Search results for: the spherical Kadomtsev-Petviashvili equation

Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Ilze Pelece, Imants Ziemelis, Henriks Putans

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Traditionally the solar energy has been used in southern countries, but it has been used also in northern ones. Most popular kind of use of solar energy in Latvia is solar collector for water heating. Traditionally flat-plate solar collectors are used because of simplicity of manufacturing. However, some peculiarities in use of solar energy in northern countries must be taken into account. In northern countries, there is lower irradiance, but longer day and longer path of the sun during summer. Therefore traditional flat-plate solar collectors are not appropriate enough in northern countries, but new forms must be developed. There are two forms of solar collectors - cylindrical and semi-spherical – proposed in this work. Such collectors can be made both for water or air heating. Theoretical calculations and measurements of energy gain from those two collectors have been done. Results show that daily energy sum received by the semi-spherical collector from the sun at the middle of summer is 1.43 times more than that of the flat one, but for the cylindrical collector, it is 1.74 times more than that of the flat one or equal to that of the tracking to sun flat-plate collector. The resulting difference in energy gain from collector will be not so large because of the difference in heat loses. Heat can be decreased by switching off the water circulation pump when the sun is covered by clouds. For this purpose solar batteries, powered pump can be used instead of complicated and expensive automatics. Even more important than overall energy gain is the fact that semi-spherical and cylindrical collectors work all day (17 hours in the middle of summer at 57 northern latitudes), while flat-plate collector only about 11 hours. Yearly energy sum received by the collector from the sun is 1.5 and 1.9 times larger for the semi-spherical and cylindrical collector respectively as for the flat one. The cylindrical solar collector is easier to manufacture, but semi-spherical one is more aesthetical and durable against the impact of the wind. Although solar collectors for water and air heating are studied in this article, main ideas are applicable also for solar batteries.

Keywords: cylindric, semi-spherical, solar collector, solar energy, water heating

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: O. Altuntaş, A. Güral

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The hardness-microstructure relationships of spherical cementite in bainitic matrix obtained by a different heat treatment cycles carried out to high carbon powder metallurgy (P/M) steel were investigated. For this purpose, 1.5 wt.% natural graphite powder admixed in atomized iron powders and the mixed powders were compacted under 700 MPa at room temperature and then sintered at 1150 °C under a protective argon gas atmosphere. The densities of the green and sintered samples were measured via the Archimedes method. A density of 7.4 g/cm³ was obtained after sintering and a density of 94% was achieved. The sintered specimens having primary cementite plus lamellar pearlitic structures were fully quenched from 950 ^°C temperature and then over-tempered at 705 °C temperature for 60 minutes to produce spherical-fine cementite particles in the ferritic matrix. After by this treatment, these samples annealed at 735 °C temperature for 3 minutes were austempered at 300 °C salt bath for a period of 1 to 5 hours. As a result of this process, it could be able to produced spherical cementite particle in the bainitic matrix. This microstructure was designed to improve wear and toughness of P/M steels. The microstructures were characterized and analyzed by SEM and micro and macro hardness.

Keywords: powder metallurgy steel, bainite, cementite, austempering and spheroidization heat treatment

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Andrey V. Samokhin, Nikolay V. Alekseev, Mikhail A. Sinaiskii

