Search results for: Permittivity tensor.

Authors: Arti Vaish, Harish Parthasarathy

Abstract:

In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.

Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.

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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: Rasoul Abazari

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In this paper, we show that C*-tensor product of an arbitrary C*-algebra A, (not unital necessary) and C*-algebra B without ground state, have no approximately inner strongly continuous one-parameter group of *-automorphisms.

Keywords: One–parameter group, C*– tensor product, Approximately inner, Ground state.

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Authors: Chiharu Okuma, Naoki Yamamoto, Jun Murakami

Abstract:

As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

Keywords: Singular value decomposition (SVD), higher-orderSVD (HOSVD), outer product expansion, power method.

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Authors: Manisha Kankarej

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The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, Integrability condition & Nijenhuis tensor.

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Authors: Sreedevi P. Chakyar, Jolly Andrews, V. P. Joseph

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A compact method for measuring the relative permittivity of a dielectric material at different temperatures using a single circular Split Ring Resonator (SRR) metamaterial unit working as a test probe is presented in this paper. The dielectric constant of a material is dependent upon its temperature and the LC resonance of the SRR depends on its dielectric environment. Hence, the temperature of the dielectric material in contact with the resonator influences its resonant frequency. A single SRR placed between transmitting and receiving probes connected to a Vector Network Analyser (VNA) is used as a test probe. The dependence of temperature between 30 ^oC and 60 ^oC on resonant frequency of SRR is analysed. Relative permittivities ‘ε’ of test samples for different temperatures are extracted from a calibration graph drawn between the relative permittivity of samples of known dielectric constant and their corresponding resonant frequencies. This method is found to be an easy and efficient technique for analysing the temperature dependent permittivity of different materials.

Keywords: Metamaterials, negative permeability, permittivity measurement techniques, split ring resonators, temperature dependent dielectric constant.

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Authors: Fred Lacy

Abstract:

A superconductor has the ability to conduct electricity perfectly and exclude magnetic fields from its interior. In order to understand electromagnetic characteristics of superconductors, their material properties need to be examined. To facilitate this understanding, a theoretical model based on concepts of electromagnetics is presented to explain the electrical and magnetic properties of superconductors. The permittivity response is the key aspect of the model and it describes the electrical resistance response and why it vanishes at the material’s critical temperature. The model also explains the behavior of magnetic fields and why they cannot exist inside superconducting materials. The theoretical concepts and equations associated with this model are used to demonstrate that they are sufficient in describing the behavior of both type I and type II (or high temperature) superconductors. This model is also able to explain why superconductors behave differently than perfect conductors. As a result, examining the permittivity response and understanding electromagnetic field theory provides insight into the major aspects associated with superconducting materials.

Keywords: Ampere’s law, permittivity, permeability, resistivity, Schrödinger wave equation.

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Authors: Sh. Gofurov, O. Ismailova, U. Makhmanov, A. Kokhkharov

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The refractometric method has been used to determine optical properties of concentration features of aqueous solutions of ethanol, tetrahydrofuran and dimethylformamide at the room temperature. Changes in dielectric permittivity of aqueous solutions of ethanol, tetrahydrofuran and dimethylformamide in a wide range of concentrations (0÷1.0 molar fraction) have been studied using molecular dynamics method. The curves depending on the concentration of experimental data on excess refractive indices and excess dielectric permittivity were compared. It has been shown that stable heteromolecular complexes in binary solutions are formed in the concentration range of 0.3÷0.4 mole fractions. The real and complex part of dielectric permittivity was obtained from dipole-dipole autocorrelation functions of molecules. At the concentrations of C = 0.3 / 0.4 m.f. the heteromolecular structures with hydrogen bonds are formed. This is confirmed by the extremum values of excessive dielectric permittivity and excessive refractive index of aqueous solutions.

Keywords: Refractometric method, dielectric constant, molecular dynamics, aqueous solution.

