An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed earlier by the authors. We discuss various aspects of the Hamiltonian structure of the Euler equations and show in particular that the optimal control approach leads to a standard formulation of the Euler equations -- the so-called impulse equations in their Lagrangian form. We discuss various other aspects of the Euler equations from a pedagogical point of view. We show that the Hamiltonian in the maximum principle is given by the pairing of the Eulerian impulse density with the velocity. We provide a comparative discussion of the flow equations in their Eulerian and Lagrangian form and describe how these forms occur naturally in the context of optimal control. We demonstrate that the extremal equations corresponding to the optimal control problem for the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE Conference on Decision and Contro

Asymptotic Stability, Instability and Stabilization of Relative Equilibria

In this paper we analyze asymptotic stability, instability and stabilization for the relative equilibria, i.e. equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal

Analytical solutions for the dynamics of two trapped interacting ultracold atoms

We discuss exact solutions of the Schroedinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one- and quasi-two-dimensional traps. We show that the quasi-one- and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering length we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.Comment: RevTeX, 15 pages, 15 figure

Controllable diffusion of cold atoms in a harmonically driven and tilted optical lattice: Decoherence by spontaneous emission

We have studied some transport properties of cold atoms in an accelerated optical lattice in the presence of decohering effects due to spontaneous emission. One new feature added is the effect of an external AC drive. As a result we obtain a tunable diffusion coefficient and it's nonlinear enhancement with increasing drive amplitude. We report an interesting maximum diffusion condition.Comment: 16 pages, 7 figures, revised versio

Driven Macroscopic Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices

Coherent macroscopic tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between tunneling regime and a self-trapped state of the condensate. This property of the system is explained by effectively reducing the dynamics to the nonlinear problem of a particle moving in a double square well potential. The analysis is made for both attractive and repulsive interatomic forces, and it highlights the experimental relevance of our findings

Statistics of Solar Wind Electron Breakpoint Energies Using Machine Learning Techniques

Solar wind electron velocity distributions at 1 au consist of a thermal "core" population and two suprathermal populations: "halo" and "strahl". The core and halo are quasi-isotropic, whereas the strahl typically travels radially outwards along the parallel and/or anti-parallel direction with respect to the interplanetary magnetic field. With Cluster-PEACE data, we analyse energy and pitch angle distributions and use machine learning techniques to provide robust classifications of these solar wind populations. Initially, we use unsupervised algorithms to classify halo and strahl differential energy flux distributions to allow us to calculate relative number densities, which are of the same order as previous results. Subsequently, we apply unsupervised algorithms to phase space density distributions over ten years to study the variation of halo and strahl breakpoint energies with solar wind parameters. In our statistical study, we find both halo and strahl suprathermal breakpoint energies display a significant increase with core temperature, with the halo exhibiting a more positive correlation than the strahl. We conclude low energy strahl electrons are scattering into the core at perpendicular pitch angles. This increases the number of Coulomb collisions and extends the perpendicular core population to higher energies, resulting in a larger difference between halo and strahl breakpoint energies at higher core temperatures. Statistically, the locations of both suprathermal breakpoint energies decrease with increasing solar wind speed. In the case of halo breakpoint energy, we observe two distinct profiles above and below 500 km/s. We relate this to the difference in origin of fast and slow solar wind.Comment: Published in Astronomy & Astrophysics, 11 pages, 10 figure