Simple Power-law Model Research Articles

New EMTP-RV Equivalent Circuit Model of Core-Shielding Superconducting Fault Current Limiter Taking Into Account the Flux Diffusion Phenomenon

In order to successfully integrate superconducting fault current limiters (SFCL) into electric power system networks, accurate and fast simulation models are needed. This led us to develop a generic electric circuit model of an inductive SFCL, which we implemented in the EMTP-RV software. The selected SFCL is of shielded-core type, i.e. a HTS hollow cylinder surrounds the central leg of a magnetic core, and is located inside a primary copper winding, generating an AC magnetic field proportional to the line current. The model accounts for the highly nonlinear flux diffusion phenomenon across the superconducting cylinder, governed by the Maxwell equations and the non-linear E-J relationship of HTS materials. The computational efficiency and simplicity of this model resides in a judicious 1-D approximation of the geometry, together with the use of an equivalent electric circuit that reproduces accurately the actual magnetic behavior for the flux density (B) inside the walls of the HTS cylinder. The HTS properties are not restricted to the simple power law model, but instead, any resistivity function depending on J, B and T can be used and inserted directly in the model through a non-linear resistance appearing in the equivalent circuit.

ChandraandXMM-Newtonobservations of the low-luminosity X-ray pulsators SAX J1324.4−6200 and SAX J1452.8−5949

We present results from our Chandra and XMM–Newton observations of two low-luminosity X-ray pulsators SAX J1324.4−6200 and SAX J1452.8−5949 which have spin periods of 172 and 437 s, respectively. The XMM–Newton spectra for both sources can be fitted well with a simple power-law model of photon index, Γ∼ 1.0. A blackbody model can equally well fit the spectra with a temperature, kT∼ 2 keV, for both sources. During our XMM–Newton observations, SAX J1324.4−6200 is detected with coherent X-ray pulsations at a period of 172.86 ± 0.02 s while no pulsations with a pulse fraction greater than 18 per cent (at 95 per cent confidence level) in 0.2–12 keV energy band are detected in SAX J1452.8−5949. The spin period of SAX J1324.4−6200 is found to be increasing on a time-scale of which would suggest that the accretor is a neutron star and not a white dwarf. Using subarcsec spatial resolution of the Chandra telescope, possible counterparts are seen for both sources in the near-infrared images obtained with the son of infrared spectrometer and array camera (SOFI) instrument on the New Technology Telescope. The X-ray and near-infrared properties of SAX J1324.4−6200 suggest it to be a persistent high-mass accreting X-ray pulsar at a distance ≤8 kpc. We identify the near-infrared counterpart of SAX J1452.8−5949 to be a late-type main-sequence star at a distance ≤10 kpc, thus ruling out SAX J1452.8−5949 to be a high-mass X-ray binary. However, with the present X-ray and near-infrared observations, we cannot make any further conclusive conclusion about the nature of SAX J1452.8−5949.

Nano-indentation in FCC metals: experimental study

This paper presents the results of an experimental study for nano-indentation size effects for different face centered cubic metals with different purities. The selected materials are: Silver, Copper, Aluminum, Lead, and Nickel. Nano-indentation tests are run using a Berkovich indenter with continuous stiffness measurement procedure where hardness is measured continuously with indentation depth. The results show three distinctive regions for the indentation size effects for the material, where hardness could increase or decrease with increasing indentation. This behavior is modeled through a proposed simple power law model, which includes the effect of grain boundaries.

