Simple Power-law Model Research Articles

A recommended procedure for estimating the cosmic-ray spectral parameter of a simple power law

A simple power law model with single spectral index α 1 is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10 13 eV. Two procedures for estimating α 1—the method of moments and maximum likelihood (ML)—are developed and their statistical performance are compared. The ML procedure is shown to be the superior approach and is then generalized for application to real cosmic-ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution and inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic-ray detector as they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives.

Soft X-ray variability of the bright quasar 3C273

We present the results from ROSAT observations of 3C273 in the soft X-ray band. The light variation of 3C273 was investigated for three different energy bands of soft, medium, and hard. The maximum variability with a factor of 2 for 551 days was confirmed at all three different bands. This appears to be a periodic variation within the period of roughly 6 months. However, the short-term or micro variation was not so distinct and the light variation of each band did not show any correlation between them. The hardness ratio for hard and soft bands shows irregular variation but there was no correlation between them. There is no distinct variation of the photon index in the case of simple power law model fitting. For power law + free absorption model fitting, the average photon index (Γ) is 2.08.

ASCA Observation of the Millisecond Pulsar PSR J2124$-$3358

Abstract The isolated 4.9 ms pulsar PSR J2124$-$3358 was observed with ASCA on 1998 May 9, and the X-ray spectrum in the 0.5–10 keV band was obtained. The X-ray spectrum can be fitted with a single blackbody model with a temperature $kT = 0.31^{+0.08}_{-0.06}\,\mathrm{keV}$, although a simple power-law model with a relatively large photon index $\Gamma = 2.8^{+0.6}_{-0.5}$ cannot be rejected.

Kinetics of propane combustion over La 0.66Sr 0.34Ni 0.3Co 0.7O 3 perovskite

La 0.66Sr 0.34Ni 0.3Co 0.7O 3 (LSNC) perovskite is an excellent catalyst in several oxygen involving reactions, including methane combustion. Catalytic combustion of propane based on efficient technologies using low cost catalysts could serve as a non-polluting source of energy in remote regions. To optimize reactors for catalytic combustion (combusters), reliable kinetic data are needed. In this paper are presented kinetics of a complete propane oxidation over LSNC studied at a steady state in a plug-flow reactor. The experimental data were obtained for 0.5 g catalyst at temperatures between 473 and 613 K, with propane concentration varied from 0.58 to 4.76 vol.% oxygen between 7.5 and 98 vol.%, and flowrate between 100 and 400 ml/min. The LSNC catalyst, prepared with high specific surface area of 15 m 2/g, shows again an excellent stable activity which competes favorably with that of noble metals. Several kinetic models have been tested. Best fit was obtained with the Mars–van Krevelen kinetic model. Nevertheless, the complete set of obtained data can also be fitted adequately by a simple power law model with 0.5 order in propane and 0.3 order in oxygen and apparent activation energy of 71 kJ/mol. Both water and carbon dioxide added to the feed have slight inhibiting effect, which was taken into account in a final extended Mars–van Krevelen kinetic model.

Reaction Kinetics and Chemical Equilibrium of Homogeneously and Heterogeneously Catalyzed Acetic Acid Esterification with Methanol and Methyl Acetate Hydrolysis

The reaction kinetics and chemical equilibrium of the reversible esterification of methanol with acetic acid were investigated. This system is of major importance as a model reaction for reactive distillation. The reaction has been catalyzed both homogeneously by acetic acid itself and heterogeneously by an acidic ion-exchange resin (Amberlyst 15). The chemical equilibrium composition was measured for various temperatures and starting compositions of the reactants and products. Kinetic information was obtained at temperatures between 303.15 and 343.15 K at various starting compositions covering concentration ranges from the stoichiometric regime to the dilute regions. Both the esterification and the hydrolysis reaction were investigated to yield a model which is applicable for any starting composition. The homogeneous reaction has been described with a simple power-law model. The use of activities in the kinetic model instead of mole fractions results in a much smaller residual error. To compare pseudohom...

