt which rapidly solidified, usually to amorphous material. Fig. 2 is an optical micrograph (in plane of shock) of the consolidated Ni-Ti alloy powder, showing the particles with different etching contrast.


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