Tensorial depolarization of alkali atoms by isotropic collisions with neutral hydrogen

Results. We consider the problem of isotropic collisions between an alkali atom and neutral hydrogen. We calculate the collisional tensorial components of general p and s-states, characterized by their effective principal quantum number $n^{*}$. It is found that the behaviour of the tensorial components obey simple power laws allowing quick calculations of the depolarizing collisional rates. As application, our results should allow a rigorous treatment of the atomic polarization profiles of the D1 -D2 lines of alkali atoms. Conclusions. Close coupling treatments of atomic collisions are needed to decipher the information encoded in the polarized radiation from the Sun. Important problems remain unresolved like the role of collisions in the Paschen-Back conditions.Comment: Accepted for publication in A&

Are collisions with neutral hydrogen important for modelling the Second Solar Spectrum of Ti I and Ca II ?

The physical interpretation of scattering line polarization offers a novel diagnostic window for exploring the thermal and magnetic structure of the quiet regions of the solar atmosphere. Here we evaluate the impact of isotropic collisions with neutral hydrogen atoms on the scattering polarization signals of the 13 lines of multiplet 42 of Ti I and on those of the K line and of the IR triplet of Ca II, with emphasis on the collisional transfer rates between nearby J-levels. To this end, we calculate the linear polarization produced by scattering processes considering realistic multilevel models and solving the statistical equilibrium equations for the multipolar components of the atomic density matrix. We confirm that the lower levels of the 13 lines of multiplet 42 of Ti I are completely depolarized by elastic collisions. We find that upper-level collisional depolarization turns out to have an unnoticeable impact on the emergent linear polarization amplitudes, except for the {\lambda 4536 line for which it is possible to notice a rather small depolarization caused by the collisional transfer rates. Concerning the Ca II lines, we show that the collisional rates play no role on the polarization of the upper level of the K line, while they have a rather small depolarizing effect on the atomic polarization of the metastable lower levels of the Ca II IR triplet.Comment: Accepted for publication in Astronomy and Astrophysic

A unified numerical model of collisional depolarization and broadening rates due to hydrogen atom collisions

Interpretation of solar polarization spectra accounting for partial or complete frequency redistribution requires data on various collisional processes. Data for depolarization and polarization transfer are needed but often missing, while data for collisional broadening are usually more readily available. Recent work by Sahal-Br\'echot and Bommier concluded that despite underlying similarities in the physics of collisional broadening and depolarization processes, relationships between them are not possible to derive purely analytically. We aim to derive accurate numerical relationships between the collisional broadening rates and the collisional depolarization and polarization transfer rates due to hydrogen atom collisions. Such relationships would enable accurate and efficient estimation of collisional data for solar applications. Using earlier results for broadening and depolarization processes based on general (i.e. not specific to a given atom), semi-classical calculations employing interaction potentials from perturbation theory, genetic programming (GP) has been used to fit the available data and generate analytical functions describing the relationships between them. The predicted relationships from the GP-based model are compared with the original data to estimate the accuracy of the method.Comment: 10 pages, 7 figures, Accepted for publication in Astronomy & Astrophysic

Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields

The physics of the solar chromosphere depends in a crucial way on its magnetic structure. However there are presently very few direct magnetic field diagnostics available for this region. Here we investigate the diagnostic potential of the Hanle effect on the Ba II D2 line resonance polarization for the determination of weak chromospheric turbulent magnetic fields......Comment: In press in astronomy and astrophysic

Evidence for collisional depolarization of the \ion{Ba}{ii} λ4554{\lambda}4554 line in the low chromosphere

