COMPRESSION OF GEOMETRIC DATA WITH THE USE OF PERTURBATION FUNCTIONS

2018 ◽  
Keyword(s):  
Geometric Data ◽  
Perturbation Functions

scholarly journals Bootstrap bounds on closed Einstein manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James Bonifacio ◽  
Kurt Hinterbichler
Keyword(s):  
Compact Riemannian Manifold ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Consistency Conditions ◽  
Conformal Field ◽  
Geometric Data ◽  
Conformal Bootstrap ◽  
Laplacian Operators ◽  
Kaluza Klein

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

Geometric Data of Hallux Valgus Feet

1996 ◽  
Vol 17 (9) ◽  
pp. 548-554 ◽  
Author(s):  
Kenneth S. Lamur ◽  
Anton Huson ◽  
Chris J. Snijders ◽  
Rob Stoeckart
Keyword(s):  
Hallux Valgus ◽  
Least Squares Method ◽  
Metatarsal Bone ◽  
Flexor Hallucis Longus ◽  
Independent Variables ◽  
First Metatarsal ◽  
Linear Dependency ◽  
Geometric Data ◽  
Longus Muscle ◽  
Stepwise Procedure

The aim of this study is to find basic quantitative geometric data that may contribute to the understanding of the etiology of hallux valgus. Embalmed specimens with existing hallux valgus (N = 39) were dissected; 28 variables were measured with a Vernier caliper gauge and toe goniometer. Correlations between pairs of independent variables were calculated. Linear dependency of the hallux angle, varus angle, and the width of the forefoot on a number of independent variables was analyzed by multiple linear regression. A least squares method and a stepwise procedure were used. The distance from the tendon of the flexor hallucis longus muscle to the head of the first metatarsal bone explains more than other variables the variation in hallux angle and width of the forefoot. A widened forefoot is significantly correlated with both hallux and varus angles. The interrelation of the predictor parameters illustrates the complicated hallux valgus phenomenon.

Point-based approach to enhance the quality of geometric data for CAE applications

2009 ◽  
Vol 48 (7) ◽  
pp. 2003-2010 ◽  
Author(s):  
A.A. Ball ◽  
R.J. Cripps ◽  
J. Lin ◽  
M. Loftus
Keyword(s):  
Geometric Data

3D Shape Modeling Using Perturbation Functions

2021 ◽  
Author(s):  
Pavlo Mykhaylov ◽  
Sergey Vyatkin ◽  
Roman Chekhmestruk ◽  
Ivan Perun ◽  
Tetiana Korobeinikova
Keyword(s):  
Shape Modeling ◽  
3D Shape ◽  
Perturbation Functions

Influence of Blade Deterioration on Compressor and Turbine Performance

2008 ◽  
Author(s):  
M. Morini ◽  
M. Pinelli ◽  
P. R. Spina ◽  
M. Venturini
Keyword(s):  
Gas Turbine ◽  
Mechanical Damage ◽  
Turbine Stage ◽  
Geometric Data ◽  
Turbine Performance ◽  
State Determination ◽  
Performance Curves ◽  
Common Causes ◽  
Simple Scaling ◽  
Main Effects

Gas turbine operating state determination consists of the assessment of the modification, due to deterioration and fault, of performance and geometric data characterizing machine components. One of the main effects of deterioration and fault is the modification of compressor and turbine performance maps. Since detailed information about actual modification of component maps is usually unavailable, many authors simulate the effects of deterioration and fault by a simple scaling of the map itself. In this paper, stage-by-stage models of the compressor and the turbine are used in order to assess the actual modification of compressor and turbine performance maps due to blade deterioration. The compressor is modeled by using generalized performance curves of each stage matched by means of a stage-stacking procedure. Each turbine stage is instead modeled as a couple of nozzles, a fixed one (stator) and a moving one (rotor). The results obtained by simulating some of the most common causes of blade deterioration (i.e., compressor fouling, compressor mechanical damage, turbine fouling and turbine erosion, occurring in one or more stages simultaneously) are reported in this paper. Moreover, compressor and turbine maps obtained through a stage-by-stage procedure are compared to the ones obtained by means of map scaling.

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