scholarly journals Polarization tensor vanishing structure of general shape: Existence for small perturbations of balls

2020 ◽  
pp. 1-32
Author(s):  
Hyeonbae Kang ◽  
Xiaofei Li ◽  
Shigeru Sakaguchi
Keyword(s):  
Small Volume ◽  
Expansion Method ◽  
Two Dimensions ◽  
Degree Zero ◽  
Polarization Tensor ◽  
General Shape ◽  
Small Perturbations ◽  
Geometric Quantity ◽  
The Core ◽  
Boundary Measurements

The polarization tensor is a geometric quantity associated with a domain. It is a signature of the small inclusion’s existence inside a domain and used in the small volume expansion method to reconstruct small inclusions by boundary measurements. In this paper, we consider the question of the polarization tensor vanishing structure of general shape. The only known examples of the polarization tensor vanishing structure are concentric disks and balls. We prove, by the implicit function theorem on Banach spaces, that a small perturbation of a ball can be enclosed by a domain so that the resulting inclusion of the core-shell structure becomes polarization tensor vanishing. The boundary of the enclosing domain is given by a sphere perturbed by spherical harmonics of degree zero and two. This is a continuation of the earlier work (Kang, Li, Sakaguchi) for two dimensions.

Differences in the Heat Transfer at the Core-Reflector Boundary of the PBMR Due to the Use of Different Numerical Methods

2009 ◽  
Author(s):  
Pieter S. du Toit ◽  
Onno Ubbink
Keyword(s):  
Two Dimensions ◽  
Heat Sources ◽  
Coarse Mesh ◽  
One Dimensional ◽  
Root Cause ◽  
The Core ◽  
Modified Method ◽  
The Difference ◽  
Horizontal Slice ◽  
Mesh Cell

The PBMR (Pebble Bed Modular Reactor) is a High-Temperature Gas-cooled Reactor (HTGR) concept. One of the exercises of the PBMR benchmark of the Organization for Economic Cooperation and Development (OECD) is a steady state two-dimensional (2D) thermal-hydraulics simulation of a simplified PBMR with prescribed heat sources. Two different programs were used to model this exercise. They predicted similar core temperatures but the side reflector temperatures next to the core differed by more than 30 °C (when using a relatively coarse mesh). The underlying methods define temperatures at either vertices (VC) or at mesh cell centres (CC). A study was undertaken using one-dimensional (1D) implementations of the VC and CC methods to model a horizontal slice through the core. This study revealed the root cause of the different predictions. A modified version of the 1D CC method was developed that essentially predicts the same temperatures as the VC method. The extension of the modified method to two dimensions is under investigation. If the difference in predicted temperatures next to the core can be eliminated or reduced, then the focus can shift to other differences between the results of the two programs.

General shape distributions in a plane

1991 ◽  
Vol 23 (2) ◽  
pp. 259-276 ◽  
Author(s):  
I. L. Dryden ◽  
K. V. Mardia
Keyword(s):  
Closed Form ◽  
Normal Approximation ◽  
Asymptotic Properties ◽  
Two Dimensions ◽  
General Shape ◽  
Shape Distribution ◽  
Inference Problems ◽  
Point Configurations ◽  
Exact Shape

In this paper we investigate the exact shape distribution for general Gaussian labelled point configurations in two dimensions. The shape density is written in a closed form, in terms of Kendall's or Bookstein's shape variables. The distribution simplifies considerably in certain cases, including the complex normal, isotropic, circular Markov and equal means cases. Various asymptotic properties of the distribution are investigated, including a large variation distribution and the normal approximation for small variations. The triangle case is considered in particular detail, and we compare the density with simulated densities for some examples. Finally, we consider inference problems, with an application in biology.

Nodal Expansion and its Application in AP1000 Nuclear Reactor Core Monitoring System

2013 ◽  
Vol 448-453 ◽  
pp. 1907-1911
Author(s):  
Wei Zhi Jia ◽  
Rui Wang ◽  
Yun Zhou
Keyword(s):  
Monitoring System ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Expansion Method ◽  
The Core ◽  
Nodal Model ◽  
Nuclear Reactor Core ◽  
Nodal Expansion Method ◽  
Full Core

As the core monitoring system of AP1000, BEACON always uses a full-core nodal model for core monitoring based on the ANC-NEM nodal model. The theory behind the nodal expansion method is discussed, and the application of the method in BEACON is described. Finally, an ANC-NEM calculation simulation is proposed.

