The transport of NO+ ions moving through each of the rare gases under the influence of an electrostatic field has been studied using ab initio potential energy surfaces in a rigid rotor approximation, using both Monte Carlo techniques and various velocity moment approaches. The results in helium are in very good agreement with published molecular dynamics calculations and experimental results.

Mobility and diffusion coefficients are generally extracted from experimental measurements of ion arrival time distributions using tensors of ranks one and two, i.e., in terms of the diffusion equation that is equivalent to Fick's second law. The theory is extended here to tensors of rank three. It is shown that under customary circumstances, the generalized diffusion equation only contains a single third-order transport coefficient. This equation is used to generate synthetic data for ions moving through a pure gas. The mobility and diffusion coefficients and third-order transport coefficients inferred from these data are compared with values used to simulate the arrival time distribution. Finally, an existing computer program has been modified in order to compute one component of the third-order transport coefficient, and this program has been applied to Li+ in He.

It has recently been shown that accurate theoretical calculations can be used to calibrate a drift-tube mass spectrometer (DTMS) to measure gaseous ion mobilities accurate to within 0.6%. Here we present a new method for calibrating a DTMS instrument to obtain diffusion coefficients parallel to the electric field which are accurate to within 8%. This method is developed and verified by consideration of He+ (2S1/2) ions in He. We apply these techniques to determine transport coefficients for Ar+(2P3/2) and Ar2+ (3P2,1,0) ions in Ar gas at 300 K, with results given as a function of E/N, the ratio of electrostatic field strength to gas number density, in the range 30–210 Td. The measured mobilities are accurate within 0.8%; for Ar+ they agree within 1.5% with Monte Carlo simulations, and for both the cations and dications they are in excellent agreement with previous measurements. Our method gives new diffusion coefficients that agree within 5% with quantum Monte Carlo calculations.

The vast majority of fitness-affecting mutations are deleterious. How natural populations evolve to cope is a question of fundamental interest. Previous studies have reported the evolution of mutational robustness, that is, natural selection favoring populations with less deleterious mutations. By definition, mutational robustness provides a short-term fitness advantage. However, this overlooks the fact that mutational robustness decreases finite asexual populations’ ability to purge recurrent deleterious mutations. Thus, mutational robustness also results in higher risk of long-term extinction by Muller’s ratchet. Here, we explore the tension between short- and long- term response to deleterious mutations. We first show that populations can resist the ratchet if either the selection coefficient or the ratio of beneficial to deleterious mutations increases as fitness declines. We designate these properties as ratchet robustness, which fundamentally reflects a negative feedback between mutation rate and the tendency to accumulate more mutations. We also find in simulations that populations can evolve ratchet robustness when challenged by deleterious mutations. We conclude that mutational robustness cannot be selected for in the long term, but it can be favored in the short-term, purely because of temporary fitness advantage. We also discuss other potential causes of mutational robustness in nature.

Moment theories of ion motion and reaction in ideal and stretched quadrupole ion traps are extended to the case of linear ion traps. Fortran and Mathematica computer programs based on these theories are developed. They are applied to the case of O+ ions moving through an Ar buffer gas containing a small amount of a reactive neutral, N2. The rate coefficient predicted ab initio for a common set of trap parameters is 6.4±0.9×10−13 cm3/s, which is large enough that it should be measureable.

In this paper, we give a conceptual explanation of dark energy as a small negative residual scalar curvature present even in empty spacetime. This curvature ultimately results from postulating a discrete spacetime geometry, very closely related to that used in the dynamical triangulations approach to quantum gravity. In this model, there are no states which have total scalar curvature exactly zero. Moreover, numerical evidence in dimension three suggests that, at a fixed volume, the number of discrete-spacetime microstates strongly increases with decreasing curvature. Because of the resulting entropic force, any dynamics which push empty spacetime strongly toward zero scalar curvature would instead produce typically observed states with a small negative curvature. This provides a natural explanation for the empirically observed small positive value for the cosmological constant (Lambda is about 10^(-121) in Planck units.) In fact, we derive the very rough estimate Lambda=10^(-187) from a simple model containing only the two (highly-degenerate) quantum states with total scalar-curvature closest to zero.

We present two theorems in the "discrete differential geometry" of positively curved spaces. The first is a combinatorial analog of the Bonnet-Myers theorem: $\bullet$ A combinatorial 3-manifold whose edges have degree at most five has edge-diameter at most five. When all edges have unit length, this degree bound is equivalent to an angle-deficit along each edge. It is for this reason we call such spaces positively curved. Our second main result is analogous to the sphere theorems of Toponogov and Cheng: $\bullet$ A positively curved 3-manifold, as above, in which vertices $v$ and $w$ have edge-distance five is a sphere whose triangulation is completely determined by the structure of $Lk(v)$ or $Lk(w)$. In fact, we provide a procedure for constructing a maximum diameter sphere from a suitable $Lk(v)$ or $Lk(w)$. The compactness of these spaces (without an explicit diameter bound) was first proved via analytic arguments in a 1973 paper by David Stone. Our proof is completely combinatorial, provides sharp bounds, and follows closely the proof strategy for the classical results.