EpeakESTIMATOR FOR GAMMA-RAY BURSTS OBSERVED BY THESWIFTBURST ALERT TELESCOPE

We report a correlation based on a spectral simulation study of the prompt emission spectra of gamma-ray bursts (GRBs) detected by the Swift Burst Alert Telescope (BAT). The correlation is between the Epeak energy, which is the peak energy in the \nu F_\nu spectrum, and the photon index (\Gamma) derived from a simple power-law model. The Epeak - \Gamma relation, assuming the typical smoothly broken power-law spectrum of GRBs, is \log Epeak = 3.258 - 0.829\Gamma (1.3 < \Gamma < 2.3). We take into account not only a range of Epeak energies and fluences, but also distributions for both the low-energy photon index and the high-energy photon index in the smoothly broken power-law model. The distribution of burst durations in the BAT GRB sample is also included in the simulation. Our correlation is consistent with the index observed by BAT and Epeak measured by the BAT, and by other GRB instruments. Since about 85% of GRBs observed by the BAT are acceptably fit with the simple power-law model because of the relatively narrow energy range of the BAT, this relationship can be used to estimate Epeak when it is located within the BAT energy range.

Progress and challenges in numerically modelling solid sports balls with application to softballs

Much of the work surrounding finite element simulation of bat–ball impacts has focused on techniques describing the ball. Determining the accuracy of these models has been hindered by challenges in experimentally characterizing the ball's response. In the following, dynamic mechanical analysis and an instrumented impact test were used to characterize the solid ball at deformation rates representative of play. The ball was described in the numerical model as a linear viscoelastic material. It was observed that a Prony series model based on small deformation dynamic mechanical analysis did not provide sufficient energy loss upon impact, while a simpler Power Law model, fitted to large deformation data, described the measured energy loss and impact force over a range of speeds. Results of a parametric study are presented as a guide towards tailoring the parameters of the Power Law model to match the measured energy loss and impact force. Discrepancies observed between the experiment and the numerical model suggest that the ball response should be characterized in environments closely resembling game conditions.

Role of Cytoskeletal Components in Stress-Relaxation Behavior of Adherent Vascular Smooth Muscle Cells

A number of recent studies have demonstrated the effectiveness of atomic force microscopy (AFM) for characterization of cellular stress-relaxation behavior. However, this technique's recent development creates considerable need for exploration of appropriate mechanical models for analysis of the resultant data and of the roles of various cytoskeletal components responsible for governing stress-relaxation behavior. The viscoelastic properties of vascular smooth muscle cells (VSMCs) are of particular interest due to their role in the development of vascular diseases, including atherosclerosis and restenosis. Various cytoskeletal agents, including cytochalasin D, jasplakinolide, paclitaxel, and nocodazole, were used to alter the cytoskeletal architecture of the VSMCs. Stress-relaxation experiments were performed on the VSMCs using AFM. The quasilinear viscoelastic (QLV) reduced-relaxation function, as well as a simple power-law model, and the standard linear solid (SLS) model, were fitted to the resultant stress-relaxation data. Actin depolymerization via cytochalasin D resulted in significant increases in both rate of relaxation and percentage of relaxation; actin stabilization via jasplakinolide did not affect stress-relaxation behavior. Microtubule depolymerization via nocodazole resulted in nonsignificant increases in rate and percentage of relaxation, while microtubule stabilization via paclitaxel caused significant decreases in both rate and percentage of relaxation. Both the QLV reduced-relaxation function and the power-law model provided excellent fits to the data (R(2)=0.98), while the SLS model was less adequate (R(2)=0.91). Data from the current study indicate the important role of not only actin, but also microtubules, in governing VSMC viscoelastic behavior. Excellent fits to the data show potential for future use of both the QLV reduced-relaxation function and power-law models in conjunction with AFM stress-relaxation experiments.

