RMSF Research Articles

Spin Hall effect in a thin Pt film

A density-functional-theory based relativistic scattering formalism is used to study charge transport through thin Pt films with room temperature lattice disorder. A Fuchs-Sondheimer specularity coefficient $p \sim 0.5$ is needed to describe the suppression of the charge current at the surface even in the absence of surface roughness. The charge current drives a spin Hall current perpendicular to the surface. Analysing the latter with a model that is universally used to interpret the spin Hall effect in thin films and layered materials, we are unable to recover values of the spin-flip diffusion length $l_{\rm sf}$ and spin Hall angle $\Theta_{\rm sH}$ that we obtain for bulk Pt using the same approximations. We trace this to the boundary conditions used and develop a generalized model that takes surface effects into account. A reduced value of $\Theta_{\rm sH}$ at the surface is then found to describe the first-principles transport results extremely well. The in-plane spin Hall effect is substantially enhanced at the surface.

Spin transport at finite temperatures: A first-principles study for ferromagnetic|nonmagnetic interfaces

Symmetry lowering at an interface leads to an enhancement of the effect of spin-orbit coupling and to a discontinuity of spin currents passing through the interface. This discontinuity is characterized by a "spin-memory loss" (SML) parameter $\delta$ that has only been determined directly at low temperatures. Although $\delta$ is believed to be significant in experiments involving interfaces between ferromagnetic and nonmagnetic metals, especially heavy metals like Pt, it is more often than not neglected to avoid introducing too many unknown interface parameters in addition to often poorly known bulk parameters like the spin-flip diffusion length $l_{\rm sf}$. In this work, we calculate $\delta$ along with the interface resistance $AR_{\rm I}$ and the spin-asymmetry parameter $\gamma$ as a function of temperature for Co$|$Pt and Py$|$Pt interfaces where Py is the ferromagnetic Ni$_{80}$Fe$_{20}$ alloy, permalloy. We use first-principles scattering theory to calculate the conductance as well as local charge and spin currents, modeling temperature-induced disorder with frozen thermal lattice and, for ferromagnetic materials, spin disorder within the adiabatic approximation. The bulk and interface parameters are extracted from the spin currents using a Valet-Fert model generalized to include SML.

High-efficiency Raman conversion in SF6- and CF4-filled hollow-core photonic bandgap fibers.

We present a comparative experimental investigation of vibrational stimulated Raman scattering in hollow-core photonic bandgap fibers pressurized with sulfur hexafluoride (${{\rm SF}_6}$SF6) and tetrafluoromethane (${{\rm CF}_4}$CF4) gases. Nanosecond-duration pulses at a wavelength of 1030 nm are coupled into the gas-filled fiber, and the first and second Stokes orders are measured at the fiber output. We characterize the conversion process as a function of gas, fiber length, and input power. With a 15 m fiber filled with ${{\rm SF}_6}$SF6, we obtain conversion efficiency to the first Stokes of 55.7% at an input peak power of 0.63 kW. In comparison, with ${{\rm CF}_4}$CF4, we obtained a higher conversion threshold and maximum conversion efficiency of 45.4%. To the best of our knowledge, this is the first reported conversion experiment with hollow-core fibers filled with ${{\rm SF}_6}$SF6 gas.

High magnetic field phase diagram and failure of the magnetic Grüneisen scaling in LiFePO4

We report the magnetic phase diagram of single-crystalline LiFePO$_4$ in magnetic fields up to 58~T and present a detailed study of magneto-elastic coupling by means of high-resolution capacitance dilatometry. Large anomalies at \tn\ in the thermal expansion coefficient $\alpha$ imply pronounced magneto-elastic coupling. Quantitative analysis yields the magnetic Gr\"uneisen parameter $\gamma_{\rm mag}=6.7(5)\cdot 10^{-7}$~mol/J. The positive hydrostatic pressure dependence $dT_{\rm N}/dp = 1.46(11)$~K/GPa is dominated by uniaxial effects along the $a$-axis. Failure of Gr\"uneisen scaling below $\approx 40$~K, i.e., below the peak temperature in the magneto-electric coupling coefficient [\onlinecite{toft2015anomalous}], implies several competing degrees of freedom and indicates relevance of recently observed hybrid excitations~[\onlinecite{yiu2017hybrid}]. A broad and strongly magnetic-field-dependent anomaly in $\alpha$ in this temperature regime highlight the relevance of structure changes. Upon application of magnetic fields $B||b$-axis, a pronounced jump in the magnetisation implies spin-reorientation at $B_{\rm SF} = 32$~T as well as a precursing phase at 29~T and $T=1.5$~K. In a two-sublattice mean-field model, the saturation field $B_{\rm sat,b} = 64(2)$~T enables the determination of the effective antiferromagnetic exchange interaction $J_{\rm af} = 2.68(5)$~meV as well as the anisotropies $D_{\rm b} = -0.53(4)$~meV and $D_{\rm c} = 0.44(8)$~meV.

