Related papers: The contact property for magnetic flows on surface…
We prove the existence of minimal symplectomorphisms and strictly ergodic contactomorphisms on manifolds which admit a locally free $\mathbb{S}^1$--action by symplectomorphisms and contactomorphisms, respectively. The proof adapts the…
Axisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions. To this end a set of pertinent non-linear ODEs are…
We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic curvature (also known as magnetic geodesics) on an oriented…
Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry,…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Magnetic reconnection plays an important role in converting energy while modifying field topology. This process takes place in varied plasma environments in which the transport of magnetic flux is intrinsic. Identifying active magnetic…
We studied the solar surface flows (differential rotation and meridional circulation) using a magnetic element feature tracking technique by which the surface velocity is obtained using magnetic field data. We used the line-of-sight…
We present a study of ground state energies and densities of quantum dots in a magnetic field, which takes into account correlation effects through the Current-density functional theory (CDFT). The method is first tested against exact…
Observations of parametrically excited surface waves in a magnetic fluid are presented. Under the influence of a magnetic field these waves have a non--monotonic dispersion relation, which leads to a richer behavior than in ordinary…
Using direct numerical simulations of the equations of magnetohydrodynamics, we study reversals of the magnetic field generated by the flow of an electrically conducting fluid in a sphere. We show that at low magnetic Prandtl numbers,…
Using two different configurations of temperature and magnetic field gradients, we observed that, in a quasi one-dimensional magnetic fluid, magnetic force either reduces the temperature difference across the sample when the two gradients…
The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the…
We study the evolution of turbulent magnetic fields from a topological point of view, invoking commonplace mathematical tools from general topology and dynamical systems theory which connect magnetic field evolution to time reversal…
We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach Hamiltonians are no longer functions on the contact…
Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible,…
We present results for a model that describes a quantum point contact. We show how electron-electron correlations, within the unrestricted Hartree-Fock approximation, generate a magnetic moment in the point contact. Having characterized the…
We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field…
We establish a relation between the growth of the cylindrical contact homology of a contact manifold and the topological entropy of Reeb flows on this manifold. We show that if a contact manifold $(M,\xi)$ admits a hypertight contact form…
We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or…
We construct a dynamical model for high-energy heavy-ion collision based on the relativistic resistive magneto-hydrodynamic framework. Using our newly developed (3+1)-dimensional relativistic resistive magneto-hydrodynamics code, we…