Unified Analysis of Cosmological Perturbations in Generalized Gravity

In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the scalar field and the scalar curvature in the Lagrangian, thus includes broad classes of generalized gravity theories resulting from recent attempts for the unification. We analyze both the scalar-type mode and the gravitational wave in analogous ways. For both modes the large scale evolutions are characterized by the same conserved quantities which are valid in the Einstein's gravity. This unified and simple treatment is possible due to our proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure

Cosmological Gravitational Wave in a Gravity with Quadratic Order Curvature Couplings

We present a set of equations describing the cosmological gravitational wave in a gravity theory with quadratic order gravitational coupling terms which naturally arise in quantum correction procedures. It is known that the gravitational wave equation in the gravity theories with a general $f(R)$ term in the action leads to a second order differential equation with the only correction factor appearing in the damping term. The case for a $R^{ab} R_{ab}$ term is completely different. The gravitational wave is described by a fourth order differential equation both in time and space. However, curiously, we find that the contributions to the background evolution are qualitatively the same for both terms.Comment: 4 pages, revtex, no figure

Non-abelian dynamics in first-order cosmological phase transitions

Bubble collisions in cosmological phase transitions are explored, taking the non-abelian character of the gauge fields into account. Both the QCD and electroweak phase transitions are considered. Numerical solutions of the field equations in several limits are presented.Comment: 8 pages, 2 figures. Contribution to the CosPA 2003 Cosmology and Particle Astrophysics Symposium. Typos correcte

First principles numerical model of avalanche-induced arc discharges in electron-irradiated dielectrics

The model consists of four phases: single electron dynamics, single electron avalanche, negative streamer development, and tree formation. Numerical algorithms and computer code implementations are presented for the first three phases. An approach to developing a code description of fourth phase is discussed. Numerical results are presented for a crude material model of Teflon

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte