Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure

A major regional air pollution event in the northeastern United States caused by extensive forest fires in Quebec, Canada

During early July 2002, wildfires burned ∼1 × 106 ha of forest in Quebec, Canada. The resultant smoke plume was seen in satellite images blanketing the U.S. east coast. Concurrently, extremely high CO mixing ratios were observed at the Atmospheric Investigation, Regional Modeling, Analysis and Prediction (AIRMAP) network sites in New Hampshire and at the Harvard Forest Environmental Measurement Site (HFEMS) in Massachusetts. The CO enhancements were on the order of 525–1025 ppbv above low mixing ratio conditions on surrounding days. A biomass burning source for the event was confirmed by concomitant enhancements in aerosol K+, NH4+, NO3−, and C2O42− mixing ratios at the AIRMAP sites. Additional data for aerosol K, organic carbon, and elemental carbon from the Interagency Monitoring of Protected Visual Environments network and CO data from Environmental Protection Agency sites indicated that the smoke plume impacted much of the U.S. east coast, from Maine to Virginia. CO mixing ratios and K concentrations at stations with 10-year or longer records suggested that this was the largest biomass burning plume to impact the U.S. east coast in over a decade. Furthermore, CO mixing ratios and aerosol particles with diameters 2.5) mass and scattering coefficients from the AIRMAP network and HFEMS indicated that this event was comparable to the large anthropogenic combustion and haze events which intermittently impact rural New England. The degree of enhancement of O3, NOy, NO3−, NH4+, and SO42− in the biomass plume showed significant variation with elevation and latitude that is attributed to variations in transport and surface depositional processes

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Sufficiently dimerized quantum antiferromagnets display elementary S=1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1=-2.3meV, J2=1.2meV, J3=2.9meV and J4=-0.3meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S=1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.Comment: 6 pages, 5 figure

Covariant gauge fixing and Kuchar decomposition

The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A geometrical definition of gauge fixing at the constraint manifold is given; it is equivalent to a definition of a background (spacetime) manifold for each topological sector of a model. Every gauge fixing defines a decomposition of the constraint manifold into the physical phase space and the space of embeddings of the Cauchy manifold into the background manifold (Kuchar decomposition). Extensions of every gauge fixing and the associated Kuchar decomposition to a neighbourhood of the constraint manifold are shown to exist.Comment: Revtex, 35 pages, no figure