Development of the Trident 1 aerodynamic saike mechanism

The Aerospike drag reduction mechanism was designed and developed for use on the Trident I submarine launched ballistic missile. This mechanism encounters a unique combination of environments necessitating unique design solutions to ensure satisfactory operation over its design life. The development of the Aerospike is reviewed emphasizing the unique and interesting problems encountered and their solutions

Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice

We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system remains short-range ordered independent of the sign and the strength of the interlayer coupling

Molecular observation of contour-length fluctuations limiting topological confinement in polymer melts

In order to study the mechanisms limiting the topological chain confinement in polymer melts, we have performed neutron-spin-echo investigations of the single-chain dynamic-structure factor from polyethylene melts over a large range of chain lengths. While at high molecular weight the reptation model is corroborated, a systematic loosening of the confinement with decreasing chain length is found. The dynamic-structure factors are quantitatively described by the effect of contour-length fluctuations on the confining tube, establishing this mechanism on a molecular level in space and time

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice

We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization and a variational mean-field approach. We find evidence that the star lattice is (besides the \kagome lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star exhibits a huge non-trivial degeneracy like on the \kagome lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.Comment: new extended version (6 pages, 6 figures) as published in Physical Review

Localized-magnon states in strongly frustrated quantum spin lattices

Recent developments concerning localized-magnon eigenstates in strongly frustrated spin lattices and their effect on the low-temperature physics of these systems in high magnetic fields are reviewed. After illustrating the construction and the properties of localized-magnon states we describe the plateau and the jump in the magnetization process caused by these states. Considering appropriate lattice deformations fitting to the localized magnons we discuss a spin-Peierls instability in high magnetic fields related to these states. Last but not least we consider the degeneracy of the localized-magnon eigenstates and the related thermodynamics in high magnetic fields. In particular, we discuss the low-temperature maximum in the isothermal entropy versus field curve and the resulting enhanced magnetocaloric effect, which allows efficient magnetic cooling from quite large temperatures down to very low ones.Comment: 21 pages, 10 figures, invited paper for a special issue of "Low Temperature Physics " dedicated to the 70-th anniversary of creation of concept "antiferromagnetism" in physics of magnetis