415,683 research outputs found
Modelling Rod-like Flexible Biological Tissues for Medical Training
This paper outlines a framework for the modelling of slender rod-like biological tissue structures in both global and local scales. Volumetric discretization of a rod-like structure is expensive in computation and therefore
is not ideal for applications where real-time performance is essential. In our approach, the Cosserat rod model is introduced to capture the global shape changes, which models the structure as a one-dimensional entity, while the
local deformation is handled separately. In this way a good balance in accuracy and efficiency is achieved. These advantages make our method appropriate for
the modelling of soft tissues for medical training applications
Raviart-Thomas finite elements of Petrov-Galerkin type
The mixed finite element method for the Poisson problem with the
Raviart-Thomas elements of low-level can be interpreted as a finite volume
method with a non-local gradient. In this contribution, we propose a variant of
Petrov-Galerkin type for this problem to ensure a local computation of the
gradient at the interfaces of the elements. The shape functions are the
Raviart-Thomas finite elements. Our goal is to define test functions that are
in duality with these shape functions: Precisely, the shape and test functions
will be asked to satisfy a L2-orthogonality property. The general theory of
Babu\v{s}ka brings necessary and sufficient stability conditions for a
Petrov-Galerkin mixed problem to be convergent. We propose specific constraints
for the dual test functions in order to ensure stability. With this choice, we
prove that the mixed Petrov-Galerkin scheme is identical to the four point
finite volumes scheme of Herbin, and to the mass lumping approach developed by
Baranger, Maitre and Oudin. Finally, we construct a family of dual test
functions that satisfy the stability conditions. Convergence is proven with the
usual techniques of mixed finite elements
An advanced meshless technique for large deformation analysis of metal forming
The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Although the finite element method (FEM) is a well-established method for modeling nonlinear problems, it often encounters difficulties for large deformation analyses due to the mesh distortion issues. Because no mesh is used, the meshless methods show very good potential for the large deformation analysis. In this paper, a local meshless formulation is developed for the large deformation analysis. The Radial Basis Function (RBF) is employed to construct the meshless shape functions, and the spline function with high continuity is used as the weight function in the construction of the local weak form. The discrete equations for large deformation of solids are obtained using the local weak-forms, RBF shape functions, and the total Lagrangian (TL) approach, which refers all variables to the initial (undeformed) configuration. This formulation requires no explicit mesh in computation and therefore fully avoids mesh distortion difficulties in the large deformation analysis of metal forming. Several example problems are presented to demonstrate the effectiveness of the developed meshless technique. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems in metal forming
The shape of primordial non-Gaussianity and the CMB bispectrum
We present a set of formalisms for comparing, evolving and constraining
primordial non-Gaussian models through the CMB bispectrum. We describe improved
methods for efficient computation of the full CMB bispectrum for any general
(non-separable) primordial bispectrum, incorporating a flat sky approximation
and a new cubic interpolation. We review all the primordial non-Gaussian models
in the present literature and calculate the CMB bispectrum up to l <2000 for
each different model. This allows us to determine the observational
independence of these models by calculating the cross-correlation of their CMB
bispectra. We are able to identify several distinct classes of primordial
shapes - including equilateral, local, warm, flat and feature (non-scale
invariant) - which should be distinguishable given a significant detection of
CMB non-Gaussianity. We demonstrate that a simple shape correlator provides a
fast and reliable method for determining whether or not CMB shapes are well
correlated. We use an eigenmode decomposition of the primordial shape to
characterise and understand model independence. Finally, we advocate a
standardised normalisation method for based on the shape
autocorrelator, so that observational limits and errors can be consistently
compared for different models.Comment: 32 pages, 20 figure
ASTErIsM - Application of topometric clustering algorithms in automatic galaxy detection and classification
We present a study on galaxy detection and shape classification using
topometric clustering algorithms. We first use the DBSCAN algorithm to extract,
from CCD frames, groups of adjacent pixels with significant fluxes and we then
apply the DENCLUE algorithm to separate the contributions of overlapping
sources. The DENCLUE separation is based on the localization of pattern of
local maxima, through an iterative algorithm which associates each pixel to the
closest local maximum. Our main classification goal is to take apart elliptical
from spiral galaxies. We introduce new sets of features derived from the
computation of geometrical invariant moments of the pixel group shape and from
the statistics of the spatial distribution of the DENCLUE local maxima
patterns. Ellipticals are characterized by a single group of local maxima,
related to the galaxy core, while spiral galaxies have additional ones related
to segments of spiral arms. We use two different supervised ensemble
classification algorithms, Random Forest, and Gradient Boosting. Using a sample
of ~ 24000 galaxies taken from the Galaxy Zoo 2 main sample with spectroscopic
redshifts, and we test our classification against the Galaxy Zoo 2 catalog. We
find that features extracted from our pipeline give on average an accuracy of ~
93%, when testing on a test set with a size of 20% of our full data set, with
features deriving from the angular distribution of density attractor ranking at
the top of the discrimination power.Comment: 20 pages, 13 Figures, 8 Tables, Accepted for publication in the
Monthly Notices of the Royal Astronomical Societ
The second order local-image-structure solid
Characterization of second order local image structure by a 6D vector ( or jet) of Gaussian derivative measurements is considered. We consider the affect on jets of a group of transformations - affine intensity-scaling, image rotation and reflection, and their compositions - that preserve intrinsic image structure. We show how this group stratifies the jet space into a system of orbits. Considering individual orbits as points, a 3D orbifold is defined. We propose a norm on jet space which we use to induce a metric on the orbifold. The metric tensor shows that the orbifold is intrinsically curved. To allow visualization of the orbifold and numerical computation with it, we present a mildly-distorting but volume-preserving embedding of it into euclidean 3-space. We call the resulting shape, which is like a flattened lemon, the second order local-image-structure solid. As an example use of the solid, we compute the distribution of local structures in noise and natural images. For noise images, analytical results are possible and they agree with the empirical results. For natural images, an excess of locally 1D structure is found
Stability analysis in the inverse Robin transmission problem
In this paper, we consider the conductivity problem with piecewiseâconstant conductivity and Robinâtype boundary condition on the interface of discontinuity. When the quantity of interest is the jump of the conductivity, we perform a local stability estimate for a parameterized nonâmonotone family of domains. We give also a quantitative stability result of local optimal solution with respect to a perturbation of the Robin parameter. In order to find an optimal solution, we propose a KohnâVogeliusâtype cost functional over a class of admissible domains subject to two boundary values problems. The analysis of the stability involves the computation of firstâorder and secondâorder shape derivative of the proposed cost functional, which is performed rigorously by means of shapeâLagrangian formulation without using the shape sensitivity of the states variables
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