Comment on Counterintuitive consequence of heating in strongly driven intrinsic junctions of Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} mesas

In a recent paper [Phys.Rev.B 81, 224518 (2010)], C. Kurter et al, analyzed the effect of strong self-heating in large-area Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) mesa structures. They conclude that $dI/dV$ conductance peaks in their mesas occur when mesas are heated to the superconducting critical temperature $T_c$. Further on they extrapolate this statement for all mesas, including much smaller and much better thermally anchored mesas used in Intrinsic Tunnelling Spectroscopy (ITS). Here I show that their conclusion does not hold neither for previously reported data, nor even for their own mesas; the very remote extrapolation to ITS is invalid. I also point out a number of inconsistencies and misleading references.Comment: 2 page

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model