Upper Limits of Iron Line Flux in X-Ray Afterglow of Two Gamma-Ray Bursts with ASCA

The iron emission line in the X-ray afterglow spectra of a Gamma-Ray Burst is thought to be a key to understanding the environment of progenitors. Although two independent observations with BeppoSAX and ASCA reported strong red-shifted iron emission line, the statistical significance of these detections was not very high. Further observations were expected and two more GRBs, GRB 990123 and GRB 990704, were observed with the X-ray satellite ASCA in 1999. The spectra of these two afterglows can be explained by a simple power-law model with excess absorption, but without any iron emission-line feature. The 90% upper limit for the iron line flux is as low as FFe = 3.3 × 10−6 photons cm−2 s−1, or less than ∼ 100 eV in equivalent width (EW). This upper limit is an order-of-magnitude smaller than the previous two detections of 1–3 keV in EW.

Subarcsecond Imaging of 3C 123: 108 GHz Continuum Observations of the Radio Hot Spots

We present the results of subarcsecond 108 GHz continuum interferometric observations toward the radio-luminous galaxy 3C 123. Using multiarray observations, we utilize the high-u,v dynamic range of the BIMA millimeter array to sample fully spatial scales ranging from 05 to 50''. This allows us to make one-to-one comparisons of millimeter-wavelength emission in the radio lobes and hot spots to VLA centimeter observations at 1.4, 4.9, 8.4, and 15 GHz. At 108 GHz, the bright, eastern double hot spot in the southern lobe is resolved. This is only the second time that a multiple hot spot region has been resolved in the millimeter regime. We model the synchrotron spectra of the hot spots and radio lobes using simple broken power-law models with high-energy cutoffs and discuss the hot spot spectra and their implications for models of multiple hot spot formation.

Viscoelastic Properties of a Resin Commonly Used in the Single Fiber Fragmentation Test

The fiber-matrix interface can play an important role in the performance of a composite, and consequently, it has been the subject of considerable study. One of the experiments often used to characterize the strength or quality of the interface is the single-fiber fragmentation test. The models used to analyze the data from this test involve a number of assumptions, one of which is the constitutive behavior of the matrix resin. To evaluate this assumption, a fragmentation apparatus was modified to include a load cell so both stress and strain could be measured during the experiment. Surprisingly, the results show that not only is the behavior viscoelastic, but virtually all of the fragmentation takes place in a range where the response is non-linear. To characterize this behavior, single-step, stress-relaxation experiments were conducted on a resin system often used in such tests. The results indicate that a simple power law model with strain-dependent parameters could describe the behavior over a very wide range of conditions. By using this characterization and the strain history, a crude fit to the actual loading curve in a fragmentation test could be obtained. In order to achieve quantitative agreement, however, a modified power law model was required. Such a relationship was shown to describe the loading curve for two quite different loading procedures.

Discovery of an X-Ray Pulsar in the SMC: AX J0058-7203

We report on the discovery and analysis of an X-ray pulsar, AX J0058–7203, in the Small Magellanic Cloud. This pulsar exhibits coherent pulsations at P = 280.3 s with a double-peak structure. The X-ray spectrum is well fitted with a simple power-law model of photon index Γ ∼ 0.7. No significant change of the pulsation period over the observation was found. A comparison with ROSAT observations in the same field reveals that AX J0058–7203 is highly variable, and is most likely a Be star binary pulsar.

Discovery of a Hard X‐Ray Source, SAX J0635+0533, in the Error Box of the Gamma‐Ray Source 2EG 0635+0521

We have discovered an X-ray source, SAX J0635+0533, with a hard spectrum within the error box of the GeV gamma-ray source in Monoceros, 2EG J0635+0521. The unabsorbed flux from the source is 1.2 x 10(exp -11) ergs /sq cm s in the 2-10 keV band. The X-ray spectrum is consistent with a simple power-law model with absorption. The photon index is 1.50 +/- 0.08, and we detect emission out to 40 keV. Optical observations identify a counterpart with a V magnitude of 12.8. The counterpart has broad emission lines and the colors of an early B-type star. If the identification of the X-ray/optical source with the gamma-ray source is correct, then the source would be a gamma-ray-emitting X-ray binary.