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Authors: Mohammed Boutalline, Imad Badi, Belaid Bouikhalene, Said Safi

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In this paper we describe the Levenvberg-Marquardt (LM) algorithm for identification and equalization of CDMA signals received by an antenna array in communication channels. The synthesis explains the digital separation and equalization of signals after propagation through multipath generating intersymbol interference (ISI). Exploiting discrete data transmitted and three diversities induced at the reception, the problem can be composed by the Block Component Decomposition (BCD) of a tensor of order 3 which is a new tensor decomposition generalizing the PARAFAC decomposition. We optimize the BCD decomposition by Levenvberg-Marquardt method gives encouraging results compared to classical alternating least squares algorithm (ALS). In the equalization part, we use the Minimum Mean Square Error (MMSE) to perform the presented method. The simulation results using the LM algorithm are important.

Keywords: Identification and equalization, communication channel, Levenvberg-Marquardt, tensor decomposition

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Authors: Y. S. Lee, F. Malek, E. M. Cheng, W. W. Liu, F. H. Wee, M. N. Iqbal, Z. Liyana, B. S. Yew, F. S. Abdullah

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This paper presents the electromagnetic interference (EMI) shielding effectiveness of rice husk and carbon nanotubes (RHCNTs) composites in the X-band region (8.2-12.4 GHz). The difference weight ratio of carbon nanotubes (CNTs) were mix with the rice husk. The rectangular waveguide technique was used to measure the complex permittivity of the RHCNTs composites materials. The complex permittivity is represented in terms of both the real and imaginary parts of permittivity in X-band frequency. The conductivity of RHCNTs shows increasing when the ratio of CNTs mixture increases. The composites materials were simulated using Computer Simulation Technology (CST) Microwave Studio simulation software. The shielding effectiveness of RHCNTs and pure rice husk was compared. The highest EMI SE of 30 dB is obtained for RHCNTs composites of 10 wt % CNTs with 10mm thickness.

Keywords: EMI Shielding effectiveness, Carbon nanotube, Composite materials, Waveguide, X-band.

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Authors: Erhan Ata, H. Hilmi Hacisalihoğlu, Yusuf Yayli

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In this work some characterizations of semi Riemannian curvature tensor on almost split quaternion Kaehler manifolds and some characterizations of Ricci tensor on almost split quaternion Kaehler manifolds are given.

Keywords: Almost split quaternion Kaehler manifold, Riemann curvature, Ricci curvature.

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Authors: Hiren Mewada, Suprava Patnaik

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Object identification and segmentation application requires extraction of object in foreground from the background. In this paper the Bhattacharya distance based probabilistic approach is utilized with an active contour model (ACM) to segment an object from the background. In the proposed approach, the Bhattacharya histogram is calculated on non-linear structure tensor space. Based on the histogram, new formulation of active contour model is proposed to segment images. The results are tested on both color and gray images from the Berkeley image database. The experimental results show that the proposed model is applicable to both color and gray images as well as both texture images and natural images. Again in comparing to the Bhattacharya based ACM in ICA space, the proposed model is able to segment multiple object too.

Keywords: Active Contour, Bhattacharya Histogram, Structure tensor, Image segmentation.

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

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This paper is aimed at proposing a rhombus shaped wearable fractal antenna for wireless communication systems. The geometrical descriptors of the antenna have been obtained using bacterial foraging optimization (BFO) for wide band operation. The method of moment based IE3D software has been used to simulate the antenna and observed that miniaturization of 13.08% has been achieved without degrading the resonating properties of the proposed antenna. An analysis with different substrates has also been done in order to evaluate the effectiveness of electrical permittivity on the presented structure. The proposed antenna has low profile, light weight and has successfully demonstrated wideband and multiband characteristics for wearable electronic applications.

Keywords: BFO, bandwidth, electrical permittivity, fractals, wearable antenna.

