Measurements of the scattering of pulsar radio emission

Measurements of the broadening of pulsar pulses by scattering in the interstellar medium are presented for a complete sample of 100 pulsars with Galactic longitudes from 6° to 311° and distances to three kiloparsec. The dependences of the scattering on the dispersion measure (τ _sc(DM) ∝ DM^α), frequency (τ _sc(v) ∝ v ^?γ ), Galactic longitude, and distance to the pulsar are analyzed. The dependence of the scattering on the dispersion measure in the near-solar neighbourhood can be represented by the power law τ _sc(DM) ∝ DM^2.2±0.1). Measurements at the low frequencies 111, 60, and 40 MHz and literature data are used to derive the frequency dependence of the scattering (τ _sc(v) ∝ V ^?γ ) over a wide frequency interval (covering a range of less than 10: 1) with no fewer than five frequencies. The index for the frequency dependence, γ = 4.1 ± 0.3, corresponds to a normal distribution for inhomogeneities in the turbulence in the scattering medium. Based on an analysis of the dependence of the scattering on the distance to the pulsar and on Galactic longitude, on average, the turbulence level C _n ² is the same in all directions and at all distances out to about three kpc, testifying to the statistical homogeneity of the turbulence of the scattering medium in the near-solar region of the Galaxy.     

The spectra of hard radiation from radio pulsars

The kinetic equation for the distribution function of relativistic electrons is solved taking into account quasi-linear interactions with waves and radiative processes. Mean values of the pitch angles ψ are calculated. If the particles of the primary beam with Lorentz factors γ_b～10⁶ are resonant, then the condition γ_bψ_b?1 is satisfied, the particle distribution is described by the function f _‖(γ) ∝ γ^?4, and the synchrotron radiation spectrum is characterized by the spectral index α=3/2. On the other hand, if a cyclotron resonance is associated with particles of the high-energy tail of the secondary plasma (γ_t～10⁵), then γ_tψ_t?1, and the distribution function has two parts—f _‖(γ) ∝ γ and f _‖(γ) ∝ γ^?2—which correspond to the spectral indices α₁=+1 and α₂=?0.5. This behavior is similar to that observed for the pulsar B0656+14. The predicted frequency of the maximum ν_m=7.5×10¹⁶ Hz coincides with the peak frequency for this pulsar. The model estimate for the total synchrotron luminosity of a typical radio pulsar with hard radiation L _s =3×10³³ erg/s is in agreement with observed values.     

Modeling the frequency dependence of the durations of solar radio spikes

The dependence of the durations of millisecond narrow-band solar radio spikes τ on the frequency f at which they are emitted is studied. A regression analysis of available experimental data at 0.3–3 GHz yields the relationship τ ∝ f ^?1.29±0.08, refining the known Güdel-Benz law. This relationship differs at a statistically significant level from the intuitive expectation τ ∝ f ^?1; this requires a physical interpretation. The frequency dependences of the pulse durations for various modes of cyclotron maser emission near the first, second, and third harmonics of the electron cyclotron frequency have been modeled. The model relationships for different cyclotron maser emission modes are different; only the results of the model for the second harmonic of the extraordinary wave are consistent with the observed behavior. Thus, this wave is a probable candidate for the dominant mode in spike bursts.     

A finite temperature chandrasekhar model: Determining the parameters and calculation of the characteristics of degenerate dwarfs

We suggest a generalization of the standard Chandrasekhar model for degenerate dwarfs. We apply an equation of state for a degenerate ideal electron gas in the form of a Sommerfeld expansion in the parameter k _B T(r)/m ₀ c ². The radial temperature distribution T(r) is modeled taking into account the presence of the isothermal core. The model has four dimensionless parameters, two microscopic (the relativistic parameter at the stellar center x ₀ and the chemical-composition parameter ?? _e = A/Z) and two macroscopic (the dimensionless temperature T ₀ ^* = k _B T _c /m ₀ c ² and dimensionless radius ?? ₀ = R _c /R of the core, where R _c and R are the radii of the core and dwarf). We found x ₀, ?? _e , and T ₀ ^* for about 3000 DA white dwarfs, based on their masses, radii, and effective temperatures from the Sloan Digital Sky Survey Data Release 4; ?? ₀ was treated as a free parameter. The influence of temperature effects on the macroscopic characteristics is analyzed, in particular, the minimum mass and maximum radii of the stars. Based on our computed energy-radius dependence, we suggest an interpretation of the observed radius distribution for these dwarfs.     

