Search results for: cubic method

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Bharti Gupta, V. K. Kukreja

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A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.

Keywords: cubic B-spline basis, spectral norms, shifted Chebyshev polynomials, collocation points, error estimates

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

Abstract:

The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: A. Chillali, M. Sahmoudi

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In this paper we will give a method for encoding the elements of the ring of integers of sextic extension, namely L = Q(a,b) which is a rational quadratic over cubic field K =Q(a) where a^{2} is a rational square free integer and b is a root of irreducible polynomiale of degree 3.

Keywords: coding, integral bases, sextic, quadratic

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Authors: K. N. S. Kasi Viswanadham

Abstract:

Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords: collocation method, coupled system, cubic b-splines, mesh points

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Authors: Mitat Uysal

Abstract:

A new met heuristic optimization algorithm called as Migrating Birds Optimization is used for curve fitting by rational cubic Bezier Curves. This requires solving a complicated multivariate optimization problem. In this study, the solution of this optimization problem is achieved by Migrating Birds Optimization algorithm that is a powerful met heuristic nature-inspired algorithm well appropriate for optimization. The results of this study show that the proposed method performs very well and being able to fit the data points to cubic Bezier Curves with a high degree of accuracy.

Keywords: algorithms, Bezier curves, heuristic optimization, migrating birds optimization

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Authors: Jihad H. Asad

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An expression for the Green’s function (GF) of anisotropic face cantered cubic (IFCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.

Keywords: lattice Green's function, elliptic integral, physics, cubic lattice

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Authors: B. Bouadjemi, S. Bentata, W. Benstaali, A. Abbad, T. Lantri, A. Zitouni

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The purpose of this study was to investigate the structural,electronic and magnetic properties of the cubic praseodymium oxides perovskites PrMnO3. It includes our calculations based on the use of the density functional theory (DFT) with both generalized gradient approximation (GGA) and GGA+U approaches, The spin polarized electronic band structures and densities of states as well as the integer value of the magnetic moment of the unit cell (6 μB) illustrate that PrMnO3 is half-metallic ferromagnetic. The study prove that the compound is half-metallic ferromagnetic however the results obtained, make the cubic PrMnO3 a promising candidate for application in spintronics.

Keywords: cubic, DFT, electronic properties, magnetic moment, spintronics

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Authors: Bin Sheng, Changhong Lu

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Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

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Authors: B. Bouadjemi, S. Bentata, W. Benstaali, A. Abbad

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The electronic and magnetic properties of the cubic praseodymium oxides perovskites PrMnO3 were calculated using the density functional theory (DFT) with both generalized gradient approximation (GGA) and GGA+U approaches, where U is on-site Coulomb interaction correction. The results show a half-metallic ferromagnetic ground state for PrMnO3 in GGA+U approached, while semi-metallic ferromagnetic character is observed in GGA. The results obtained, make the cubic PrMnO3 a promising candidate for application in spintronics.

Keywords: first-principles, electronic properties, transition metal, materials science

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Authors: M. Khundadze, V. Varazashvili, N. Lejava, R. Jorbenadze

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Phase transitions of cerium and neodymium are investigated by using high-temperature scanning calorimeter (HT-1500 Seteram). For cerium two types of transformation are detected: at 350-372 K - hexagonal close packing (hcp) - face-centered cubic lattice (fcc) transition, and at 880-960K the face-centered cubic lattice (fcc) transformation into body-centered cubic lattice (bcc). For neodymium changing of hexagonal close packing (hcp) into the body-centered cubic lattice (bcc) is detected at 1093-1113K. The thermal characteristics of transitions – enthalpy, entropy, temperature domains – are reported.

Keywords: cerium, calorimetry, enthalpy of phase transitions, neodymium

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Authors: M. Khundadze, V. Varazashvili, N. Lejava, R. Jorbenadze

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Phase transitions of cerium and neodymium are investigated by using high temperature scanning calorimeter (HT-1500 Seteram). For cerium two types of transformation are detected: at 350-372 K - hexagonal close packing (hcp) - face-centered cubic lattice (fcc) transition, and in 880-960K the face-centered cubic lattice (fcc) transformation into body-centered cubic lattice (bcc). For neodymium changing of hexagonal close packing (hcp) into body-centered cubic lattice (bcc) is detected at 1093-1113K. The thermal characteristics of transitions – enthalpy, entropy, temperature domains – are reported.