Context. Rigorous modeling of the \ion{Ba}{ii} ${\lambda}4554$ formation is potentially interesting since this strongly polarized line forms in the solar chromosphere where the magnetic field is rather poorly known. Aims. To investigate the role of isotropic collisions with neutral hydrogen in the formation of the polarized \ion{Ba}{ii} ${\lambda}4554$ line and, thus, in the determination of the magnetic field. Methods. Multipole relaxation and transfer rates of the $d$ and p-states of \ion{Ba}{ii} by isotropic collisions with neutral hydrogen are calculated. We consider a plane parallel layer of \ion{Ba}{ii} situated at the low chromosphere and anisotropically illuminated from below which produces linear polarization in the ${\lambda}4554$ line by scattering processes. To compute that polarization, we solve the statistical equilibrium equations for \ion{Ba}{ii} levels including collisions, radiation and magnetic field effects. Results. Variation laws of the relaxation and transfer rates with hydrogen number density $n_{\textrm {\scriptsize H}}$ and temperature are deduced. The polarization of the ${\lambda}4554$ line is clearly affected due to isotropic collisions with neutral hydrogen although the collisional depolarization of its upper level $^2P_{3/2}$ is negligible. This is because the alignment of the metastable levels $^2D_{3/2}$ and $^2D_{5/2}$ of the \ion{Ba}{ii} are vulnerable to collisions. At the height of formation of the ${\lambda}4554$ line where $n_{\textrm {\scriptsize H}} \sim 2 \times 10^{14}$ cm$^{-3}$, we find that the neglecting of the collisions induces inaccuracy of $\sim$ 25% on the calculation of the polarization and $\sim$ 35 % inaccuracy on microturbulent magnetic field determination.Comment: 12 pages, 4 figures, accepted for publication in A&

Collisional depolarization and transfer rates of spectral lines by atomic hydrogen. II: application to d states of neutral atoms

The theory of collisional depolarization of spectral lines by atomic hydrogen (Derouich et al. \cite{derouich1}) is extended to $d$ $(l$=2) atomic levels. Depolarization rates, polarization and population transfer rates are calculated and results are given as a function of the temperature. Cross sections as a function of the effective quantum number for a relative velocity of 10 $\textrm{km s}^{-1}$ are also given together with velocity exponents $\lambda$, if \textbf{they exist}, on the assumption that the cross section varies with velocity as $v^{-\lambda}$. A discussion of our results is presented.Comment: 11 pages including 3 figures and 2 tables, accepted in A&

Collisional depolarization and transfer rates of spectral lines by atomic hydrogen. IV: application to ionised atoms

The semi-classical theory of collisional depolarization of spectral lines of neutral atoms by atomic hydrogen (Derouich et al. 2003a; Derouich et al. 2003b; Derouich et al. 2004 and references therein) is extended to spectral lines of singly ionised atoms. In this paper we apply our general method to the particular cases of the 3d $^2D$ and $4p$ $^2P$ states of the CaII ion and to the $5p$ $^2P$ state of the SrII ion. Analytical expressions of all rates as a function of local temperature are given. Our results for the CaII ion are compared to recent quantum chemistry calculations. A discussion of our results is presented.Comment: 19 pages, 14 figures, submitted to Astronomy and Astrophysic

A model of dengue fever

BACKGROUND: Dengue is a disease which is now endemic in more than 100 countries of Africa, America, Asia and the Western Pacific. It is transmitted to the man by mosquitoes (Aedes) and exists in two forms: Dengue Fever and Dengue Haemorrhagic Fever. The disease can be contracted by one of the four different viruses. Moreover, immunity is acquired only to the serotype contracted and a contact with a second serotype becomes more dangerous. METHODS: The present paper deals with a succession of two epidemics caused by two different viruses. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the human and the mosquito populations. RESULTS: Stability of the equilibrium points is given and a simulation is carried out with different values of the parameters. The epidemic dynamics is discussed and illustration is given by figures for different values of the parameters. CONCLUSION: The proposed model allows for better understanding of the disease dynamics. Environment and vaccination strategies are discussed especially in the case of the succession of two epidemics with two different viruses

The Effect of Physical Exercise on the Dynamics of Glucose and Insulin

Abstract Regular physical activity is indicated either to prevent and delay the onset of non-insulin-dependent diabetes or to assure a good control of diabetes by increasing insulin sensitivity and ameliorating the metabolism of glucose disappearance. Many studies and experiments have dealt with this subject. In this paper, we introduce the effect of physical activity via parameters of a mathematical model which allows us to compare the behaviour of blood glucose in normal, non-insulin-dependent diabetes and insulin-dependent diabetes people, with and without physical effort. Extreme cases of physical activity leading to hypoglycaemia or aggravating hyperglycaemia are also underlined.