Characteristic scale of heterogeneity of seismically active fault and its manifestation in scaling of earthquake source spectra

Previously, similarity of source spectra of Kamchatka earthquakes with respect to the common corner frequency f_c1 and the expressed deviations from similarity for the second f_c2 and the third f_c3 corner frequencies were revealed. The value of f_c3 reflects the characteristic size L_is of fault surface; correspondingly, L_is ≈ v_rT_is, where v_r is the rupture speed and T_is ≈ 1/f_c3 is characteristic time. The estimates of f_c3 are used for normalizing f_c1 and f_c2. In this way one obtains dimensionless rupture temporal parametres τ₁ and τ₂ and can further study the dependence τ₂ (τ₁). The growth of a rupture is considered as a process of aggregation of elementary fault spots of the size L_is. The dimensionless width of the random front of aggregation is on the order of τ₂. The relationship τ₂ (τ₁) approximately follows power law with exponent β. The estimates of β derived from earthquake populations of Kamchatka, USA and Central Asia (β = 0.35–0.6) agree with values expected from the known Eden’s theory of random aggregation growth and from its generalizations.     

Strmömgren zones of type II supernovae

The emission measures EM in the directions of supernova remnants and pulsars are considered as functions of their ages t. The resulting plot has a well-defined lower boundary, which can be approximated by the expression EM_min∝1/t. The quantity EM_min increases with decreasing age t and does not level off or reach a maximum until t?500 yr. It is concluded that the bulk of the radiative energy that goes into ionizing and heating the interstellar gas is released at early stages of the supernova remnant’s evolution. We suggest that most of the kinetic energy of the supernova shell is converted into thermal energy and radiated at remnant ages t<100 yr, when the supernova shell, which is expanding at an enormous speed (about 10⁴ km/s), overtakes the shell produced by the presupernova in the supergiant stage. We have estimated the ionization energy E?10⁵¹ erg, diameter L?60 pc, and electron density N_e?7 cm^?3 of the HII regions around the supernovae (the supernova Strömgren zones). A list of objects that can be reliably identified as Strömgren zones of type II supernovae is presented. The plot of pulsar pulse broadening τ as a function of the pulsar age t also has a well-defined lower boundary, for which τ∝t^?2 when t≥1000 yr. This suggests that turbulence develops during the first thousand years after the supernova outburst. It is also concluded that turbulence plays an important role in the formation and evolution of the Strömgren zones of type II supernovae.     

The critical scale of fluctuation for active lateral forces in spatially variable undrained clays

This study addresses the phenomenon of the critical scale of fluctuation (SOF) for active lateral force (P_a) in undrained clay when there is a spatial variability in the clay. The phenomenon is significant under shear strength (τ_f) random fields but is insignificant under unit weight (γ) random fields. It is found that the phenomenon of the critical SOF is connected to the nature of the spatial averaging, which is “line averaging” under τ_f random fields and is “area averaging” under γ random fields. The former averaging effect (line) is significantly weaker than the latter (area), so the tendency for the critical slip plane to seek for a favorable location is stronger for the τ_f random field than for the γ random field. Hence, the phenomenon of the critical SOF is more pronounced under τ_f random fields than under γ random fields. The underlying mechanisms for the phenomenon of the critical SOF will be explored in this paper.     

The Influence of Benthic Macrofauna on the Erodibility of Intertidal Sediments with Varying mud Content in Three New Zealand Estuaries

