Search results for: spherical symmetry

Authors: B. Zare-Farsani, M. Valieghbal, M. Tarkashvand, A. H. Farahbod

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To provide the conditions for nuclear fusion by high energy and powerful laser beams, it is required to have a high degree of symmetry and surface uniformity of the spherical capsules to reduce the Rayleigh-Taylor hydrodynamic instabilities. In this paper, we have used the digital microscopic holography based on Mach-Zehnder interferometer to study the quality of targets for inertial fusion. The interferometric pattern of the target has been registered by a CCD camera and analyzed by Holovision software. The uniformity of the surface and shell thickness are investigated and measured in reconstructed image. We measured shell thickness in different zone where obtained non uniformity 22.82 percent.  

Keywords: inertial confinement fusion, mach-zehnder interferometer, digital holographic microscopy, image reconstruction, holovision

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Authors: Anas Ibrahim Yahaya, Christophe Soligo

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A substantial body of literature has reported on facial symmetry and asymmetry and their role in human mate choice. However, major gaps persist, with nearly all data originating from the WEIRD (Western, Educated, Industrialised, Rich and Developed) populations, and results remaining largely equivocal when compared across studies. This study is aimed at quantifying facial asymmetry from the 3D faces of the Hausa of northern Nigeria and also aimed at determining their (Hausa) perceptions and judgements of standardised facial images with different levels of asymmetry using questionnaires. Data were analysed using R-studio software and results indicated that individuals with lower levels of facial asymmetry (near facial symmetry) were perceived as more attractive, more suitable as marriage partners and more caring, whereas individuals with higher levels of facial asymmetry were perceived as more aggressive. The study conclusively asserts that all faces are asymmetric including the most beautiful ones, and the preference of less asymmetric faces was not just dependent on single facial trait, but rather on multiple facial traits; thus the study supports that physical attractiveness is not just an arbitrary social construct, but at least in part a cue to general health and possibly related to environmental context.

Keywords: face, asymmetry, symmetry, Hausa, preference

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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: Pratibha, Jyoti Kori

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Particles in industry, harvesting, coal mines, etc. may not necessarily be spherical in shape. In general, it is difficult to find perfectly spherical particle. The prediction of movement and deposition of non spherical particle in distinct airway generation is much more difficult as compared to spherical particles. Moreover, there is extensive inflexibility in deposition between ducts of a particular generation and inside every alveolar duct since particle concentrations can be much bigger than the mean acinar concentration. Consequently, a large number of particles fail to be exhaled during expiration. This study presents a mathematical model for the movement and deposition of those non-spherical particles by using particle aspect ratio and shape factor. We analyse the pulsatile behavior underneath sinusoidal wall oscillation due to periodic breathing condition through a non-Darcian porous medium or inside pulmonary region. Since the fluid is viscous and Newtonian, the generalized Navier-Stokes equation in two-dimensional coordinate system (r, z) is used with boundary-layer theory. Results are obtained for various values of Reynolds number, Womersley number, Forchsheimer number, particle aspect ratio and shape factor. Numerical computation is done by using finite difference scheme for very fine mesh in MATLAB. It is found that the overall air velocity is significantly increased by changes in aerodynamic diameter, aspect ratio, alveoli size, Reynolds number and the pulse rate; while velocity is decreased by increasing Forchheimer number.

Keywords: deposition, interstitial lung diseases, non-Darcian medium, numerical simulation, shape factor

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Authors: Ouardi Okkacha, Kaarour Abedlkrim, Meskine Mohamed

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The effective Hamiltonians are widely used in molecular spectroscopy for the interpretation of the vibration-rotation spectra. Their construction is an ambiguous procedure due to the existence of unitary transformations that change the effective Hamiltonian but do not change its eigenvalues. As a consequence of this ambiguity, it may happen that some parameters of effective Hamiltonians cannot be recovered from experimental data in a unique way. The type of admissible transformations which keeps the operator form of the effective Hamiltonian unaltered and the number of empirically determinable parameters strongly depend on the symmetry type of a molecule (asymmetric top, spherical top, and so on) and on the degeneracy of the vibrational state. In this work, we report the study of the ambiguity of effective Hamiltonian for the fundamental degenerate states v3 of the Molecule 12CD4.

