Implications upon theory discrimination of an accurate measurement of the time rate of change of the gravitational “constant” G and other cosmological parameters

A substantial improvement in the accuracy of ˙ G tests (The dot denotes the time derivative.) would make it realistic to speak in terms of a measurement of ˙G , rather than merely a smaller upper bound on | ˙G|. We show that the accuracy Δ | ˙G/G|≈? 10^‐14 yr^‐1 may be sufficient, given the accuracy of other cosmological parameters, to observe effects predicted by higher dimensions theories and, hence, to discriminate among different models. The ˙G design goal for the SEE (Satellite Energy Exchange) mission is Δ (˙G/G) ≈? 10^‐14 yr^‐1.     

The strength of compactness in Computability Theory and Nonstandard Analysis

Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers. The most basic question is: how hard is it to compute a finite sub-cover from such a cover of $2^{\mathbb{N}}$? Another natural question is: how hard is it to compute a sequence that covers $2^{\mathbb{N}}$ minus a measure zero set from such a cover? The special and weak fan functionals respectively compute such finite sub-covers and sequences. In this paper, we establish the connection between these new fan functionals on one hand, and various well-known comprehension axioms on the other hand, including arithmetical comprehension, transfinite recursion, and the Suslin functional. In the spirit of Reverse Mathematics, we also analyse the logical strength of compactness in Nonstandard Analysis. Perhaps surprisingly, the results in the latter mirror (often perfectly) the computational properties of the special and weak fan functionals. In particular, we show that compactness (nonstandard or otherwise) readily brings us to the outer edges of Reverse Mathematics (namely ${\mathrm{\Pi }}_2^1{\text{-}\mathsf{\text{CA}}}_0$), and even into Schweber's higher-order framework (namely ${\mathrm{\Sigma }}_1^2$-separation).     

Effects of bundling on the properties of the SPC water model

Simultaneous representation of molecules at an all-atom and coarse-grained level, as required by multiscaling molecular dynamics simulations, poses problems for the treatment of small molecules. If more than one of these molecules are mapped to a single coarse-grained interaction site, unrestricted movement in the all-atom representation can make a meaningful correspondence of the coordinates between the two representations impossible. Restricting the relative movement of molecules mapped to the same coarse-grained interaction site solves that problem, but will have consequences for the properties of the model. Here we investigate the effects of introducing bundling to the common simple point charge (SPC) water model and present a bundled water model that preserves important properties of SPC water relevant for multiscaling.