Interactions of satellite-speed helium atoms with satellite surfaces. 2: Energy distributions of reflected helium atoms

Energy transfer in collisions of satellite-speed (7,000 m/sec) helium atoms with a cleaned 6061-T6 satellite-type aluminum surface was investigated using the molecular-beam technique. The amount of energy transferred was determined from the measured energy of the molecular-beam and the measured spatial and energy distributions of the reflected atoms. Spatial distributions of helium atoms scattered from a 6061-T6 aluminum surface were measured. The scattering pattern exhibits a prominent backscattering, probably due to the gross surface roughness and/or the relative lattice softness of the aluminum surface. Energy distributions of reflected helium atoms from the same surface were measured for six different incidence angles. For each incidence angle, distributions were measured at approximately sixty scattering positions. At a given scattering position, the energy spectra of the reflected helium atoms and the background gas were obtained using the retarding-field energy analyzer

Researches on interactions of satellite-speed helium atoms with aluminum and quartz surfaces

Three major areas were experimentally studied: (1) energy transfer in collisions of satellite-speed (700 m/sec) helium atoms with a cleaned satellite-type aluminum surface was investigated using the molecular-beam technique. Spatial and energy distributions of reflected helium atoms were measured and analyzed, (2) The gross accommodation coefficient for a satellite-speed (7000 m/sec) helium beam entering a 2-inch-diameter aluminum spherical cavity was determined by measuring the exit velocity distribution of the leaving helium atoms using a metastable time-of-flight method. Results indicate that the 7000-m/sec satellite-speed helium atoms entering the cavity gain full accommodation with the room-temperature inner surface of the sphere through a large number of collisions before leaving the spherical cavity; and (3) the feasibility of producing a satellite-speed atomic hydrogen beam by arc-heating, for use in studies of interactions of satellite-surfaces with hydrogen atoms under laboratory conditions, was investigated. It was found that a stable arc-heated molecular hydrogen beam can be obtained using the arc-heater, and that a partially dissociated hydrogen beam can be produced. Photographs of laboratory equipment are shown

A Spinorial Formulation of the Maximum Clique Problem of a Graph

We present a new formulation of the maximum clique problem of a graph in complex space. We start observing that the adjacency matrix A of a graph can always be written in the form A = B B where B is a complex, symmetric matrix formed by vectors of zero length (null vectors) and the maximum clique problem can be transformed in a geometrical problem for these vectors. This problem, in turn, is translated in spinorial language and we show that each graph uniquely identifies a set of pure spinors, that is vectors of the endomorphism space of Clifford algebras, and the maximum clique problem is formalized in this setting so that, this much studied problem, may take advantage from recent progresses of pure spinor geometry

Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

Noncooperative algorithms in self-assembly

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar non-cooperative variant of Winfree's abstract Tile Assembly Model. This model has been the center of several open problems and conjectures in the last fifteen years, and the first fully general results on its computational power were only proven recently (SODA 2014). These results, as well as ours, exemplify the intricate connections between computation and geometry that can occur in self-assembly. In this model, tiles can stick to an existing assembly as soon as one of their sides matches the existing assembly. This feature contrasts with the general cooperative model, where it can be required that tiles match on \emph{several} of their sides in order to bind. In order to describe our algorithms, we also introduce a generalization of regular expressions called Baggins expressions. Finally, we compare this model to other automata-theoretic models.Comment: A few bug fixes and typo correction

On the π\pi and KK as qqˉq \bar q Bound States and Approximate Nambu-Goldstone Bosons

We reconsider the two different facets of $\pi$ and $K$ mesons as $q \bar q$ bound states and approximate Nambu-Goldstone bosons. We address several topics, including masses, mass splittings between $\pi$ and $\rho$ and between $K$ and $K^*$, meson wavefunctions, charge radii, and the $K-\pi$ wavefunction overlap.Comment: 15 pages, late

Complementary algorithms for graphs and percolation

A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph representation and so, in concert, can arbitrarily modify any graph. Since the clusters of a percolation model may be described as simple connected graphs, an efficient Monte Carlo scheme can be constructed that uses the algorithms to sweep the occupation probability back and forth between two turning points. This approach concentrates computational sampling time within a region of interest. A high precision value of pc = 0.59274603(9) was thus obtained, by Mersenne twister, for the two dimensional square site percolation threshold.Comment: 5 pages, 3 figures, poster version presented at statphys23 (2007