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Barchetti, A. Bucciero, A. L. Guido, L. Mainetti and L. Patrono",authors:[{id:"18608",title:"Dr.",name:"Alberto",middleName:null,surname:"Bucciero",fullName:"Alberto Bucciero",slug:"alberto-bucciero"},{id:"22648",title:"Eng.",name:"Ugo",middleName:null,surname:"Barchetti",fullName:"Ugo Barchetti",slug:"ugo-barchetti"},{id:"22649",title:"Eng.",name:"Anna Lisa",middleName:null,surname:"Guido",fullName:"Anna Lisa Guido",slug:"anna-lisa-guido"},{id:"22650",title:"Prof.",name:"Luca",middleName:null,surname:"Mainetti",fullName:"Luca Mainetti",slug:"luca-mainetti"},{id:"22651",title:"Prof.",name:"Luigi",middleName:null,surname:"Patrono",fullName:"Luigi Patrono",slug:"luigi-patrono"}]},{id:"15543",title:"Strategic Fit in Supply Chain Management: A Coordination Perspective",slug:"strategic-fit-in-supply-chain-management-a-coordination-perspective",signatures:"S. Kamal Chaharsooghi and Jafar Heydari",authors:[{id:"15869",title:"Dr.",name:"Seyed Kamal",middleName:null,surname:"Chaharsooghi",fullName:"Seyed Kamal Chaharsooghi",slug:"seyed-kamal-chaharsooghi"},{id:"18801",title:"Dr.",name:"Jafar",middleName:null,surname:"Heydari",fullName:"Jafar Heydari",slug:"jafar-heydari"}]},{id:"15544",title:"Towards Improving Supply Chain Coordination through Business Process Reengineering",slug:"towards-improving-supply-chain-coordination-through-business-process-reengineering",signatures:"Marinko Maslaric and Ales Groznik",authors:[{id:"18677",title:"Dr.",name:"Marinko",middleName:null,surname:"Maslaric",fullName:"Marinko Maslaric",slug:"marinko-maslaric"},{id:"22725",title:"Dr.",name:"Ales",middleName:null,surname:"Groznik",fullName:"Ales Groznik",slug:"ales-groznik"}]},{id:"15545",title:"Integrated Revenue Sharing Contracts to Coordinate a Multi-Period Three-Echelon Supply Chain",slug:"integrated-revenue-sharing-contracts-to-coordinate-a-multi-period-three-echelon-supply-chain",signatures:"Mei-Shiang Chang",authors:[{id:"22157",title:"Prof.",name:"Mei-Shiang",middleName:null,surname:"Chang",fullName:"Mei-Shiang Chang",slug:"mei-shiang-chang"}]},{id:"15546",title:"The Impact of Demand Information Sharing on the Supply Chain Stability",slug:"the-impact-of-demand-information-sharing-on-the-supply-chain-stability",signatures:"Jing Wang and Ling Tang",authors:[{id:"22160",title:"Prof.",name:"Jing",middleName:null,surname:"Wang",fullName:"Jing Wang",slug:"jing-wang"},{id:"22889",title:"Miss",name:"Ling",middleName:null,surname:"Tang",fullName:"Ling Tang",slug:"ling-tang"}]},{id:"15547",title:"Complexity in Supply Chains: A New Approachto Quantitative Measurement of the Supply-Chain-Complexity",slug:"complexity-in-supply-chains-a-new-approachto-quantitative-measurement-of-the-supply-chain-complexity",signatures:"Filiz Isik",authors:[{id:"19462",title:"Mrs",name:"Filiz",middleName:null,surname:"Isik",fullName:"Filiz Isik",slug:"filiz-isik"}]},{id:"15548",title:"A Multi-Agent Model for Supply Chain Ordering Management: An Application to the Beer Game",slug:"a-multi-agent-model-for-supply-chain-ordering-management-an-application-to-the-beer-game",signatures:"Mohammad Hossein Fazel Zarandi, Mohammad Hassan Anssari, Milad Avazbeigi and Ali Mohaghar",authors:[{id:"8321",title:"Mr.",name:"Miludin",middleName:null,surname:"Milankovic",fullName:"Miludin Milankovic",slug:"miludin-milankovic"},{id:"23527",title:"Prof.",name:"Mohammad Hossein",middleName:null,surname:"Fazel Zarandi",fullName:"Mohammad Hossein Fazel Zarandi",slug:"mohammad-hossein-fazel-zarandi"},{id:"23528",title:"M",name:"Mohammad Hassan",middleName:null,surname:"Anssari",fullName:"Mohammad Hassan Anssari",slug:"mohammad-hassan-anssari"},{id:"24043",title:"Dr.",name:"Ali",middleName:null,surname:"Mohaghar",fullName:"Ali Mohaghar",slug:"ali-mohaghar"}]},{id:"15549",title:"A Collaborative Vendor – Buyer Deteriorating Inventory Model for Optimal Pricing, Shipment and Payment Policy with Two – Part Trade Credit",slug:"a-collaborative-vendor-buyer-deteriorating-inventory-model-for-optimal-pricing-shipment-and-payment-",signatures:"Nita H. Shah and Kunal T. Shukla",authors:[{id:"19031",title:"Dr.",name:"Nita",middleName:null,surname:"Shah",fullName:"Nita Shah",slug:"nita-shah"},{id:"19499",title:"Mr",name:"Kunal",middleName:null,surname:"Shukla",fullName:"Kunal Shukla",slug:"kunal-shukla"}]},{id:"15550",title:"Quantifying the Demand Fulfillment Capability of a Manufacturing Organization",slug:"quantifying-the-demand-fulfillment-capability-of-a-manufacturing-organization",signatures:"César Martínez-Olvera",authors:[{id:"18528",title:"Dr.",name:"Cesar",middleName:null,surname:"Martinez-Olvera",fullName:"Cesar Martinez-Olvera",slug:"cesar-martinez-olvera"},{id:"127345",title:"Prof.",name:"Cesar",middleName:null,surname:"Martinez-Olvera",fullName:"Cesar Martinez-Olvera",slug:"cesar-martinez-olvera"}]},{id:"15551",title:"Continuum-Discrete Models for Supply Chains and Networks",slug:"continuum-discrete-models-for-supply-chains-and-networks",signatures:"Ciro D’Apice, Rosanna Manzo and Benedetto Piccoli",authors:[{id:"11309",title:"Dr.",name:"Benedetto",middleName:null,surname:"Piccoli",fullName:"Benedetto Piccoli",slug:"benedetto-piccoli"},{id:"11311",title:"Prof.",name:"Ciro",middleName:null,surname:"D'Apice",fullName:"Ciro D'Apice",slug:"ciro-d'apice"},{id:"11312",title:"Dr.",name:"Rosanna",middleName:null,surname:"Manzo",fullName:"Rosanna Manzo",slug:"rosanna-manzo"},{id:"117681",title:"Prof.",name:"Benedetto",middleName:null,surname:"Piccoli",fullName:"Benedetto Piccoli",slug:"benedetto-piccoli"},{id:"117684",title:"Dr.",name:"Rosanna",middleName:null,surname:"Manzo",fullName:"Rosanna Manzo",slug:"rosanna-manzo"}]},{id:"15552",title:"Services and Support Supply Chain Design for Complex Engineering Systems",slug:"services-and-support-supply-chain-design-for-complex-engineering-systems",signatures:"John P.T. Mo",authors:[{id:"6394",title:"Prof.",name:"John P.T.",middleName:null,surname:"Mo",fullName:"John P.T. Mo",slug:"john-p.t.