Keywords: 12CD4, high-resolution infrared spectra, tetrahedral tensorial formalism, vibrational states, rovibrational line position analysis, XTDS, SPVIEW

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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: Rinku Maji, Joydeep Chakrabortty, Stephen F. King

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The grand unified theory (GUT) rationales the arbitrariness of the standard model (SM) and explains many enigmas of nature at the outset of a single gauge group. The GUTs predict the proton decay and, the spontaneous symmetry breaking (SSB) of the higher symmetry group may lead to the formation of topological defects, which are indispensable in the context of the cosmological observations. The Super-Kamiokande (Super-K) experiment sets sacrosanct bounds on the partial lifetime (τ) of the proton decay for different channels, e.g., τ(p → e+ π0) > 1.6×10³⁴ years which is the most relevant channel to test the viability of the nonsupersymmetric GUTs. The GUTs based on the gauge groups SO(10) and E(6) are broken to the SM spontaneously through one and two intermediate gauge symmetries with the manifestation of the left-right symmetry at least at a single intermediate stage and the proton lifetime for these breaking chains has been computed. The impact of the threshold corrections, as a consequence of integrating out the heavy fields at the breaking scale alter the running of the gauge couplings, which eventually, are found to keep many GUTs off the Super-K bound. The possible topological defects arising in the course of SSB at different breaking scales for all breaking chains have been studied.

Keywords: grand unified theories, proton decay, threshold correction, topological defects

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

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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: David C. Ni

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The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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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: Alireza Abdikian

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By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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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: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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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: M. Riaz, Inamur Rehman, Abhishek Sharma

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The present work is the development of an experimental method for determining the thermal diffusivity variations with temperature of selected regular shaped solid fruits and vegetables subjected to forced convection cooling. Experimental investigations were carried on the sample chosen (potato and brinjal), which is approximately of spherical geometry. The variation of temperature within the food product is measured at several locations from centre to skin, under forced convection environment using a deep freezer, maintained at -10°C.This method uses one dimensional Fourier equation applied to regular shapes. For this, the experimental temperature data obtained from cylindrical and spherical shaped products during pre-cooling was utilised. Such temperature and thermal diffusivity profiles can be readily used with other information such as degradation rate, etc. to evaluate thermal treatments based on cold air cooling methods for storage of perishable food products.

Keywords: thermal diffusivity, skin temperature, precooling, forced convection, regular shaped

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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: Wenhao Lan, Ning Li, Qiang Tong

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To improve the registration accuracy of a source point cloud and template point cloud when the initial relative deflection angle is too large, a PointNetLK algorithm combined with an oriented bounding box (PointNetLK-OBB) is proposed. In this algorithm, the OBB of a 3D point cloud is used to represent the macro feature of source and template point clouds. Under the guidance of the iterative closest point algorithm, the OBB of the source and template point clouds is aligned, and a mirror symmetry effect is produced between them. According to the fitting degree of the source and template point clouds, the mirror symmetry plane is detected, and the optimal rotation and translation of the source point cloud is obtained to complete the 3D point cloud registration task. To verify the effectiveness of the proposed algorithm, a comparative experiment was performed using the publicly available ModelNet40 dataset. The experimental results demonstrate that, compared with PointNetLK, PointNetLK-OBB improves the registration accuracy of the source and template point clouds when the initial relative deflection angle is too large, and the sensitivity of the initial relative position between the source point cloud and template point cloud is reduced. The primary contribution of this paper is the use of PointNetLK to avoid the non-convex problem of traditional point cloud registration and leveraging the regularity of the OBB to avoid the local optimization problem in the PointNetLK context.