Fine sediment inputs can alter estuarine ecosystem structure and function. However, natural variations in the processes that regulate sediment transport make it difficult to predict their fate. In this study, sediments were sampled at different times (2011–2012) from 45 points across intertidal sandflat transects in three New Zealand estuaries (Whitford, Whangamata, and Kawhia) encompassing a wide range in mud (≤63 μm) content (0–56 %) and macrofaunal community structure. Using a core-based erosion measurement device (EROMES), we calculated three distinct measures of sediment erosion potential: erosion threshold (? _c ; N m^?2), erosion rate (ER; g m^?2 s^?1), and change in erosion rate with increasing bed shear stress (m _e ; g N^?1 s^?1). Collectively, these measures characterized surface (? _c and ER) and sub-surface (m _e ) erosion. Benthic macrofauna were grouped by functional traits (size and motility) and data pooled across estuaries to determine relationships between abiotic (mud content, mean grain size) and biotic (benthic macrofauna, microbial biomass) variables and erosion measures. Results indicated that small bioturbating macrofauna (predominantly freely motile species <5 mm in size) destabilized surface sediments, explaining 23 % of the variation in ? _c (p ≤ 0.01) and 59 % of the variation in ER (p ≤ 0.01). Alternatively, mud content and mean grain size cumulatively explained 61 % of the variation in m _e (p ≤ 0.01), where increasing mud and grain size stabilized sub-surface sediments. These results highlight that the importance of biotic and abiotic predictors vary with erosion stage and that functional group classifications are a useful way to determine the impact of benthic macrofauna on sediment erodibility across communities with different species composition.     

Scaling properties of corner frequencies of Kamchatka earthquakes

Scaling properties of earthquake populations bear the major information on the physics of the source process of an earthquake. To determine scaling properties, source spectra of more than 400 earthquakes of Kamchatka were determined in a frequency range 0.1–30 Hz using materials of digital registration of PET station, and characteristic frequencies of earthquakes were estimated. The range of magnitudes is 4–6.5, the range of distances is 80–220 km. To enable reduction of a spectrum to the source, attenuation properties of the medium around PET were determined beforehand. It is revealed that source spectra show several corner (characteristic) frequencies: f _c1, f _c2 and f _c3; where the spectral trend changes: from f ⁰ to f ^?1, from f ^?1 to f ^?2, and from f ^?2 to f ^?3, respectively. Although in some cases f _c1 ≈ f _c2 in agreement with the usual ω^?2 spectral model, the main part of spectra has more complicated character. For a large part of the studied earthquakes a source-controlled upper cutoff of acceleration spectrum, or corner frequency f _c3, is observed. This is an important fact, as the existence of f _c3 (source-controlled f _max) is not recognized in the bulk of the seismological literature. For f _c1, the observed scaling agrees with the usual hypothesis of similarity of the earthquake sources of different size (magnitude); it is close to f _c1 ～ M ₀ ^?1/3 , where M ₀ is seismic moment. For f _c2, scaling is close to f _c2 ～ M ₀ ^?0.17 ～ f _c1 ^0.5 , that indicates an expressed violation of similarity. For f _c3, scaling is close to f _c2 ～ M ₀ ^?0.08 ～ f _c1 ^0.25 , so that similarity is broken even sharper in this case. Hypotheses about possible causes of the observed scaling are discussed.     

Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method

In this research, the reliability analysis of seismic ultimate bearing capacity of strip footing is assessed with implementing slip lines method coupled with random field theory. The probability density functions of seismic and static bearing capacities which are log-normal and nearly normal distribution respectively are compared to each other. The predicted Probability Density Function (PDF) of the seismic bearing capacity by slip line method is verified, with those of the Terzaghi equation and Monte Carlo simulation (MCs). For uncertainties analysis by Terzaghi equation the N_c, N_q and N_γ are assessed stochastically.     

Deviation of the arrival-time delay of pulses for the Crab pulsar from a quadratic frequency region

Our measurements of the arrival-time delays of radio pulses from the Crab pulsar, PSR B0531+21, at low frequencies 111, 63, and 44 MHz revealed additional delays compared to the usual quadratic frequency relation, Δt(v) ∝ v ^?2. These additional delays are 65 ms between 63 MHz and 111 MHz—i.e., a factor of two longer than the pulsar’s period, i.e., a factor of five longer than the pulsar period—and cannot be explained by the “twisting” of the magnetic-field lines by the rotation of the pulsar. We suggest the model in which a previously unknown high-density plasma layer with a high electron concentration is present along the line of sight in the Crab nebula, causing an additional frequency-dependent delay of the observed radio pulses at low frequencies due to the contribution of the n _e ² v ^?4 term in the dispersion-delay formula. The parameters of this inferred layer have been derived: emission measure EM ? 4 × 10⁶ pc/cm⁶, electron density n _e ? 10⁶ cm^?3, depth along the line of sight d ? 4 × 10^?6 pc, and electron temperature T _e ≥ 2 × 10⁶ K.     

