Related papers: The contact property for magnetic flows on surface…
We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.
We study Hamiltonian systems near a compact symplectic Morse-Bott minimum. Our first result shows that if the flow is Zoll (that is, it induces a free circle action) along a sequence of energy levels converging to the minimum, then the…
The need for reliable predictions of the solar activity cycle motivates the development of dynamo models incorporating a representation of surface processes sufficiently detailed to allow assimilation of magnetographic data. In this series…
The contact value theorem was originally derived for Coulomb fluids of mobile charged particles in thermal equilibrium, in the presence of interfaces carrying a {\em uniform} surface charge density and in the absence of dielectric…
We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties…
Aims: To investigate the relationship between surges and magnetic reconnection during the emergence of small-scale active regions. In particular, to examine how the large-scale geometry of the magnetic field, shaped by different phases of…
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has non-vanishing symplectic homology. As a consequence, we establish the existence of contractible closed…
In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
This chapter is build from three 1.5 hours lectures given in Udine in april 2018 on various aspects of Earth's core dynamics. The chapter starts with a short historical note on the discovery of Earth's magnetic field and core (section 1).…
We study the low-temperature behavior of a magnetic impurity which is weakly coupled to correlated conduction electrons. To account for conduction electron interactions a diagrammatic approach in the frame of the 1/N expansion is developed.…
Using the linear fractional transformation, connecting effective conductivities sigma_{e} of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for sigma_{e} in a magnetic field are obtained. They…
By modelling the coronal structures by "slowly" evolving Double-Beltrami two-fluid equilibria (created by the interaction of the magnetic and velocity fields), the conditions for catastrophic transformations of the original state are…
Rotating magnetic structures are common in astrophysics, from vortex tubes and tornados in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure and…
Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not…
We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Ma\~n\'e…
The thermomagnetic convection of magnetic fluids in a cylindrical geometry subjected to a homogeneous magnetic field is studied. The study is motivated by a novel thermal instability [W. Luo et al., Phys. Rev. Lett. 82, 4134 (1999)]. As…
We discuss some elementary examples of interactions (at low velocity) between point charges and magnetic dipoles using potentials, along the lines indicated by Konopinsky, and show that the physical interpretation might look quite different…
These are notes for a course on contact manifolds and torus actions delivered at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems at Centre de Recerca Matem\`atica in Barcelona in July 2001. To be published by…
The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative…