On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

Study of the relation between the shape of lacosamide crystals and the composition of crystallization medium

Crystallization is the critical process used by pharmaceutical industries to achieve the desired size, size distribution, shape and polymorphism of a product material. Control of these properties presents a major challenge since they influence considerably downstream processing factors. Experimental work aimed at finding ways to control the crystal shape of Lacosamide, an active pharmaceutical ingredient developed by UCB Pharma, during crystallization was carried out. It was found that the crystal lattice displayed a very strong unidirectional double hydrogen bonding, which was at the origin of the needle shape of the Lacosamide crystals. Two main strategies were followed to hinder the hydrogen bonding and compete with the addition of a Lacosamide molecule along the crystal length axis: changing the crystallization medium or weakening the hydrogen bonding. Various solvents were tested to check whether the solvent used to crystallize Lacosamide had an influence on the final crystal shape. Solvent molecules seemed to slow down the growth in the length axis by hindering the unidirectional hydrogen bonding of Lacosamide crystals, but not enough to promote the crystal growth in the width axis. Additives were also tested. Certain additives have shown to compete in a more efficient way than solvent molecules with the hydrogen bonding of Lacosamide. The additive effect has also shown to be compatible with the solvent effect. In parallel, hydrogen atoms in Lacosamide were changed into deuterium atoms in order to weaken the hydrogen bonds strength. Weakening the hydrogen bonds of Lacosamide allowed to let the crystal grow in the width axis. Deuteration was found to be combinable with solvent effect while being in competition with the additive effect. The Lacosamide molecule was eventually deemed an absolute needle by the terms of Lovette and Doherty. The results of this dissertation are aimed at contributing to this classification.

Shape-keeping elements in tRNA

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Permafrost cores and active layer pits on Herschel Island: link to shape files

Twelve permafrost cores and active layer pits were drilled/dug on Herschel Island in order to estimate the soil organic carbon and total nitrogen contents in the first 30, 100 and 200 cm of ground. The data are shapefile points with attribute table, which contains different core information.

Performance Evaluation of a Statistical and a Neural Network Model for Nonrigid Shape-Based Registration

Shape-based registration methods frequently encounters in the domains of computer vision, image processing and medical imaging. The registration problem is to find an optimal transformation/mapping between sets of rigid or nonrigid objects and to automatically solve for correspondences. In this paper we present a comparison of two different probabilistic methods, the entropy and the growing neural gas network (GNG), as general feature-based registration algorithms. Using entropy shape modelling is performed by connecting the point sets with the highest probability of curvature information, while with GNG the points sets are connected using nearest-neighbour relationships derived from competitive hebbian learning. In order to compare performances we use different levels of shape deformation starting with a simple shape 2D MRI brain ventricles and moving to more complicated shapes like hands. Results both quantitatively and qualitatively are given for both sets.

Dynamic Distance-Based Shape Features for Gait Recognition

We propose a novel skeleton-based approach to gait recognition using our Skeleton Variance Image. The core of our approach consists of employing the screened Poisson equation to construct a family of smooth distance functions associated with a given shape. The screened Poisson distance function approximation nicely absorbs and is relatively stable to shape boundary perturbations which allows us to define a rough shape skeleton. We demonstrate how our Skeleton Variance Image is a powerful gait cycle descriptor leading to a significant improvement over the existing state of the art gait recognition rate.

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.