Contact Discontinuities in Models of Contact Binaries Undergoing Thermal Relaxation Oscillations

In this paper we pursue the suggestion by Shu, Lubow & Anderson (1979) and Wang (1995) that contact discontinuity (DSC) may exist in the secondary in the expansion TRO (thermal relaxation oscillation) state. It is demonstrated that there is a mass exchange instability in some range of mass ratio for the two components. We show that the assumption of {\it constant} volume of the secondary should be relaxed in DSC model. For {\it all} mass ratio the secondary alway satisfies the condition that no mass flow returns to the primary through the inner Lagrangian point. The secondary will expand in order to equilibrate the interaction between the common convective envelope and the secondary. The contact discontinuity in contact binary undergoing thermal relaxation does not violate the second law of thermodynamics. The maintaining condition of contact discontinuity is derived in the time-dependent model. It is desired to improve the TRO model with the advanced contact discontinuity layer in future detailed calculations.Comment: 5 pages in emulateapj, 1 figur

Coupled-channels effects in elastic scattering and near-barrier fusion induced by weakly bound nuclei and exotic halo nuclei

The influence on fusion of coupling to the breakup process is investigated for reactions where at least one of the colliding nuclei has a sufficiently low binding energy for breakup to become an important process. Elastic scattering, excitation functions for sub-and near-barrier fusion cross sections, and breakup yields are analyzed for $^{6,7}$Li+$^{59}$Co. Continuum-Discretized Coupled-Channels (CDCC) calculations describe well the data at and above the barrier. Elastic scattering with $^{6}$Li (as compared to $^{7}$Li) indicates the significant role of breakup for weakly bound projectiles. A study of $^{4,6}$He induced fusion reactions with a three-body CDCC method for the $^6$He halo nucleus is presented. The relative importance of breakup and bound-state structure effects on total fusion is discussed.Comment: 29 pages, 9 figure

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Separability and entanglement of four-mode Gaussian states

The known Peres-Horodecki criterion and scaling criterion of separability are considered on examples of three-mode and four-mode Gaussian states of electromagnetic field. It is shown that the principal minors of the photon quadrature dispersion matrix are sensitive to the change of scaling parameters. An empirical observation has shown that the bigger the modulus of negative principal minors, the more entangled the state.Comment: 14 pages, 11 figure

Simulation of Lablab Pastures

The potential of legume-based pastures to address declining soil nitrogen on marginal cropping soils is increasingly recognised in northern Australia, as such there is a need for cost benefit analysis of pastures and crops in a mixed farming system. In highly variable rainfall environments, biophysical modelling may be the best way of identifying and quantifying interactions with mixed crop-livestock systems on a seasonal basis. This paper describes a case study where both animal productivity and lablab pasture production is simulated. Lablab (Lablab purpureus) is an annual tropical legume widely used as a short-term legume phase in crop-pasture rotations, providing high quality forage for animal production and a low risk nitrogen input for crop production

Post-Newtonian Theory for Precision Doppler Measurements of Binary Star Orbits

The determination of velocities of stars from precise Doppler measurements is described here using relativistic theory of astronomical reference frames so as to determine the Keplerian and post-Keplerian parameters of binary systems. We apply successive Lorentz transformations and the relativistic equation of light propagation to establish the exact treatment of Doppler effect in binary systems both in special and general relativity theories. As a result, the Doppler shift is a sum of (1) linear in $c^{-1}$ terms, which include the ordinary Doppler effect and its variation due to the secular radial acceleration of the binary with respect to observer; (2) terms proportional to $c^{-2}$, which include the contributions from the quadratic Doppler effect caused by the relative motion of binary star with respect to the Solar system, motion of the particle emitting light and diurnal rotational motion of observer, orbital motion of the star around the binary's barycenter, and orbital motion of the Earth; and (3) terms proportional to $c^{-2}$, which include the contributions from redshifts due to gravitational fields of the star, star's companion, Galaxy, Solar system, and the Earth. After parameterization of the binary's orbit we find that the presence of periodically changing terms in the Doppler schift enables us disentangling different terms and measuring, along with the well known Keplerian parameters of the binary, four additional post-Keplerian parameters, including the inclination angle of the binary's orbit, $i$. We briefly discuss feasibility of practical implementation of these theoretical results, which crucially depends on further progress in the technique of precision Doppler measurements.Comment: Minor changes, 1 Figure included, submitted to Astrophys.