Hamiltonian and linear-space structure for damped oscillators: I. General theory

Hamiltonian dynamics and spectral theory for spin-oscillators

We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have infinitely many transversally elliptic singularities, exactly one elliptic-elliptic singularity and one focus-focus singularity. The most interesting dynamical featu...

Target Space Duality I : General Theory ∗

We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and M̃ arises because of the existence of a very special symplectic manifold. This manifold locally looks like M×M̃ and admits a double fibration. We analyze the local geometric requirements necessary for target space duality and prove that both manifol...

Linear Scale - Space I : Basic Theory 1

0 i 1 LINEAR SCALE - SPACE I : BASIC THEORY 1

Polynomial Chaos Expansions For Damped Oscillators

Uncertainty quantification is the state-of-the-art framework dealing with uncertainties arising in all kind of real-life problems. One of the framework’s functions is to propagate uncertainties from the stochastic input factors to the output quantities of interest, hence the name uncertainty propagation. To this end, polynomial chaos expansions (PCE) have been effectively used in a wide variety...