Transport in ultradilute solutions of 3^3He in superfluid 4^4He

We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $\tilde < 10^{-9}$ and temperatures $\sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.Comment: NORDITA PREPRINT 2015-37, 9 pages, 6 figure

Low Temperature Transport Properties of Very Dilute Classical Solutions of 3^3He in Superfluid 4^4He

We report microscopic calculations of the thermal conductivity, diffusion constant and thermal diffusion constant for classical solutions of $^3$He in superfluid $^4$He at temperatures T \la 0.6~K, where phonons are the dominant excitations of the $^4$He. We focus on solutions with $^3$He concentrations \la \,10^{-3}, for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of $^3$He-phonon scattering, which is crucial for determining the $^3$He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a $^3$He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the $^3$He distribution function, which we show has an analytical solution in terms of Sonine polynomials. We also calculate the corrections to the Fokker-Planck results for the transport coefficients.Comment: 29 pages, 2 figure

Transport in very dilute solutions of 3^3He in superfluid 4^4 He

Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-$^3$He capture in a dilute solution of $^3$He in superfluid $^4$He, we derive the transport properties of dilute solutions in the regime where the $^3$He are classically distributed and rapid $^3$He-$^3$He scatterings keep the $^3$He in equilibrium. Our microscopic framework takes into account phonon-phonon, phonon-$^3$He, and $^3$He-$^3$He scatterings. We then apply these calculations to measurements by Rosenbaum et al. [J.Low Temp.Phys. {\bf 16}, 131 (1974)] and by Lamoreaux et al. [Europhys.Lett. {\bf 58}, 718 (2002)] of dilute solutions in the presence of a heat flow. We find satisfactory agreement of theory with the data, serving to confirm our understanding of the microscopics of the helium in the future nEDM experiment.Comment: 10 pages, 5 figures, v

Aurelius Augustine\u27s-Use or Discarding of the Classical Methodology of Education to Promote the Christian Faith

Thesis statement: It is the purpose of this paper to examine Augustine’s use or discarding of the classical methodology of education as found in his works de Ordine and de Doctrines Christiana. Introduction: The tension in the early church between the Christian faith and pagan culture found a compromise in Augustine\u27s declaration: Every good and true Christian should understand that wherever he may find truth, it is the Lord\u27s . This he declared in de Doctrines Christiana, 396

Wonder, Aesthetics, and Ethics: A Meditation on Technological Thinking, Psychical Distance, and the Moral Imagination

Senior Project submitted to The Division of Social Studies of Bard College

Modeling the total and polarized emission in evolving galaxies: "spotty" magnetic structures

Future radio observations with the SKA and its precursors will be sensitive to trace spiral galaxies and their magnetic field configurations up to redshift $z\approx3$. We suggest an evolutionary model for the magnetic configuration in star-forming disk galaxies and simulate the magnetic field distribution, the total and polarized synchrotron emission, and the Faraday rotation measures for disk galaxies at z\la 3. Since details of dynamo action in young galaxies are quite uncertain, we model the dynamo action heuristically relying only on well-established ideas of the form and evolution of magnetic fields produced by the mean-field dynamo in a thin disk. We assume a small-scale seed field which is then amplified by the small-scale turbulent dynamo up to energy equipartition with kinetic energy of turbulence. The large-scale galactic dynamo starts from seed fields of 100 pc and an averaged regular field strength of 0.02\,$\mu$G, which then evolves to a "spotty" magnetic field configuration in about 0.8\,Gyr with scales of about one kpc and an averaged regular field strength of 0.6\,$\mu$G. The evolution of these magnetic spots is simulated under the influence of star formation, dynamo action, stretching by differential rotation of the disk, and turbulent diffusion. The evolution of the regular magnetic field in a disk of a spiral galaxy, as well as the expected total intensity, linear polarization and Faraday rotation are simulated in the rest frame of a galaxy at 5\,GHz and 150\,MHz and in the rest frame of the observer at 150\,MHz. We present the corresponding maps for several epochs after disk formation. (abridged)Comment: 13 pages, 6 figures, 2 tables, revised version is accepted for publication in Astronomische Nachrichte

Spectral radiative properties of cirrus clouds deduced from interferometric measurements

July, 1994.Includes bibliographical references.Sponsored by National Aeronautics and Space Administration NAG 1-1146.Sponsored by Office of Naval Research N00014-91-J-1422.Sponsored by Dept. of Energy DE-FG02-90ER60970

Help for the heartland? The employment and electoral effects of the Trump tariffs in the United States

We study the economic and political consequences of the 2018-2019 trade war between the United States, China and other U.S. trade partners at the detailed geographic level, exploiting measures of local exposure to U.S. import tariffs, foreign retaliatory tariffs, and U.S. compensation programs. So far, the trade-war has not provided economic help to the U.S. heartland: import tariffs on foreign goods neither raised nor lowered U.S. employment in newly-protected sectors; retaliatory tariffs had clear negative employment impacts, primarily in agriculture; and these harms were only partly mitigated by compensatory U.S. agricultural subsidies. Nevertheless, consistent with expressive views of politics, the tariff war appears to have been a political success for the governing Republican party. Residents of regions more exposed to import tariffs became less likely to identify as Democrats, more likely to vote to reelect Donald Trump in 2020, and more likely to elect Republicans to Congress. Foreign retaliatory tariffs only modestly weakened that support