Launching of hot gas outflow by disc-wide supernova explosions

Galactic gas outflows are driven by stellar feedback with dominant contribution from supernovae (SN) explosions. The question of whether the energy deposited by SNe initiates a large scale outflow or gas circulation on smaller scales -- between discs and intermediate haloes, depends on SN rate and their distribution in space and time. We consider here gas circulation by disc-wide unclustered SNe with galactic star formation rate in the range from {$\simeq 6\times 10^{-4}$ to $\simeq 6\times 10^{-2}~M_\odot$~yr$^{-1}$~kpc$^{-2}$, corresponding to mid-to-high star formation observed in galaxies. We show that such disc-wide SN explosion regime can form circulation of warm ($T\sim 10^4$ K) and cold ($T<10^3$ K) phases within a few gas scale heights, and elevation of hot {($T>10^5$ K)} gas at higher ($z>1$ kpc) heights. We found that the threshold energy input rate for hot gas outflows with disc-wide supernovae explosions is estimated to be of the order $\sim 4\times 10^{-4}$~erg~s$^{-1}$~cm$^{-2}$. We discuss the observational manifestations of such phenomena in optical and X-ray bands. In particular, we found that for face-on galaxies with SF ($\Sigma_{_{\rm SF}}>0.02~M_\odot$~yr$^{-1}$~kpc$^{-2}$), the line profiles of ions typical for warm gas show a double-peak shape, corresponding to out-of-plane outflows. In the X-ray bands, galaxies with high SF rates ($\Sigma_{_{\rm SF}}>0.006~M_\odot$~yr$^{-1}$~kpc$^{-2}$) can be bright, with a smooth surface brightness in low-energy bands ($0.1\hbox{--}0.3$~keV) and patchy at higher energies ($1.6\hbox{--}8.3$~keV).}

Calculating spin transport properties from first principles: Spin currents

Local charge and spin currents are evaluated from the solutions of fully relativistic quantum mechanical scattering calculations for systems that include temperature-induced lattice and spin disorder as well as intrinsic alloy disorder. This makes it possible to determine material-specific spin transport parameters at finite temperatures. Illustrations are given for a number of important materials and parameters at 300 K. The spin-flip diffusion length $l_{\rm sf}$ of Pt is determined from the exponential decay of a spin current injected into a long length of thermally disordered Pt; we find $l_{\rm sf}^{\rm Pt}= 5.3\pm0.4 \,$nm. For the ferromagnetic substitutional disordered alloy Permalloy (Py), we inject currents that are fully polarized parallel and antiparallel to the magnetization and calculate $l_{\rm sf}$ from the exponential decay of their difference; we find $l_{\rm sf}^{\rm Py}= 2.8 \pm 0.1 \,$nm. The transport polarization $\beta$ is found from the asymptotic polarization of a charge current in a long length of Py to be $\beta = 0.75 \pm 0.01$. The spin Hall angle $\Theta_{\rm sH}$ is determined from the transverse spin current induced by the passage of a longitudinal charge current in thermally disordered Pt; our best estimate is $\Theta_{\rm sH}^{\rm Pt}=4.5 \pm 1 \%$ corresponding to the experimental room temperature bulk resistivity $\rho =10.8 \mu \Omega \,$cm.

