Publications related to Ideal knots and other packing problems of tubes

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

Medial axis transformation as a solid modeling representation method for computer aided design software

Paul Xirouchakis, Mihai-Bogdan Lazar, Ian Anthony Stroud, Florian Barras, Guillaume Goualard

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...

2016

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Jan Sickmann Hesthaven, Paolo Gatto

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...

Springer Verlag2015

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

Alfio Quarteroni, Luca Dede', Andrea Bartezzaghi

We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...

MATHICSE2015

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to q ...

American Physical Society2015

High-Precision MRI Reconstruction Algorithm for 3D Sphere Packings

Daniele Mari, Arnaud Comment, Riccardo Balzan, Alessandro Luigi Sellerio

Packings of granular materials are complex systems consisting of large sets of particles interacting via contact forces. Their internal structure is interesting for several theoretical and practical reasons, especially when the model system consists in a l ...

Springer Verlag2015

Algebraic twists of modular forms and Hecke orbits

Philippe Michel

We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistri ...

Springer Verlag2015

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

Full blow-up range for co-rotaional wave maps to surfaces of revolution

Can Gao

We construct blow-up solutions of the energy critical wave map equation on

\mathbb{R}^{2+1}\to \mathcal N

with polynomial blow-up rate (

t^{-1-\nu}

for blow-up at

t=0

) in the case when

\mathcal N

is a surface of revolution. Here we extend the blow-u ...

2014

Ideal knots and other packing problems of tubes

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An Inner-Product Calculus for Periodic Functions and Curves

Medial axis transformation as a solid modeling representation method for computer aided design software

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

High-Precision MRI Reconstruction Algorithm for 3D Sphere Packings

Algebraic twists of modular forms and Hecke orbits

Similarity-Based Shape Priors for 2D Spline Snakes

Constructing reparameterization invariant metrics on spaces of plane curves

Full blow-up range for co-rotaional wave maps to surfaces of revolution

Medial axis transformation as a solid modeling representation method for computer aided design software

An Inner-Product Calculus for Periodic Functions and Curves

Constructing reparameterization invariant metrics on spaces of plane curves

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Similarity-Based Shape Priors for 2D Spline Snakes

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Algebraic twists of modular forms and Hecke orbits

Full blow-up range for co-rotaional wave maps to surfaces of revolution

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

High-Precision MRI Reconstruction Algorithm for 3D Sphere Packings