Keywords: mirror symmetry, oriented bounding box, point cloud registration, PointNetLK-OBB

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Authors: J. Ranjbarn, A. Alibeigloo

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In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock, dynamic response

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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: 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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Authors: Mahsa Mahtab, Morteza Habibi

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The effect of different anode tip geometries on the intensity of soft and hard x-ray emitted from a 4 kJ plasma focus device is investigated. For this purpose, 5 different anode tips are used. The shapes of the uppermost region of these anodes have been cylindrical-flat, cylindrical-hollow, spherical-convex, cone-flat and cone-hollow. Analyzed data have shown that cone-flat, spherical-convex and cone-hollow anodes significantly increase X-ray intensity respectively in comparison with cylindrical-flat anode; while the cylindrical-hollow tip decreases. Anode radius reduction at its end in conic or spherical anodes enhance SXR by increasing plasma density through collecting a greater mass of gas and more gradual transition phase to form a more stable dense plasma pinch. Also, HXR is enhanced by increasing the energy of electrons colliding with the anode surface through raise of induced electrical field. Finally, the cone-flat anode is introduced to use in cases in which the plasma focus device is used as an X-ray source due to its highest yield of X-ray emissions.

Keywords: plasma focus, anode tip, HXR, SXR, pinched plasma

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Authors: B. F. Nteumagne, E. Pindza, E. Mare

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We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.

Keywords: fractional brownian model, symmetry, transaction cost, option pricing

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: Olga V. Korotkaya

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This article is devoted to an important problem of calculation of deflected mode of the combustion chamber and the nozzle end of a new liquid-propellant rocket cruise engine. A special attention is given to the methodology of calculation. Three operating modes are considered. The analysis has been conducted in ANSYS software. The methods of conducted research are mathematical modelling, substructure method, cyclic symmetry, and finite element method. The calculation has been carried out to order of S. P. Korolev Rocket and Space Corporation «Energia». The main results are practical. Proposed methodology and created models would be able to use for a wide range of strength problems.

Keywords: combustion chamber, cyclic symmetry, finite element method, liquid-propellant rocket engine, nozzle end, substructure

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Authors: Mohan L. Jayatiake, Judd Storrs, Jing-Huei Lee

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The optimal MRI resolution relies on a homogeneous magnetic field. However, local susceptibility variations can lead to field inhomogeneities that cause artifacts such as image distortion and signal loss. The effects of local susceptibility variation notoriously increase with magnetic field strength. Active shimming improves homogeneity by applying corrective fields generated from shim coils, but requires calculation of optimal current for each shim coil. FASTMAP (fast automatic shimming technique by mapping along projections) is an effective technique for finding optimal currents works well at high-field, but is restricted to shimming spherical regions of interest. The 3D gradient-echo pulse sequence was modified to reduce sensitivity to eddy currents and used to obtain susceptibility field maps at 4T. Measured fields were projected onto first-and second-order spherical harmonic functions corresponding to shim hardware. A spherical phantom was used to calibrate the shim currents. Susceptibility maps of a volunteer’s brain with and without FASTMAP shimming were obtained. Simulations indicate that optimal shim currents derived from the field map may provide better overall shimming of the human brain.

Keywords: shimming, high-field, active, passive

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Authors: Parvathy Anitha, Nilesh J. Vasa, M. S. Ramachandra Rao