-mo"}]},{id:"15553",title:"Lifecycle Based Distributed Cooperative Service Supply Chain for Complex Product",slug:"lifecycle-based-distributed-cooperative-service-supply-chain-for-complex-product",signatures:"Pengzhong Li, Rongxin Gu and Weimin Zhang",authors:[{id:"19636",title:"Prof.",name:"Pengzhong",middleName:null,surname:"Li",fullName:"Pengzhong Li",slug:"pengzhong-li"},{id:"22403",title:"Dr.",name:"Weimin",middleName:null,surname:"Zhang",fullName:"Weimin Zhang",slug:"weimin-zhang"},{id:"22404",title:"Dr.",name:"Rongxin",middleName:null,surname:"Gu",fullName:"Rongxin Gu",slug:"rongxin-gu"}]},{id:"15554",title:"A Generalized Algebraic Model for Optimizing Inventory Decisions in a Centralized or Decentralized Three-Stage Multi-Firm Supply Chain with Complete Backorders for Some Retailers",slug:"a-generalized-algebraic-model-for-optimizing-inventory-decisions-in-a-centralized-or-decentralized-t",signatures:"Kit Nam Francis Leung",authors:[{id:"21408",title:"Dr.",name:"Kit-nam Francis",middleName:null,surname:"Leung",fullName:"Kit-nam Francis Leung",slug:"kit-nam-francis-leung"}]},{id:"15555",title:"Life Cycle Costing, a View of Potential Applications: from Cost Management Tool to Eco-Efficiency Measurement",slug:"life-cycle-costing-a-view-of-potential-applications-from-cost-management-tool-to-eco-efficiency-meas",signatures:"Francesco Testa, Fabio Iraldo, Marco Frey and Ryan O’Connor",authors:[{id:"9825",title:"Dr.",name:"Francesco",middleName:null,surname:"Testa",fullName:"Francesco Testa",slug:"francesco-testa"},{id:"10764",title:"Prof.",name:"Fabio",middleName:null,surname:"Iraldo",fullName:"Fabio Iraldo",slug:"fabio-iraldo"},{id:"22437",title:"Prof.",name:"Marco",middleName:null,surname:"Frey",fullName:"Marco Frey",slug:"marco-frey"},{id:"22438",title:"Dr.",name:"Ryan",middleName:null,surname:"O'Connor",fullName:"Ryan 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Márquez",slug:"fausto-pedro-garcia-marquez",fullName:"Fausto Pedro García Márquez"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],publishedBooksByAuthor:[]},onlineFirst:{chapter:{type:"chapter",id:"82335",title:"Straight Rectangular Waveguide for Circular Dielectric Material in the Cross Section and for Complementary Shape of the Cross Section",doi:"10.5772/intechopen.104815",slug:"straight-rectangular-waveguide-for-circular-dielectric-material-in-the-cross-section-and-for-complem",body:'We begin with a review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments as published in [1]. Six groups of methods were reviewed: the finite-element method, the finite-difference method, the integral-equation method, methods based on series expansion, approximate methods based on separation of variables, and methods that do not fit the above groups.
The use of wavelet-like basis functions for solving electromagnetics problems is demonstrated in [2]. The modes of an arbitrarily shaped hollow metallic waveguide use a surface integral equation and the method of moments. A class of wavelet-like basis functions produces a sparse method of moments. A technique for efficient computation of an integral wavelet transform of a finite-energy function on a dense set of the time-scale domain is proposed [3] by using compactly supported spline wavelets. Application of principal component analysis and wavelet transform to fatigue crack detection in waveguides is proposed in [4]. Ultrasonic guided waves are a useful tool in structural health monitoring applications that can benefit from built-in transduction, moderately large inspection ranges, and high sensitivity to small flaws. An accurate full-wave integral formulation was developed [5] for the study of integrated planar dielectric waveguide structures with printed metalized sections, which are of practical interest for millimeter-wave and submillimeter-wave applications. An advantageous finite element method for the rectangular waveguide problem was developed [6] by which complex propagation characteristics may be obtained for arbitrarily shaped waveguides. The finite-element method has been used to derive approximate values of the possible propagation constant for each frequency. The impedance characteristics of the fundamental mode in a rectangular waveguide were computed using this finite element method. The extension to higher-order elements is straightforward, and by modifications of the method it is possible to treat other types of waveguides as well, e.g., dielectric waveguides with impedance walls and open unbounded dielectric waveguides properties treating the region of infinity.
