Fabrication of a glycerol from CO2 reaction system, supplement

The fabrication, installation, and testing of a glycerol hydrogenation and a CO2 hydrogenation - CH4 partial oxidation units are reported. The glycerol system proved to be operational while the CO2 system was installed but not bought on operational steam

Biological effects of prolonged expoure of small animals to unusual gaseous environments semiannual report, 1 sep. 1964 - 28 feb. 1965

Biological effect of prolonged exposure of man and small animals to pure oxygen and helium - oxygen environmen

Mercury in the environs of the north slope of Alaska

The analysis of Greenland ice suggests that the flux of mercury from the continents to the atmosphere has increased in recent times, perhaps partly as a result of the many of man’s activities that effect an alteration of terrestrial surfaces. Upon the exposure of fresh crustal matter, the natural outgassing of mercury vapor from the earth’s surface could be enhanced. Accordingly, mercury was measured in a variety of environmental materials gathered from the North Slope of Alaska to provide background data prior to the anticipated increase of activity in this environment. The materials were collected during the U. S. Coast Guard WEBSEC 72-73 cruises as well as through the facilities provided by Naval Arctic Research Laboratory in the spring of 1973. The method of measurement depended upon radioactivation of mercury with neutrons and the subsequent quantification of characteristic gamma radiations after radiochemical purification. Mercury concentrations in seawater at several locations in the vicinity of 151°W, 71°N averaged 20 parts per trillion. The waters from all stations east of this location showed a significantly smaller concentration. This difference may relate to penetration o f Bering- Chukchi Sea water into the southern Beaufort Sea to 151°W. Marine sediments on the shelf and slope between 143°W and 153°W contained about 100 parts per billion mercury, except for those on the continental shelf between Barter Island and the Canning River, where the concentration was less than half this value. These results are consistent with sediment input from the respective rivers when their mercury content and mineralogy are considered. The mercury content of river waters was 18 ppt and in reasonable agreement with the average of snow samples (13 ppt). The burden of mercury in plankton was 37 ppb.This work was supported by the office of Naval Research under grant N R 083-290

Ground state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved rigorously that the commonly accepted leading order term of the ground state energy is correct in the zero-density-limit. Here, strong indications are given that also the next to leading term is correct. It is shown that the first terms obtained in a perturbative treatment provide contributions which are lost in the Bogoliubov approach.Comment: 6 pages, accepted for publication in Europhys. Lett. http://www.epletters.ch

A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems

Classical small systems coupled to finite baths

We have studied the properties of a classical $N_S$-body system coupled to a bath containing $N_B$-body harmonic oscillators, employing an $(N_S+N_B)$ model which is different from most of the existing models with $N_S=1$. We have performed simulations for $N_S$-oscillator systems, solving $2(N_S+N_B)$ first-order differential equations with $N_S \simeq 1 - 10$ and $N_B \simeq 10 - 1000$, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence. Detailed calculations of the stationary energy distribution of the system $f_S(u)$ ($u$: an energy per particle in the system) have shown that its properties are mainly determined by $N_S$ but weakly depend on $N_B$. The calculated $f_S(u)$ is analyzed with the use of the $\Gamma$ and $q$-$\Gamma$ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where $q$ stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the $N_S$-body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional ($N_S+N_B$) models which include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.Comment: 30 pages, 16 figures; the final version accepted in Phys. Rev.