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We consider the existence of a force that could produce a non-null result in the Eötvös experiment while producing a null result in the Eöt-Wash experiment. We introduce a general force, in the form of its Taylor series expansion, and determine the response of each experiment to that force. We can then determine which terms of the expansion are important to each experiment. A trial force, in the form of a mixed vector-scalar interaction is introduced and we analyze the resulting Eötvös parameters for various values of the strengths and ranges of the interactions. We find that under certain conditions the Eötvös parameter for the Eöt-Wash experiment can be made zero while the Eötvös parameter for the Eötvös experiment is nonzero. Next, we examine the possibility of a wind force appearing in the MICROSCOPE experiment. This wind would be due to the satellite's motion through a particle background which couples to the differential accelerometer through a baryon-number dependent interaction. We determine the signal that would be measured by MICROSCOPE satellite and compare the power spectrum density of this signal to the published power spectrum density of the experiment. Additionally, we present a new theoretical framework for the time-variation of nuclear decay rates. This new framework is motivated by the results of numerous experiments which show a periodicity of one year. The fractional decay rate of these experiments are constant, regardless of isotope. We find that a novel neutrino interaction, in the form of an index of refraction, successfully generates the constant fractional decay rates. Using the optical theorem and the relativistic Breit-Wigner distribution makes the index of refraction consistent with neutrino speed measurements. We conclude by describing other systems where the index of refraction could create observable oscillations. Finally, we consider the suppression of beta decay rates through the Pauli exclusion principle due to the presence of background cosmic and solar neutrinos. We derive the suppression factor for both thermalized and non-thermalized neutrinos.