2,772 research outputs found
Development, fabrication and test of a high purity silica heat shield
Get PDFA highly reflective hyperpure ( 25 ppm ion impurities) slip cast fused silica heat shield material developed for planetary entry probes was successfully scaled up. Process development activities for slip casting large parts included green strength improvements, casting slip preparation, aggregate casting, strength, reflectance, and subscale fabrication. Successful fabrication of a one-half scale Saturn probe (shape and size) heat shield was accomplished while maintaining the silica high purity and reflectance through the scale-up process. However, stress analysis of this original aggregate slip cast material indicated a small margin of safety (MS. = +4%) using a factor of safety of 1.25. An alternate hyperpure material formulation to increase the strength and toughness for a greater safety margin was evaluated. The alternate material incorporates short hyperpure silica fibers into the casting slip. The best formulation evaluated has a 50% by weight fiber addition resulting in an 80% increase in flexural strength and a 170% increase in toughness over the original aggregate slip cast materials with comparable reflectance
Divergences in QED on a Graph
Full text linkWe consider a model of quantum electrodynamics (QED) on a graph. The one-loop
divergences in the model are investigated by use of the background field
method.Comment: 14 pages, no figures, RevTeX4. References and typos adde
Some Exact Results on the Potts Model Partition Function in a Magnetic Field
Full text linkWe consider the Potts model in a magnetic field on an arbitrary graph .
Using a formula of F. Y. Wu for the partition function of this model as a
sum over spanning subgraphs of , we prove some properties of concerning
factorization, monotonicity, and zeros. A generalization of the Tutte
polynomial is presented that corresponds to this partition function. In this
context we formulate and discuss two weighted graph-coloring problems. We also
give a general structural result for for cyclic strip graphs.Comment: 5 pages, late
Some Exact Results for Spanning Trees on Lattices
Full text linkFor -vertex, -dimensional lattices with , the number
of spanning trees grows asymptotically as
in the thermodynamic limit. We present an exact closed-form result for the
asymptotic growth constant for spanning trees on the
-dimensional body-centered cubic lattice. We also give an exact integral
expression for on the face-centered cubic lattice and an exact
closed-form expression for on the lattice.Comment: 7 pages, 1 tabl
Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice
Full text linkWe present exact solutions for the zero-temperature partition function of the
-state Potts antiferromagnet (equivalently, the chromatic polynomial ) on
tube sections of the simple cubic lattice of fixed transverse size and arbitrarily great length , for sizes and and boundary conditions (a) and (b)
, where () denote free (periodic) boundary
conditions. In the limit of infinite-length, , we calculate the
resultant ground state degeneracy per site (= exponent of the ground-state
entropy). Generalizing from to , we determine
the analytic structure of and the related singular locus which
is the continuous accumulation set of zeros of the chromatic polynomial. For
the limit of a given family of lattice sections, is
analytic for real down to a value . We determine the values of
for the lattice sections considered and address the question of the value of
for a -dimensional Cartesian lattice. Analogous results are presented
for a tube of arbitrarily great length whose transverse cross section is formed
from the complete bipartite graph .Comment: 28 pages, latex, six postscript figures, two Mathematica file
Acyclic orientations on the Sierpinski gasket
Full text linkWe study the number of acyclic orientations on the generalized
two-dimensional Sierpinski gasket at stage with equal to
two and three, and determine the asymptotic behaviors. We also derive upper
bounds for the asymptotic growth constants for and -dimensional
Sierpinski gasket .Comment: 20 pages, 8 figures and 6 table
Optimal path planning for nonholonomic robotics systems via parametric optimisation
Get PDFAbstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping
Redshifted formaldehyde from the gravitational lens B0218+357
Full text linkThe gravitational lens toward B0218+357 offers the unique possibility to
study cool moderately dense gas with high sensitivity and angular resolution in
a cloud that existed half a Hubble time ago. Observations of the radio
continuum and six formaldehyde (H2CO) lines were carried out with the VLA, the
Plateau de Bure interferometer, and the Effelsberg 100-m telescope. Three radio
continuum maps indicate a flux density ratio between the two main images, A and
B, of ~ 3.4 +/- 0.2. Within the errors the ratio is the same at 8.6, 14.1, and
43 GHz. The 1_{01}-0_{00} line of para-H2CO is shown to absorb the continuum of
image A. Large Velocity Gradient radiative transfer calculations are performed
to reproduce the optical depths of the observed two cm-wave "K-doublet" and
four mm-wave rotational lines. These calculations also account for a likely
frequency-dependent continuum cloud coverage. Confirming the diffuse nature of
the cloud, an n(H2) density of < 1000 cm^{-3} is derived, with the best fit
suggesting n(H2) ~ 200 cm^{-3}. The H2CO column density of the main velocity
component is ~5 * 10^{13} cm^{-2}, to which about 7.5 * 10^{12} cm^{-2} has to
be added to also account for a weaker feature on the blue side, 13 km/s apart.
N(H2CO)/N(NH3) ~ 0.6, which is four times less than the average ratio obtained
from a small number of local diffuse (galactic) clouds seen in absorption. The
ortho-to-para H2CO abundance ratio is 2.0 - 3.0, which is consistent with the
kinetic temperature of the molecular gas associated with the lens of B0218+357.
With the gas kinetic temperature and density known, it is found that optically
thin transitions of CS, HCN, HNC, HCO+, and N2H+ (but not CO) will provide
excellent probes of the cosmic microwave background at redshift z=0.68.Comment: Accepted for A&A, 8 Pages, 3 Figures, 5 Table
Positive Influence Of Education Partnerships For Teaching Integrated STEM Through Drone Competition
Get PDFWhile enhancing the STEM career pipeline through improved quality and quantity of STEM teaching available to an ever-widening diversity is K-12 students is garnering significant attention across the U.S., there lacks widely adopted implementation and support models that efficiently make full advantage of the vast human and fiscal resources available. A wide swath of STEM education stake-holding partnersâschools, businesses, government agencies, non-profit organizations, and institutions of higher educationâfrequently are compelled to provide support and guidance but lack easy to follow pathways in order to do so. This research study describes and documents a unique vehicle to bring often disparate partners to a unified effort under the banner of drone education designed to improve STEM and technology-oriented career pathways. Identified barriers that the collaborative partnership helped overcome to ensure success include providing: modest start-up costs for modern high-tech equipment for participating schools (drones); an infrastructure for leveraging the consistently successful approach to providing regional and statewide competitive events (precision drone flight and knowledge competitions); large-scale buildings and facilities to host competitive festivals and events (e.g., indoor sports stadiums); and K-12 teacher professional development programs along with classroom-ready instructional materials needed to nurture and sustain student drone education programs
Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs
Full text linkWe present exact calculations of chromatic polynomials for families of cyclic
graphs consisting of linked polygons, where the polygons may be adjacent or
separated by a given number of bonds. From these we calculate the (exponential
of the) ground state entropy, , for the q-state Potts model on these graphs
in the limit of infinitely many vertices. A number of properties are proved
concerning the continuous locus, , of nonanalyticities in . Our
results provide further evidence for a general rule concerning the maximal
region in the complex q plane to which one can analytically continue from the
physical interval where .Comment: 27 pages, Latex, 17 figs. J. Phys. A, in pres
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