Symmetries of the WDVV equations and Chazy-type equations

We investigate the symmetry structure of the WDVV equations. We obtain an $r$-parameter group of symmetries, where $r = (n^2 + 7n + 2)/2 + \lfloor n/2 \rfloor$. Moreover it is proved that for $n=3$ and $n=4$ these comprise all symmetries. We determine a subgroup, which defines an $SL_2$-action on the space of solutions. For the special case $n=3$ this action is compared to the $SL_2$-symmetry of the Chazy equation. For $n=4$ and $n=5$ we construct new, Chazy-type, solutions

Polynomial solutions to the WDVV equations in four dimensions

All polynomial solutions of the WDVV equations for the case n = 4 are determined. We find all five solutions predicted by Dubrovin, namely those corresponding to Frobenius structures on orbit spaces of finite Coxeter groups. Moreover we find two additional series of polynomial solutions of which one series is of semi-simple type (massive). This result supports Dubrovin's conjecture if modified appropriately

Evaluation of potassium titanate as a component of alkaline fuel cell matrices

Various forms of potassium titanate were found to have almost complete resistance to chemical attack in 45 wt % KOH at 150 C (423 K) for up to 9600 hours. Electron microscopy and X-ray diffraction disclosed important differences with respect to fibricity and stability. The octatitanate appeared to possess the best combination of properties. It was concluded that potassium titanate could be produced in a more asbestos-like form. Fiber dispersion is important in matrix manufacture

Effects of temperature and electrolyte concentration on performance of a fuel cell of the Bacon type

Effects of temperature and electrolyte concentration on performance of fuel cel

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange

Effects of carbon dioxide on trapped electrolyte hydrogen-oxygen, alkaline fuel cells

Effects of carbon dioxide on trapped electrolyte hydrogen-oxygen alkaline fuel cell

Radiation Rates for Low Z Impurities in Edge Plasmas

The role of impurity radiation in the reduction of heat loads on divertor plates in present experiments such as DIII-D, JET, JT-60, ASDEX, and Alcator C-Mod, and in planned experiments such as ITER and TPX places a new degree of importance on the accuracy of impurity radiation emission rates for electron temperatures below 250 eV for ITER and below 150 eV for present experiments. We have calculated the radiated power loss using a collisional radiative model for Be, B, C, Ne and Ar using a multiple configuration interaction model which includes density dependent effects, as well as a very detailed treatment of the energy levels and meta-stable levels. The "collisional radiative" effects are very important for Be at temperatures below 10 eV. The same effects are present for higher Z impurities, but not as strongly. For some of the lower Z elements, the new rates are about a factor of two lower than those from a widely used, simpler average-ion package (ADPAK) developed for high Z ions and for higher temperatures. Following the approach of Lengyel for the case where electron heat conduction is the dominant mechanism for heat transport along field lines, our analysis indicates that significant enhancements of the radiation losses above collisional radiative model rates due to such effects as rapid recycling and charge exchange recombination will be necessary for impurity radiation to reduce the peak heat loads on divertor plates for high heat flux experiments such as ITER.Comment: Preprint for the 11th PSI meeting, gzipped postscript with 11 figures, 14 page

Calculations of Energy Losses due to Atomic Processes in Tokamaks with Applications to the ITER Divertor

Reduction of the peak heat loads on the plasma facing components is essential for the success of the next generation of high fusion power tokamaks such as the International Thermonuclear Experimental Reactor (ITER) 1 . Many present concepts for accomplishing this involve the use of atomic processes to transfer the heat from the plasma to the main chamber and divertor chamber walls and much of the experimental and theoretical physics research in the fusion program is directed toward this issue. The results of these experiments and calculations are the result of a complex interplay of many processes. In order to identify the key features of these experiments and calculations and the relative role of the primary atomic processes, simple quasi-analytic models and the latest atomic physics rate coefficients and cross sections have been used to assess the relative roles of central radiation losses through bremsstrahlung, impurity radiation losses from the plasma edge, charge exchange and hydrogen radiation losses from the scrape-off layer and divertor plasma and impurity radiation losses from the divertor plasma. This anaysis indicates that bremsstrahlung from the plasma center and impurity radiation from the plasma edge and divertor plasma can each play a significant role in reducing the power to the divertor plates, and identifies many of the factors which determine the relative role of each process. For instance, for radiation losses in the divertor to be large enough to radiate the power in the divertor for high power experiments, a neutral fraction of 10-3 to 10-2 and an impurity recycling rate of netrecycle of ~ 10^16 s m^-3 will be required in the divertor.Comment: Preprint for the 1994 APSDPP meeting, uuencoded and gzipped postscript with 22 figures, 40 pages