The stability of sublittoral, fine-grained sediments in a subarctic estuary

The erodibility of natural estuarine sediments was measured in sit along a longitudinal transect of Manitounuk Sound, Hudson Bay, using the benthic flume Sea Carousel. Sedimentation processes along the transect varied from continuous, rapid, post-glacial sedimentation in the inner Sound, to glacial outcrops and seabed reworking of the outer Sound. The grain size and physical bulk properties reflect changes in depositional environment and correlate with sediment erosion threshold stress (τ_c), erosion rate (E), erosion type and still-water mass settling rate. There was a steady increase in τ_c (0·8–2·0 Pa) with distance down the Sound in parallel with the decreasing sedimentation rate (0·003–0·001 m yr^?1) and increasing sediment bulk density (1650–2010 kg m^?3). The near-surface friction coefficient varied up to 68° in proportion to the clay content of post-glacial material. Glacial sediments were characterized by variable results and generally higher friction coefficients. Seabed erosion in Sea Carousel began with surface creep of loose aggregates, pellets and organic debris. This was followed by Type I bed erosion at rates that varied between 0·0002 and 0·0032 kg m^?2 s^?1 (mean 0·0015). Type I peak erosion rate was inversely related to applied bed shear stress (τ_o). Type II erosion succeeded Type I, often after a broad transitional period. Simulations of suspended sediment concentration in Sea Carousel were made using four commonly used erosion (E) algorithms. The best results were obtained using Krone's dimensionless ratio relationship: E=M(τ_o/τ_c-1). Simulations were highly sensitive to the definition of erosion threshold with sediment depth [τ_c(z)]. Small errors in definition of τ_c(z) caused large errors in the prediction of suspended sediment concentration which far exceeded differences between the methods tested.     

Evolution of the isotopic composition of carbon and oxygen in a calcite precipitating H2O-CO2-CaCO3 solution and the related isotopic composition of calcite in stalagmites

The isotopic composition of carbon and oxygen in a calcite precipitating CO₂-H₂O-CaCO₃ solution is preserved in the calcite precipitated. For the interpretation of isotopic proxies from stalagmites knowledge of the evolution of δ¹³C and δ¹⁸O in the solution during precipitation is required. A system of differential equations is presented from which this evolution can be derived. Both, irreversible loss of carbon and oxygen from the solution with precipitation time τ and exchange of oxygen in the carbonates with the oxygen in the water with exchange time T are considered. For carbon, where no exchange is active, a modified equation of Rayleigh-distillation is found, which takes into account that precipitation stops at c_eq, the saturation concentration of DIC with respect to calcite, and that c_eq as well as the precipitation time τ is slightly different for the heavy and the light isotope. This, however, requires introducing a new parameter γ = (A_eq/B_eq)/(A₀/B₀), which has to be determined experimentally. (A_eq/B_eq) is the isotopic ratio for the heavy (A) and the light isotope (B) at both chemical and isotopic equilibrium and (A₀/B₀) is the initial isotopic ratio of the solution. In the case of oxygen, where exchange is present, the isotopic shifts are reduced with increasing values of the precipitation time τ. For τ ? T the solution stays in isotopic equilibrium with the oxygen in the water during the entire time in which precipitation is active. The isotopic ratios in a calcite precipitating solution R(t)/R₀ = (1 + δ(t)/1000) for carbon are plotted versus those of oxygen. R₀ is the isotopic ratio at time t = 0, when precipitation starts and δ(t) the isotopic shift in the solution after time t. These show positive correlations for the first 50% of calcite, which can precipitate. Their slopes increase with increasing values of τ and they closely resemble Hendy-tests performed along growth layers of stalagmites. Our results show that stalagmites, which grow by high supply of water with drip times less than 50 s, exhibit positive correlations between δ¹³C and δ¹⁸O along a growth layer. But in spite of this the isotopic composition of oxygen in the solution at the apex is in isotopic equilibrium with the oxygen in the water, and therefore also that of calcite deposited at the apex.     