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The report presents the results of R&D of plasma-chemical production of W, W-Cu, W-Ni-Fe nanopowders as well as spherical micropowders of these compounds for their use in modern 3D printing technologies. Plasma-chemical synthesis of nanopowdersis based on the reduction of tungsten oxide compounds powders in a stream of hydrogen-containing low-temperature thermal plasma generated in an electric arc plasma torch. The synthesis of W-Cu and W-Ni-Fe nanocompositesiscarried out using the reduction of a mixture of the metal oxides. Using the synthesized tungsten-based nanocomposites powders, spherical composite micropowders with a submicron structure canbe manufactured by spray dryinggranulation of nanopowder suspension and subsequent densification and spheroidization of granules by melting in a low-temperature thermal plasma flow. The DC arc plasma systems are usedfor the synthesis of nanopowdersas well as for the spheroidization of microgranuls. Plasma systems have a capacity of up to 1 kg/h for nanopowder and up to 5 kg/h for spheroidized powder. All synthesized nanopowders consist of aggregated particles with sizes less than 100 nm, and nanoparticles of W-Cu and W-Ni-Fe composites have core (W) –shell (Cu or Ni-Fe) structures. The resulting dense spherical microparticles with a size of 20-60 microns have a submicron structure with a uniform distribution of metals over the particle volume. The produced tungsten-based nano- and spherical micropowderscan be used to develop new materials and manufacture products using advanced modern technologies.

Keywords: plasma, powders, production, tungsten-based

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Michael Williams

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The ability to control a flowing well is of the utmost important. During the kill phase, heavy weight kill mud is circulated around the well. While increasing bottom hole pressure near wellbore formation, the damage is increased. The addition of high density spherical objects has the potential to minimise this near wellbore damage, increase bottom hole pressure and reduce operational time to kill the well. This operational time saving is seen in the rapid deployment of high density spherical objects instead of building high density drilling fluid. The research aims to model the well kill process using a Computational Fluid Dynamics software. A model has been created as a proof of concept to analyse the flow of micron sized spherical objects in the drilling fluid. Initial results show that this new methodology of spherical objects in drilling fluid agrees with traditional stream lines seen in non-particle flow. Additional models have been created to demonstrate that areas of higher flow rate around the bit can lead to increased probability of wash out of formations but do not affect the flow of micron sized spherical objects. Interestingly, areas that experience dimensional changes such as tool joints and various BHA components do not appear at this initial stage to experience increased velocity or create areas of turbulent flow, which could lead to further borehole stability. In conclusion, the initial models of this novel well control methodology have not demonstrated any adverse flow patterns, which would conclude that this model may be viable under field conditions.

Keywords: well control, fluid mechanics, safety, environment

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: A. Selmi, A. Bisharat

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Using Fourier transform and based on the Mindlin's 2^nd gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

Keywords: Eshelby tensor, Eshelby-like tensor, Green’s function, Mindlin’s 2nd gradient model, spherical inclusion

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: A. Bentabet, A. Aydin, N. Fenineche

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The mean penetration depth has a most important in the absorption transport phenomena. Analytical model of light ion backscattering coefficients from solid targets have been made by Vicanek and Urbassek. In the present work, we showed a mathematical expression (deterministic model) for Z1/2. In advantage, in the best of our knowledge, relatively only one analytical model exit for electron or positron mean penetration depth in solid targets. In this work, we have presented a simple geometric spherical model of absorbed particles based on CSDA scheme. In advantage, we have showed an analytical expression of the mean penetration depth by combination between our model and the Vicanek and Urbassek theory. For this, we have used the Relativistic Partial Wave Expansion Method (RPWEM) and the optical dielectric model to calculate the elastic cross sections and the ranges respectively. Good agreement was found with the experimental and theoretical data.

Keywords: Bentabet spherical geometric model, continuous slowing down approximation, stopping powers, ranges, mean penetration depth

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Authors: Sirapat Lookrak, Anol Paisal

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Space debris has numerous manifestations, including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's Law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane, so the Gaussian surface is a very small cylinder, and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless maneuvering space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: near-field approximation, far-field approximation, localized Gauss’s law, electric charge density

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

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Authors: S. V. Patil , S. K. Sahoo, K. Y. Chougule, S. S. Patil

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Spherically agglomerated crystals of Pioglitazone hydrochloride (PGH) with improved flowability and compactibility were successfully prepared by emulsion solvent diffusion method. Plane agglomerates and agglomerates with additives: polyethylene glycol 6000 (PEG), polyvinyl pyrrolidone (PVP) and β cyclodextrin (β-CD) were prepared using methanol, chloroform and water as good solvent, bridging liquid and poor solvent respectively. Particle size, flowability, compactibility and packability of plane, PEG and β-CD agglomerates were preferably improved for direct tableting compared with raw crystals and PVP agglomerates of PGH. These improved properties of spherically agglomerated crystals were due to their large and spherical shape and enhanced fragmentation during compaction which was well supported by increased tensile strength and less elastic recovery of its compact. X-ray powder diffraction and differential scanning calorimetry study were indicated polymorphic transition of PGH from form II to I during recrystallization but not associated with chemical transition indicated by fourier transforms infrared spectra.