Study of the ecological gas for MRPCs

The Multigap Resistive Plate Chamber (MRPC) is a gaseous detector; the performance depends very much on the gas mixture as well as the design. MRPCs are used as a timing device in several collider experiments and cosmic ray experiments thanks to the excellent timing performance. The typical gas mixtures of RPC-type detectors at current experiments are based on the gases $\rm C_2F_4H_2$ and $\rm SF_6$. These gases have very high Global Warming Potential (GWP) values of 1430 and 23900 respectively. The present contribution has been performed as a part of efforts to reduce the amount of greenhouse gases used in high energy experiments. The performance of MRPC has been measured with two different gas mixtures; $\rm C_2F_4H_2$ based gas mixtures and the ecological $\rm C_3F_4H_2$ (HFO-1234ze). A small MRPC was used for the tests. It has an sensitive area of 20 $\times$ 20 $\rm cm^2$; it was been built with 6 gaps of 220 $\mu$m. In normal operation, the strong space charge created within the gas avalanche limits the avalanche's growth. $\rm SF_6$ plays an important part in the process due to its high attachment coefficient at low electric fields. It is thus necessary to find another gas that has a similar attachment coefficient. $\rm CF_{3}I$ is a possible candidate. Tests were performed with this gas added to $\rm C_3F_4H_2$.

Induced energy gap in finite-sized superconductor/ferromagnet hybrids

We theoretically study self-consistent proximity effects in finite-sized systems consisting of ferromagnet ($\rm F$) layers coupled to an $s$-wave superconductor ($\rm S$). We consider both $\rm SF_1F_2$ and $\rm SH$ nanostructures, where the $\rm F_1 F_2$ bilayers are uniformly magnetized, and the ferromagnetic $\rm H$ layer possesses a helical magnetization profile. We find that when the $\rm F_1 F_2$ layers are weakly ferromagnetic, a hard gap can emerge when the relative magnetization directions are rotated from parallel to antiparallel. Moreover, the gap is most prominent when the thicknesses of $\rm F_1$ and $\rm F_2$ satisfy $\rm d_{F1}\leq d_{F2}$, respectively. For the $\rm SH$ configuration, increasing the spatial rotation period of the exchange field can enhance the induced hard gap. Our investigations reveal that the origin of these findings can be correlated with the propagation of quasiparticles with wavevectors directed along the interface. To further clarify the source of the induced energy gap, we also examine the spatial and energy resolved density of states, as well as the spin-singlet, and spin-triplet superconducting correlations, using experimentally accessible parameter values. Our findings can be beneficial for designing magnetic hybrid structures where a tunable superconducting hard gap is needed.

Active galactic nuclei vs. host galaxy properties in the COSMOS field

The coeval AGN and galaxy evolution and the observed local relations between SMBHs and galaxy properties suggest some connection or feedback between SMBH growth and galaxy build-up. We looked for correlations between properties of X-ray detected AGN and their FIR detected host galaxies, to find quantitative evidences for this connection, highly debated in the latest years. We exploit the rich multi-wavelength data set available in the COSMOS field for a large sample (692 sources) of AGN and their hosts, in the redshift range $0.1<z<4$. We use X-ray data to select AGN and determine their properties (intrinsic luminosity and nuclear obscuration), and broad-band SED fitting to derive host galaxy properties (stellar mass $M_*$ and star formation rate SFR). We find that the AGN 2-10 keV luminosity ($L_{\rm X}$) and the host $8-1000~\mu m$ star formation luminosity ($L_{\rm IR}^{\rm SF}$) are significantly correlated. However, the average host $L_{\rm IR}^{\rm SF}$ has a flat distribution in bins of AGN $L_{\rm X}$, while the average AGN $L_{\rm X}$ increases in bins of host $L_{\rm IR}^{\rm SF}$, with logarithmic slope of $\sim0.7$, in the redshifts range $0.4<z<1.2$. We also discuss the comparison between the distribution of these two quantities and the predictions from hydro-dynamical simulations. Finally we find that the average column density ($N_H$) shows a positive correlation with the host $M_*$, at all redshifts, but not with the SFR (or $L_{\rm IR}^{\rm SF}$). This translates into a negative correlation with specific SFR. Our results are in agreement with the idea that BH accretion and SF rates are correlated, but occur with different variability time scales. The presence of a positive correlation between $N_H$ and host $M_*$ suggests that the X-ray $N_H$ is not entirely due to the circum-nuclear obscuring torus, but may also include a contribution from the host galaxy.