A correlation between the spectral and timing properties of AGN

We present the results from a combined study of the average X-ray spectral and timing properties of 14 nearby AGN. For 11 of the sources in the sample, we used all the available data from the RXTE archive, which were taken until the end of 2006. There are 7795 RXTE observations in total for these AGN, obtained over a period of ~7-11 years. We extracted their 3-20 keV spectra and fitted them with a simple power-law model, modified by the presence of a Gaussian line (at 6.4 keV) and cold absorption, when necessary. We used these best-fit slopes to estimate the mean spectral slope for each object, while we used results from the literature to estimate the average spectral slope of the three objects without archival, monitorin RXTE data. Our results show that the AGN average spectral slopes are not correlated either with the black hole mass or the characteristic frequencies that were detected in the power spectra.They are positively correlated, though, with the characteristic frequency when normalised to the sources black hole mass. This is similar to the spectral-timing correlation that has been observed in Cyg X-1, but not the same.The AGN spectral-timing correlation can be explained if we assume that the accretion rate determines both the average spectral slope and the characteristic time scales in AGN. The spectrum should steepen and the characteristic frequency should increase, proportionally, with increasing accretion rate. We also provide a quantitative expression between spectral slope and accretion rate. Thermal Comptonisation models are broadly consistent with our result, but only if the ratio of the soft photons' luminosity to the power injected to the hot corona is proportionally related to the accretion rate.

X-RAY SPECTRAL PROPERTIES OF THE BAT AGN SAMPLE

The 9-month Swift Burst Alert Telescope (BAT) catalog provides the first unbiased (log N_H < 24) look at local (<z> = 0.03) AGN. In this paper, we present the collected X-ray properties (0.3 - 12keV) for the 153 AGN detected. In addition, we examine the X-ray properties for a complete sample of non-beamed sources, above the Galactic plane. Of these, 45% are best fit by simple power law models while 55% require the more complex partial covering model. One of our goals was to determine the fraction of "hidden" AGN, which we define as sources with scattering fractions < 0.03 and ratios of soft to hard X-ray flux < 0.04. We found that "hidden" AGN constitute a high percentage of the sample (24%), proving that they are a very significant portion of local AGN. Further, we find that the fraction of absorbed sources does increase at lower unabsorbed 2-10 keV luminosities, as well as accretion rates. Some of the most interesting results for the BAT AGN sample involve the host galaxy properties. We found that 33% are hosted in peculiar/irregular galaxies and only 5/74 hosted in ellipticals. Further, 54% are hosted in interacting/merger galaxies. Finally, we present both the average X-ray spectrum (0.1-10 keV) and log N-log S in the 2-10 keV band. With our average spectrum, we have the remarkable result of reproducing the measured CXB X-ray power law slope of ~ 1.4 (Marshall et al. 1980). From the log N-log S relationship, we show that we are complete to log S < -11 in the 2-10 keV band. Both the collected X-ray properties of our uniform sample and the log N-log S relationship will now provide valuable input to X-ray background models for z ~ 0. (abridged)

Probing the 3.6 μm CIRB withSpitzerin Three DIRBE Dark Spots

We observed three regions of the sky with Spitzer in which the cosmic infrared background (CIRB) has been determined at 3.5 μm using the method of subtracting 2MASS stellar fluxes from zodiacal light-subtracted maps. For each of these regions we have obtained 270 s of integration time per pixel with IRAC on Spitzer over the central square degree. We present galaxy counts in each of these approximately 1 deg2 IRAC surveys. Along with deep galaxy counts in the extended Groth strip and GOODS North, we are able to compare the galactic contribution to the CIRB with the DIRBE minus 2MASS-determined L-band CIRB. Using the profile-fit photometry package GIM2D, we find a substantially larger flux contribution to the CIRB than that determined using aperture photometry. We have also made the first rigorous analysis of the uncertainties in determining the CIRB via galaxy counts in Spitzer images using a Monte Carlo Markov chain simulation of our data analysis. Using a simple broken power law model for galaxy counts as a function of magnitude we find a most probable contribution to the CIRB from galaxies at 3.6 μm of 10.8+2.1−1.1 kJy sr−1 (9.0+1.7−0.9 nW m−2 sr−1). Even with this restricted model, however, we find that galaxy counting does not strongly constrain the CIRB from above. We are able to find solutions in which the CIRB runs away to large intensities without the need for an additional diffuse source.

