Concept

Poisson manifold

Related publications (71)

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

Two dimensional quantum mechanical simulation of low dimensional tunneling devices

Mihai Adrian Ionescu, Cem Alper, Livio Lattanzio, José Luis Padilla de la Torre, Pierpaolo Palestri

We present a 2-D quantum mechanical simulation framework based on self-consistent solutions of the Schrodinger and Poisson equations, using the Finite Element Method followed by tunneling current (direct and phonon assisted) calculation in post-processing. ...

Elsevier2015

Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Cedric Jean-François Hernalsteens, Massimo Giovannozzi

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinea ...

American Physical Society2014

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

Extensions of Lie-Rinehart algebras and cotangent bundle reduction

Tudor Ratiu

Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...

Oxford University Press2013

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

Calibration by Correlation Using Metric Embedding from Nonmetric Similarities

Davide Scaramuzza

This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time correlat ...

2013

The Leaf Space Of A Multiplicative Foliation

Madeleine Jotz

We show that if a smooth multiplicative subbundle S subset of T G on a groupoid G P is involutive and satisfies completeness conditions, then its leaf space G/S inherits a groupoid structure over the space of leaves of TP boolean AND S in P. As an applicat ...

Amer Inst Mathematical Sciences2012

Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems

In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of evera and Weinstein in Progr Theoret Phys Suppl 144:145 154 2001) to construct different ...

Springer Verlag2012

Stability of Equilibria for the so(4) Free Rigid Body

Tudor Ratiu, Murat Turhan

The stability for all generic equilibria of the Lie-Poisson dynamics of the so(4) rigid body dynamics is completely determined. It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium ...

2012

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