A comprehensive study of the design and performance of a multilayer dielectric rod waveguide with a rectangular cross section is proposed in [7]. The design is comprised of a high permittivity core encased by a low permittivity cladding. A mathematical model was proposed to predict the fundamental mode cutoff frequency in terms of the core dimensions and the core and cladding permittivity. The model is useful for design purposes and it offers an excellent match to full-wave electromagnetic simulation results.
The characteristics of the effective-medium-clad dielectric waveguides, including dispersion, cross-polarization, crosstalk between parallel waveguides, bending loss, and wave leakage at the crossing, have been comprehensively investigated and measured [8].
Mode matching has been done at all the air and dielectric interfaces and thus the characteristic equations have been derived [9]. Two ratios are introduced in the characteristic equations and the new set of characteristic equations thus obtained are then plotted and graphical solutions are obtained for the propagation parameters assuming certain numerical values for the introduced ratios.
A fundamental and accurate technique to compute the propagation constant of waves in a dielectric rectangular waveguide was proposed [10]. The formulation is based on matching the fields to the constitutive properties of the material at the boundary.
The method of lines for the analysis of dielectric waveguides was proposed [11]. These waveguides are uniform along the direction of propagation, are loss-free and passive. Hybrid-mode dispersion curves, field and intensity distributions for integrated optical waveguides were presented.
The problem of normal waves in a closed regular waveguide of arbitrary cross section has been considered [12]. It was reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. The solutions were defined using the variational formulation of the problem. The problem was reduced to the study of an operator function. The properties of the operators involved in the operator function were examined. Theorems were proved concerning the discrete character of the spectrum and the distribution of characteristic numbers of the operator function on the complex plane. The completeness of the system of Eigen- and associated vectors of the operator function was investigated.
TE-wave propagation in a hollow waveguide with a graded dielectric layer using a hyperbolic tangent function is proposed in Ref. [13]. General formulas for the electric field components of the TE-waves, applicable to hollow waveguides with arbitrary cross sectional shapes were presented. The exact analytical results for the electric field components were illustrated in the special case of a rectangular waveguide. The exact analytical results for the reflection and transmission coefficients are valid for waveguides of arbitrary cross sectional shapes. The obtained reflection and transmission coefficients are in exact asymptotic agreement with those obtained for a very thin homogeneous dielectric layer using mode-matching and cascading. The proposed method gives analytical results that are directly applicable without the need of mode-matching, and it has the ability to model realistic, smooth transitions.
Rectangular waveguides were the earliest mode of transmission lines used for compact systems like radars and inside equipment shelters [14]. An air-filled rectangular waveguide WR-90 is simulated using HFSS simulation software to obtain different parameters. The electric and magnetic field patterns are analyzed: intrinsic impedance and wavelength for the first four modes of the waveguide are also obtained.
The diffraction of electromagnetic waves by rectangular waveguides with a longitudinal slit has been simulated [15]. The results allow determining the patterns of change in frequency bands in which the structure can be used as a directional coupler and as a power divider when changing the number of slots, their sizes and provisions. Modeling the characteristics of such kinds of structures allows predicting the creation of directional couplers and power dividers with high integral characteristics.
Several methods of propagation along the straight waveguides were developed, based on Maxwell’s equations. A transfer matrix function for the analysis of electromagnetic wave propagation along the straight dielectric waveguide with arbitrary profiles has been proposed in Ref. [16].
In this chapter, the main objective is to generalize the mode model method [16] in order to solve also complicated and practical problems of circular dielectric material and a circular hollow core in the center of the cross section of the rectangular waveguide. It is important to distinguish between the mode-model method and the proposed technique. The proposed technique deals only with calculating the dielectric profile in the cross section of the inhomogeneous case. In order to solve any inhomogeneous problem in the cross section, more than one technique can be proposed for the same mode-model method. The technique proposed in this chapter will refer to two interesting practical applications. In the first case, the cross section consists of circular dielectric material in the center of the cross section. In the second case, the cross section shows the complementary shape of the cross section of the first case, as an example of a hollow waveguide in which the circular hollow core is located in the center of the cross section. These examples show two discontinuous cross sections and complementary shapes that cannot be solved by analytical methods. We will explain in detail the special technique for calculating the dielectric profile in all cases. After receiving the expressions of the proposed technique for each inhomogeneous problem in the cross section, we will explain how and where the technique can be integrated into the proposed mode-model. The second objective is to find the relevant parameters in order to obtain the Gaussian behavior of the output field in the interesting cases of circular dielectic material and a circular hollow core in the rectangular cross section.
The wavelet transform creates a representation of the signal in both the time and frequency domain in order to allow efficient access to localized information about the signal. A set of waveforms comprising a transform is called a basis function. Fourier transforms use only sine and cosine waves as their basis functions, namely a signal is decomposed into a series sine and cosine functions or wavelets by the FFT. Examples for the applications of wavelet transform are demonstrated in [2, 3, 4, 5]. The proposed method in this chapter is based on the Fourier transform that creates a representation of the signal in the frequency domain. Two complicated and complementary shapes are given in this section.