FLOW PROPERTIES OF ORANGE DIETARY FIBER SUSPENSIONS

ABSTRACTThe flow behavior of 7–20% orange dietary fiber (DF) suspensions at 15–65C was most adequately described by the simple power law model. The effect of the temperature on the apparent coefficient of viscosity (ηapp) followed an Arrhenius‐type relationship. The flow activation energy (Ea) was in the range 3.0–14. 7kJ/mol, depending on the concentration. The ηapp increased exponentially with concentration within the temperature range studied. The combined effect of temperature and concentration on the ηapp could be represented by an exponential equation. In all the cases, the effect of concentration on ηapp was more pronounced than that of the temperature.

Ionized ultraviolet and soft X-ray absorption in the low-redshift active galactic nucleus PG 1126−041

We present here the analysis of ultraviolet spectra from IUE and an X-ray spectrum from ROSAT PSPC observations of the X-ray weak, far-infrared loud AGN, PG 1126-041 (Mrk 1298). The first UV spectra taken in June 1992, simultaneously with ROSAT, show strong absorption lines of NV, CIV and SiIV, extending over a velocity range from -1000 to -5000 km/s with respect to the corresponding line centre. Our analysis shows that the Broad Emission Line Region (BELR) is, at least partially, covered by the material causing these absorption lines. In the IUE spectrum taken in Jan. 1995, the continuum was a factor of two brighter and the UV absorption lines are found to be considerably weaker than in 1992, but only little variation in the emission line fluxes is found. With UV spectral indices of A_{uv} \simeq 1.82 and 1.46 for the 1992 and 1995 data, the far UV spectrum is steep. Based on the emission line ratios and the broad band spectral energy distribution, we argue that the steepness of the UV spectrum is unlikely to be due to reddening. The soft X-ray emission in the ROSAT band is weak. A simple power-law model yields a very poor fit with a UV-to-X-ray spectral index A_{uvx}=2.32. Highly ionized (warm) absorption is suggested by the ROSAT data. After correcting for a warm absorber, the optical to X-ray spectral slope is close to the average of A{uvx}\simeq 1.67 for radio quiet quasars.

Values of [ITAL]H[/ITAL][TINF]0[/TINF] from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of H0 produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply imaged sources that have been detected. We obtain the first adequate fit to all the observations only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models that are consistent with observations to 95% confidence level (CL) indicate H0 = 104(1 - ) km s-1 Mpc-1. Previous weak-lensing measurements constrain the mean mass density within 30'' of G1 to be = 0.26 ? 0.16 (95% CL), implying H0 = 77 km s-1 Mpc-1 (95% CL). The best-fitting models span the range 65?80 km s-1 Mpc-1. Further observations will shrink the confidence interval for both the mass model and . The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power-law density profiles. We therefore caution against using simple isothermal or power-law mass models to derive H0 from other time-delay systems. High signal-to-noise ratio imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.

On the Theory of Pulse Propagation and Two‐Frequency Field Statistics in Irregular Interstellar Plasmas