Determination of the degree of Al,Si order Q od in kinetically disordered albite using hard mode infrared spectroscopy

Hard Mode Infrared Spectroscopy (HMIS) is used to correlate the line shifts Δω, the intensity changes ΔA and the variations of spectral line widths Γ of infrared absorption bands with the degree of Al, Si ordering, Q _od, in kinetically disordered Na-feldspar. A simple relationship Δω∝ΔA∝ΔΓ∝Q _od ² was found with the phonon band around 650 cm^?1 being particularly sensitive to small changes of the degree of Al, Si ordering. It is shown that the average degree of Al, Si order can be determined from HMIS with an accuracy of ca. 8 percent using 50 mg of Na-feldspar. The experimental results agree well with recent X-ray determinations using identical samples. The significance of HMIS for the study of kinetic processes in minerals is explained.     

Time constant of hydraulic-head response in aquifers subjected to sudden recharge change: application to large basins

Analytical formulae are proposed to describe the first-order temporal evolution of the head in large groundwater systems (such as those found in North Africa or eastern Australia) that are subjected to drastic modifications of their recharge conditions (such as those in Pleistocene and Holocene times). The mathematical model is based on the hydrodynamics of a mixed-aquifer system composed of a confined aquifer connected to an unconfined one with a large storage capacity. The transient behaviour of the head following a sudden change of recharge conditions is computed with Laplace transforms for linear one-dimensional and cylindrical geometries. This transient evolution closely follows an exponential trend exp(?t/τ). The time constant τ is expressed analytically as a function of the various parameters characterizing the system. In many commonly occurring situations, τ depends on only four parameters: the width a _c of the main confined aquifer, its transmissivity T _c, the integrated storage situated upstream in the unconfined aquifer M?=?S _u a _u, and a curvature parameter accounting for convergence/divergence effects. This model is applied to the natural decay of large aquifer basins of the Sahara and Australia following the end of the mid-Holocene humid period. The observed persistence of the resource is discussed on the basis of the time constant estimated with the system parameters. This comparison confirms the role of the upstream water reserve, which is modelled as an unconfined aquifer, and highlights the significant increase of the time constant in case of converging flow.     

Eifelite,KNa3Mg4Si12O30, a new mineral of the osumilite group with octahedral sodium

Eifelite of variable composition is uniaxial positive withn ₀ near 1.543 andn _e near 1.544, a between 10.14 and 10.15 Å, andc about 14.22 Å, space groupP 6/m 2/c 2/c. There is a complete series of solid solution between the eifelite end member KNa₃Mg₄Si₁₂O₃₀ and roedderite, KNaMg₅Si₁₂O₃₀, following the 2 Na?Mg substitution. Both eifelite and roedderite have milarite-type structures, but Na is always in six-coordinated sites: In roedderite Na occupies solely a newly defined B′^[6]-position which is slightly displaced alongc from the ideal B_[9]-position lying on the (001/2)-mirror plane in K₂Mg₅Si₁₂O₃₀. In eifelite Na is located both inB′^[6] and in theA _[6]-positions, where it partially replaces Mg. Eifelite has the highest cation occupancy of all osumilite group minerals known thus far. Both eifelite and roedderite occur in vesicles of contact metamorphosed basement xenoliths ejected with the leucite tephrite lava of the Quaternary Bellerberg volcano in the Eifel, West Germany. They are considered to be precipitates from highly alkaline, MgSi-rich, but Al-deficient gas phases that originated through interaction of gaseous igneous differentiates with the xenoliths.     

X-ray crystallography and mineral chemistry of bastnaesite from Kanigiri granite,Prakasam district,Andhra Pradesh,India