Figure 1(a) and (b) shows two complementary shapes of profiles in the cross section of the straight rectangular waveguide and their relevant parameters. The circular dielectric material in the center of the cross section is shown in Figure 1(a) and the circular hollow core in the center of the cross section is shown in Figure 1(b). The two examples are demonstrated as a response to a half-sine (
Complementary shapes of profiles in the cross section of the straight rectangular waveguide and their relevant parameters. (a) Circular dielectric material in the center of the cross section. (b) A circular hollow core in the center of the cross section.
The main objective is to generalize the mode model method [16] in order to also solve complicated problems of circular dielectric material and a circular hollow core in the rectangular cross section. All the mathematical development relates to the frequency domain. The main points are given in Appendix A.
It is important to separate between mode-model method and the proposed technique. The proposed technique refers only to calculating of the dielectric profile in the cross section of the inhomogeneous problem. In order to solve any inhomogeneous problem in the cross section, more than one technique can be proposed for the same mode-model method. After receiving the expressions of the proposed technique for eace inhomogeneous problem in the cross section, we will explain how and where the technique can be integrated into the proposed mode-model. The second objective is to find the relevant parameters in order to obtain the Gaussian behavior of the output field in the interesting cases of circular dielectic profile and circular hollow profile in the rectangular cross section.
The method is based on Maxwell’s equations for the computation of output fields at each point along the straight waveguide. This method relates the wave profile at the output to the input wave in the Laplace space. A Laplace transform is necessary to obtain convenient and simple input–output connections of the fields. The method consists of Fourier coefficients of the transverse dielectric profile and of the input–output profile. Thus, the accuracy of the method depends on the number of the modes in the system.
The output transverse field profiles are computed by the inverse Laplace and Fourier transforms. The output components of the electric field are given finally by
where
The modified wave-number matrices are given by
where the diagonal matrices
and where
Similarly, the other components of the magnetic field are obtained. The output transverse field profiles are given by the inverse Laplace and Fourier transforms, as follows
where the inverse Laplace transform is calculated according to the Salzer method [17, 18]. The inverse Laplace transform is performed in this study by a direct numerical integration on the Laplace transform domain by using the method of Gaussian Quadrature. The integration path in the right side of the Laplace transform domain includes all the singularities.
where
The relation between the functions f (t) and F (p) is given by
The function F(p) may be either known only numerically or too complicated for evaluating f(t) by Cauchy’s theorem. The function F(p) behaves like a Polynomial without a constant term, in the variable 1/p, along (
In Eq. (10),
A sufficient condition for Eq. (12) to hold is obviously the “Orthogonality” of
A Fortran code is developed using NAG subroutines (The Numerical Algorithms Group (NAG)) [19].
The proposed technique will introduce details for all the interesting cases of a discontinuous cross section, as shown in Figure 1(a) and (b).
This section explains the proposed technique for calculating the dielectric profile for the two different inhomogeneous and complicated shapes of the cross section, as shown in Figure 1(a) and (b).
The technique is based on Fourier transform and uses the image method and periodic replication for fulfilling the boundary conditions of the metallic waveguide. Periodicity and symmetry properties are chosen to force the boundary conditions at the location of the walls in a real problem, by extending the waveguide region (
The image method for (a) an arbitrary profile in the cross section, and (b) the specific case of circular dielectric material in the center of the cross section.
The dielectric profile
If
where
The radius of the circle is given by
The dielectric profile for the cross section (Figure 1(a)) is given by.
where
The cyclic matrix
The components are organized in a vectorial notation as follows
The Fourier components of the dielectric profile are calculated in the Fourier space. The convolution operation
is written in a matrix form as
and the matrix order is (2 N + 1)(2 M + 1), where
The convolution operation is expressed by the cyclic matrix
The derivative of the dielectric profile is given by
where
Figure 3(a)–(c) shows the extending of the waveguide region in all cases to a four-fold larger region, according to the image method. The image method and periodic replication are needed for fulfilling the boundary condition of the metallic waveguide. Figure 3(a) shows the hollow waveguide where the circular hollow core is located in the center of the cross section. This figure represents an example of the complementary shape of Figure 3(c). Figure 3(b) shows the cross section entirely filled with the dielectric material. Figure 3(c) shows the cross section where the circular dielectric material is located in the center.
Extending the waveguide region in all cases to a four-fold larger region, according to the image method. (a) The hollow waveguide where the circular hollow core is located in the center of the cross section. (b) The cross section entirely filled with dielectric material. (c) Circular dielectric material is located in the center of the cross section.
Note that the problem shown in Figure 3(a) is more complicated than the problem shown in Figure 3(c), and the technique for solving this inhomogeneous problem in the cross section based on the image method is not effective for the specific case shown in Figure 3(a). Thus the proposed technique for calculating the dielectric profile of this problem is based on the fact that this figure represents an example of the complementary shape of Figure 3(c).
In order to solve any inhomogeneous problem in the cross section (e.g., Figure 3(a) and (c)), more than one technique can be proposed for the same mode-model method.
The proposed technique to calculate the dielectric profile for the cross section as shown in Figure 3(a) for hollow waveguide is based on subtracting the dielectric profile of the waveguide with the dielectric material in the core (Figure 3(c)) from the dielectric profile of the waveguide filled entirely with the dielectric material (Figure 3(b)).
This section presents several examples for the different geometries of two specific examples of the complementary shapes of dielectric profile in the cross section, as shown in Figure 1(a) and (b). The solutions are demonstrated as a response to a half-sine (
A comparison with the known transcendental Equation [20] according to Figure 4(a) is given in order to examine the validity of the theoretical model. The known solution for the dielectric slab modes based on the transcendental Equation [20] is given as follows:
(a) A dielectric slab in a rectangular metallic waveguide. (b) A comparison between the theoretical model (
where
The solution obtained for the wave profile ((25)–(27)) describes a symmetrical mode of the dielectric slab. This mode is substituted as an input wave at z = 0 to the solution of the proposed theoretical model Eq. (2).