The ALHAMBRA survey:B-band luminosity function of quiescent and star-forming galaxies at 0.2 ≤ z &lt; 1 by PDF analysis

Our goal is to study the evolution of the $B-$band luminosity function (LF) since $z=1$ using ALHAMBRA data. We used the photometric redshift and the $I-$band selection magnitude probability distribution functions (PDFs) of those ALHAMBRA galaxies with $I\leq24$ mag to compute the posterior LF. We statistically studied quiescent and star-forming galaxies using the template information encoded in the PDFs. The LF covariance matrix in redshift-magnitude-galaxy type space was computed, including the cosmic variance. That was estimated from the intrinsic dispersion of the LF measurements in the 48 ALHAMBRA sub-fields. The uncertainty due to the photometric redshift prior is also included in our analysis. We modelled the LF with a redshift-dependent Schechter function affected by the same selection effects than the data. The measured ALHAMBRA LF at $0.2\leq z<1$ and the evolving Schechter parameters both for quiescent and star-forming galaxies agree with previous results in the literature. The estimated redshift evolution of $M_B^* \propto Qz$ is $Q_{\rm SF}=-1.03\pm0.08$ and $Q_{\rm Q}=-0.80\pm0.08$, and of $\log \phi^* \propto Pz$ is $P_{\rm SF}=-0.01\pm0.03$ and $P_{\rm Q}=-0.41\pm0.05$. The measured faint-end slopes are $\alpha_{\rm SF}=-1.29\pm0.02$ and $\alpha_{\rm Q}=-0.53\pm0.04$. We find a significant population of faint quiescent galaxies, modelled by a second Schechter function with slope $\beta=-1.31\pm0.11$. We find a factor $2.55\pm0.14$ decrease in the luminosity density $j_B$ of star-forming galaxies, and a factor $1.25\pm0.16$ increase in the $j_B$ of quiescent ones since $z=1$, confirming the continuous build-up of the quiescent population with cosmic time. The contribution of the faint quiescent population to $j_B$ increases from 3% at $z=1$ to 6% at $z=0$. The developed methodology will be applied to future multi-filter surveys such as J-PAS.

Development and Type Test of a Single-Break 126-kV/40-kA–2500-A Vacuum Circuit Breaker

The objective of this paper is to present a 126-kV/40-kA–2500-A single-break vacuum circuit breaker (VCB) and its type test results based on the IEC 62271-100: 2006 and GB1984-2003 standards. A single-break 126-kV vacuum interrupter (VI), with a pair of 2/3 coil-type contacts, is used in the 126-kV VCB. The external insulation of the VI is provided by ${\rm SF}_{6}$ at 0.1 MPa. A spring-type operating mechanism is used to provide a closing velocity of 1.15 m/s, which is an average velocity for 4 mm before the moving contact mates with the stationary contact. The opening velocity within 20 mm, which is 1/3 of a full contact stroke of 60 mm, is 3.5 m/s. Two kinds of test circuits are used in the type tests to verify the making and breaking capabilities of this 126-kV VCB prototype. One is a direct test circuit for test duty cycles, such as out-of-phase making and breaking test duties, that is, OP1 and OP2; capacitive current switching test of class C1, that is, CC1/LC1 and CC2/LC2. The other is a synthetic circuit, used for tests, such as the terminal fault test, the short-line fault test, the double earth fault test, and the electrical endurance test of class E2. The dielectric tests of a 230-kV/1 min power frequency voltage withstand test and a 550-kV lightning impulse voltage withstand test were used to verify the dielectric withstand performance of the VCB. Experiment results presented in this paper showed that the 126-kV/40 kA–2500 A single-break VCB passed the type tests according to IEC 62271-100 and GB1984-2003.

Quantum electrodynamical corrections to a magnetic dipole in general relativity

Magnetized neutron stars are privileged places where strong electromagnetic fields as high as $\BQ=4.4\times10^9$~T exist, giving rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). These corrections need to be included to the general relativistic (GR) description of a magnetic dipole supposed to be anchored in the neutron star. In this paper, these QED and GR perturbations to the standard flat space-time dipole are calculated to the lowest order in the fine structure constant~$\alpha_{\rm sf}$ and to any order in the ratio $\Rs/R$ where $R$ is the neutron star radius and $\Rs$ its Schwarzschild radius. Following our new 3+1~formalism developed in a previous work, we compute the multipolar non-linear corrections to this dipole and demonstrate the presence of a small dipolar~$\ell=1$ and hexapolar~$\ell=3$ component.

