Partition asymptotics from one-dimensional quantum entropy and energy currents

We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p(n,a), defined as the number of decompositions of a positive integer 'n' into integer summands, with each summand appearing at most 'a' times in a given decomposition. The derivation involves mapping to an equivalent physical problem concerning the quantum entropy and energy currents of particles flowing in a one-dimensional channel connecting thermal reservoirs, and which obey Gentile's intermediate statistics with statistical parameter 'a'. The method is also applied to partitions associated with Haldane's fractional exclusion statistics.Comment: Published versio

Martin Company Nuclear Division Reports

From summary: An analysis has been performed to determine the ability of the fuel container to withstand the various thermal, mechanical and chemical forces imposed upon the generator by vehicle failures. Where theoretical analysis was impossible, and where experimental evidence was desired, capsules and generators were tested under simulated missile-failure conditions. Thus, the safety limits of SNAP III in a satellite application were defined

Final Safety Analysis Report. SNAP III Thermoelectric Generator

The SNAP-III thermoelectric generator procedures power from the decay heat of 2100 curies of Po/sup 210/. This generator is to be used as a source of auxiliary power in a terrestrial satellite. For purposes of analysis, the satellite system postulated is launched from the Pacific Missile Bange into a 275- statute mile polar orbit with an orbital lifetime of about 1 year. Po/sup 210/ is an alpha emitter having a half life of 138 days and alpha and gamma decay energies of 5.3 and 0.8 mev, respectively. It is a natural component of the earth's crust, as a member of the uranium disintegration series. Sampling of polonium in the biosphere was conducted specifically for this program to determine background radiation levels. Since the fuel is primarily an alpha emitter, there is no direct radiation problem. An analysis was performed to determine the ability of the fuel container to withstand the various thermal, mechanical, and chemical forces imposed upon the generator by vehicle failures. Where theoretical analysis was impossible and experimental evidence was desired, capsules and generators were tested under simulated missile-failure conditions, Thus, the safety limits of SNAP-III in a satellite application were defined. SNAP-III is designed to be aerothermodynamically consumed on reentry into the earth's atmosphere so that the polonium will be dispersed as aerosols in the upper stratosphere. Since heating rates will be lower for aborts occurring prior to orbiting, 65 abort cases have been considered to define the general consequences of vehicle failures. The spatial and temporal relations of vehicle aborts are summarized in cartographic and tabular form. (auth