Cosmological Imprints of a Generalized Chaplygin Gas Model for the Early Universe

We propose a phenomenological model for the early universe where there is a smooth transition between an early "quintessence" phase and a radiation dominated era. The matter content is modelled by an appropriately modified Chaplygin gas for the early universe. We constrain the model observationally by mapping the primordial power spectrum of the scalar perturbations to the latest data of WMAP7. We compute as well the spectrum of the primordial gravitational waves as would be measured today. We show that the high frequencies region of the spectrum depends on the free parameter of the model and most importantly this region of the spectrum can be within the reach of future gravitational waves detectors.Comment: 10 pages, 8 figures. RevTex

Constraints on millicharged particles with low threshold germanium detectors at Kuo-Sheng Reactor Neutrino Laboratory

Relativistic millicharged particles ($\chi_q$) have been proposed in various extensions to the Standard Model of particle physics. We consider the scenarios where they are produced at nuclear reactor core and via interactions of cosmic-rays with the earth's atmosphere. Millicharged particles could also be candidates for dark matter, and become relativistic through acceleration by supernova explosion shock waves. The atomic ionization cross section of $\chi_q$ with matter are derived with the equivalent photon approximation. Smoking-gun signatures with significant enhancement in the differential cross section are identified. New limits on the mass and charge of $\chi_q$ are derived, using data taken with a point-contact germanium detector with 500g mass functioning at an energy threshold of 300~eV at the Kuo-Sheng Reactor Neutrino Laboratory.Comment: 8 pages, 7 figure

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

Exact analytical approach to differential equations with variable coefficients

This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the analytical expression presented in the paper. The formalism can be easily extended to the infinite dimensional case such as the quantum time-dependent Hamiltonian problem.Comment: 16 pages, 4 figure