We propose a mathematical scheme to classify the eigenmodes of linear adiabatic oscillations of spherically symmetric stars, with fully taking account of the perturbation to the gravitational potential. The scheme allows us to allocate a unique and continuous integral index (the radial order) to each eigenmode with a positive squared eigenfrequency of any stellar structure, which is invariant a...

A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal comp...

Quillen’s local index theorem is used to study the charge transport coefficients (adiabatic curvature) associated to the ground state of a Schrödinger operator for a charged (spinless) particle on a closed, multiply connected surface. The formula splits the adiabatic curvature into an explicit integral part and a fluctuating part which has a natural interpretation in terms of quantum chaos. PAC...

Active optical tuning of silicon racetrack resonators clad in dye-doped blue phase liquid crystals (BPLCs) is experimentally demonstrated. An adiabatic racetrack resonator geometry that allows for enhanced tuning is presented and analyzed. The resonance shift of an unmodified geometry racetrack is Δλ=0.7 nm, while an adiabatic racetrack achieves a Δλ=1.23 nm resonance shift because of a greater...

for the log derivative of the FRW scale factor, the famous Hubble parameterH(η) = da/dη a . The independent variable is the conformal time η, c is simply related to the adiabatic index of the cosmological fluid, c = 3 2 γ − 1 which was assumed constant by Faraoni, and κ = 0,±1 is the curvature index of the flat, closed, open FRW universe, respectively. For the mathematical considerations of thi...

The adiabatic limit refers to the geometric degeneration in which the metric is been blown up along certain directions. The study of the adiabatic limit of geometric invariants is initiated by E. Witten [39], who relates the adiabatic limit of the η-invariant to the holonomy of determinant line bundle, the so called “global anomaly”. In this case the manifold is fibered over a circle and the me...

We prove that the sonic surface of axisymmetric meridional stationary flows is always attached to the accretor, however small, if the adiabatic index of the gas is = 5=3. Using local expansions near a point-like accretor, we extend Bondi’s classification of spherically symmetric flows to axisymmetric flows, introducing the possibility of angular sectors reached by no flow lines, and singular di...

We prove that the sonic surface of axi-symmetric meridional stationary flows is always attached to the accretor, however small, if the adiabatic index of the gas is γ = 5/3. Using local expansions near a point-like accretor, we extend Bondi's classification of spherically symmetric flows to axisymmetric flows, introducing the possibility of angular sectors reached by no flow lines, and singular...

The evolution of a class of inhomogeneous spherically symmetric universe models possessing a varying cosmological term and a material fluid, with an adiabatic index either constant or not, is studied.