This article presents a comparative analysis of solar activity data, Mt Wilson diameter data, Super-Kamiokande solar neutrino data, and nuclear decay data acquired at the Lomonosov Moscow State University (LMSU). We propose that salient periodicities
in all of these datasets may be attributed to r-mode oscillations. Periodicities in the solar activity data and in Super-Kamiokande solar neutrino data may be attributed to r-mode oscillations in the known tachocline, with normalized radius in the range 0.66 to 0.74, where the sidereal rotation rate is in the range 13.7 to 14.6 year-1. We propose that periodicities in the Mt Wilson and LMSU data may be attributed to similar r-mode oscillations where the sidereal rotation rate is approximately which we attribute to a hypothetical inner tachocline separating a slowly rotating core from the radiative zone. We also discuss the possible role of the RSFP (Resonant Spin Flavor Precession) process, which leads to estimates of the neutrino magnetic moment and of the magnetic field strength in or near the solar core.
The recently suggested modification of the transverse electric contribution to the Lifshitz formula (S. K. Lamoreaux, arXiv:0801.1283) is discussed. We show that this modification is inconsistent with the data of two precise experiments, and violates
the Nernst heat theorem. The preprints suggestion concerning the resolution of the apparent violation of the Third Law of Thermodynamics is shown to be incorrect.
We review new constraints on the Yukawa-type corrections to Newtonian gravity obtained recently from gravitational experiments and from the measurements of the Casimir force. Special attention is paid to the constraints following from the most precis
e dynamic determination of the Casimir pressure between the two parallel plates by means of a micromechanical torsional oscillator. The possibility of setting limits on the predictions of chameleon field theories using the results of gravitational experiments and Casimir force measurements is discussed.