A CONNECTION BETWEEN OBSCURATION AND STAR FORMATION IN LUMINOUS QUASARS

We present a measurement of the star formation properties of a uniform sample of mid-IR selected, unobscured and obscured quasars (QSO1s and QSO2s) in the Bo\"otes survey region. We use an spectral energy distribution (SED) analysis for photometric data spanning optical to far-IR wavelengths to decompose AGN and host galaxy components. We find that when compared to a matched sample of QSO1s, the QSO2s have higher far-IR detection fractions, far-IR fluxes and infrared star formation luminosities ($L_{\rm IR}^{\rm SF}$) by a factor of $\sim2$. Correspondingly, we show that the AGN obscured fraction rises from 0.3 to 0.7 between $4-40\times10^{11}L_\odot$. We also find evidence associating the absorption in the X-ray emission with the presence of far-IR emitting dust. Overall, these results are consistent with galaxy evolution models in which quasar obscurations can be associated with a dust-enshrouded starburst galaxies.

EARLY SCIENCE WITH THE LARGE MILLIMETER TELESCOPE: EXPLORING THE EFFECT OF AGN ACTIVITY ON THE RELATIONSHIPS BETWEEN MOLECULAR GAS, DUST, AND STAR FORMATION

The molecular gas, H$_2$, that fuels star formation in galaxies is difficult to observe directly. As such, the ratio of $L_{\rm IR}$ to $L^\prime_{\rm CO}$ is an observational estimation of the star formation rate compared with the amount of molecular gas available to form stars, which is related to the star formation efficiency and the inverse of the gas consumption timescale. We test what effect an IR luminous AGN has on the ratio $L_{\rm IR}/L^\prime_{\rm CO}$ in a sample of 24 intermediate redshift galaxies from the 5 mJy Unbiased Spitzer Extragalactic Survey (5MUSES). We obtain new CO(1-0) observations with the Redshift Search Receiver on the Large Millimeter Telescope. We diagnose the presence and strength of an AGN using Spitzer IRS spectroscopy. We find that removing the AGN contribution to $L_{\rm IR}^{\rm tot}$ results in a mean $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$ for our entire sample consistent with the mean $L_{\rm IR}/L^\prime_{\rm CO}$ derived for a large sample of star forming galaxies from $z\sim0-3$. We also include in our comparison the relative amount of polycyclic aromatic hydrocarbon emission for our sample and a literature sample of local and high redshift Ultra Luminous Infrared Galaxies and find a consistent trend between $L_{6.2}/L_{\rm IR}^{\rm SF}$ and $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$, such that small dust grain emission decreases with increasing $L_{\rm IR}^{\rm SF}/L^\prime_{\rm CO}$ for both local and high redshift dusty galaxies.

Multiplex Real-Time PCR to Diagnose Rickettsial Disease from Skin Biopsies

In the U.S., the diseases most often caused by spotted-fever group Rickettsia (SFGR) species are Rocky Mountain spotted fever (RMSF; Rickettsia

Low-temperature properties of single-crystalCrB2

We report the low-temperature properties of $^{11}$B-enriched single-crystal CrB$_{2}$ as prepared from high-purity Cr and B powder by a solid-state reaction and optical float zoning. The electrical resistivity, $\rho_{\rm xx}$, Hall effect, $\rho_{\rm xy}$, and specific heat, $C$, are characteristic of an exchange-enhanced Fermi liquid ground state, which develops a slightly anisotropic spin gap $\Delta \approx 220\,{\rm K}$ below $T_{\rm N}=88\,{\rm K}$. This observation is corroborated by the absence of a Curie dependence in the magnetization for $T\to0$ reported in the literature. Comparison of $C$ with $d\rho_{\rm xx}/dT$, where we infer lattice contributions from measurements of VB$_2$, reveals strong antiferromagnetic spin fluctuations with a characteristic spin fluctuation temperature $T_{\rm sf}\approx 257\,{\rm K}$ in the paramagnetic state, followed by a pronounced second-order mean-field transition at $T_{\rm N}$, and unusual excitations around $\approx T_{\rm N}/2$. The pronounced anisotropy of $\rho_{\rm xx}$ above $T_{\rm N}$ is characteristic of an easy-plane anisotropy of the spin fluctuations consistent with the magnetization. The ratio of the Curie-Weiss to the N$\acute{\rm{e}}$el temperatures, $f=-\Theta_{\rm CW}/T_{\rm N}\approx 8.5$, inferred from the magnetization, implies strong geometric frustration. All physical properties are remarkably invariant under applied magnetic fields up to $14\,\,{\rm T}$, the highest field studied. In contrast to earlier suggestions of local-moment magnetism our study identifies CrB$_{2}$ as a weak itinerant antiferromagnet par excellence with strong geometric frustration.

