Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Planetary/DOD entry technology flight experiments. Volume 4: DOD entry flight experiments

For abstract, see vol. 1

Planetary/DOD entry technology flight experiments. Volume 1: Executive summary

The feasibility of using the space shuttle to launch planetary and DoD entry flight experiments was examined. The results of the program are presented in two parts: (1) simulating outer planet environments during an earth entry test, the prediction of Jovian and earth radiative heating dominated environments, mission strategy, booster performance and entry vehicle design, and (2) the DoD entry test needs for the 1980's, the use of the space shuttle to meet these DoD test needs, modifications of test procedures as pertaining to the space shuttle, modifications to the space shuttle to accommodate DoD test missions and the unique capabilities of the space shuttle. The major findings of this program are summarized

Crop-phenology and LANDSAT-based irrigated lands inventory in the high plains

Optimal LANDSAT image dates for 1980 were identified based on the weekly crop-weather reports for Colorado, New Mexico, South Dakota, Texas, Oklahoma, Kansas, Nebraska, and Wyoming. The 1979 agricultural statistics data were entered into computer files and a revised questionnaire was developed and mailed to ASCS county agents. A set of computer programs was developed to allow the preparation of computer-assisted graphic displays of much of the collected data

Crop phenology and LANDSAT-based irrigated lands inventory in the high plains

The activity concentrated on identifying crop and irrigation data sources for the eight states within the High Plains Aquifer and making contacts concerning the nature of these data. A mail questionnaire was developed to gather specific data not routinely reported through standard data collection channels. Input/output routines were designed for High Plains crop and irrigation data and initial statistical data on crops were input to computer files

The design and evaluation of grazing incidence relay optics

X-ray astronomy, both solar and celestial, has many needs for high spatial resolution observations which have to be performed with electronic detectors. If the resolution is not to be detector limited, plate scales in excess of 25 microns arc/sec, corresponding to focal lengths greater than 5 m, are required. In situations where the physical size is restricted, the problem can be solved by the use of grazing incidence relay optics. A system was developed which employs externally polished hyperboloid-hyperboloid surfaces to be used in conjunction with a Wolter-Schwarzschild primary. The secondary is located in front of the primary focus and provides a magnification of 4, while the system has a plate scale of 28 microns arc/sec and a length of 1.9 m. The design, tolerance specification, fabrication and performance at visible and X-ray wavelengths of this optical system are described

Sofic-Dyck shifts

We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck shifts are shifts of sequences whose finite factors form unambiguous context-free languages. We show that they correspond exactly to the class of shifts of sequences whose sets of factors are visibly pushdown languages. We give an expression of the zeta function of a sofic-Dyck shift

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

Color television study Final report, Nov. 1965 - Mar. 1966

Color television camera for transmission from lunar and earth orbits and lunar surfac

Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime

Point contact spectroscopy on a H2O molecule bridging Pt electrodes reveals a clear crossover between enhancement and reduction of the conductance due to electron-vibration interaction. As single channel models predict such a crossover at transmission probability of t=0.5, we used shot noise measurements to analyze the transmission and observed at least two channels across the junction where the dominant channel has t=0.51+/-0.01 transmission probability at the crossover conductance, which is consistent with the predictions for single-channel models.Comment: 4 pages, 1 table, 4 figure