First principles simulations of liquid Fe-S under Earth's core conditions

First principles electronic structure calculations, based upon density functional theory within the generalized gradient approximation and ultra-soft Vanderbilt pseudopotentials, have been used to simulate a liquid alloy of iron and sulfur at Earth's core conditions. We have used a sulfur concentration of $\approx 12$wt, in line with the maximum recent estimates of the sulfur abundance in the Earth's outer core. The analysis of the structural, dynamical and electronic structure properties has been used to report on the effect of the sulfur impurities on the behavior of the liquid. Although pure sulfur is known to form chains in the liquid phase, we have not found any tendency towards polymerization in our liquid simulation. Rather, a net S-S repulsion is evident, and we propose an explanation for this effect in terms of the electronic structure. The inspection of the dynamical properties of the system suggests that the sulfur impurities have a negligible effect on the viscosity of Earth's liquid core.Comment: 24 pages (including 8 figures

Deterministic Chaos in Blood Pressure Signals During Different Physiological Conditions

Several coupled and nonlinear controlling mechanisms are involved in the regulation of blood pressure. The possible presence of chaos in physiological signals has been the subject of some research. In this study, blood pressure signals were analysed using a range of nonlinear time series analysis techniques. Individual effectors of blood pressure were either experimentally removed or enhanced, so that the controlling mechanisms that are responsible for the chaotic nature of the signals may be identified by chaotic analysis of the signals. The level of chaos varied across the different experimental conditions, showing a distinct decrease from control conditions to all other experimental conditions

Deterministic Chaos in Blood Pressure Signals During Different Physiological Conditions

Several coupled and nonlinear controlling mechanisms are involved in the regulation of blood pressure. The possible presence of chaos in physiological signals has been the subject of some research. In this study, blood pressure signals were analysed using a range of nonlinear time series analysis techniques. Individual effectors of blood pressure were either experimentally removed or enhanced, so that the controlling mechanisms that are responsible for the chaotic nature of the signals may be identified by chaotic analysis of the signals. The level of chaos varied across the different experimental conditions, showing a distinct decrease from control conditions to all other experimental conditions

Equations of State and Crystal Structures of High-Pressure Phases of Shocked Silicates and Oxides

Shock-wave data are now available for a variety of rocks, minerals, and oxides of geophysical interest in the pressure range appropriate for the lower mantle. These data are analyzed to obtain equation-of-state parameters with emphasis on the shock-induced high-pressure phases. Of twenty-four materials for which Hugoniot data are analyzed, all but MgO, Al_2O_3, and MnO_2 undergo at least one shock-induced phase change below 800 kb. Birch-Murnaghan parameters for the raw Hugoniots, metastable Hugoniots, adiabats, and 25°C isotherms are obtained for the high-pressure phases. On correcting the raw Hugoniot data for MgO and Al_2O_3 for strength effects, we find that the calculated adiabatic equations of state are in good agreement with recent ultrasonic data. The zero-pressure densities of high-pressure phases are obtained by constraining the adiabats calculated from the Hugoniot data such that the zero-pressure densities and the zero-pressure slopes of the adiabats satisfy Anderson's seismic equation of state. Probable crystallographic structures of the high-pressure phases are inferred from the classical laws of crystal chemistry and, in some cases, from static high-pressure recovery experiments on analog compounds. Shock data for SiO_2 (stishovite) indicate that transformation to the fluorite-type structure (observed in TiO_2) does not take place under shock, at least to ∼2000 kb. Fe_2O_3 probably transforms to either the perovskite or B rare earth structure with a zero-pressure density of 5.96 g/cm^³. MgAl_2O_4 (spinel) may transform to the CaFe_2O_4 structure with a zero-pressure density of 4.19 g/cm_³. Feldspars transform to the hollandite structure (density, of ∼3.85 g/cm^³). Olivine-rich rocks containing greater than 10% FeO either disproportionate to the ilmenite and rock salt structure or transform to a new post-spinel polymorph having the Sr_2PbO_4 structure. Pyroxenes containing greater than 10% FeO probably transform to the ilmenite structure. High-pressure forms of sillimanite and andalusite have calculated densities of 4.00 and 3.95 g/cm^³, respectively. This probably represents disproportionation reaction products, Al_2O_3 + SiO_2 (stishovite), which would give a density of 4.09 g/cm^³. The Birch-Murnaghan second-order parameter ξ is nearly zero for MgO and Al_2O_3. 0.73 for stishovite, and ∼1 for the high-pressure phases of the olivines and pyroxenes. The values of K′ = dK/dP are calculated along the Hugoniots and adiabats and are found to decrease at a rate of −0.5 to −1.6 cm³/g when the density is increased either by compression or by iron substitution

Dynamic baroreflex control of blood pressure: influence of the heart vs. peripheral resistance

The aim in the present experiments was to assess the dynamic baroreflex control of blood pressure, to develop an accurate mathematical model that represented this relationship, and to assess the role of dynamic changes in heart rate and stroke volume in giving rise to components of this response. Patterned electrical stimulation [pseudo-random binary sequence (PRBS)] was applied to the aortic depressor nerve (ADN) to produce changes in blood pressure under open-loop conditions in anesthetized rabbits. The stimulus provided constant power over the frequency range 0–0.5 Hz and revealed that the composite systems represented by the central nervous system, sympathetic activity, and vascular resistance responded as a second-order low-pass filter (corner frequency ≈0.047 Hz) with a time delay (1.01 s). The gain between ADN and mean arterial pressure was reasonably constant before the corner frequency and then decreased with increasing frequency of stimulus. Although the heart rate was altered in response to the PRBS stimuli, we found that removal of the heart's ability to contribute to blood pressure variability by vagotomy and β1-receptor blockade did not significantly alter the frequency response. We conclude that the contribution of the heart to the dynamic regulation of blood pressure is negligible in the rabbit. The consequences of this finding are examined with respect to low-frequency oscillations in blood pressure

Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method