We have computed two-frequency second moments and pulse profiles for plane and spherical waves both propagating in an extended plasma and incident on a thin plasma phase screen located between the source and the observer. The various models we consider for the power spectrum of the interstellar electron density fluctuations versus wavenumber are the simple power-law model, the power-law model with an inner scale, the model, and the square-law structure function model. The power-law model with spectral exponent β=11/3 corresponds to the Kolmogorov turbulence spectrum. The β=4 model describes the random distribution in location and orientation of discrete objects with relatively sharp boundaries, such as shocks, across the line of sight. An outer scale is included in the β=4 model to account for the average size of such objects. The results for the various spectral models generally lie between the extremes represented by the simple Kolmogorov and square-law structure function models. In the strong scattering limit, the diffractive decorrelation bandwidth is related to the scattering broadening time via a Fourier uncertainty relation. We have computed numerical values for the uncertainty constant for the various geometries and spectral models and find values ranging over a factor of 2. For the Kolmogorov spectrum, the value is less than that in the widely-used Taylor, Manchester, & Lyne (1993) catalog by factors of 1.98 and 2.34 for a point source in an extended medium and in screen geometries, respectively. Thus observers must use the appropriate constant when comparing observations with a specific spectral and geometrical model. We also note that high signal-to-noise ratio observations of the scattering tails of pulsar pulses may be used to constrain the various spectral models of the Galactic electron density fluctuations, independent of the distribution of the scattering material along the line of sight.

Two cosmological models for clusters of galaxies

We investigate the properties of clusters of galaxies in two cosmological models using N-body simulations and the Press--Schecter (PS) theory. In the first model, the initial power spectrum of density fluctuations is in the form P(k) ∝ k−2 at wavelengths λ <120 h−1 Mpc. In the second model, the initial linear power spectrum of density fluctuations contains a feature (bump) at wavelengths λ~30–60, h−1 Mpc, which correspond to the scale of superclusters of galaxies. We examine the mass function, peculiar velocities, the power spectrum and the correlation function of clusters in both models for different values of the density parameter Ο0 and σ8 (the rms fluctuation on the 8, h−1Mpc scale). The results are compared with observations. We find that in many aspects the power spectrum of density fluctuations in model (2) fits the observed data better than the simple power-law model (1). In the first model, the mass function and peculiar velocities of clusters are consistent with observations only if Ο0<0.6. In the second model, the permitted region in the (Ο0, σ8) plane is larger. In this model, the power spectrum of clusters is in good agreement with the observed power spectrum of the APM clusters. This model predicts that there is a bump in the correlation function of clusters at separations r ~20–35, h−1 Mpc. In the future, accurate measurements of the cluster correlation function at these distances can serve as a discriminating test for this model. We examine the linear theory predictions for the peculiar velocities of peaks in the Gaussian field and compare these to the peculiar velocities of clusters in N-body simulations. We determine the clusters as the maxima of the density field smoothed on the scale R ~1.5, h−1 Mpc, and define their peculiar velocities using the same smoothing scale as for the density field. The numerical results show that in this case the rms peculiar velocities of clusters increase with cluster richness. The rms peculiar velocity of small clusters is similar to the linear theory expectations, while the rms peculiar velocity of rich clusters is higher than that predicted in the linear theory (~18 per cent for clusters with a mean intercluster separation dcl=30 h−1 Mpc).

Rheological behaviour of date-water concentrates

The rheological behaviour of date-water concentrates of three date cultivars has been determined using a Haake VT 181 concentric-cylinder rotational viscometer. The date cultivars used were Khudary, Sufri, and Serri; and the date-water concentrates were 20, 30, 40, 50, 60, and 70 °Brix. The 20 and 30 °Brix concentrates exhibited Newtonian flow in the temperature range 25–85 °C while the other concentrates (40, 50, 60 and 70 °Brix) were well described by the simple power law model in the temperature range 25–95 °C and their flow was non-Newtonian exhibiting pseudoplastic behaviour. Temperature had a pronounced effect on consistency coefficient of samples at 40 °Brix concentrations from the three cultivars. The magnitude of the consistency coefficient decreased with increase in temperature. The Arrhenius model described the effect of temperature on the apparent viscosity with activation energies from 1.9 × 10 4 to 3.1 × 10 4 kJ kg −1 mol −1 at 50 s −1, from 1.9 × 10 4 to 3.2 × 10 4 kJ kg −1 mol −1 at 100 s −1, and from 1.9 × 10 4 to 3.3 × 10 4 kJ kg −1 mol −1 at 200 s −1. The magnitude of activation energy increased with increase in concentration.

