Quarterly Progress Report No.6

Signal intensity operations have stopped and the preliminary reduction of all field intensity records completed . The 12 me back-scatter equipment is described and operating conditions stated. Tentative interpretations of ob served echoes in terms of possible reflection mechanisms are given.Section I Purposes – Section II Abstract – Section III Publications, Lectures, Reports and Conferences – Section IV Factual Data : Task A Transmission of H.F. Radio Waves ; Task B Pulse Techniques Backscatter at 12 mc ; Task B Visual Observations of Aurora – Section V Conclusions and Recommendations – Section VI Plans for Next Quarter – Section VII PersonnelYe

Plane wave stability of some conservative schemes for the cubic Schr\"{o}dinger equation

The plane wave stability properties of the conservative schemes of Besse and Fei et al. for the cubic Schr\"{o}dinger equation are analysed. Although the two methods possess many of the same conservation properties, we show that their stability behaviour is very different. An energy preserving generalisation of the Fei method with improved stability is presented.Comment: 12 pages, 6 figure

Geometric integration of non-autonomous Hamiltonian problems

Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of dimensions. We show that one possible extension of symplectic methods in the autonomous setting to the non-autonomous setting is obtained by using canonical transformations. Many existing methods fit into this framework. We also perform experiments which indicate that for exponential integrators, the canonical and symmetric properties are important for good long time behaviour. In particular, the theoretical and numerical results support the well documented fact from the literature that exponential integrators for non-autonomous linear problems have superior accuracy compared to general ODE schemes.Comment: 20 pages, 3 figure

Task A, Analysis of C-W Data, Final Report

The object of this investigation is to obtain additional information concerning the effects of aurora on high frequency radio signals which is essential to a complete understanding of new modes of propagation that have tactical and strategic applications.Signal Corps Contract No. DA-36-039-SC-71137 Department of the Army Project No. 3-99-03-022 Signal Corps Project No. 182BLIST OF FIGURES -- [SECTION I] PURPOSE -- [SECTION II] ABSTRACT -- [SECTION III] PUBLICATIONS. LECTURES, REPORTS AND CONFERENCES -- [SECTION IV] FACTUAL DATA : 1. Signal Outage Time on Short Paths and Blackouts Compared for Years of High and Low Solar Activity. ; 2. Study of Possible Relations between Transmission over Long Paths and Ionospheric,Magnetic and Solar Phenomena. ; 3. Study of Fluctuation Indices. ; 4. Effects of Ionospheric Absorption and Irregularities on 4 Mc/s Short Path Transmission. ; 5. F2 Region Parameters at College for the Period June 1941 Through December 1956. ; 6. Tables of Monthly Medians Signal Strength June 1949-December 1950 and January 1954-October 1955. -- [SECTION V] OVERALL CONCLUSIONS -- [SECTION VI] RECOMMENDATIONS -- [SECTION VII] PERSONNELYe

Pumping for gestural origins: The well may be rather dry.

Corballis's explanation for right-handedness in humans relies heavily on the gestural protolanguage hypothesis, which he argues for by a series of “intuition pumps.” Scrutinizing the mirror system hypothesis and modern gesture as components of the argument, we find that they do not provide the desired evidence of a gestural precursor to speech

Adaptive Energy Preserving Methods for Partial Differential Equations

A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used with both finite difference and partition of unity approaches, thereby also including finite element approaches. The schemes are then extended to accommodate $r$-, $h$- and $p$-adaptivity. The method is applied to the Korteweg-de Vries equation and the Sine-Gordon equation and results from numerical experiments are presented.Comment: 27 pages; some changes to notation and figure