Keywords: spherical crystallization, pioglitazone hydrochloride, compactibility, packability

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Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Eric Huang, Coleman DeLude, Justin Romberg, Saibal Mukhopadhyay, Madhavan Swaminathan

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High performance computing (HPC) based emulators can be used to model the scattering from multiple stationary and moving targets for RADAR applications. These emulators rely on the RADAR Cross Section (RCS) of the targets being available in complex scenarios. Representing the RCS using tables generated from electromagnetic (EM) simulations is often times cumbersome leading to large storage requirement. This paper proposed a spherical harmonic based anisotropic scatterer model to represent the RCS of complex targets. The problem of finding the locations and reflection profiles of all scatterers can be formulated as a linear least square problem with a special sparsity constraint. This paper solves this problem using a modified Orthogonal Matching Pursuit algorithm. The results show that the spherical harmonic based scatterer model can effectively represent the RCS data of complex targets.

Keywords: RADAR, RCS, high performance computing, point scatterer model

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: N. N. M. Pauzi, M. R. Karim, M. Jamil, R. Hamid, M. F. M. Zain

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The aim of this study is to conduct an experimental investigation on the influence of complete replacement of natural coarse aggregate with spherically-shape and crushed waste cathode ray tube (CRT) glass to the aspect of workability, density, and compressive strength of the concrete. After characterizing the glass, a group of concrete mixes was prepared to contain a 40% spherical CRT glass and 60% crushed CRT glass as a complete (100%) replacement of natural coarse aggregates. From a total of 16 types of concrete mixes, the optimum proportion was selected based on its best performance. The test results showed that the use of spherical and crushed glass that possesses a smooth surface, rounded, irregular and elongated shape, and low water absorption affects the workability of concrete. Due to a higher specific gravity of crushed glass, concrete mixes containing CRT glass had a higher density compared to ordinary concrete. Despite the spherical and crushed CRT glass being stronger than gravel, the results revealed a reduction in compressive strength of the concrete. However, using a lower water to binder (w/b) ratio and a higher superplasticizer (SP) dosage, it is found to enhance the compressive strength of 60.97 MPa at 28 days that is lower by 13% than the control specimen. These findings indicate that waste CRT glass in the form of spherical and crushed could be used as an alternative of coarse aggregate that may pave the way for the disposal of hazardous e-waste.

Keywords: cathode ray tube, glass, coarse aggregate, compressive strength

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Weiping Liu

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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

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Authors: Kasirga Yildirak, Ismail Gur

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We propose a model to measure hail risk of an Agricultural Insurance portfolio. Hail is one of the major catastrophic event that causes big amount of loss to an insurer. Moreover, it is very hard to predict due to its strange atmospheric characteristics. We make use of parcel based claims data on apricot damage collected by the Turkish Agricultural Insurance Pool (TARSIM). As our ultimate aim is to compute the loadings assigned to specific parcels, we build a portfolio risk model that makes use of PD and the severity of the exposures. PD is computed by Spherical-Linear and Circular –Linear regression models as the data carries coordinate information and seasonality. Severity is mapped into integer brackets so that Probability Generation Function could be employed. Individual regressions are run on each clusters estimated on different criteria. Loss distribution is constructed by Panjer Recursion technique. We also show that one risk-one crop model can easily be extended to the multi risk–multi crop model by assuming conditional independency.

Keywords: hail insurance, spherical regression, circular regression, spherical clustering

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