Mass Flux Measurements in Solid $^4$He

There has been considerable attention given to solid helium over the past decade. Our approach to study the solid has been to sandwich solid helium between two reservoirs of superfluid helium. With this approach, we found and explored the characteristics of mass flux that takes place from one reservoir to the other\footnote{M.W. Ray and R.B. Hallock, Phys. Rev. Letters 100, 235301 (2008); 105, 145301 (2010); Phys. Rev. B 79, 224302 (2009).}. We observed flow that has the characteristics of one-dimensional conductivity\footnote{Ye. Vekhov and R.B. Hallock, Phys. Rev. Letters 109, 045303 (2012); Phys. Rev. B 90, 134511 (2014).} and we have documented the effects that various concentrations of $^3$He impurity have on the temperature dependence of the flow\footnote{Ye. Vekhov, W.J. Mullin and Hallock, Phys. Rev. Letters 113, 035302 (2014); Ye. Vekhov and R.B Hallock, Phys. Rev. B 92, 104509 (2015).} These experiments continue and we will report on this work and new results that may be available.