Keywords: cerium, calorimetry, neodymium, enthalpy of phase transitions, neodymium

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Arnab Majumdar, Srimani Sen

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In this paper, a vivid simulated study has been made on 35 GHz Ka-band window frequency in order to judge and compare the DC and high frequency properties of cubic ZnB-GaN with the existing hexagonal 4H-SiC. A flat profile p⁺pnn⁺ DDR structure of impatt is chosen and is optimized at a particular bias current density with respect to efficiency and output power taking into consideration the effect of mobile space charge also. The simulated results obtained reveals the strong potentiality of impatts based on both cubic ZnB-GaN and hexagonal 4H-SiC. The DC-to-millimeter wave conversion efficiency for cubic ZnB-GaN impatt obtained is 50% with an estimated output power of 2.83 W at an optimized bias current density of 2.5×10⁸ A/m². The conversion efficiency and estimated output power in case of hexagonal 4H-SiC impatt obtained is 22.34% and 40 W respectively at an optimum bias current density of 0.06×10⁸ A/m².

Keywords: cubic ZnB-GaN, hexagonal 4H-SiC, double drift impatt diode, millimetre wave, optimised bias current density, wide band gap semiconductor

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Authors: Fakharuddin Ibrahim, Jamaludin Md. Ali, Ahmad Ramli

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In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G¹ continuity. The conditions considered are known as the G¹ Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

Keywords: data interpolation, rational ball curve, hermite condition, continuity

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Authors: M. A. Ghebouli, A. Bouhemadou, H. Choutri, L. Louaila

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Some physical properties of the cubic perovskites CsXF3 (X = Sr, Ca, and Hg) have been investigated using pseudopotential plane–wave (PP-PW) method based on the density functional theory (DFT). The calculated lattice constants within GGA (PBE) and LDA (CA-PZ) agree reasonably with the available experiment data. The elastic constants and their pressure derivatives are predicted using the static finite strain technique. We derived the bulk and shear moduli, Young’s modulus, Poisson’s ratio and Lamé’s constants for ideal polycrystalline aggregates. The analysis of B/G ratio indicates that CsXF3 (X = Ca, Sr, and Hg) are ductile materials. The thermal effect on the volume, bulk modulus, heat capacities CV, CP, and Debye temperature was predicted.

Keywords: perovskite, PP-PW method, elastic constants, electronic band structure

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Authors: B. Bouadjemi, S. Bentata, W. Benstaali, A. Abbad, T. Lantri, A. Zitouni

Abstract:

The purpose of this study was to investigate the structural,electronic and magnetic properties of the cubic praseodymium oxides perovskites PrMnO3. It includes our calculations based on the use of the density functional theory (DFT) with both generalized gradient approximation (GGA) and GGA+U approaches, The spin polarized electronic band structures and densities of states aswellas the integer value of the magnetic moment of the unit cell (6 μB) illustrate that PrMnO3 is half-metallic ferromagnetic. The study shows that the robust half-metallicity makes the cubic PrMnO3 a promising candidate for application in spintronics.

Keywords: Perovskite, DFT, electronic properties, Magnetic moment, half-metallic

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Authors: Edamana Vasudevan Krishnan

Abstract:

This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: Raghvendra Singh Yadav, Ivo Kuřitka

Abstract:

In this report, we studied the impact of Gd3+ substitution on structural, magnetic and electrical properties of CoFe2O4 nanoparticles synthesized by sonochemical method. X-ray diffraction pattern confirmed the formation of cubic spinel structure at low concentration of Gd3+ ions, however, GdFeO3 additional phase was observed at higher concentration of Gd3+ ions. Raman and Fourier Transform Infrared spectroscopy study also confirmed cubic spinel structure of Gd3+ substituted CoFe2O4 nanoparticles. The field emission scanning electron microscopy study revealed that Gd3+ substituted CoFe2O4 nanoparticles were in the range of 5-20 nm. The magnetic properties of Gd3+ substituted CoFe2O4 nanoparticles were investigated by using vibrating sample magnetometer. The variation in saturation magnetization, coercivity and remanent magnetization with Gd3+ concentration in CoFe2O4 nanoparticles was observed. The variation of real and imaginary part of dielectric constant, tan δ, and AC conductivity were studied at room temperature.