The comparison between the theoretical model (Eq. (2)) and the transcendental equation (Eqs (25)–(27)) is shown in Figure 4(b) for the dielectric slab in a rectangular metallic waveguide (Figure 4(a)) and the convergence of our theoretical results is shown in Figure 4(c).
The comparison is demonstrated for every order (
The convergence of the solution is verified by the criterion
where the number of the modes is equal to
If the value of the criterion (Eq. (29)) is less than −2, then the numerical solution is well converged. When
Figure 5(a)–(e) shows the output field where the circular dielectric material is located in the center of the cross section of the straight rectangular waveguide, where a = b = 20 mm,
The output field where the circular dielectric material is located in the center of the cross section of the straight rectangular waveguide, where a = b = 20 mm, and r = 2.5 mm, r is the radius of the circular dielectric material, and for (a)
The output field where the circular dielectric material is located in the center of the cross section of the straight rectangular waveguide, where a = b = 20 mm, and r = 2 mm, where r is the radius of the circular dielectric material, and for (a)
Figure 7(a)–(e) shows the output field where the circular hollow core is located in the center of the cross section of the straight rectangular waveguide, where a = b = 20 mm,
The output field where the circular hollow core is located in the center of the cross section of the straight rectangular waveguide, where a = b = 20 mm, and r = 2.5 mm, where r is the radius of the circular hollow core, and for (a)
The output field where the circular hollow core is located in the center of the cross section of the straight rectangular waveguide, where a = b = 20 mm, and r = 2 mm, where r is the radius of the circular hollow core, and for (a)
By increasing only the dielectric constant from
We can predict the waveguide parameters (
These results are strongly affected by the different parameters
The wavelet transform creates a representation of the signal in both the time and frequency domain in order to allow efficient access of localized information about the signal. A set of waveforms comprising a transform is called a basis function. Fourier transforms use only sine and cosine waves as their basic functions, namely a signal is decomposed into a series of sine and cosine functions or wavelets by the FFT. Examples for the applications of wavelet transform are demonstrated in [2, 3, 4, 5]. The proposed method in this chapter is based on the Fourier transform that creates a representation of the signal in the frequency domain.
Two specific examples of complementary shapes of dielectric profile in the cross section were introduced in this chapter. In the first case, the cross section consists of circular dielectric material in the center of the cross section. In the second case, the cross section shows the complementary shape of the cross section of the first case, as an example of a hollow waveguide in which the circular hollow core is located in the center of the cross section.
Note that the problem shown in Figure 3(a) is more complicated than the problem shown in Figure 3(c), and the technique for solving this inhomogeneous problem in the cross section based on the image method is not effective for the specific case shown in Figure 3(a). The proposed technique for calculating the dielectric profile of the problem shown in Figure 3(a) is based on the fact that this figure represents an example of the complementary shape of Figure 3(c).
In order to solve any inhomogeneous problem in the cross section (e.g., Figure 3(a) and (c)), more than one technique can be proposed for the same mode-model method.
The proposed technique to calculate the dielectric profile for the cross section as shown in Figure 3(a) for hollow waveguide is based on subtracting the dielectric profile of the waveguide from the dielectric material in the core (Figure 3(c)) from the dielectric profile of the waveguide filled entirely with the dielectric material (Figure 3(b)).
Figures 5(a)–(e) and 6(a)–(e) demonstrate the output fields, where the circular dielectric material is located in the center of the cross section of the straight rectangular waveguide, where the parameter r refers to the radius of the circular dielectric material. Figures 7(a)–(e) and 8(a)–(e) demonstrate the output fields, where the circular hollow core is located in the center of the cross section of the straight rectangular waveguide, where the parameter r refers to the radius of the circular hollow core. The other parameters are a = b = 20 mm,
By increasing only the dielectric constant from
We can predict the waveguide parameters (
The results are strongly affected by the different parameters
The applications are useful for straight rectangular waveguides in millimeter regimes, where the circular dielectric material is located in the center of the cross section, and also for hollow waveguides, where the circular hollow core is located in the center of the cross section.
The wavelet transform creates a representation of the signal in both the time and frequency domain in order to allow efficient access of localized information about the signal. A set of waveforms comprising a transform is called a basis function. Fourier transforms use only sine and cosine waves as its basic functions, namely a signal is decomposed into a series sine and cosine functions or wavelets by the FFT. Examples for the applications of wavelet transform are demonstrated in [2, 3, 4, 5]. The proposed method in this chapter is based on the Fourier transform that creates a representation of the signal in the frequency domain. The main points of the proposed method and the proposed technique are:
A Laplace transform is necessary to obtain convenient and simple input–output connections of the fields. The method consists of Fourier coefficients of the transverse dielectric profile and of the input–output profile. Thus, the accuracy of the method depends on the number of the modes in the system.
The Laplace transform
is applied on the z-dimension, where
A Fourier transform is applied on the transverse dimension
and the differential equations are transformed to an algebraic form in the (
The method of images is applied to satisfy the conditions
The region
The output transverse field profiles are given by the inverse Laplace and Fourier transforms, as follows
where the inverse Laplace transform is calculated according to the Salzer method [17, 18].
The main objective is to generalize the mode model method [16] in order to solve also complicated and practical problems of circular dielectic material and a circular hollow core (Figure 1(a) and (b)) in the center of the cross section of the rectangular waveguide.
The second objective is to find the relevant parameters in order to obtain the Gaussian behavior of the output field in the interesting cases of circular dielectic material and a circular hollow core in the rectangular cross section.
