Recently a WENO scheme, with smoothness indicators constructed based on L1 measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), ...referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations.
Summary
In this paper, we have proposed a new problem independent discontinuity locator for hybridization. Along with this, a new global smoothness indicator is proposed. The hybrid weighted ...essentially nonoscillatory (WENO) scheme works on the principle of applying linear upwind scheme in smooth regions and WENO algorithm in nonsmooth regions to save computational cost, which is reflected in the time taken for the computation of the numerical solution. A problem independent discontinuity locator has been designed based on the properties of the existing smoothness indicators. In addition, to attain the required order of accuracy, a new global smoothness indicator is proposed, which produces a solution with better resolution at discontinuities. Numerical experiments have been included to demonstrate the application of the proposed theory to some benchmark problems. It has been shown that the newly proposed hybrid WENO scheme works faster and gives a solution of higher resolution than WENO‐JS, WENO‐Z, and few other more recent third‐order WENO schemes.
To save computational cost and time, the WENO reconstruction is implemented only at the region of discontinuities, which are identified based on newly proposed problem independent discontinuity locator that does not require any threshold assumptions. The global smoothness indicator is proposed that has a lower total variation and hence is expected to give better results. Figure 1 shows located grid points by discontinuity locator in discontinuous and critical point region, whereas Figure 2 shows high resolution result with hybrid WENO scheme for Shu entropy problem.
•The article presents a new seventh-order weighted essentially non-oscillatory scheme.•The local and global smoothness indicators are constructed based on L1-norm.•A global smoothness indicator is of ...O(Δx8) constructed.•The resulted scheme attains the desired order of accuracy in presence of critical points.•Numerical examples are presented with one and two-dimensional system of Euler equations.
In this article, the construction and implementation of a seventh order weighted essentially non-oscillatory scheme is reported for solving hyperbolic conservation laws. Local smoothness indicators are constructed based on L1-norm, where a higher order interpolation polynomial is used with each derivative being approximated to the fourth order of accuracy with respect to the evaluation point. The global smoothness indicator so constructed ensures the scheme achieves the desired order of accuracy. The scheme is reviewed in the presence of critical points and verified the numerical accuracy, convergence with the help of linear scalar test cases. Further, the scheme is implemented to non-linear scalar and system of equations in one and two dimensions. As the formulation is based on method of lines, to move forward in time linear strong-stability-preserving Runge–Kutta scheme (lSSPRK) for the linear problems and the fourth order nonlinear version of five stage strong stability preserving Runge–Kutta scheme (SSPRK(5, 4)) for nonlinear problems is used.
Zinc selenium phosphate glasses added with the traces of Au
2
O
3
were prepared and heat-treated. XRD, TEM, DSC, FT-IR and optical absorption (OA) spectroscopy methods were used for the structural ...assessment of these samples. Later, different dielectric parameters viz., dielectric constant (
ε′
), electric moduli (
M
), impedance (
Z
) and a.c. conductivity (
σ
ac
) were measured over wide regions of frequency (
ω
) and temperature (
T
) as functions of Au
2
O
3
concentration. Dielectric breakdown strength (DBS) of these samples was also measured at ambient conditions. The characterization studies indicated that multiple crystal grains were entrenched in the residual amorphous phase of the samples. The X-ray diffraction studies revealed that the bulk glasses consisted of Au
2
(SeO
3
)
3
crystal phase and Au
0
metallic particles (MPs). As Au
2
O
3
content was raised, the intensity of the XRD peak related to Au
3+
crystal phase indicated a growing trend, whereas that of Au
0
MPs showed a decreasing trend. The results of XPS studies revealed similar inferences. The FT-IR results pointed out an improved degree of augmentation of the glass network as the content of Au
2
O
3
was increased. Optical absorption (OA) - spectra of the glasses indicated a broad absorption band in the spectral range of 500–600 nm due to the surface plasmon resonance (SPR) of Au
0
MPs. The intensity of the band was observed to decrease as Au
2
O
3
content was increased and indicated decreasing proportion of Au
0
metallic particles in the samples. The dielectric parameters exhibited a decreasing trend, whereas the dielectric breakdown strength (DBS) and electrical impedance indicated a substantial hike due to the increasing concentration of Au
2
O
3
. Overall, the presence of Au
2
O
3
caused a significant improvement in the insulating strength of the ZnO added SeO
2
-P
2
O
5
glasses and hence such glasses may be considered as insulating layers in the display panel devices.