Dependence of nucleation rates on sulfuric acid vapor concentration in diverse atmospheric locations

Correlations between concentrations of newly formed particles and sulfuric acid vapor were analyzed for twenty one nucleation events measured in diverse continental and marine atmospheric environments. A simple power law model for formation rates of 1 nm particles, J1 = K · [H2SO4]P, where P and K are least squares parameters, was tested for each environment. We found that, to within experimental uncertainty, P = 2. Constraining P to 2, the prefactor Kkinetic ranges from 10−14 to 10−11 cm3s−1. According to the nucleation theorem, an exponent value of 2 indicates that the critical cluster contains two sulfuric acid molecules. Existing nucleation rate expressions based on classical nucleation theory predict significantly larger values of P. The prefactor values vary with environment and are 1 to 4 orders of magnitude below the hard‐sphere collision limit. These results provide a simple parameterization for atmospheric new particle formation that could be used in global climate models.

Quasi-Dynamic Visualization of Crack Propagation and Wake Evolution in Y-TZP Ceramic by Mechano-Luminescence

The propagation of a macro-scale crack was visualized in yittria-tettragonal zirconia polycrystal (Y-TZP) ceramics using a mechano-luminescence (ML) of SrAl2O4:Eu, Dy. The transformation zone around the crack was also clearly detected in both the crack front and side areas of the Y-TZP in a realistic time frame. The ML made it possible to precisely detect a relatively fast crack propagating in the speed range from 20 m/s to 140 m/s, thereby realizing so-called quasi-dynamic R-curve. Effective toughening then commenced and the applied stress intensity factor increased to 20 MPa \(\sqrt m \). The ho values obtained from the ML observation deviated slightly from those predicted by the Evans-McMeeking model, and support Marshall's simple power law model of quasi-static crack propagation.

The FirstSwiftBAT Gamma‐Ray Burst Catalog

We present the first Swift Burst Alert Telescope (BAT) catalog of gamma ray bursts (GRBs), which contains bursts detected by the BAT between 2004 December 19 and 2007 June 16. This catalog (hereafter BAT1 catalog) contains burst trigger time, location, 90% error radius, duration, fluence, peak flux, and time averaged spectral parameters for each of 237 GRBs, as measured by the BAT. The BAT-determined position reported here is within 1.75' of the Swift X-ray Telescope (XRT)-determined position for 90% of these GRBs. The BAT T(sub 90) and T(sub 50) durations peak at 80 and 20 seconds, respectively. From the fluence-fluence correlation, we conclude that about 60% of the observed peak energies, E(sup obs)(sub peak) of BAT GRBs could be less than 100 keV. We confirm that GRB fluence to hardness and GRB peak flux to hardness are correlated for BAT bursts in analogous ways to previous missions' results. The correlation between the photon index in a simple power-law model and E(sup obs)(sub peak) is also confirmed. We also report the current status for the on-orbit BAT calibrations based on observations of the Crab Nebula.

The Very Soft X‐Ray Spectrum of the Double Pulsar System J0737−3039

We present the results of an 80 ks Chandra ACIS-S observation of the double pulsar system J0737-3039. Furthermore, we report on spectral, spatial and timing analysis of the combined X-ray observations performed so far for this system. Fitting a total of similar to 1100 photons, we show that the X-ray spectrum of the J0737 similar to 3039 system is very soft, and not satisfactorily modeled by a simple blackbody or an atmospheric model. However, it is not possible yet to discriminate between a predominantly nonthermal and a predominantly thermal origin for the X-ray emission. Adopting a simple power-law emission model, the photon index (Gamma = 3.7 +/- 0: 4; 90% confidence interval) and the implied conversion efficiency of the rotational energy of PSR J0737-3039A into X-ray emission ( 4: 1 +/- 0: 5; 10(-4), for a distance to the source of 500 pc) are compatible with the X-ray photons being emitted in the magnetosphere of PSR J0737-3039A. This hypothesis is also supported by the absence of detectable X-ray orbital modulation ( up to similar to 20%, 3 sigma) or any X-ray nebular emission and it is in agreement with the high (>= 75%) X-ray pulsed fraction of PSR J0737-3039A. A two blackbody or a Comptonized blackbody model also reproduce the data, and the upper limit to the value of the hydrogen column density, N-H less than or similar to 1; 10(20) cm(-2), is in better agreement ( with respect to the power- law model) with the Galactic NH in that direction and at that distance. For the two blackbody model the implied emission radii and temperatures are also compatible with those seen in other recycled pulsars, calling for the bulk of the X-ray photons being originated from heated regions at the surface of pulsar A. On the other hand, in the Comptonized blackbody model, the electron temperature seems to be significantly smaller than in other similar objects.