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From 1985 to 1986, he was a Research Fellow in the Research Institute for Electronic Equipment, ZZU AD, Plovdiv, Bulgaria. In 1986, he joined the Department of Control Systems, Technical University of Sofia at the Plovdiv campus, where he is presently a Full Professor. He has held long-term visiting Professor/Scholar positions at various institutions in South Korea, Turkey, Mexico, Greece, Belgium, UK, and Germany. And he has coauthored one book and authored or coauthored more than 80 research papers in conference proceedings and journals. 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After finishing his P. hD degree in 1992, he served in the Industry as a Scientific Officer and continued his academic career as a visiting scholar for a number of educational institutions. In 1996 he joined National University of Science & Technology Pakistan (NUST) as an Associate Professor; NUST is one of the top few universities in Pakistan. In 1999 he joined an International Company Lineo Inc, Canada as Manager Compiler Group, where he headed the group for developing Compiler Tool Chain and Porting of Operating Systems for the BLACKfin processor. The processor development was a joint venture by Intel and Analog Devices. In 2002 Lineo Inc., was taken over by another company, so he joined Aalborg University Denmark as an Assistant Professor.\nProfessor Akbar has truly a multi-disciplined career and he continued his legacy and making progress in many areas of his interests both in teaching and research. 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The literature source was Web of Science and SSCI, SCI-EXPANDED, A&HCI, CPCI-S, CPCI-SSH, and ESCI indexes. Fifty-two articles were reviewed; however, 14 of them were not been included in the study. As a result, 38 articles were examined. Level of education, field of education, and material types of AR used in education and reported educational advantages of AR have been investigated. All articles are categorized according to target groups, which are early childhood education, primary education, secondary education, high school education, graduate education, and others. AR technology has been mostly carried out in primary and graduate education. “Science education” is the most explored field of education. Mobile applications and marker-based materials on paper have been mostly preferred. The major advantages indicated in the articles are “Learning/Academic Achievement,” “Motivation,” and “Attitude”.",book:{id:"6543",slug:"state-of-the-art-virtual-reality-and-augmented-reality-knowhow",title:"State of the Art Virtual Reality and Augmented Reality Knowhow",fullTitle:"State of the Art Virtual Reality and Augmented Reality Knowhow"},signatures:"Rabia M. Yilmaz",authors:[{id:"225838",title:"Dr.",name:"Rabia",middleName:null,surname:"Yilmaz",slug:"rabia-yilmaz",fullName:"Rabia Yilmaz"}]},{id:"63639",doi:"10.5772/intechopen.81086",title:"Cooperative Learning: The Foundation for Active Learning",slug:"cooperative-learning-the-foundation-for-active-learning",totalDownloads:3475,totalCrossrefCites:18,totalDimensionsCites:24,abstract:"The role of instructors is evolving from the presenter of information to the designer of active learning processes, environments, and experiences that maximize student engagement. The more active a lesson, the more students tend to engage intellectually and emotionally in the learning activities. Cooperative learning is the foundation on which many of the active learning procedures are based. Cooperative learning is the instructional use of small groups so that students work together to maximize their own and each other’s learning. Most of the active learning procedures, such as problem-based learning, team-learning, collaborative learning, and PALS, require that students work cooperatively in small groups to achieve joint learning goals. Cooperative learning is based on two theories: Structure-Process-Outcome theory and Social Interdependence theory. Four types of cooperative learning have been derived: formal cooperative learning, informal cooperative learning, cooperative base groups, and constructive controversy. There is considerable research confirming the effectiveness of cooperative learning. To be cooperative, however, five basic elements must be structured into the situation: positive interdependence, individual accountability, promotive interaction, social skills, and group processing.",book:{id:"6929",slug:"active-learning-beyond-the-future",title:"Active Learning",fullTitle:"Active Learning - Beyond the Future"},signatures:"David W. Johnson and Roger T. 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Currently, you can hear a lot of criticism that the classroom has not changed significantly compared to the last century or even like two centuries ago. Do the teachers succeed in modern changes? The purpose of the chapter is to summarize the current changes in didactics for the use of innovative teaching methods and study the understanding of changes by teachers. In this chapter, we consider four areas: the expansion of the subject of pedagogy, environmental approach to teaching, the digital generation and the changes taking place, and innovation in teaching. The theory of education, figuratively speaking, has two levels. At the macro-level, in the “education-society” relationship, decentralization and diversification, internationalization of education, and the introduction of digital technologies occur. At the micro-level in the “teacher-learner” relationship, there is an active mix of traditional and innovative methods, combination of an activity approach with an energy-informational environment approach, cognition with constructivism and connectivism.",book:{id:"5980",slug:"new-pedagogical-challenges-in-the-21st-century-contributions-of-research-in-education",title:"New Pedagogical Challenges in the 21st Century",fullTitle:"New Pedagogical Challenges in the 21st Century - Contributions of Research in Education"},signatures:"Aigerim Mynbayeva, Zukhra Sadvakassova and Bakhytkul\nAkshalova",authors:[{id:"201997",title:"Dr.",name:"Aigerim",middleName:null,surname:"Mynbayeva",slug:"aigerim-mynbayeva",fullName:"Aigerim Mynbayeva"},{id:"209208",title:"Dr.",name:"Zukhra",middleName:null,surname:"Sadvakassova",slug:"zukhra-sadvakassova",fullName:"Zukhra Sadvakassova"},{id:"209210",title:"Dr.",name:"Bakhytkul",middleName:null,surname:"Akshalova",slug:"bakhytkul-akshalova",fullName:"Bakhytkul Akshalova"}]},{id:"59468",doi:"10.5772/intechopen.74344",title:"Virtual