General Issues in the Evolution of Fermion Masses and Mixings

General issues in the renormalization group evolution of fermion masses and mixings is discussed. An effective fixed point in the top quark Yukawa coupling can strongly constrain its value at the electroweak scale. Predictions following from Yukawa coupling unification are affected by threshold corrections at the grand unified scale. The Landau pole translates into an upper limit on the strong gauge coupling $\alpha _3(M_Z)$. Given the hierarchy in the fermion sector, the evolution of the Cabbibo-Kobayashi-Maskawa matrix can be expressed in terms of a single scaling parameter $S$. Using this scaling factor and analogous scaling factors for the quark and lepton masses, we outline a systematic strategy that readily yields electroweak predictions for any GUT scale texture.}Comment: (Talk given at the SUSY93 Conference MSB), 9 pages + 3 PS figures not included (available on request), MAD/PH/75

Supersymmetry with Grand Unification

Supersymmetry (SUSY) has many well known attractions, especially in the context of Grand Unified Theories (GUTs). SUSY stabilizes scalar mass corrections (the hierarchy problem), greatly reduces the number of free parameters, facilitates gauge coupling unification, and provides a plausible candidate for cosmological dark matter. In this conference report we survey some recent examples of progress in SUSY-GUT applications.Comment: Talk V. Barger at the Workshop on Physics at Current Accelerators and the Supercollider, Argonne, June 1993, 15 pages + 12 PS figures included (uuencoded), (correct author list in header) MAD/PH/78

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on T3×RT^3 \times R

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to ftp://vela.acs.oakland.edu/pub/berger/u1genfig

Classification of symmetric periodic trajectories in ellipsoidal billiards

We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display a selection of 3D minimal SPTs. Some of them have properties that cannot take place in the 2D case.Comment: 26 pages, 77 figures, 17 table

Analysis Of Measured Transport Properties Of Domain Walls In Magnetic Nanowires And Films

Existing data for soft magnetic materials of critical current for domain-wall motion, wall speed driven by a magnetic field, and wall electrical resistance, show that all three observable properties are related through a single parameter: the wall mobility $\mu$. The reciprocal of $\mu$ represents the strength of viscous friction between domain wall and conduction-electron gas. And $\mu$ is a function of the wall width, which depends in turn on the aspect ratio t/w, where t and w are the thickness and width of the sample. Over four orders of magnitude of $\mu$, the data for nanowires show $\mu\propto (t/w)^{-2.2}$. This dependence is in approximate agreement with the prediction of the 1984 Berger theory based on s-d exchange. On the other hand, it is inconsistent with the prediction of the 2004 Tatara and Kohno theory, and of the 2004 Zhang and Li theory.Comment: 7 pages, 1 figure; submitted to Phys. Rev.