A systematic approach to determining the properties of an iodine absorption cell for high-precision radial velocity measurements

Absorption cells filled with diatomic iodine are frequently employed as wavelength reference for high-precision stellar radial velocity determination due their long-term stability and low cost. Despite their wide-spread usage in the community, there is little documentation on how to determine the ideal operating temperature of an individual cell. We have developed a new approach to measuring the effective molecular temperature inside a gas absorption cell and searching for effects detrimental to a high precision wavelength reference, utilizing the Boltzmann distribution of relative line depths within absorption bands of single vibrational transitions. With a high resolution Fourier transform spectrometer, we took a series of 632 spectra at temperatures between 23{\deg}C and 66{\deg}C. These spectra provide a sufficient basis to test the algorithm and demonstrate the stability and repeatability of the temperature determination via molecular lines on a single iodine absorption cell. The achievable radial velocity precision is found to be independent of the cell temperature and a detailed analysis shows a wavelength dependency, which originates in the resolving power of the spectrometer in use and the signal-to-noise ratio. Two effects were found to cause apparent absolute shifts in radial velocity, a temperature-induced shift of the order of 1 m/s/K and a more significant effect resulting in abrupt jumps of 50 m/s is determined to be caused by the temperature crossing the dew point of the molecular iodine.Comment: 8 pages, 9 figures accepted for publication in MNRA

Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio

Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the main difference between the mixtures and pure fluids lies in the existence of stable three dimensional patterns near onset in a wide range of the parameter space. We evaluated the stationary solutions of roll, crossroll, and square convection and we determined the location of the stability boundaries for many parameter combinations thereby obtaining the Busse balloon for roll and square patterns.Comment: 19 pages + 15 figures, accepted by Journal of Fluid Mechanic

Roll convection of binary fluid mixtures in porous media

We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh-B\'enard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared to one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh--B\'enard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios which are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism

Magnetization and susceptibility of ferrofluids

A second-order Taylor series expansion of the free energy functional provides analytical expressions for the magnetic field dependence of the free energy and of the magnetization of ferrofluids, here modelled by dipolar Yukawa interaction potentials. The corresponding hard core dipolar Yukawa reference fluid is studied within the framework of the mean spherical approximation. Our findings for the magnetic and phase equilibrium properties are in quantitative agreement with previously published and new Monte Carlo simulation data.Comment: 8 pages including 4 figure

Faraday instability in a two-component Bose Einstein condensate

Motivated by recent experiments on Faraday waves in Bose Einstein condensates (BEC) we investigate the dynamics of two component cigar shaped BEC subject to periodic modulation of the strength of the transverse confinement. It is shown that two coupled Mathieu equations govern the dynamics of the system. We found that the two component BEC in a phase mixed state is relatively more unstable towards pattern formation than the phase segregated state.Comment: 6 pages, 4 figure

Scaling and interleaving of sub-system Lyapunov exponents for spatio-temporal systems

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a sub-system in a very cost effective way. In this work we present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. It is inspired by the stability analysis of the homogeneous evolution in a one-dimensional coupled map lattice but appears to be equally valid in a much wider range of cases. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative sub-system volume) for one and two-dimensional lattices in spatio-temporal chaotic regimes. In doing so we notice that the Lyapunov spectra for consecutive sub-system sizes are interleaved and we discuss the possible ways in which this may arise. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension and Kolmogorov-Sinai entropy) finding better convergence as the sub-system size is increased than with conventional rescaling.Comment: 18 pages, double column, REVTeX, 27 embedded postscript figures with psfig. Submitted to Chao