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Stochastic Shape Analysis
The chapter describes stochastic models of shapes from a Hamiltonian viewpoint, including Langevin models, Riemannian Brownian motions and stochastic...
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A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized...
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Shape Analysis by Computing Geodesics on a Manifold via Cubic B-splines
When a parameterized probability density function is used to represent a landmark-based shape, the shape can be viewed as a point on the manifold...
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Shape Sensitivity Analysis of a 2D Fluid–Structure Interaction Problem
We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes–elasticity system with...
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Boundary shape reconstruction with Robin condition: existence result, stability analysis, and inversion via multiple measurements
This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region...
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Analysis of General Shape Optimization Problems in Nonlinear Acoustics
In various biomedical applications, precise focusing of nonlinear ultrasonic waves is crucial for efficiency and safety of the involved procedures....
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Shape Gradient Methods for Shape Optimization of an Unsteady Multiscale Fluid–Structure Interaction Model
We consider numerical shape optimization of a fluid–structure interaction model. The constrained system involves multiscale coupling of a...
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Exploring how ecological and epidemiological processes shape multi-host disease dynamics using global sensitivity analysis
We use global sensitivity analysis (specifically, Partial Rank Correlation Coefficients) to explore the roles of ecological and epidemiological...
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Modeling, analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators
Existing quasi-zero stiffness (QZS) isolators are reviewed. In terms of their advantages, a novel X-shape QZS isolator combined with the...
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Stochastic Shape Analysis
The chapter describes stochastic models of shapes from a Hamiltonian viewpoint, including Langevin models, Riemannian Brownian motions and stochastic...
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Geometric Aspects of Shape Optimization
We present a review of known results in shape optimization from the point of view of Geometric Analysis. This paper is devoted to the mathematical...
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Shape analysis and fairness metric of generalized fractional Bézier curve
In the areas of engineering and architecture, smooth curves and surfaces are crucial to produce sleek products and to prevent the structures from...
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Contact Shape Optimization
Contact shape optimization problems in 3D have a structure that can be effectively exploited by the TFETI-based methods introduced in Part III. The...
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Mathematical Methods for the Shape Analysis and Indexing of Tangible CH Artefacts
Thanks to continuous efforts towards 3D digitisation in the Cultural Heritage (CH) domain, we have experienced increasing interest in mathematical...
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PDE-Constrained Shape Optimization: Toward Product Shape Spaces and Stochastic Models
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which a...
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A Sheaf-Theoretic Construction of Shape Space
We present a sheaf-theoretic construction of shape space—the space of all shapes. We do this by describing a homotopy sheaf on the poset category of...
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Shape-Programming in Hyperelasticity Through Differential Growth
This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation...
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Recent Development of Medical Shape Analysis via Computational Quasi-conformal Geometry
Medical analysis is closely related to mathematics in many aspects. Over the past decades, mathematicians have designed numerous mathematical models...
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Mechanical-Mathematical Modeling of the Shape of Dental Arches for Orthognathic Occlusion
We perform mathematical modeling of the shape of dental arches. It is assumed that dental arches can be modeled by second-order curves. As a result...
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Deep neural networks on diffeomorphism groups for optimal shape reparametrization
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding...
