Synthesis for Polynomial Lasso Programs

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities). Central to this approach is the discovery of non-linear (algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's template-based approach and prove a completeness criterion. We perform program synthesis by generating a constraint whose solution is a synthesized program together with a loop invariant that proves the program's correctness. This constraint is non-linear and is passed to an SMT solver. Moreover, we can enforce the termination of the synthesized program with the support of test cases.Comment: Paper at VMCAI'14, including appendi

Initial Investigation of Reaction Control System Design on Spacecraft Handling Qualities for Earth Orbit Docking

A program of research, development, test, and evaluation is planned for the development of Spacecraft Handling Qualities guidelines. In this first experiment, the effects of Reaction Control System design characteristics and rotational control laws were evaluated during simulated proximity operations and docking. Also, the influence of piloting demands resulting from varying closure rates was assessed. The pilot-in-the-loop simulation results showed that significantly different spacecraft handling qualities result from the design of the Reaction Control System. In particular, cross-coupling between translational and rotational motions significantly affected handling qualities as reflected by Cooper-Harper pilot ratings and pilot workload, as reflected by Task-Load Index ratings. This influence is masked but only slightly by the rotational control system mode. While rotational control augmentation using Rate Command Attitude Hold can reduce the workload (principally, physical workload) created by cross-coupling, the handling qualities are not significantly improved. The attitude and rate deadbands of the RCAH introduced significant mental workload and control compensation to evaluate when deadband firings would occur, assess their impact on docking performance, and apply control inputs to mitigate that impact

On the formation/dissolution of equilibrium droplets

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\sim(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model; to appear in Europhys. Let

Investigation of Control System and Display Variations on Spacecraft Handling Qualities for Docking with Stationary and Rotating Targets

This paper documents the investigation into the manual docking of a preliminary version of the Crew Exploration Vehicle with stationary and rotating targets in Low Earth Orbit. The investigation was conducted at NASA Langley Research Center in the summer of 2008 in a repurposed fixed-base transport aircraft cockpit and involved nine evaluation astronauts and research pilots. The investigation quantified the benefits of a feed-forward reaction control system thruster mixing scheme to reduce translation-into-rotation coupling, despite unmodeled variations in individual thruster force levels and off-axis center of mass locations up to 12 inches. A reduced rate dead-band in the phase-plane attitude controller also showed some promise. Candidate predictive symbology overlaid on a docking ring centerline camera image did not improve handling qualities, but an innovative attitude status indicator symbol was beneficial. The investigation also showed high workload and handling quality problems when manual dockings were performed with a rotating target. These concerns indicate achieving satisfactory handling quality ratings with a vehicle configuration similar to the nominal Crew Exploration Vehicle may require additional automation

Finite-size scaling of the helicity modulus of the two-dimensional O(3) model

Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus $\Upsilon$ of the two-dimensional O(3) model and compare it to the low temperature expansion prediction. From this, we estimate the range of validity for the leading terms of the low temperature expansion of the finite-size scaling function and for the low temperature expansion of the correlation length. Our results strongly suggest that a Kosterlitz-Thouless transition at a temperature $T > 0$ is extremely unlikely in this model.Comment: 4 pages, 3 Postscript figures, to appear in Phys. Rev. B Jan. 1997 as a Brief Repor

Ground-state properties of tubelike flexible polymers

In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects