Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints

Figure of Merit for Dark Energy Constraints from Current Observational Data

Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. Here we show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) is the covariance matrix of {f_i}. The {f_i} should be minimally correlated. We demonstrate two useful choices of {f_i} using 182 SNe Ia (compiled by Riess et al. 2007), [R(z_*), l_a(z_*), \Omega_b h^2] from the five year Wilkinson Microwave Anisotropy Probe (WMAP) observations, and SDSS measurement of the baryon acoustic oscillation (BAO) scale, assuming the HST prior of H_0=72+/-8 km/s Mpc^{-1} and without assuming spatial flatness. We find that the correlation of (w_0,w_{0.5}) [w_0=w_X(z=0), w_{0.5}=w_X(z=0.5), w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a] is significantly smaller than that of (w_0,w_a) [w_X(a)=w_0+(1-a)w_a]. In order to obtain model-independent constraints on DE, we parametrize the DE density function X(z)=\rho_X(z)/\rho_X(0) as a free function with X_{0.5}, X_{1.0}, and X_{1.5} [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated from data. If one assumes a linear DE equation of state, current data are consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a free function parametrized by (X_{0.5}, X_{1.0}, X_{1.5}), current data deviate from a cosmological constant at z=1 at 68% C.L., but are consistent with a cosmological constant at 95% C.L.. Future DE experiments will allow us to dramatically increase the FoM of constraints on (w_0,w_{0.5}) and of (X_{0.5}, X_{1.0}, X_{1.5}). This will significantly shrink the DE parameter space to enable the discovery of DE evolution, or the conclusive evidence for a cosmological constant.Comment: 7 pages, 3 color figures. Submitte

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

Uncorrelated Measurements of the Cosmic Expansion History and Dark Energy from Supernovae

We present a method for measuring the cosmic expansion history H(z) in uncorrelated redshift bins, and apply it to current and simulated type Ia supernova data assuming spatial flatness. If the matter density parameter Omega_m can be accurately measured from other data, then the dark energy density history X(z)=rho_X(z)/rho_X(0) can trivially be derived from this expansion history H(z). In contrast to customary ``black box'' parameter fitting, our method is transparent and easy to interpret: the measurement of H(z)^{-1} in a redshift bin is simply a linear combination of the measured comoving distances for supernovae in that bin, making it obvious how systematic errors propagate from input to output. We find the Riess et al. (2004) ``gold'' sample to be consistent with the ``vanilla'' concordance model where the dark energy is a cosmological constant. We compare two mission concepts for the NASA/DOE Joint Dark Energy Mission (JDEM), the Joint Efficient Dark-energy Investigation (JEDI), and the Supernova Accelaration Probe (SNAP), using simulated data including the effect of weak lensing (based on numerical simulations) and a systematic bias from K-corrections. Estimating H(z) in seven uncorrelated redshift bins, we find that both provide dramatic improvements over current data: JEDI can measure H(z) to about 10% accuracy and SNAP to 30-40% accuracy.Comment: 7 pages, 4 color figures. Expanded and revised version; PRD in pres

Angle-dependence of the Hall effect in HgBa2CaCu2O6 thin films

Superconducting compounds of the family Hg-Ba-Ca-Cu-O have been the subject of intense study since the current record-holder for the highest critical temperature of a superconductor belongs to this class of materials. Thin films of the compound with two adjacent copper-oxide layers and a critical temperature of about 120 K were prepared by a two-step process that consists of the pulsed-laser deposition of precursor films and the subsequent annealing in mercury-vapor atmosphere. Like some other high-temperature superconductors, Hg-Ba-Ca-Cu-O exhibits a specific anomaly of the Hall effect, a double-sign change of the Hall coefficient close to the superconducting transition. We have investigated this phenomenon by measurements of the Hall effect at different angles between the magnetic field direction and the crystallographic c-axis. The results concerning the upper part of the transition, where the first sign change occurs, are discussed in terms of the renormalized fluctuation model for the Hall conductivity, adapted through the field rescaling procedure in order to take into account the arbitrary orientation of the magnetic field.Comment: to be published in Phys. Rev.

Neutral Gas Properties and Lyα\alpha Escape in Extreme Green Pea Galaxies

Mechanisms regulating the escape of Ly$\alpha$ photons and ionizing radiation remain poorly understood. To study these processes we analyze VLA 21cm observations of one Green Pea (GP), J160810+352809 (hereafter J1608), and HST COS spectra of 17 GP galaxies at $z<0.2$. All are highly ionized: J1608 has the highest [O III] $\lambda5007$/[O II] $\lambda3727$ for star-forming galaxies in SDSS, and the 17 GPs have [O III]/[O II] $\geq6.6$. We set an upper limit on J1608's HI mass of $\log M_{HI}/M_\odot=8.4$, near or below average compared to similar mass dwarf galaxies. In the COS sample, eight GPs show Ly$\alpha$ absorption components, six of which also have Ly$\alpha$ emission. The HI column densities derived from Ly$\alpha$ absorption are high, $\log N_{HI}/$cm$^{-2}=19-21$, well above the LyC optically thick limit. Using low-ionization absorption lines, we measure covering fractions (f_{\mbox{cov}}) of $0.1-1$, and find that f_{\mbox{cov}} strongly anti-correlates with Ly$\alpha$ escape fraction. Low covering fractions may facilitate Ly$\alpha$ and LyC escape through dense neutral regions. GPs with f_{\mbox{cov}}\sim1 all have low neutral gas velocities, while GPs with lower f_{\mbox{cov}}=0.2-0.6 have a larger range of velocities. Conventional mechanical feedback may help establish low f_{\mbox{cov}} in some cases, whereas other processes may be important for GPs with low velocities. Finally, we compare f_{\mbox{cov}} with proposed indicators of LyC escape. Ionizing photon escape likely depends on a combination of neutral gas geometry and kinematics, complicating the use of emission-line diagnostics for identifying LyC emitters.Comment: 21 pages, 11 figures, accepted for publication in Ap

Dynamic and Stagnating Plasma Flow Leading to Magnetic Flux Tube Collimation

Highly collimated, plasma-filled magnetic flux tubes are frequently observed on galactic, stellar and laboratory scales. We propose that a single, universal magnetohydrodynamic pumping process explains why such collimated, plasma-filled magnetic flux tubes are ubiquitous. Experimental evidence from carefully diagnosed laboratory simulations of astrophysical jets confirms this assertion and is reported here. The magnetohydrodynamic process pumps plasma into a magnetic flux tube and the stagnation of the resulting flow causes this flux tube to become collimated.Comment: to be published in PRL; color figures on electronic versio