The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

In this paper, we calculate the explicit expression for the fugacity for two- and three-dimensional weakly interacting Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of analytic functions --- the homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein condensation phase transition of three-dimensional hard-sphere Bose gases.Comment: 24 pages, 9 figure

Modeling Pressure-Ionization of Hydrogen in the Context of Astrophysics

The recent development of techniques for laser-driven shock compression of hydrogen has opened the door to the experimental determination of its behavior under conditions characteristic of stellar and planetary interiors. The new data probe the equation of state (EOS) of dense hydrogen in the complex regime of pressure ionization. The structure and evolution of dense astrophysical bodies depend on whether the pressure ionization of hydrogen occurs continuously or through a ``plasma phase transition'' (PPT) between a molecular state and a plasma state. For the first time, the new experiments constrain predictions for the PPT. We show here that the EOS model developed by Saumon and Chabrier can successfully account for the data, and we propose an experiment that should provide a definitive test of the predicted PPT of hydrogen. The usefulness of the chemical picture for computing astrophysical EOS and in modeling pressure ionization is discussed.Comment: 16 pages + 4 figures, to appear in High Pressure Researc

Regions of significant influence on unforced global mean surface air temperature variability in climate models

We document the geographic regions where local variability is most associated with unforced global mean surface air temperature (GMT) variability in Coupled Model Intercomparison Project Phase 5 coupled global climate models (GCMs) at both the subdecadal and interdecadal timescales. For this purpose, Regions of Significant Influence on GMT are defined as locations that have a statistically significant correlation between local surface air temperature (SAT) and GMT (with a regression slope greater than 1), and where local SAT variation leads GMT variation in time. In both GCMs and observations, subdecadal timescale GMT variability is most associated with SAT variation over the eastern equatorial Pacific. At the interdecadal timescale, GMT variability is also linked with SAT variation over the Pacific in many GCMs, but the particular spatial patterns are GCM dependent, and several GCMs indicate a primary association between GMT and SAT over the Southern Ocean. We find that it is difficult to validate GCM behavior at the interdecadal timescale because the pattern derived from observations is highly depended on the method used to remove the forced variability from the record. The magnitude of observed GMT variability is near the ensemble median at the subdecadal timescale but well above the median at the interdecadal timescale. GCMs with a stronger subdecadal relationship between GMT and SAT over the Pacific tend to have more variable subdecadal GMT while GCMs with a stronger interdecadal relationship between GMT and SAT over parts of the Southern Ocean tend to have more variable GMT

Poly[hexa­aqua­copper(II) [di-μ3-sulfato-disodiate(I)]]

The title compound, {[Cu(H2O)6][Na2(SO4)2]}n, has been prepared under mild hydro­thermal conditions and has been structurally characterized. It exhibits a structure in which the inorganic frameworks are three-dimensional, participating in extensive hydrogen bonding. Copper occupies a special position (). The Na atom is coordinated by five O atoms of four sulfates [Na—O distances are between 2.825 (3) and 2.983 (3) Å]. The four O atoms of the sulfate ligand are coordinated to four Na atoms, the sulfate ligands coordinating in a chelating/bridging tetra­dentate mode

Electromagnetic Transition in Waveguide with Application to Lasers

The electromagnetic transition of two-level atomic systems in a waveguide is calculated. Compared with the result in free space, the spontaneous emission rate decrease because the phase space is smaller, and meanwhile, some resonance appears in some cases. Moreover, the influence of non-uniform electromagnetic field in a waveguide on absorption and stimulated emission is considered. Applying the results to lasers, a method to enhance the laser power is proposed.Comment: 4 pages, 2 figure