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Authors: Jonghyun Park, Soonyoung Park, Sanggyun Kim, Wanhyun Cho, Sunworl Kim

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In general, image-based 3D scenes can now be found in many popular vision systems, computer games and virtual reality tours. So, It is important to segment ROI (region of interest) from input scenes as a preprocessing step for geometric stricture detection in 3D scene. In this paper, we propose a method for segmenting ROI based on tensor voting and Dirichlet process mixture model. In particular, to estimate geometric structure information for 3D scene from a single outdoor image, we apply the tensor voting and Dirichlet process mixture model to a image segmentation. The tensor voting is used based on the fact that homogeneous region in an image are usually close together on a smooth region and therefore the tokens corresponding to centers of these regions have high saliency values. The proposed approach is a novel nonparametric Bayesian segmentation method using Gaussian Dirichlet process mixture model to automatically segment various natural scenes. Finally, our method can label regions of the input image into coarse categories: “ground", “sky", and “vertical" for 3D application. The experimental results show that our method successfully segments coarse regions in many complex natural scene images for 3D.

Keywords: Region segmentation, tensor voting, image-based 3D, geometric structure, Gaussian Dirichlet process mixture model

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Authors: Mohamed Gouskir, Belaid Bouikhalene, Hicham Aissaoui, Benachir Elhadadi

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In this paper, we present an application of Riemannian geometry for processing non-Euclidean image data. We consider the image as residing in a Riemannian manifold, for developing a new method to brain edge detection and brain extraction. Automating this process is a challenge due to the high diversity in appearance brain tissue, among different patients and sequences. The main contribution, in this paper, is the use of an edge-based anisotropic diffusion tensor for the segmentation task by integrating both image edge geometry and Riemannian manifold (geodesic, metric tensor) to regularize the convergence contour and extract complex anatomical structures. We check the accuracy of the segmentation results on simulated brain MRI scans of single T1-weighted, T2-weighted and Proton Density sequences. We validate our approach using two different databases: BrainWeb database, and MRI Multiple sclerosis Database (MRI MS DB). We have compared, qualitatively and quantitatively, our approach with the well-known brain extraction algorithms. We show that using a Riemannian manifolds to medical image analysis improves the efficient results to brain extraction, in real time, outperforming the results of the standard techniques.

Keywords: Riemannian manifolds, Riemannian Tensor, Brain Segmentation, Non-Euclidean data, Brain Extraction.

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Authors: Qing Liu, Jean-Fabien Capsal, Claude Richard

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In this current contribution, authors are dedicated to investigate influence of the crystal lamellae orientation on electromechanical behaviors of relaxor ferroelectric Poly (vinylidene fluoride –trifluoroethylene -chlorotrifluoroethylene) (P(VDF-TrFE-CTFE)) films by control of polymer microstructure, aiming to picture the full map of structure-property relationship. In order to define their crystal orientation films, terpolymer films were fabricated by solution-casting, stretching and hot-pressing process. Differential scanning calorimetry, impedance analyzer, and tensile strength techniques were employed to characterize crystallographic parameters, dielectric permittivity, and elastic Young’s modulus respectively. In addition, large electrical induced out-of-plane electrostrictive strain was obtained by cantilever beam mode. Consequently, as-casted pristine films exhibited surprisingly high electrostrictive strain 0.1774% due to considerably small value of elastic Young’s modulus although relatively low dielectric permittivity. Such reasons contributed to large mechanical elastic energy density. Instead, due to 2 folds increase of elastic Young’s modulus and less than 50% augmentation of dielectric constant, fullycrystallized film showed weak electrostrictive behavior and mechanical energy density as well. And subjected to mechanical stretching process, Film C exhibited stronger dielectric constant and out-performed electrostrictive strain over Film B because edge-on crystal lamellae orientation induced by uniaxially mechanical stretch. Hot-press films were compared in term of cooling rate. Rather large electrostrictive strain of 0.2788% for hot-pressed Film D in quenching process was observed although its dielectric permittivity equivalent to that of pristine as-casted Film A, showing highest mechanical elastic energy density value of 359.5 J/m3. In hot-press cooling process, dielectric permittivity of Film E saw values at 48.8 concomitant with ca.100% increase of Young’s modulus. Films with intermediate mechanical energy density were obtained.

