Nonlinear Young integrals via fractional calculus

For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.Comment: arXiv admin note: substantial text overlap with arXiv:1404.758

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints

Propagating waves in an extremal black string

We investigate the black string in the context of the string theories. It is shown that the graviton is the only propagating mode in the (2+1)--dimensional extremal black string background. Both the dilation and axion turn out to be non-propagating modes.Comment: Minor corrections, 11 pages in ReVTeX, no figure

Quantization of spontaneously broken gauge theory based on the BFT-BFV Formalism

We quantize the spontaneously broken abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We have constructed the BFT physical fields, and obtain the first class observables including the Hamiltonian in terms of these fields. We have also explicitly shown that there are exact form invariances between the second class and first class quantities. Then, according to the BFV formalism, we have derived the corresponding Lagrangian having U(1) gauge symmetry. We also discuss at the classical level how one easily gets the first class Lagrangian from the symmetry-broken second class Lagrangian.Comment: 16 pages, latex, final version published in Mod. Phys. Lett.

Low Temperature Susceptibility of the Noncentrosymmetric Superconductor CePt_3Si

We report ac susceptibility measurements of polycrystalline CePt_3Si down to 60 mK and in applied fields up to 9 T. In zero field, a full Meissner state emerges at temperatures T/Tc < 0.3, where Tc=0.65 K is the onset transition temperature. Though transport measurements show a relatively high upper critical field Bc2 ~ 4-5 T, the low temperature susceptibility, \chi', is quite fragile to applied field, with \chi' diminishing rapidly in fields of a few kG. Interestingly, the field dependence of \chi' is well described by the power law, 4\pi\chi'=(B/B_c)^{1/2}, where Bc is the field at which the onset of resistance is observed in transport measurements.Comment: 5 figure