Keywords: spinel ferrites, nanoparticles, sonochemical method, magnetic properties

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Authors: Shyh Ming Chern

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Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

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Authors: A. Yazdanmehr, H. Jahed

Abstract:

Being made with the lightest commercially available industrial metal, Magnesium (Mg) alloys are of interest for light-weighting. Expanding their application to different material processing methods requires Mg properties at large strains. Several room-temperature processes such as shot and laser peening and hole cold expansion need compressive large strain data. Two methods have been proposed in the literature to obtain the stress-strain curve at high strains: 1) anti-buckling guides and 2) small cubic samples. In this paper, an anti-buckling fixture is used with the help of digital image correlation (DIC) to obtain the compression-tension (C-T) of AZ31B-H24 rolled sheet at large strain values of up to 10.5%. The effect of the anti-bucking fixture on stress-strain curves is evaluated experimentally by comparing the results with those of the compression tests of cubic samples. For testing cubic samples, a new fixture has been designed to increase the accuracy of testing cubic samples with DIC strain measurements. Results show a negligible effect of anti-buckling on stress-strain curves, specifically at high strain values.

Keywords: large strain, compression-tension, loading-unloading, Mg alloys

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Authors: Kunwar Mrityunjai Sharma, Trilok Nath Singh

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The Navier-Stokes equation is used to study nonlinear fluid flow in rough 2D fractures. The major goal is to investigate the influence of inertial flow owing to fracture wall roughness on nonlinear flow behavior. Roughness profiles are developed using Barton's Joint Roughness Coefficient (JRC) and used as fracture walls to assess wall roughness. Four JRC profiles (5, 11, 15, and 19) are employed in the study, where a higher number indicates higher roughness. A parametric study has been performed using varying pressure gradients, and the corresponding Forchheimer number is calculated to observe the nonlinear behavior. The results indicate that the fracture roughness has a significant effect on the onset of nonlinearity. Additionally, the validity of the cubic law is evaluated and observed that it overestimates the flow in rough fractures and should be used with utmost care.

Keywords: fracture flow, nonlinear flow, cubic law, Navier-stokes equation

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Authors: Darsh N. Patel, Eric Olson

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Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: Raghvendra Singh Yadav, Ivo Kuřitka, Jarmila Vilcakova, Pavel Urbánek, Michal Machovsky, Milan Masař, Martin Holek

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Herein, we reported the influence of La³⁺ substitution on structural, magnetic and dielectric properties of CoFe₂O₄ nanoparticles synthesized by starch-assisted sol-gel combustion method. X-ray diffraction pattern confirmed the formation of cubic spinel structure of La³⁺ ions doped CoFe₂O₄ nanoparticles. Raman and Fourier Transform Infrared spectroscopy study also confirmed cubic spinel structure of La³⁺ substituted CoFe₂O₄ nanoparticles. The field emission scanning electron microscopy study revealed that La³⁺ substituted CoFe2O4 nanoparticles were in the range of 10-40 nm. The magnetic properties of La³⁺ substituted CoFe₂O₄ nanoparticles were investigated by using vibrating sample magnetometer. The variation in saturation magnetization, coercivity and remanent magnetization with La³⁺ concentration in CoFe2O4 nanoparticles was observed. The variation of real and imaginary part of dielectric constant, tan δ, and AC conductivity were studied with change of concentration of La³⁺ ions in CoFe₂O₄ nanoparticles. The variation in optical properties was studied via UV-Vis absorption spectroscopy. Acknowledgment: This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic – Program NPU I (LO1504).