Keywords: Crystal orientation, electrostrictive strain, mechanical energy density, permittivity, relaxor ferroelectric.

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Authors: Nisha Goyal, R.K. Gupta

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Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Chiharu Okuma, Jun Murakami, Naoki Yamamoto

Abstract:

In digital signal processing it is important to approximate multi-dimensional data by the method called rank reduction, in which we reduce the rank of multi-dimensional data from higher to lower. For 2-dimennsional data, singular value decomposition (SVD) is one of the most known rank reduction techniques. Additional, outer product expansion expanded from SVD was proposed and implemented for multi-dimensional data, which has been widely applied to image processing and pattern recognition. However, the multi-dimensional outer product expansion has behavior of great computation complex and has not orthogonally between the expansion terms. Therefore we have proposed an alterative method, Third-order Orthogonal Tensor Product Expansion short for 3-OTPE. 3-OTPE uses the power method instead of nonlinear optimization method for decreasing at computing time. At the same time the group of B. D. Lathauwer proposed Higher-Order SVD (HOSVD) that is also developed with SVD extensions for multi-dimensional data. 3-OTPE and HOSVD are similarly on the rank reduction of multi-dimensional data. Using these two methods we can obtain computation results respectively, some ones are the same while some ones are slight different. In this paper, we compare 3-OTPE to HOSVD in accuracy of calculation and computing time of resolution, and clarify the difference between these two methods.

Keywords: Singular value decomposition (SVD), higher-order SVD (HOSVD), higher-order tensor, outer product expansion, power method.

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Authors: Jay Prakash Singh

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The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Keywords: LP-Sasakian manifolds, coefficient α, quasi conformal curvature tensor, concircular vector field, torse forming vector field, η-Einstein manifold.

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Authors: Yan Xu, Toshihiro Nishimura

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Segmentation in ultrasound images is challenging due to the interference from speckle noise and fuzziness of boundaries. In this paper, a segmentation scheme using fuzzy c-means (FCM) clustering incorporating both intensity and texture information of images is proposed to extract breast lesions in ultrasound images. Firstly, the nonlinear structure tensor, which can facilitate to refine the edges detected by intensity, is used to extract speckle texture. And then, a spatial FCM clustering is applied on the image feature space for segmentation. In the experiments with simulated and clinical ultrasound images, the spatial FCM clustering with both intensity and texture information gets more accurate results than the conventional FCM or spatial FCM without texture information.

Keywords: fuzzy c-means, spatial information, structure tensor, ultrasound image segmentation

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Authors: V. V. Lyahov, V. M. Neshchadim

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We offer a new technique for research of stability of current sheaths in space plasma taking into account the effect of polarization. At the beginning, the found perturbation of the distribution function is used for calculation of the dielectric permeability tensor, which simulates inhomogeneous medium of a current sheath. Further, we in the usual manner solve the system of Maxwell's equations closed with the material equation. The amplitudes of Fourier perturbations are considered to be exponentially decaying through the current sheath thickness. The dispersion equation follows from the nontrivial solution requirement for perturbations of the electromagnetic field. The resulting dispersion equation allows one to study the temporal and spatial characteristics of instability modes of the current sheath (within the limits of the proposed model) over a wide frequency range, including low frequencies.

Keywords: Current sheath, distribution function, effect of polarization, instability modes, low frequencies, perturbation of electromagnetic field dispersion equation, space plasma, tensor of dielectric permeability.