Suzaku Wide-Band Observations of SN 1006

Abstract We report on the wide-band spectra of SN1006, as observed by Suzaku. Thermal and nonthermal emissions were successfully resolved thanks to the excellent spectral response of Suzaku's X-ray CCD XIS. The nonthermal emission could not be reproduced by a simple power-law model, but needed a roll-off at 5.7$\times$10$^{16}$Hz $=$ 0.23keV. The roll-off frequency is significantly higher in the northeastern rim than in the southwestern rim. We also placed the most stringent upper limit of the flux above 10keV using the Hard X-ray Detector.

Validity of strong lensing statistics for constraints on the galaxy evolution model

We examine the usefulness of the strong lensing statistics to constrain the evolution of the number density of lensing galaxies by adopting the values of the cosmological parameters determined by recent Wilkinson Microwave Anisotropy Probe observation. For this purpose, we employ the lens-redshift test proposed by Kochanek and constrain the parameters in two evolution models, simple power-law model characterized by the power-law indexes νn and νv, and the evolution model by Mitchell et al. based on cold dark matter structure formation scenario. We use the well-defined lens sample from the Sloan Digital Sky Survey (SDSS) and this is similarly sized samples used in the previous studies. Furthermore, we adopt the velocity dispersion function of early-type galaxies based on SDSS DR1 and DR5. It turns out that the indexes of power-law model are consistent with the previous studies, thus our results indicate the mild evolution in the number and velocity dispersion of early-type galaxies out to z= 1. However, we found that the values for p and q used by Mitchell et al. are inconsistent with the presently available observational data. More complete sample is necessary to withdraw more realistic determination on these parameters.

Catalytic oxidation of butyl acetate over silver-loaded zeolites

The performance of silver-loaded zeolite (HY and HZSM-5) catalysts in the oxidation of butyl acetate as a model volatile organic compound (VOC) was studied. The objective was to find a catalyst with superior activity, selectivity towards deep oxidation product and stability. The catalyst activity was measured under excess oxygen condition in a packed bed reactor operated at gas hourly space velocity (GHSV) = 15,000–32,000 h −1, reaction temperature between 150 and 500 °C and butyl acetate inlet concentration of 1000–4000 ppm. Both AgY and AgZSM-5 catalysts exhibited high activity in the oxidation of butyl acetate. Despite lower silver content, AgY showed better activity, attributed to better metal dispersion, surface characteristics and acidity, and its pore system. Total conversion of butyl acetate was achieved at above 400 °C. The oxidation of butyl acetate followed a simple power law model. The reaction orders, n and m were evaluated under differential mode by varying the VOC partial pressure between 0.004 and 0.018 atm and partial pressure of oxygen between 0.05 and 0.20 atm. The reaction rate was independent of oxygen concentration and single order with respect to VOC concentration. The activation energies were 19.78 kJ/mol for AgY and 32.26 kJ/mol for AgZSM-5, respectively.

Can photo-ionisation explain the decreasing fraction of X-ray obscured AGN with luminosity?

Chandra and XMM-Newton surveys show that the fraction of obscured AGN decreases rapidly with increasing luminosity. Although this is usually explained by assuming that the covering factor of the central engine is much smaller at luminous QSOs, the exact origin of this effect remains unknown. We perform toy simulations to test whether photo-ionisation of the obscuring screen in the presence of a strong radiation field can reproduce this effect. In particular, we create X-ray spectral simulations using a warm absorber model assuming a range of input column densities and ionisation parameters. We fit instead the simulated spectra with a simple cold absorption power-law model that is the standard practice in X-ray surveys. We find that the fraction of absorbed AGN should fall with luminosity as L −0.16±0.03 in rough agreement with the observations. Furthermore, this apparent decrease in the obscuring material is consistent with the dependence of the FeKα narrow-line equivalent width on luminosity, i.e. the X-ray Baldwin effect.

