Feedback local optimality principle applied to rocket vertical landing VTVL

Vertical landing is becoming popular in the last fifteen years, a technology known under the acronym VTVL, Vertical Takeoff and Vertical Landing [1,2]. The interest in such landing technology is dictated by possible cost reductions [3,4], that impose spaceship’s recycling. The rockets are not generally de- signed to perform landing operations, rather their design is aimed at takeoff operations, guaranteeing a very high forward acceleration to gain the velocity needed to escape the gravitational force. In this paper a new control method based on Feedback Local Optimality Principle, named FLOP is applied to the rocket landing problem. The FLOP belongs to a special class of optimal controllers, developed by the mechatronic and vehicle dynamics lab of Sapienza, named Variational Feedback Controllers - VFC, that are part of an ongoing research and are recently applied in different field: nonlinear system [5], marine and terrestrial autonomous vehicles [6,7,8], multi agents interactions and vibration control [9, 10]. The paper is devoted to show the robustness of the nonlinear controlled system, comparing the performances with the LQR, one of the most acknowledged methods in optimal control

A compactness theorem for complete Ricci shrinkers

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF

A Note on the Generalization of the GEMS Approach

This paper is a supplement of our earlier work JHEP 0410 (2004) 011[gr-qc/0409107].We map the vector potential of charged black holes into GEMS and find that its effect on the thermal spectrum is the same as that on the black hole side, i.e., it will induce a chemical potential in the thermal spectrum which is the same as that in the charged black holes.We also argue that the generalization of GEMS approach to non-stationary motions is not possible.Comment: Latex file, 10 pages, no figure; v2: minor corrections; v3: revised with title changed, one new section added and references adde

Field Dependent Phase Diagram of the Quantum Spin Chain (CH3)2NH2CuCl3

Although (CH3)2NH2CuCl3 (MCCL) was first examined in the 1930's [1], there are open questions regarding the magnetic dimensionality and nature of the magnetic properties. MCCL is proposed to be a S=1/2 alternating ferromagnetic antiferromagnetic spin chain alternating along the crystalline a-axis [2,3]. Proposed ferromagnetic (JFM =1.3 meV) and antiferromagnetic (JAFM =1.1 meV) exchange constants make this system particularly interesting for experimental study. Because JFM and JAFM are nearly identical, the system should show competing behavior between S=1/2 (AFM) and S=1(FM) effects. We report low temperature magnetic field dependent susceptibility, chi(H), and specific heat, Cp, of MCCL. These provide an initial magnetic-field versus temperature phase diagram. A zero-field phase transition consistent with long range magnetic order is observed at T=0.9 K. The transition temperature can be reduced via application of a magnetic field. We also present comparisons to a FM/AFM dimer model that accounts for chi(T,H=0) and Cp(H,T).Comment: 2 pages, 1 figure included in text. Submitted to proceedings of 24th International Conference on Low Temperature Physics, August 200

The K\"ahler-Ricci flow with positive bisectional curvature

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.Comment: 15 page

Some remarks on second order linear difference equations

We obtain some further results for comparison theorems and oscillation criteria of second order linear difference equations

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Adenosine Triphosphate and Carbon Efficient Route to Second Generation Biofuel Isopentanol.

Climate change necessitates the development of CO2 neutral or negative routes to chemicals currently produced from fossil carbon. In this paper we demonstrate a pathway from the renewable resource glucose to next generation biofuel isopentanol by pairing the isovaleryl-CoA biosynthesis pathway from Myxococcus xanthus and a butyryl-CoA reductase from Clostridium acetobutylicum. The best plasmid and Escherichia coli strain combination makes 80.50 ± 8.08 (SD) mg/L of isopentanol after 36 h under microaerobic conditions with an oleyl alcohol overlay. In addition, the system also shows a strong preference for isopentanol production over prenol in microaerobic conditions. Finally, the pathway requires zero adenosine triphosphate and can be paired theoretically with nonoxidative glycolysis, the combination being redox balanced from glucose thus avoiding unnecessary carbon loss as CO2. These pathway properties make the isovaleryl-CoA pathway an attractive isopentanol production route for further optimization