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Optimal control of geodesics in Riemannian manifolds

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Interactive design exploration for constrained meshes

Mark Pauly, Sofien Bouaziz, Bailin Deng, Yuliy Gennadievich Schwartzburg, Mario Moacir Deuss, Alexandre Kaspar

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modif ...

Elsevier2015

Cell Shape Dynamics Reveal Balance of Elasticity and Contractility in Peripheral Arcs

Jean-Jacques Meister, Chiara Gabella, Benoît Vianay, Céline Jeanne Labouesse

The mechanical interaction between adherent cells and their substrate relies on the formation of adhesion sites and on the stabilization of contractile acto-myosin bundles, or stress fibers. The shape of the cell and the orientation of these fibers can be ...

Cell Press2015

Igatools: an isogeometric analysis library

Pablo Antolin Sanchez

We present the design of an object oriented general purpose library for isogeometric analysis, where the mathematical concepts of the isogeometric method and their relationships are directly mapped into classes and their interactions. The encapsulation of ...

2015

Discrete variational Lie group formulation of geometrically exact beams dynamics

Yves Weinand, Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...

Springer Verlag2015

The Fluid Joint: The Soft Spot of Micro- and Nanosystems

Massimo Mastrangeli

Fluid bridges are ubiquitous soft structures of finite size that conform to and link the surfaces of neighboring objects. Fluid joints, the specific type of fluid bridge with at least one extremity constrained laterally, display even more pronounced reacti ...

2015

Fiber connectivity and bifurcation diagrams of almost toric integrable systems

Tudor Ratiu

We describe the bifurcation diagrams of almost toric integrable Hamiltonian systems on a four dimensional symplectic manifold M, not necessarily compact. We prove that, under a weak assumption, the connectivity of the fibers of the induced singular Lagrang ...

Int Press Boston, Inc2015

Principal Flows

Victor Panaretos, Tung Huy Pham, Zhigang Yao

We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...

American Statistical Association2014

Optimal control for power generating kites

Sanket Sanjay Diwale

Numerical solutions for optimal power generation in a pumping power cycle for Airborne Wind Energy is presented. The problem is essentially an infinite horizon optimal control problem which is then attempted to solve by three methods, finite time horizon a ...

2014

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martins Bruveris, Martin Bauer

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...

Springer Verlag2014

Principal Polynomial Analysis

Devis Tuia

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...

World Scientific Publ Co Pte Ltd2014