Finite element approximation of nonlocal dynamic fracture models

In this work we estimate the convergence rate for time stepping schemes applied to nonlocal dynamic fracture modeling. Here we use the nonlocal formulation given by the bond based peridynamic equation of motion. We begin by establishing the existence of H2 peridynamic solutions over any finite time interval. For this model the gradients can become large and steep slopes appear and localize when the non-locality of the model tends to zero. In this treatment spatial approximation by finite elements are used. We consider the central-difference scheme for time discretization and linear finite elements for discretization in the spatial variable. The fully discrete scheme is shown to converge to the actual H2 solution in the mean square norm at the rate CtΔt + Csh2=/2. Here h is the mesh size, Δ is the length scale of nonlocal interaction and Δt is the time step. The constants Ct and Cs are independent of Δt, and h. In the absence of nonlinearity a CFL like condition for the energy stability of the central difference time discretization scheme is developed. As an example we consider Plexiglass and compute constants in the a-priori error bound

Optical Spectroscopy of Type Ia Supernovae

We present 432 low-dispersion optical spectra of 32 Type Ia supernovae (SNe Ia) that also have well-calibrated light curves. The coverage ranges from 6 epochs to 36 epochs of spectroscopy. Most of the data were obtained with the 1.5m Tillinghast telescope at the F. L. Whipple Observatory with typical wavelength coverage of 3700-7400A and a resolution of ~7A. The earliest spectra are thirteen days before B-band maximum; two-thirds of the SNe were observed before maximum brightness. Coverage for some SNe continues almost to the nebular phase. The consistency of the method of observation and the technique of reduction makes this an ideal data set for studying the spectroscopic diversity of SNe Ia.Comment: Accepted for publication in the Astronomical Journal, 109 pages (including data table), 44 figures, full resolution figures at http://www.noao.edu/noao/staff/matheson/Iaspec.ps.g

Soil Chemical Properties Under Conservation Agriculture and Cereal-Based Cropping System in Eastern Tarai of Nepal

Field experiments were conducted for four years (2014-2017) at five locations namely Salbani, Bhokraha, Simariya, Bhaluwa and Kaptanganj of Sunsari district to assess the changes in soil chemical properties under conservation agriculture (CA)-based practices in two cropping systems namely rice-kidney bean-maize at Salbani and rice-wheat at rest of the locations. In rice-wheat cropping system, there were four treatments: (1) conventional tillage (CT) for rice transplantation and subsequent wheat sowing, (2) conventional tillage rice transplantation followed by zero tillage (ZT) wheat, (3) unpuddled rice transplantation followed by zero tillage wheat, (4) zero tillage in both rice and wheat. Similarly, in rice-kidney bean-maize cropping system, there were four treatments; (1) conventional tillage for rice transplantation and sowing of both kidney bean and maize, (2) conventional tillage rice transplantation followed by zero tillage in both kidney bean and maize, (3) unpuddled rice transplantation followed by zero tillage in both kidney bean and maize, (4) zero tillage in all three crops. Soil samples were taken at initial and every year after rice harvest.The soil samples were analyzed for total nitrogen, available phosphorus, available potassium, pH and soil organic matter.Total nitrogen (N) showed a slightly decreasing trend in the first three years and showed a slight increase at the end of experiment under ZT in all locations. The total N under ZT changed from 0.12 to 0.13%, 0.05 to 0.06%, 0.10 to 0.12%, 0.11 to 0.08% and 0.09 to 0.13% in Salbani, Bhokraha, Simariya, Bhaluwa and Kaptanganj, respectively.  All locations showed the positive values of available potassium; Salbani  revealing considerable change of 64.3 to 78.5 mg/kg in CT while 68.4 to 73.3 mg/kg in ZT condition. The treatment where rice was transplanted in unpuddled condition and zero tilled to wheat, had a mean value of available phosphorus and potassium as 87.3 and 81.9 mg/kg respectively. Soil pH ranged from 4.8 to 7.1 in CT while it was 5.2 to 6.8 in ZT across the locations. The change in soil organic matter in CT of all locations except Salbani was narrower as compared to ZT

The Peculiar Type Ic Supernova 1997ef: Another Hypernova

SN 1997ef has been recognized as a peculiar supernova from its light curve and spectral properties. The object was classified as a Type Ic supernova (SN Ic) because its spectra are dominated by broad absorption lines of oxygen and iron, lacking any clear signs of hydrogen or helium line features. The light curve is very different from that of previously known SNe Ic, showing a very broad peak and a slow tail. The strikingly broad line features in the spectra of SN 1997ef, which were also seen in the hypernova SN 1998bw, suggest the interesting possibility that SN 1997ef may also be a hypernova. The light curve and spectra of SN 1997ef were modeled first with a standard SN~Ic model assuming an ordinary kinetic energy of explosion $E_{\rm K} = 10^{51}$ erg. The explosion of a CO star of mass $M_{\rm CO} \approx 6 M_\odot$ gives a reasonably good fit to the light curve but clearly fails to reproduce the broad spectral features. Then, models with larger masses and energies were explored. Both the light curve and the spectra of SN 1997ef are much better reproduced by a C+O star model with $E_{\rm K} =$ 8 \e{51} erg and $M_{\rm CO} = 10 M_\odot$. Therefore, we conclude that SN 1997ef is very likely a hypernova on the basis of its kinetic energy of explosion. Finally, implications for the deviation from spherical symmetry are discussed in an effort to improve the light curve and spectral fits.Comment: "To appear in the Astrophysical Journal, Vol.534 (2000)