Keywords: starch, sol-gel combustion method, nanoparticles, magnetic properties, dielectric properties

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Authors: Samaneh Poormohammadi, Farid Golkar, Vahideh Khatibi Sarabi

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Climate change and consecutive droughts have increased the importance of using rainwater harvesting methods. One of the methods of rainwater harvesting and, in other words, the management of atmospheric water resources is the use of weather modification technologies. Weather modification (also known as weather control) is the act of intentionally manipulating or altering the weather. The most common form of weather modification is cloud seeding, which increases rain or snow, usually for the purpose of increasing the local water supply. Cloud seeding operations in Iran have been married since 1999 in central Iran with the aim of harvesting rainwater and reducing the effects of drought. In this research, we analyze the results of cloud seeding operations in the Simindashtplain in northern Iran. Rainwater harvesting with the help of cloud seeding technology has been evaluated through its effects on surface water and underground water. For this purpose, two different methods have been used to estimate runoff. The first method is the US Soil Conservation Service (SCS) curve number method. Another method, known as the reasoning method, has also been used. In order to determine the infiltration rate of underground water, the balance reports of the comprehensive water plan of the country have been used. In this regard, the study areas located in the target area of each province have been extracted by drawing maps of the influence coefficients of each area in the GIS software. It should be mentioned that the infiltration coefficients were taken from the balance sheet reports of the country's comprehensive water plan. Then, based on the area of each study area, the weighted average of the infiltration coefficient of the study areas located in the target area of each province is considered as the infiltration coefficient of that province. Results show that the amount of water extracted from the rain with the help of cloud seeding projects in Simindasht is as follows: an increase in runoff 63.9 million cubic meters (with SCS equation) or 51.2 million cubic meters (with logical equation) and an increase in ground water resources: 40.5 million cubic meters.

Keywords: rainwater harvesting, ground water, atmospheric water resources, weather modification, cloud seeding

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Authors: Raghvendra Singh Yadav, Ivo Kuřitka, Jaromir Havlica, Zuzana Kozakova, Jiri Masilko, Lukas Kalina, Miroslava Hajdúchová, Vojtěch Enev, Jaromir Wasserbauer

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In this work, we investigated the structural and magnetic properties of CoFe2O4:Nd3+/Dy3+/Pr3+/Gd3+ nanoparticles synthesized by starch-assisted sol-gel combustion method. X-ray diffraction pattern confirmed the formation of cubic spinel structure of rare-earth ions (Nd3+, Dy3+, Pr3+, Gd3+) doped CoFe2O4 spinel ferrite nanoparticles. Raman and Fourier Transform Infrared spectroscopy study also confirmed cubic spinel structure of rare-earth ions (Nd3+, Dy3+, Pr3+, Gd3+) substituted CoFe2O4 nanoparticles. The field emission scanning electron microscopy study revealed the effect of annealing temperature on size of rare-earth ions (Nd3+, Dy3+, Pr3+, Gd3+) substituted CoFe2O4 nanoparticles and particles were in the range of 10-100 nm. The magnetic properties of rare-earth ions (Nd3+, Dy3+, Pr3+, Gd3+) substituted CoFe2O4 nanoparticles were investigated by using vibrating sample magnetometer. The variation in saturation magnetization, coercivity and remanent magnetization with annealing temperature/ particle size of rare-earth ions (Nd3+, Dy3+, Pr3+, Gd3+) substituted CoFe2O4 nanoparticles was observed. Acknowledgment: This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic – Program NPU I (LO1504).

Keywords: starch, sol-gel combustion method, rare-earth ions, spinel ferrite nanoparticles, magnetic properties

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Authors: M. Guler, E. Guler

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We report some elastic parameters of cubic fluorite type neptunium dioxide (NpO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other relevant elastic parameters were also calculated during research. After calculations, we have compared our results with the available theoretical data. Our results agree well with the previous theoretical findings of the considered quantities of NpO2.

Keywords: NpO2, elastic properties, bulk modulus, mechanical properties

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Authors: E. Güler, M. Güler

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We present some elastic parameters of cubic fluorite type uranium dioxide (UO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic parameters were calculated during research. After calculations, we compared our results not only with the available theoretical data but also with previous experimental results. Our results are consistent with experiments and compare well the former theoretical results of the considered parameters of UO2.

Keywords: UO2, elastic constants, bulk modulus, mechanical properties

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Authors: E. Güler, M. Güler

Abstract:

We report some elastic quantities of cubic fluorite type plutonium dioxide (PuO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic quantities were calculated during present research. After present calculations, we have compared our results with the existing theoretical data of literature. Our results are consistent with previous theoretical findings of the considered parameters of PuO2.

Keywords: PuO2, elastic properties, bulk modulus, mechanical properties

Procedia PDF Downloads 273