and Augmented Reality: New Frontiers for Clinical Psychology",slug:"virtual-and-augmented-reality-new-frontiers-for-clinical-psychology",totalDownloads:2359,totalCrossrefCites:13,totalDimensionsCites:21,abstract:"In the last decades, the applied approach for the use of virtual reality (VR) and augmented reality (AR) on clinical and health psychology has grown exponentially. These technologies have been used to treat several mental disorders, for example, phobias, stress-related disorders, depression, eating disorders, and chronic pain. The importance of VR/AR for the mental health field comes from three main concepts: (1) VR/AR as an imaginal technology, people can feel “as if they are” in a reality that does not exist in external world; (2) VR/AR as an embodied technology, the experience to feel user’s body inside the virtual environment; and (3) VR/AR as connectivity technology, the “end of geography’. In this chapter, we explore the opportunities provided by VR/AR as technologies to improve people’s quality of life and to discuss new frontiers for their application in mental health and psychological well-being promotion.",book:{id:"6543",slug:"state-of-the-art-virtual-reality-and-augmented-reality-knowhow",title:"State of the Art Virtual Reality and Augmented Reality Knowhow",fullTitle:"State of the Art Virtual Reality and Augmented Reality Knowhow"},signatures:"Sara Ventura, Rosa M. Baños and Cristina Botella",authors:[{id:"106036",title:"Dr.",name:"Rosa Maria",middleName:null,surname:"Baños",slug:"rosa-maria-banos",fullName:"Rosa Maria Baños"},{id:"227763",title:"Ph.D.",name:"Sara",middleName:null,surname:"Ventura",slug:"sara-ventura",fullName:"Sara Ventura"},{id:"229056",title:"Dr.",name:"Cristina",middleName:null,surname:"Botella",slug:"cristina-botella",fullName:"Cristina Botella"}]},{id:"64583",doi:"10.5772/intechopen.81714",title:"Evaluating a Course for Teaching Advanced Programming Concepts with Scratch to Preservice Kindergarten Teachers: A Case Study in Greece",slug:"evaluating-a-course-for-teaching-advanced-programming-concepts-with-scratch-to-preservice-kindergart",totalDownloads:1419,totalCrossrefCites:13,totalDimensionsCites:18,abstract:"Coding is a new literacy for the twenty-first century, and as a literacy, coding enables new ways of thinking and new ways of communicating and expressing ideas, as well as new ways of civic participation. A growing number of countries, in Europe and beyond, have established clear policies and frameworks for introducing computational thinking (CT) and computer programming to young children. In this chapter, we discuss a game-based approach to coding education for preservice kindergarten teachers using Scratch. The aim of using Scratch was to excite students’ interest and familiarize them with the basics of programming in an open-ended, project-based, and personally meaningful environment for a semester course in the Department of Preschool Education in the University of Crete. For 13 weeks, students were introduced to the main Scratch concepts and, afterward, were asked to prepare their projects. For the projects, they were required to design their own interactive stories to teach certain concepts about mathematics or physical science to preschool-age students. The results we obtained were more satisfactory than expected and, in some regards, encouraging if one considers the fact that the research participants had no prior experiences with computational thinking.",book:{id:"6936",slug:"early-childhood-education",title:"Early Childhood Education",fullTitle:"Early Childhood Education"},signatures:"Stamatios Papadakis and Michail Kalogiannakis",authors:null}],mostDownloadedChaptersLast30Days:[{id:"58060",title:"Pedagogy of the Twenty-First Century: Innovative Teaching Methods",slug:"pedagogy-of-the-twenty-first-century-innovative-teaching-methods",totalDownloads:8818,totalCrossrefCites:17,totalDimensionsCites:21,abstract:"In the twenty-first century, significant changes are occurring related to new scientific discoveries, informatization, globalization, the development of astronautics, robotics, and artificial intelligence. This century is called the age of digital technologies and knowledge. How is the school changing in the new century? How does learning theory change? Currently, you can hear a lot of criticism that the classroom has not changed significantly compared to the last century or even like two centuries ago. Do the teachers succeed in modern changes? The purpose of the chapter is to summarize the current changes in didactics for the use of innovative teaching methods and study the understanding of changes by teachers. In this chapter, we consider four areas: the expansion of the subject of pedagogy, environmental approach to teaching, the digital generation and the changes taking place, and innovation in teaching. The theory of education, figuratively speaking, has two levels. At the macro-level, in the “education-society” relationship, decentralization and diversification, internationalization of education, and the introduction of digital technologies occur. At the micro-level in the “teacher-learner” relationship, there is an active mix of traditional and innovative methods, combination of an activity approach with an energy-informational environment approach, cognition with constructivism and connectivism.",book:{id:"5980",slug:"new-pedagogical-challenges-in-the-21st-century-contributions-of-research-in-education",title:"New Pedagogical Challenges in the 21st Century",fullTitle:"New Pedagogical Challenges in the 21st Century - Contributions of Research in Education"},signatures:"Aigerim Mynbayeva, Zukhra Sadvakassova and Bakhytkul\nAkshalova",authors:[{id:"201997",title:"Dr.",name:"Aigerim",middleName:null,surname:"Mynbayeva",slug:"aigerim-mynbayeva",fullName:"Aigerim Mynbayeva"},{id:"209208",title:"Dr.",name:"Zukhra",middleName:null,surname:"Sadvakassova",slug:"zukhra-sadvakassova",fullName:"Zukhra Sadvakassova"},{id:"209210",title:"Dr.",name:"Bakhytkul",middleName:null,surname:"Akshalova",slug:"bakhytkul-akshalova",fullName:"Bakhytkul Akshalova"}]},{id:"61746",title:"Facilitation of Teachers’ Professional Development through Principals’ Instructional Supervision and Teachers’ Knowledge- Management Behaviors",slug:"facilitation-of-teachers-professional-development-through-principals-instructional-supervision-and-t",totalDownloads:3378,totalCrossrefCites:2,totalDimensionsCites:2,abstract:"With the rise of global competition and the focus on teacher quality, teacher professional development is becoming