Flake Drying Temperature Affects Mat Properties during Pressing

Holzforschung ◽  
2002 ◽  
Vol 56 (5) ◽  
pp. 558-562 ◽  
Author(s):  
C. J. Martino ◽  
S. Shrauti ◽  
S. Banerjee ◽  
L. P. Otwell ◽  
E. W. Price
Keyword(s):  
Contact Angle ◽  
High Temperature ◽  
Surface Hydrophobicity ◽  
Environmental Benefits ◽  
General Shape ◽  
Drying Temperature ◽  
The Core ◽  
Pore Closure ◽  
Lower Temperature ◽  
High Temperature Drying

Summary The contact angle of water on wood rises sharply as the wood approaches dryness. The general shape of the rise can be reproduced through thermodynamic calculations that consider the presence of extractives on the surface. SEM work confirms that extractives move progressively to the surface with increasing drying temperature. Other factors such as pore closure also contribute to surface hydrophobicity. The temperature profile within a stack of flakes during accelerated pressing shows a break at 100°C when flakes dried at high temperature are processed. Moisture is known to be driven from the outer layers of the stack to the core during early pressing. If the flake surface is hydrophobic then this moisture would film on the surface rather than penetrate into the flake. Subsequent evaporation of the moisture would lead to high pressure. Hence, flakes dried at high temperature should be more prone to delamination. High-temperature drying also promotes VOC emissions and there should be operational and environmental benefits to drying at lower temperature.

The Core and the Stability of Group Choice in Spatial Voting Games

1988 ◽  
Vol 82 (1) ◽  
pp. 195-211 ◽  
Author(s):  
Norman Schofield ◽  
Bernard Grofman ◽  
Scott L. Feld
Keyword(s):  
Political Stability ◽  
Simple Majority ◽  
Small Perturbations ◽  
The Core ◽  
Spatial Voting ◽  
Voting Games ◽  
Voting Game ◽  
Stable Core ◽  
The Stability ◽  
Structurally Stable

The core of a voting game is the set of undominated outcomes, that is, those that once in place cannot be overturned. For spatial voting games, a core is structurally stable if it remains in existence even if there are small perturbations in the location of voter ideal points. While for simple majority rule a core will exist in games with more than one dimension only under extremely restrictive symmetry conditions, we show that, for certain supramajorities, a core must exist. We also provide conditions under which it is possible to construct a structurally stable core. If there are only a few dimensions, our results demonstrate the stability properties of such frequently used rules as two-thirds and three-fourths. We further explore the implications of our results for the nature of political stability by looking at outcomes in experimental spatial voting games and at Belgian cabinet formation in the late 1970s.

Identification of border-zone corridors in the left ventricle using the core expansion method

2017 ◽  
Author(s):  
L. Serra ◽  
R. M. Figueras i Ventura ◽  
X. Planes ◽  
M. Steghöfer ◽  
J. Fernández-Armenta ◽  
...  
Keyword(s):  
Left Ventricle ◽  
Expansion Method ◽  
Border Zone ◽  
The Core

To Improve the Accuaracy of Harmonic Synthesis Method by Using More Detectors in Azimuthal Direction in HTR

2014 ◽  
Author(s):  
Kai Fan ◽  
Fu Li ◽  
Xuhua Zhou
Keyword(s):  
Power Distribution ◽  
Synthesis Method ◽  
Expansion Method ◽  
Azimuthal Direction ◽  
Neutron Detectors ◽  
Tsinghua University ◽  
The Core ◽  
Demonstration Plant ◽  
Polynomial Expansion Method ◽  
High Temperature Gas

Modular high temperature gas cooled reactor HTR-PM demonstration plant, designed by INET, Tsinghua University, is being built in Shidaowan, Shandong province, China. HTR-PM adopts pebble bed concept. Like other HTR, monitoring the core power distribution of HTR-PM is very important but challenging, as there is no in-core neutron detectors. There are some proposals to reconstruct the power distribution using the readings of ex-core neutron detectors. One method is harmonic synthesis method. In HTR, the neutron detectors are arranging symmetrically; and the power distribution of the core is also symmetrical. So in the before, only one set of detectors were used to reconstruct the power distribution, for considering the readings of different sets were almost same. In this paper, all readings of the neutron detectors were used, and new results were calculated and evaluated. It is showed that using more detector readings has no help to the accuracy of the harmonic synthesis method but improve the robustness of the method obvious. Using more detectors could improve both the robustness and the accuracy to the harmonics’ coefficients polynomial expansion method.

The diffraction of SH waves by an arbitrary shaped crack in two dimensions

1992 ◽  
Vol 340 (1659) ◽  
pp. 503-529 ◽  
Keyword(s):  
Function Method ◽  
Scattering Problem ◽  
Elastic Solid ◽  
Two Dimensions ◽  
General Shape ◽  
Sh Waves ◽  
Green Function Method ◽  
Rigid Barrier ◽  
Shaped Crack ◽  
Scalar Scattering

In this paper we consider the two-dimensional scalar scattering problem for Helmholtz’s equation exterior to a smooth open arc of general shape. The problem has a number of physical applications including the diffraction of sound by a rigid barrier immersed in a compressible fluid and by a crack in an elastic solid which supports a state of anti-plane strain (SH-motion). The mathematical method used here is the crack Green function method introduced by G. R. Wickham. This enables the scattering problem to be reduced to the solution of a Fredholm integral equation of the second kind with a continuous kernel. The numerical solution of this equation is discussed and a number of examples are computed.

Existence of weakly neutral coated inclusions of general shape in two dimensions

2020 ◽  
pp. 1-24 ◽  
Author(s):  
Hyeonbae Kang ◽  
Xiaofei Li ◽  
Shigeru Sakaguchi
Keyword(s):  
Two Dimensions ◽  
General Shape
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