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Authors: M. Emami, R. Tarighi, R. Goodarzi

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Maximal radar wave absorbing cannot be achieved by shaping alone. We have to focus on the parameters of absorbing materials such as permittivity, permeability, and thickness so that best absorbing according to our necessity can happen. The real and imaginary parts of the relative complex permittivity (ε_r' and ε_r") and permeability (µ_r' and µ_r") were obtained by simulation. The microwave absorbing property of carbon and Ni(C) is simulated in this study by MATLAB software; the simulation was in the frequency range between 2 to 12 GHz for carbon black (C), and carbon coated nickel (Ni(C)) with different thicknesses. In fact, we draw reflection loss (RL) for C and Ni-C via frequency. We have compared their absorption for 3-mm thickness and predicted for other thicknesses by using of electromagnetic wave transmission theory. The results showed that reflection loss position changes in low frequency with increasing of thickness. We found out that, in all cases, using nanocomposites as absorbance cannot get better results relative to pure nanoparticles. The frequency where absorption is maximum can determine the best choice between nanocomposites and pure nanoparticles. Also, we could find an optimal thickness for long wavelength absorbing in order to utilize them in protecting shields and covering.

Keywords: Absorbing, carbon, carbon nickel, frequency, thicknesses.

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Authors: Mohd Tarmizi Ali, Mohd Khairul Mohd Salleh, Md. Mahfudz Md. Zan

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Dielectric sheet perturbation to the dominant TE111 mode resonant frequency of a circular cavity is studied and presented in this paper. The dielectric sheet, placed at the middle of the airfilled cavity, introduces discontinuities and disturbs the configuration of electromagnetic fields in the cavity. For fixed dimensions of cavity and fixed thickness of the loading dielectric, the dominant resonant frequency varies quite linearly with the permittivity of the dielectric. This quasi-linear relationship is plotted using Maple software and verified using 3D electromagnetic simulations. Two probes are used in the simulation for wave excitation into and from the cavity. The best length of probe is found to be 3 mm, giving the closest resonant frequency to the one calculated using Maple. A total of fourteen different dielectrics of permittivity ranging from 1 to 12.9 are tested one by one in the simulation. The works show very close agreement between the results from Maple and the simulation. A constant difference of 0.04 GHz is found between the resonant frequencies collected during simulation and the ones from Maple. The success of this project may lead to the possibility of using the middle loaded cavity at TE111 mode as a microwave non-destructive testing of solid materials.

Keywords: Middle-loaded cavity, dielectric sheet perturbation.

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Authors: Bijay Kumar Sahoo, Ashok Kumar Srivastav

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We have investigated the effect of piezoelectric (PZ) polarization property in binary as well as in ternary wurtzite nitrides. It is found that with the presence of PZ polarization property, the phonon group velocity is modified. The change in phonon group velocity due to PZ polarization effect directly depends on piezoelectric tensor value. Using different piezoelectric tensor values recommended by different workers in the literature, percent change in group velocities of phonons has been estimated. The Debye temperatures and frequencies of binary nitrides GaN, AlN and InN are also calculated using the modified group velocities. For ternary nitrides AlxGa(1-x)N, InxGa(1-x)N and InxAl(1-x)N, the phonon group velocities have been calculated as a functions of composition. A small positive bowing is observed in phonon group velocities of ternary alloys. Percent variations in phonon group velocities are also calculated for a straightforward comparison among ternary nitrides. The results are expected to show a change in phonon relaxation rates and thermal conductivity of III-nitrides when piezoelectric polarization property is taken into consideration.

Keywords: Wirtzite nitrides, piezoelectric polarization, Phonon group velocity, Debye frequency and Debye temperature.

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Authors: N.Subramanian, U.K.Misra

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The precise form of tensorial transformations acting on a given collection of infinite matrices into another ; for such classical ideas connected with the summability field of double gai sequence spaces. In this paper the results are impose conditions on the tensor g so that it becomes a tensorial transformations from the metric space χ2 to the metric space C

Keywords: tensorial transformations, double gai sequences , double analytic, dual.