Li2SO4–MgO–P2O5 glasses mixed with a varied quantity of NiO were prepared. Detailed spectroscopic investigations (viz., OA, IR and Raman) spectra were carried out. Optical absorption spectral results ...indicated that Ni2+ ions in the glass network reside in octahedral (Oh) as well as tetrahedral (Td) sites; these results have also pointed out the growing concentration of Ni2+ ions in Oh sites as NiO concentration is increased up to 0.8 mol%. Results of infrared and Raman spectral studies indicated increased internal chaos in the sulpho-phosphate glass network with an increase of NiO concentration up to 0.8 mol%. Values of dielectric permittivity (both real and imaginary components), a.c. conductivity, σac, are observed to be gradually increasing with NiO content in the concentration range 0–0.8 mol%. Electric moduli spectra have exhibited dipolar relaxation effects and the dipolar relaxation time τ estimated from these spectra exhibited a decreasing trend with the raise of NiO quantity up to 0.8 mol%. The complexes of octahedral Ni2+ ions with oxygen ions are predicted to be the possible dipoles responsible for the dipolar effects. Variation of σac with NiO content exhibited an increasing trend up to 0.8 mol%. Quantitative analysis of this observation indicated ionic contribution to σac is dominant in the glasses containing small quantities of NiO (< 0.8 mol%), whereas in the glasses containing higher quantities of NiO (> 0.8 mol%) polaronic contribution to the conductivity seems to be present. Overall, the results of dielectric properties of studied glass system indicted that the glass with low quantities of NiO (< 0.8 mol%) can be considered as useful material as electrolytes in the solid-state batteries.
An illustration of entrenchment of SO42− structural unit in the disrupted phosphate glass network consisting of PO43− (Q0) units. Display omitted
•Spectral studies of Li2SO4–MgO–P2O5:NiO glasses indicated Ni2+ ions act as modifiers.•ε and σac found to increase with NiO content due to increased internal chaos in glass.•Dielectric studies indicated glasses with NiO (<0.8 mol%) are useful as electrolytes.
A total of 158 serum samples of newly diagnosed type 2 diabetes patients and control subjects were analyzed using Synchrotron Radiation X-ray Fluorescence (SRXRF) technique. The microprobe XRF beam ...line-16 of Indus-2 synchrotron radiation facility at Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India, was used to identify and quantify the elements K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Br, Rb, Sr, and Pb. A significant decrease in the mean concentrations of K, Ca, Ti, Cr, Mn, Ni, Zn, and As and an increase in the concentrations of V, Fe, Co, Cu, Se, and Pb were observed in the serum samples of the patient group when compared to the control group. It is hypothesized that the observed alterations in the elemental concentrations might have led to ineffective uptake of insulin and have interfered with glucose homeostasis by either directly or indirectly causing oxidative stress.
A comparative study of trace elements in Singareni and Talcher coals was carried out using Particle Induced X-ray Emission technique with a 3 MeV proton beam. Concentrations of sixteen elements, K, ...Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Rb, Sr and Pb were obtained and compared with Clarke’s values to ascertain the enrichment factor for each. Pearson correlation and hierarchical cluster analyses were used to understand the relationship between the inorganic constituents of coal. It is anticipated that this study of trace elements in coals will be useful to protect environment and to regulate the emission of toxic elements during coal combustion and utilization.