The authors report the results of X-ray diffraction (XRD) and geochemical studies on bastnaesites (lanthanum cerium fluoro-carbonate) hosted in alkali Kanigiri Granite of the Prakasam district in Andhra Pradesh, India. The XRD pattern of the investigated bastnaesite displays sharply-defined reflections. The observed d-spacings of the bastnaesite are in very close agreement with those published for bastnaesite standard in International Centre for Diffraction Data (ICDD) Card No. 11–340. The calculated unit cell parameters (a _o ; c _o ) and unit cell volume (V) of the studied bastnaesite (a _o 7.1301–7.1413 Å, c _o 9.7643–9.7902Å and V 429.8940–432.3875 ų) are almost equal to values published for bastnaesite standard (c _o 7.1290 Å, c _o 9.7744 Å and V 430.19 ų) in the relevant data card. Geochemical data of bastnaesite reveals high content of Ce (mean 27.22%) followed by La (mean 16.82%), Nd (mean 6.12%) and Pr (mean 1.91%). Compared to light REE (LREE) content (mean 437165 ppm), heavy REE (HREE) content (mean 5867 ppm) is drastically low, with unusually high LREE/HREE ratio (mean 80). The chondrite-normalised plot also exhibits drastic enrichment of LREE relative to HREE with pronounced negative Euanomaly (mean Eu/Eu* = 0.15). High (LREE) _N / (HREE) _N , (La/Lu) _N , (La/Yb) _N and (Ce/Yb) _N ratios reveal higher fractionation of LREE relative to HREE. The rare earth element (REE) contents of the studied bastnaesite are very close to REE contents of bastnaesite hosted in alkali syenite from Madagascar. The presence of bastnaesite in Kanigiri Granite and soils derived from it enhances the scope of further exploration for bastnaesite in several bodies of alkaline rocks and alkali granitoids present along the eastern margins of the Cuddapah basin, Andhra Pradesh.     

Probabilistic evaluation of primary consolidation settlement of Songdo New City by using kriged estimates of geologic profiles

The uncertainty in the spatial distributions of consolidation settlement (s _c) and time (t _p) for Songdo New City is evaluated by using a probabilistic procedure. Ordinary kriging and three theoretical semivariogram models are used to estimate the spatial distributions of geo-layers which affect s _c and t _p in this study. The spatial map of mean (μ) and standard deviation (σ) for s _c and t _p are determined by using a first-order second moment method based on the evaluated statistics and probability density functions (PDFs) of soil properties. It is shown that the coefficients of variation (COVs) of the compression ratio [C _c/(1 + e ₀)] and the coefficient of consolidation (c _v) are the most influential factors on the uncertainties of s _c and t _p, respectively. The μ and σ of the s _c and t _p, as well as the probability that s _c exceeds 100 cm [P(s _c > 100 cm)] and the probability that t _p exceeds 36 months [P(t _p > 36 months)] in Sect. 1, are observed to be larger than those of other sections because the thickness of the consolidating layer in Sect. 1 is the largest in the entire study area. The area requiring additional fill after the consolidation appears to increase as the COV of C _c/(1 + e ₀) increases and as the probabilistic design criterion (α) decreases. It is also shown that the area requiring the prefabricated vertical drains installation increases as the COV of c _v increases and as the α decreases. The design procedure presented in this paper could be used in the decision making process for the design of geotechnical structures at coastal reclamation area.     

Compression behavior of reconstituted soils mixed with bentonite for a cutoff wall in a landfill site

Soil-bentonite (SB) backfill is used extensively in cutoff walls at landfill sites; the walls are used as engineered geotechnical barriers for contaminant control. With increasing bentonite content, the coefficient of consolidation and hydraulic conductivity of the SB decrease. However, when the bentonite content is increased beyond a certain percentage, the hydraulic conductivity of the SB decreases very little. One of the aims of this paper is to introduce the concept of optimal bentonite content (OBC) for SB cutoff walls, in which the hydraulic conductivity (k_h) is expected to be lower than 1?×?10^?9 m/s. Additionally, the paper introduces a new index consolidation stress ratio, c_vσ′, which is used to obtain the OBC. For this study, the initial water contents of the SB backfill material are selected to be 0.8, 1.0, and 1.2 times their corresponding liquid limits. The clayey soils are amended with different bentonite contents, 0, 5, 8, and 10% (by dry weight basis) for the oedometer tests. Then, piezocone penetration test (CPTU) is applied in SB cutoff wall at a landfill site in Jingjiang city, China. The results of the laboratory and field studies show that the introduction of a new index, c_vσ′, is very useful for calculating the OBC and for evaluating the coefficient of consolidation and hydraulic conductivity of SB backfill. The advantage of SB backfill with OBC is that it can achieve the design requirement of very low hydraulic conductivity and improve the safety reserves.