Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we \emph{reduce} the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is \emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the system behavior by studying the system's Lie symmetrie

Raman transitions between hyperfine clock states in a magnetic trap

We present our experimental investigation of an optical Raman transition between the magnetic clock states of $^{87}$Rb in an atom chip magnetic trap. The transfer of atomic population is induced by a pair of diode lasers which couple the two clock states off-resonantly to an intermediate state manifold. This transition is subject to destructive interference of two excitation paths, which leads to a reduction of the effective two-photon Rabi-frequency. Furthermore, we find that the transition frequency is highly sensitive to the intensity ratio of the diode lasers. Our results are well described in terms of light shifts in the multi-level structure of $^{87}$Rb. The differential light shifts vanish at an optimal intensity ratio, which we observe as a narrowing of the transition linewidth. We also observe the temporal dynamics of the population transfer and find good agreement with a model based on the system's master equation and a Gaussian laser beam profile. Finally, we identify several sources of decoherence in our system, and discuss possible improvements.Comment: 10 pages, 7 figure

Low-field microwave absorption in epitaxial La-Sr-Mn-O films resulting from the angle-tuned ferromagnetic resonance in the multidomain state

We studied magnetic-field induced microwave absorption in 100-200 nm thick La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ films on SrTiO$_{3}$ substrate and found a low-field absorption with a very peculiar angular dependence: it appears only in the oblique field and is absent both in the parallel and in the perpendicular orientations. We demonstrate that this low-field absorption results from the ferromagnetic resonance in the multidomain state (domain-mode resonance). Its unusual angular dependence arises from the interplay between the parallel component of the magnetic field that drives the film into multidomain state and the perpendicular field component that controls the domain width through its effect on domain wall energy. The low-field microwave absorption in the multidomain state can be a tool to probe domain structure in magnetic films with in-plane magnetization.Comment: 9 pages, 9 Figure

Ventilatory Phenotypes among Four Strains of Adult Rats.

Our purpose in this study was to identify different ventilatory phenotypes among four different strains of rats. We examined 114 rats from three in-house, inbred strains and one outbred strain: Brown Norway (BN;n = 26), Dahl salt-sensitive (n = 24), Fawn-hooded Hypertensive (FHH: n = 27), and outbred Sprague-Dawley rats (SD; n = 37). We measured eupneic (room air) breathing and the ventilatory responses to hypoxia (12% O2-88% N2), hypercapnia (7% CO2), and two levels of submaximal exercise. Primary strain differences were between BN and the other strains. BN rats had a relatively attenuated ventilatory response to CO2 (P \u3c 0.001), an accentuated ventilatory response to exercise (P \u3c 0.05), and an accentuated ventilatory roll-off during hypoxia (P \u3c 0.05). Ventilation during hypoxia was lower than other strains, but hyperventilation during hypoxia was equal to the other strains (P \u3e 0.05), indicating that the metabolic rate during hypoxia decreased more in BN rats than in other strains. Another strain difference was in the frequency and timing components of augmented breaths, where FHH rats frequently differed from the other strains, and the BN rats had the longest expiratory time of the augmented breaths (probably secondary to the blunted CO2 sensitivity). These strain differences not only provide insight into physiological mechanisms but also indicate traits (such as CO2 sensitivity) that are genetically regulated. Finally, the data establish a foundation for physiological genomic studies aimed at elucidating the genetics of these ventilatory control mechanisms

Magnetic anisotropies and magnetization reversal of the Co2_2Cr0.6_{0.6}Fe0.4_{0.4}Al Heusler compound

Magnetic anisotropies and magnetization reversal properties of the epitaxial Heusler compound Co$_2$Cr$_{0.6}$Fe$_{0.4}$Al (CCFA) deposited on Fe and Cr buffer layers are studied. Both samples exhibit a growth-induced fourfold anisotropy, and magnetization reversal occurs through the formation of stripy domains or 90 degree domains. During rotational magnetometric scans the sample deposited on Cr exhibits about 2 degree sharp peaks in the angular dependence of the coercive field, which are oriented along the hard axis directions. These peaks are a consequence of the specific domain structure appearing in this particular measurement geometry. A corresponding feature in the sample deposited on Fe is not observed.Comment: 11 pages, 7 figure

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism investigation of size effects on field-induced N\'eel-cap reversal

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism is used to investigate the influence of an applied magnetic field on N\'eel caps (i.e., surface terminations of asymmetric Bloch walls). Self-assembled micron-sized Fe(110) dots displaying a moderate distribution of size and aspect ratios serve as model objects. Investigations of remanent states after application of an applied field along the direction of N\'eel-cap magnetization give clear evidence for the magnetization reversal of the N\'eel caps around 120 mT, with a $\pm$20 mT dispersion. No clear correlation could be found between the value of the reversal field and geometrical features of the dots

Domain structure of epitaxial Co films with perpendicular anisotropy

Epitaxial hcp Cobalt films with pronounced c-axis texture have been prepared by pulsed lased deposition (PLD) either directly onto Al2O3 (0001) single crystal substrates or with an intermediate Ruthenium buffer layer. The crystal structure and epitaxial growth relation was studied by XRD, pole figure measurements and reciprocal space mapping. Detailed VSM analysis shows that the perpendicular anisotropy of these highly textured Co films reaches the magnetocrystalline anisotropy of hcp-Co single crystal material. Films were prepared with thickness t of 20 nm < t < 100 nm to study the crossover from in-plane magnetization to out-of-plane magnetization in detail. The analysis of the periodic domain pattern observed by magnetic force microscopy allows to determine the critical minimum thickness below which the domains adopt a pure in-plane orientation. Above the critical thickness the width of the stripe domains is evaluated as a function of the film thickness and compared with domain theory. Especially the discrepancies at smallest film thicknesses show that the system is in an intermediate state between in-plane and out-of-plane domains, which is not described by existing analytical domain models

Mars lander survey

The requirements, issues, and design options are reviewed for manned Mars landers. Issues such as high 1/d versus low 1/d shape, parking orbit, and use of a small Mars orbit transfer vehicle to move the lander from orbit to orbit are addressed. Plots of lander mass as a function of Isp, destination orbit, and cargo up and down, plots of initial stack mass in low Earth orbit as a function of lander mass and parking orbit, detailed weight statements, and delta V tables for a variety of options are included. Lander options include a range from minimum landers up to a single stage reusable design. Mission options include conjunction and Venus flyby trajectories using all-cryogenic, hybrid, NERVA, and Mars orbit aerobraking propulsion concepts