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We propose a new interconnection relation for infinite-dimensional port-Hamiltonian systems that enables the coupling of ports with different spatial dimensions by integrating over the the surplus dimensions. To show the practical…

Dynamical Systems · Mathematics 2023-01-12 Jens Jäschke , Nathanael Skrepek , Matthias Ehrhardt

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…

Differential Geometry · Mathematics 2007-05-23 Simon P. Morgan

Fast Magnetic Reconnection is currently regarded as an important process also beyond the solar system, specially in magnetically dominated regions of galactic and extragalactic sources like the surrounds of black holes and relativistic…

This paper is the first input towards an open analogue of the quantum Kirwan map. We consider the adiabatic limit of the symplectic vortex equation over the unit disk for a Hamiltonian G-manifold with Lagrangian boundary condition, by…

Symplectic Geometry · Mathematics 2018-01-12 Dongning Wang , Guangbo Xu

This article is devoted to characterize all possible effective behaviors of composite materials by means of periodic homogenization. This is known as a $G$-closure problem. Under convexity and $p$-growth conditions ($p>1$), it is proved…

Analysis of PDEs · Mathematics 2015-06-26 Jean-Francois Babadjian , Marco Barchiesi

We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $\delta$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike…

Quantum Physics · Physics 2022-10-27 Etienne Granet

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…

Numerical Analysis · Mathematics 2020-09-30 Andrea Brugnoli , Ghislain Haine , Anass Serhani , Xavier Vasseur

We prove the existence of infinitely many periodic orbits of symplectomorphisms isotopic to the identity if they admit at least one hyperbolic periodic orbit and satisfy some condition on the flux. Our result is proved for a certain class…

Symplectic Geometry · Mathematics 2015-08-27 Marta Batoréo

We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic…

Condensed Matter · Physics 2015-06-25 I. S. Tupitsyn , N. V. Prokof'ev , P. C. E. Stamp

We study the contact geometry of the connected components of the energy hypersurface, in the symmetric restricted 3-body problem on $\mathbb{S}^2$, for a specific type of motion of the primaries. In particular, we show that these components…

Dynamical Systems · Mathematics 2024-11-19 Kursat Yilmaz , Alessandro Arsie

Motivated by a path planning problem we consider the following procedure. Assume that we have two points $s$ and $t$ in the plane and take $\mathcal{K}=\emptyset$. At each step we add to $\mathcal{K}$ a compact convex set that does not…

Computational Geometry · Computer Science 2015-02-13 Sergio Cabello , Michael Kerber

This work presents a 2.5-dimensional simulation study of the instability of current-sheets located in a medium with a strong density variation along the current layer. The initial force-free configuration is observed to undergo a two-stage…

Solar and Stellar Astrophysics · Physics 2015-05-13 Lapo Bettarini , Giovanni Lapenta

We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length $mn$ for all $n$, and certain $\12-$order Sobolev norms on the graph paper lines. We also…

Functional Analysis · Mathematics 2016-11-26 Robert S. Strichartz

We present a constructive numerical example of fast magnetic reconnection in a three dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines. The solution is intrinsically three…

Plasma Physics · Physics 2015-05-18 Bijia Pang , Ue-Li Pen , Ethan T. Vishniac

A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then…

Differential Geometry · Mathematics 2019-07-05 Casey Blacker

The port-Hamiltonian formulation is a powerful method for modeling and interconnecting systems of different natures. In this paper, the port-Hamiltonian formulation in tensorial form of a thick plate described by the Mindlin-Reissner model…

Analysis of PDEs · Mathematics 2020-10-07 Andrea Brugnoli , Daniel Alazard , Valérie Pommier-Budinger , Denis Matignon

In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of…

Differential Geometry · Mathematics 2007-05-23 Ely Kerman

The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (pHs), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac…

Analysis of PDEs · Mathematics 2020-10-07 Andrea Brugnoli , Daniel Alazard , Valérie Pommier-Budinger , Denis Matignon

Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…

Algebraic Topology · Mathematics 2019-11-13 Stefan Papadima , Alexander I. Suciu

Magnetic reconnection is invoked as one of the primary mechanisms to produce energetic particles. We employ large-scale three-dimensional (3D) particle-in-cell simulations of reconnection in magnetically-dominated ($\sigma=10$) pair plasmas…

High Energy Astrophysical Phenomena · Physics 2021-12-15 Hao Zhang , Lorenzo Sironi , Dimitrios Giannios