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Authors: A.S.A. Khiar, A.K. Arof

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Starch/chitosan blend have been prepared via the solution casting technique. Ionic conductivity for the system was conducted over a wide range of frequency between 50 Hz-1 MHz and at temperatures between 303 K and 373 K. Sample with 35 wt% of NH4NO3 shows the highest conductivity of 3.89 ± 0.79 x 10-5 Scm-1 at room temperature. Conductivity-temperature relationship suggests that samples are Arrhenian. Power law exponent was obtained through dielectric loss variation and the trend suggests that the conduction mechanism of the ions can be represented by the correlated barrier hopping (CBH) model.

Keywords: starch, chitosan, permittivity, power exponent law

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Authors: Carmen D. Pricinâ, E. Corina Cipu, Victor Ţigoiu

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The flow of a third grade fluid in an orthogonal rheometer is studied. We employ the admissible velocity field proposed in [5]. We solve the problem and obtain the velocity field as well as the components for the Cauchy tensor. We compare the results with those from [9]. Some diagrams concerning the velocity and Cauchy stress components profiles are presented for different values of material constants and compared with the corresponding values for a linear viscous fluid.

Keywords: Non newtonian fluid flow, orthogonal rheometer, third grade fluid.

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

Abstract:

To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.

Keywords: BFO, electrical permittivity, fractals, Koch curve.

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Authors: Vahid Sabermand, Yousef Hojjat, Majid Hasanzadeh

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This paper contains 2 main parts. In the first part of paper we simulated and studied three types of electrode patterns used in various industries for suspension and handling of the semiconductor and glass and we selected the best pattern by evaluating the electrostatic force, which was comb pattern electrode. In the second part we investigated the parameters affecting the amount of electrostatic force such as the gap between surface and electrode (g), the electrode width (w), the gap between electrodes (t), the surface permittivity and electrode length and methods of improvement of adhesion force by changing these values.

Keywords: Electrostatic force, electrostatic adhesion, electrostatic chuck, electrostatic application in industry, Electroadhesive grippers.

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Authors: Henok Hailemariam, Frank Wuttke

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Collapsible soils are weak soils that appear to be stable in their natural state, normally dry condition, but rapidly deform under saturation (wetting), thus generating large and unexpected settlements which often yield disastrous consequences for structures unwittingly built on such deposits. In this study, a prediction model for the relative subsidence of stressed collapsible soils based on dielectric permittivity measurement is presented. Unlike most existing methods for soil subsidence prediction, this model does not require moisture content as an input parameter, thus providing the opportunity to obtain accurate estimation of the relative subsidence of collapsible soils using dielectric measurement only. The prediction model is developed based on an existing relative subsidence prediction model (which is dependent on soil moisture condition) and an advanced theoretical frequency and temperature-dependent electromagnetic mixing equation (which effectively removes the moisture content dependence of the original relative subsidence prediction model). For large scale sub-surface soil exploration purposes, the spatial sub-surface soil dielectric data over wide areas and high depths of weak (collapsible) soil deposits can be obtained using non-destructive high frequency electromagnetic (HF-EM) measurement techniques such as ground penetrating radar (GPR). For laboratory or small scale in-situ measurements, techniques such as an open-ended coaxial line with widely applicable time domain reflectometry (TDR) or vector network analysers (VNAs) are usually employed to obtain the soil dielectric data. By using soil dielectric data obtained from small or large scale non-destructive HF-EM investigations, the new model can effectively predict the relative subsidence of weak soils without the need to extract samples for moisture content measurement. Some of the resulting benefits are the preservation of the undisturbed nature of the soil as well as a reduction in the investigation costs and analysis time in the identification of weak (problematic) soils. The accuracy of prediction of the presented model is assessed by conducting relative subsidence tests on a collapsible soil at various initial soil conditions and a good match between the model prediction and experimental results is obtained.

Keywords: Collapsible soil, relative subsidence, dielectric permittivity, moisture content.

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