Modelization of Superferromagnetism in Soft Nanocrystalline Materials Based on an Accurate Description of Magnetostatic Interactions

At high temperature, Fe-Si nanograins obtained by partial crystallization of amorphous Fe-Si-Cu-Nb-B precursor are superparamagnetic, due to the disappearance of the magnetism of the residual amorphous matrix. At a transition temperature T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> above the amorphous Curie temperature, a spontaneous polarization J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sf</sup> appears, despite a much lower blocking temperature. Dipolar interactions, or a residual ferromagnetic coupling between grains, have been invoked to explain this effect. We investigate here the dipolar hypothesis. The Lorentz field (L.f.) model is improved the idea being that the field acting on a nanograin is screened by a surrounding soft shell. The attenuation factor is calculated, leading to a decrease of T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> compared with the L.f. approximation. Moreover, a description of the spontaneous magnetization curve J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sf</sup> (T)/J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> (T) is obtained, with a slope near T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> much sharper than predicted by the (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> - T) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> law associated to an invariant molecular field factor. Comparison with the experiments shows good agreement.

Spin Pumping and Inverse Spin Hall Effect in Platinum: The Essential Role of Spin-Memory Loss at Metallic Interfaces

Through combined ferromagnetic resonance, spin pumping, and inverse spin Hall effect experiments in Co|Pt bilayers and Co|Cu|Pt trilayers, we demonstrate consistent values of ℓsfPt=3.4±0.4 nm and θSHEPt=0.056±0.010 for the respective spin diffusion length and spin Hall angle for Pt. Our data and model emphasize the partial depolarization of the spin current at each interface due to spin-memory loss. Our model reconciles the previously published spin Hall angle values and explains the different scaling lengths for the ferromagnetic damping and the spin Hall effect induced voltage.

Cosmological tests using gamma-ray bursts, the star formation rate and possible abundance evolution

The principal goal of this paper is to use attempts at reconciling the Swift long gamma-ray bursts (LGRBs) with the star formation history (SFH) to compare the predictions of $\Lambda$CDM with those in the $R_{\rm h}=ct$ Universe. In the context of the former, we confirm that the latest Swift sample of GRBs reveals an increasing evolution in the GRB rate relative to the star formation rate (SFR) at high redshifts. The observed discrepancy between the GRB rate and the SFR may be eliminated by assuming a modest evolution parameterized as $(1+z)^{0.8}$---perhaps indicating a cosmic evolution in metallicity. However, we find a higher metallicity cut of $Z=0.52Z_{\odot}$ than was seen in previous studies, which suggested that LGRBs occur preferentially in metal poor environments, i.e., $Z\sim0.1-0.3Z_{\odot}$. We use a simple power-law approximation to the high-\emph{z} ($\ga 3.8$) SFH, i.e., $R_{\rm SF}\propto[(1+z)/4.8]^{\alpha}$, to examine how the high-\emph{z} SFR may be impacted by a possible abundance evolution in the Swift GRB sample. For an expansion history consistent with $\Lambda$CDM, we find that the Swift redshift and luminosity distributions can be reproduced with reasonable accuracy if $\alpha=-2.41_{-2.09}^{+1.87}$. For the $R_{\rm h}=ct$ Universe, the GRB rate is slightly different from that in $\Lambda$CDM, but also requires an extra evolutionary effect, with a metallicity cut of $Z=0.44Z_{\odot}$. Assuming that the SFR and GRB rate are related via an evolving metallicity, we find that the GRB data constrain the slope of the high-\emph{z} SFR in $R_{\rm h}=ct$ to be $\alpha=-3.60_{-2.45}^{+2.45}$. Both cosmologies fit the GRB/SFR data rather well.

Main Scenarios of Spatial Distribution of Charged and Neutral Components in ${\rm SF}_{6}$ Plasma

Numerical modeling and theoretical analyses of spatial distribution with detailed set of plasmachemical processes in elegas have been made for a wide range of pressures. Evolution of main charged and neutral particles in time and space has been obtained. It is shown that at low pressures, the Boltzmann distribution holds for both electrons and negative ions and separation of the plasma into two regions with an almost flat profile of the electron density. At high pressures, electronegativity of plasma is extremely high and the self-consistent electric field is determined not only by the electrons, as in the conventional plasma, but also by the ions of both signs. This leads to an abnormally small potential drop in the plasma and nonmonotonic ion profiles.