By measuring ultrasonic velocity in Li
2
SO
4
-MgO-P
2
O
5
glasses doped with different concentrations of NiO, we have evaluated different elastic coefficients; the values of these coefficients ...exhibited a decreasing trend with increase of nickel oxide concentration up to 0.8 mol%. This is ascribed to increasing presence of nickel ions in octahedral positions that act as modifiers and are predicted to have induced structural defects like dangling bonds in the glass network. Such increased degree of disorder in the glass network is anticipated to be a hindrance for the propagation of ultrasonic waves and hence caused the decrease in the velocities of ultrasonic waves and elastic coefficients. Overall, there is a decrease in mechanical strength of these glasses with increased content of nickel oxide up to 0.8 mol%.
This study is mainly focused on electrical characteristics of PbO−ZrO2−SiO2: TiO2 glass ceramics embedded with Pb2Ti2O6 cubic pyrochlore crystal phases. The samples were synthesized by usual melt ...quenching technique and subsequent heat treating at crystallization temperature for prolonged times. The samples were characterized by XRD, SEM and DSC, IR, EPR and optical absorption spectroscopy techniques. Later, dielectric properties viz., dielectric constant, loss tangent, electric moduli, electrical impedance and a.c. conductivity over wide ranges of frequency and temperature, have been measured as a function of TiO2 content. The results of characterization techniques viz., XRD, SEM and DSC, indicated that the samples are embedded with multiple crystal grains (with sizes varying from 0.1 to 1 μm) cemented with residual glass phase. The volume fraction of the crystal grains is found to increase with increase of TiO2 content. The XRD studies on PbO−ZrO2−SiO2:TiO2 glass ceramics revealed that Pb2Ti2O6 cubic pyrochlore crystal phase is the principal phase present in the bulk samples. The studies have also confirmed that a small part of Pb(Zr 0.5Ti0.5)O3 and Ti2O3 crystal grains are also present in the titled glass ceramics. The results of IR spectral studies have indicated that there is an increasing degree of polymerization of glass network with increasing TiO2 content up to 0.6 mol%. This is attributed to the presence of Ti ions predominantly in Ti4+ state (in this concentration range of TiO2) that take part in the network forming positions with TiO4 and also substitutionally positioned octahedral sites. The results of optical absorption and EPR spectral studies have pointed out that a part of the Ti ions were reduced to Ti3+ state and such ions were predicted to act as modifiers. These studies have also indicated that the concentration of Ti3+ ions is higher in the samples crystallized with 0.8 and 1.0 mol%. The values of dielectric parameters are decreased with increasing of crystallizing agent. The decrease is attributed to the participation of Ti ions in the formation of Pb2Ti2O6 cubic pyrochlore crystalline phases with TiO4 structural units. Quantitative analysis of the dielectric properties of PbO−ZrO2−SiO2:TiO2 glass ceramics together with the results of spectroscopic studies indicated that the electrical insulating strength is the highest for the glass crystallized with 0.6 mol% of TiO2.
Dispersion of electric moduli M′ and M″(ω) with frequency in the temperature range 30–350 °C for the PbO-ZrO2-SiO2 glass crystallized with 0.8 mol% of TiO2. Display omitted
•Study deals with electrical characteristics of PbO−ZrO2−SiO2:TiO2 glass ceramics.•XRD, SEM studies indicated glass ceramics contain Pb2Ti2O6 pyrochlore crystal phases.•Spectroscopic studies indicated Ti ions exist in Ti3+,Ti4+ states in glass ceramics.•Dielectric parameters are decreased with increase of crystallizing agent TiO2.•Decrease is attributed to participation of Ti ions in pyrochlore crystalline phases.
Dielectric constant ('), loss (tandelta), ac conductivity (sigma) of CaO-Sb2O3-B2O3:M2O3 (Al2O3, Ga2O3 and In2O3) glasses with varying concentrations of M2O3 (0-5mol%), were measured as a function of ...frequency and temperature over moderately wide ranges. The analysis of results of these studies along with IR, Raman and optical absorption spectra and also DTA studies indicated that in the concentration ranges, 0 < =Al2O3 < =,0 < =Ga2O3 < =2 and 1 < =In2O3 < =5, Al3+, Ga3+ ions occupy tetrahedral positions whereas In3+ ions take up octahedral substitutional positions, cross-link with the other structural units in the glass network and increase the rigidity of the glass network.
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