Singularity theorems from weakened energy conditions

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the Quantum Energy Inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.Comment: v3 18 pages. Minor correction to the proof of Lemma 3.1; results are unchanged. Final version to appear in Class Quantum Gra

Improved tangent-cone method for the Aerodynamic Preliminary Analysis System (APAS) version of the hypersonic arbitrary-body program

The Aerodynamic Preliminary Analysis System (APAS) utilizes a modified version of the Hypersonic Arbitrary-Body Program (HABP) Mark 3 code in its analysis rationale. Four methods are considered for incorporation into the code as the tangent-cone method. The combination of second-order slender body theory and the approximate solution of Hammitt and Murthy shows the best agreement with the exact numerical solutions and is thus included in the APAS production version of the HABP code

How Hot is the Wind from TW Hydrae?

It has recently been suggested that the winds from Classical T Tauri stars in general, and the wind from TW Hya in particular, reaches temperatures of at least 300,000 K while maintaing a mass loss rate of $\sim 10^{-11}$ \Msol yr$^{-1}$ or larger. If confirmed, this would place strong new requirements on wind launching and heating models. We therefore re-examine spectra from the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope and spectra from the Far Ultraviolet Spectroscopic Explorer satellite in an effort to better constrain the maximum temperature in the wind of TW Hya. We find clear evidence for a wind in the \ion{C}{2} doublet at 1037 \AA and in the \ion{C}{2} multiplet at 1335 \AA. We find no wind absorption in the \ion{C}{4} 1550 \AA doublet observed at the same time as the \ion{C}{2} 1335 \AA line or in observations of \ion{O}{6} observed simultaneously with the \ion{C}{2} 1037 \AA line. The presence or absence of \ion{C}{3} wind absorption is ambiguous. The clear lack of a wind in the \ion{C}{4} line argues that the wind from TW Hya does not reach the 100,000 K characteristic formation temperature of this line. We therefore argue that the available evidence suggests that the wind from TW Hya, and probably all classical T Tauri stars, reaches a maximum temperature in the range of 10,000 -- 30,000 K.Comment: 17 pages, 3 figures, Figure 1 in 2nd version fixes a small velocity scaling error and new revision adds a reference to an additional paper recently foun

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.Comment: 13 pages, 4 figure

Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation (DFT-MD) and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry (CHA) for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.Comment: 28 pages, 5 figure