When GRB afterglows get softer, hard components come into play

Aims. We aim to investigate the ability of simple spectral models to describe the GRB early afterglow emission. Methods. We performed a time resolved spectral analysis of a bright GRB sample detected by the Swift Burst Alert Telescope and promptly observed by the Swift X‐ray Telescope,with spectroscopically measured redshift in the period April 2005 ‐ January 2007. The sample consists of 22 GRBs and a total of 214 spectra. We restricted our analysis to the softest spectra sub‐sample whi ch consists of 13 spectra with photon index > 3. Results. In this sample we found that four spectra, belonging to GRB060502A, GRB060729, GRB060904B, GRB061110A prompt‐ afterglow transition phase, cannot be modeled neither by a single power law nor by the Band model. Instead we find that the d ata present high energy (> 3 keV, in the observer frame) excesses with respect to these models. We estimated the joint statistical significance of these excesses at the level of 4.3 �. In all four cases, the deviations can be modeled well by adding either a second power law or a blackbody component to the usual synchrotron power law spectrum. The additional power law would be explained by the emerging of the afterglow, while the blackbody could be interpreted as the photospheric emission from X‐ray flares or as t he shock breakout emission. In one case these models leave a 2.2� excess which can be fit by a Gaussian line at the energy the high ly ionized Nickel recombination. Conclusions. Although the data do not allow an unequivocal interpretation, the importance of this analysis consists in the fact that w e show that a simple power law model or a Band model are insuffi cient to describe the X-ray spectra of a small homogeneous sample of GRBs at the end of their prompt phase.

Blackbody components in gamma-ray bursts spectra?

We study 7 Gamma Ray Bursts (GRBs), detected both by the BATSE instrument, on-board the Compton Gamma Ray Observatory, and by the Wide Field Camera (WFC), on-board BeppoSAX. These bursts have measured spectroscopic redshifts and are a sizeable fraction of the bursts defining the correlation between the peak energy E_peak (i.e. the peak of the vFv spectrum) and the total prompt isotropic energy E_iso (the so called Amati relation). Recent theoretical interpretations of this correlation assume that black-body emission dominates the time resolved spectra of GRBs, even if, in the time integrated spectrum, its presence may be hidden by the change of its temperature and by the dilution of a possible non-thermal power law component. We perform a time resolved spectral analysis, and show that the sum of a power-law and a black-body gives acceptable fits to the time dependent spectra within the BATSE energy range, but overpredicts the flux in the WFC X-ray range. Moreover, a fit with a cutoff power-law plus a black-body is consistent with the WFC data, but the black-body component contributes a negligible fraction of the total flux. On the contrary, we find that fitting the spectra with a Band model or a simple cutoff power-law model yields an X-ray flux and spectral slope which well matches the WFC spectra.

Shape optimization of a MHD generator based on pressure drop and power output constraints

The optimum shape and axial variation of electrical loading (power ratio) of a MHD generator are obtained for a prescribed fractional power output and pressure drop along the generator. These optimum solutions are obtained using the ADS (Automatic Design Synthesis) optimization code. The objective function (duct size) for the prescribed design conditions was obtained by Carter for a quasi 1-D flow with a simple power law model for electrical conductivity. In this work, a generalized numerical optimization scheme, capable of incorporating any arbitrary electrical conductivity model is presented. The numerical solutions obtained using this scheme is validated with analytical results obtained by Carter. We demonstrate the use of this scheme to minimize the volume of a duct with a hypothetical power law model incorporating the effect of residence time (function of inlet Mach number) on the electrical conductivity. We further demonstrate the use of this scheme for obtaining the optimum shape of a MHD generator using an E-beam generated ionized gas stream.