Flow properties of Roselle ( Hibiscus sabdariffa L.) extract

Flow properties of water extract of Roselle calyces were determined using a concentric cylinders rotational viscometer for extract concentration range of 5–65% TS, temperature range of 20–60 °C, and shear rate range of 2·5–979 s −1. Measured shear stress was within the range 0·5 to 49·7 Pa, corresponding to an apparent viscosity range of 0·0015–1·55 Pa s. Within the tested ranges of concentration, temperature, and shear rate, the extract exhibited a pseudoplastic behaviour, and was adequately described by the simple power law model. The flow behaviour index was consistently below unity (0·76–0·97), with the consistency index varying between 0.007 and 1.6 Pa s n. Activation energy of flow varied from 18·74 to 42·80 (kJ/kmol) for the extract concentration range of 5–65% TS, at a shear rate of 100 s −1. The experimental results were fitted by mathematical models to allow prediction of apparent viscosity as a function of concentration, temperature, and shear rate.

Characteristics of gamma-ray bursts at MeV energies measured by COMPTEL

We present results from the spectral analysis of 29 gamma-ray bursts measured by the COMPTEL Telescope instrument (0.75–30 MeV) during the period from April 1991 through May 1995. The time-averaged spectra of these events are consistent with a simple power law model with spectral index in the range 1.5–3.5, whereas simple thermal models are statistically inconsistent with the burst sample. We find good agreement between burst spectra measured simultaneously by BATSE, COMPTEL and EGRET, which typically show a spectral transition or “break” in the BATSE energy range around a few hundred keV followed by simple power law emission extending to hundreds of MeV. Observations of rapid intensity variations up to a few MeV in the stronger bursts are used to investigate the importance of photon-photon opacity and to place limits on the source distance and bulk Lorentz factor.

Investigation of the kinetics of a deactivating system by transient experiments

A transient approach has been applied to a system deactivating due to coke formation, in order to determine the kinetics for the main reaction. The method, which was used on a Pt Sn/Al 2O 3 catalyst deactivated during propane dehydrogenation, consisted of runs in which the gas composition and temperature were changed in steps. By separating the deactivation from the main reaction kinetics, it was possible to obtain rate equations. A simple power-law model was found to fit the data best. Finally, simulations using the model for the main reaction together with a model for the deactivation mechanism were successfully applied to original data. The paper also discusses problems with non-uniform coke profiles in integral reactors, and errors induced in kinetic parameters by using methods that utilize extrapolation to zero process time when finding mechanistic models.

Advantages of Spectrum-Röntgen-Gamma and INTEGRAL forthe Study of Narrow-Line Seyfert 1 Galaxies

This paper summarizes the spectral and timing properties of narrow-line Seyfert1 galaxies (NLS1) in view of recent ROSAT and ASCA observations. NLS1have generally steeper soft (0.1–2.4 keV) x-ray continuum slopes than Seyfert 1s with broader lines, and there exists an anticorrelation between the 0.1–2.4keV continuum slope and the FWHM of the Hβ line. Objects with steep 0.1–2.4keV continuum slopes and Hβ FWHM > 3000 km s−1 are clearly discriminated against by nature. When simple power-law models are fit to ROSAT spectra,photon indices reach values up to about 5, much higher than is usually seen inSeyfert 1s. Interestingly, the hard (2–10 keV) x-ray continuum slopes tend also to be steeper in NLS1 compared to broad-lined Seyfert 1 galaxies. We also reportevidence for giant and rapid soft x-ray variability in the narrow-line Seyfert1 galaxy IRAS 13224–3809 and the narrow-line quasar PHL 1092. The advantagesof Spectrum-Röntgen-Gamma (SRG) and INTEGRAL for the study ofNLS1 are discussed.