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ZnO is a semiconducting material with a direct wide band gap of 3.37 eV and a large exciton binding energy of 60 meV at room temperature. Microspheres with high sphericity and symmetry exhibit unique functionalities which makes them excellent omnidirectional optical resonators. Hence there is an advent interest in fabrication of single crystalline semiconductor microspheres especially magnetic ZnO microspheres, as ZnO is a promising material for semiconductor device applications. Also, ZnO is non-toxic and biocompatible, implying it is a potential material for biomedical applications. Room temperature Photoluminescence (PL) spectra of the fabricated ZnO microspheres were measured, at an excitation wavelength of 325 nm. The ultraviolet (UV) luminescence observed is attributed to the room-temperature free exciton related near-band-edge (NBE) emission in ZnO. Besides the NBE luminescence, weak and broad visible luminescence (~560nm) was also observed. This broad emission band in the visible range is associated with oxygen vacancies related to structural defects. In transition metal (TM) ion-doped ZnO, 3d levels emissions of TM ions will modify the inherent characteristic emissions of ZnO. A micron-sized ZnO crystal has generally a wurtzite structure with a natural hexagonal cross section, which will serve as a WGM (whispering gallery mode) lasing micro cavity due to its high refractive index (~2.2). But hexagonal cavities suffers more optical loss at their corners in comparison to spherical structures; hence spheres may be a better candidate to achieve effective light confinement. In our study, highly smooth spherical shaped micro particles with different diameters ranging from ~4 to 6 μm were grown on different substrates. SEM (Scanning Electron Microscopy) and AFM (Atomic Force Microscopy) images show the presence of uniform smooth surfaced spheres. Raman scattering measurements from the fabricated samples at 488 nm light excitation provide convincing supports for the wurtzite structure of the prepared ZnO microspheres. WGM lasing studies from TM-doped ZnO microparticles are in progress.

Keywords: laser ablation, microcavity, photoluminescence, ZnO microsphere

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Manuel Alejandro Taborda Ceballos, Martin Sommerfeld

Abstract:

Transport phenomena and dispersion of non-spherical particle in turbulent flows are found everywhere in industrial application and processes. Powder handling, pollution control, pneumatic transport, particle separation are just some examples where the particle encountered are not only spherical. These types of multiphase flows are wall bounded and mostly highly turbulent. The particles found in these processes are rarely spherical but may have various shapes (e.g., fibers, and rods). Although research related to the behavior of regular non-spherical particles in turbulent flows has been carried out for many years, it is still necessary to refine models, especially near walls where the interaction fiber-wall changes completely its behavior. Imaging-based experimental studies on dispersed particle-laden flows have been applied for many decades for a detailed experimental analysis. These techniques have the advantages that they provide field information in two or three dimensions, but have a lower temporal resolution compared to point-wise techniques such as PDA (phase-Doppler anemometry) and derivations therefrom. The applied imaging techniques in dispersed two-phase flows are extensions from classical PIV (particle image velocimetry) and PTV (particle tracking velocimetry) and the main emphasis was simultaneous measurement of the velocity fields of both phases. In a similar way, such data should also provide adequate information for validating the proposed models. Available experimental studies on the behavior of non-spherical particles are uncommon and mostly based on planar light-sheet measurements. Especially for elongated non-spherical particles, however, three-dimensional measurements are needed to fully describe their motion and to provide sufficient information for validation of numerical computations. For further providing detailed experimental results allowing a validation of numerical calculations of non-spherical particle dispersion in turbulent flows, a water channel test facility was built around a horizontal closed water channel. Into this horizontal main flow, a small cross-jet laden with fiber-like particles was injected, which was also solely driven by gravity. The dispersion of the fibers was measured by applying imaging techniques based on a LED array for backlighting and high-speed cameras. For obtaining the fluid velocity fields, almost neutrally buoyant tracer was used. The discrimination between tracer and fibers was done based on image size which was also the basis to determine fiber orientation with respect to the inertial coordinate system. The synchronous measurement of fluid velocity and fiber properties also allow the collection of statistics of fiber orientation, velocity fields of tracer and fibers, the angular velocity of the fibers and the orientation between fiber and instantaneous relative velocity. Consequently, an experimental study the behavior of elongated non-spherical particles in wall bounded turbulent flows was achieved. The development of a comprehensive analysis was succeeded, especially near the wall region, where exists hydrodynamic wall interaction effects (e.g., collision or lubrication) and abrupt changes of particle rotational velocity. This allowed us to predict numerically afterwards the behavior of non-spherical particles within the frame of the Euler/Lagrange approach, where the particles are therein treated as “point-particles”.

Keywords: crossflow, non-spherical particles, particle tracking velocimetry, PIV

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