increasingly crucial, and the stress and challenges for principals are more severe than ever. Teachers can improve their professional abilities through principals’ instructional supervision and their own knowledge-management (KM) behaviors to benefit students. Thus, this chapter analyzes the relationship among principals’ instructional supervision, teachers’ KM, and teachers’ professional development. The author believes that principals’ instructional supervision and effective KM can facilitate the professional development of teachers. The author also believes the readers can know the relationships among them, and teachers’ professional development can be improved through principal’s instructional supervision and teachers’ KM behaviors.",book:{id:"6674",slug:"contemporary-pedagogies-in-teacher-education-and-development",title:"Contemporary Pedagogies in Teacher Education and Development",fullTitle:"Contemporary Pedagogies in Teacher Education and Development"},signatures:"Chien-Chin Chen",authors:[{id:"232569",title:"Ph.D.",name:"Chien Chih",middleName:null,surname:"Chen",slug:"chien-chih-chen",fullName:"Chien Chih Chen"}]},{id:"75908",title:"From the Classroom into Virtual Learning Environments: Essential Knowledge, Competences, Skills and Pedagogical Strategies for the 21st Century Teacher Education in Kenya",slug:"from-the-classroom-into-virtual-learning-environments-essential-knowledge-competences-skills-and-ped",totalDownloads:515,totalCrossrefCites:0,totalDimensionsCites:0,abstract:"As teachers in Kenya begin to migrate from the classroom to virtual learning spaces following COVID 19 pandemic, there is pressing need to realign Teacher Education to requisite Knowledge, competences, skills, and attitudes that will support online teaching. This chapter explores these needs using a combination of lived experiences and literature review that captured a meta-analysis of research trends on e-learning. While trends in Teacher Education indicate progression towards adoption of technology, there are disparities between the theory and practice. Evidence from recent research and reports; and the recollected experiences confirmed knowledge, competence, skills and pedagogical gaps in the implementation of online learning, that have been exacerbated by COVID-19. The researcher recommends that teacher education should sensitize and train teacher trainees on how to access, analyze and use new knowledge emerging with technology; they also should be coached on how learners learn with technology and on fundamentals of the communication process. Particularly the course on educational technology, should focus on how to create and manage online courses. The 5-stage E-Moderator Model and Universal Design for Learning (UDL) are recommended as effective pedagogical scaffold for online teaching.",book:{id:"10229",slug:"teacher-education-in-the-21st-century-emerging-skills-for-a-changing-world",title:"Teacher Education in the 21st Century",fullTitle:"Teacher Education in the 21st Century - Emerging Skills for a Changing World"},signatures:"Catherine Adhiambo Amimo",authors:[{id:"333482",title:"Dr.",name:"Catherine Adhiambo",middleName:null,surname:"Amimo",slug:"catherine-adhiambo-amimo",fullName:"Catherine Adhiambo Amimo"}]},{id:"75224",title:"Decoding the Digital Gap in Teacher Education: Three Perspectives across the Globe",slug:"decoding-the-digital-gap-in-teacher-education-three-perspectives-across-the-globe",totalDownloads:583,totalCrossrefCites:0,totalDimensionsCites:4,abstract:"Educational use of technology is regularly assessed, and results often show a gap between educational policies and what is actually practiced. This chapter will help clarify how teacher educators experience the changing educational contexts due to the digital revolution, how their meaning-making shifts, and how outside forces influence those processes. The results are based on comparative international studies. Central for this study is practitioners’ professional digital competence, their attitudes towards digital technology and the use of digital technology in education. We found that the influence and contribution of digital practice is carried out quite differently across the globe. Our research questions were: How do practitioners experience teaching in a rapidly changing context? How do attitudes change due to top-down governing of education? and What motivates teacher educators to implement digital technology?",book:{id:"10229",slug:"teacher-education-in-the-21st-century-emerging-skills-for-a-changing-world",title:"Teacher Education in the 21st Century",fullTitle:"Teacher Education in the 21st Century - Emerging Skills for a Changing World"},signatures:"Steinar Thorvaldsen and Siri Sollied Madsen",authors:[{id:"332624",title:"Associate Prof.",name:"Siri Sollied",middleName:null,surname:"Madsen",slug:"siri-sollied-madsen",fullName:"Siri Sollied Madsen"},{id:"332626",title:"Prof.",name:"Steinar",middleName:null,surname:"Thorvaldsen",slug:"steinar-thorvaldsen",fullName:"Steinar Thorvaldsen"}]},{id:"75416",title:"Self-Study Research: Challenges and Opportunities in Teacher Education",slug:"self-study-research-challenges-and-opportunities-in-teacher-education",totalDownloads:763,totalCrossrefCites:0,totalDimensionsCites:0,abstract:"This article aims to describe what self-study research is, why self-study can be a good approach to teacher educators’ professional development and improvements in practice and highlight some challenges and opportunities in this research approach. In addition, the article will shed light on some methodological aspects related to self-study. Self-study refers to teacher educators who in an intentionally and systematically way examine their practice to improve it, based on a deeper understanding of practice, as well as the context practice takes place. In the article, I argue that engaging in self-study is a learning and development process and an approach to developing personal professionalism, collective professionalism and improvements in practice.",book:{id:"10229",slug:"teacher-education-in-the-21st-century-emerging-skills-for-a-changing-world",title:"Teacher Education in the 21st Century",fullTitle:"Teacher Education in the 21st Century - Emerging Skills for a Changing World"},signatures:"Kåre Hauge",authors:[{id:"332053",title:"Associate Prof.",name:"Kåre",middleName:null,surname:"Hauge",slug:"kare-hauge",fullName:"Kåre Hauge"}]}],onlineFirstChaptersFilter:{topicId:"265",limit:6,offset:0},onlineFirstChaptersCollection:[],onlineFirstChaptersTotal:0},preDownload:{success:null,errors:{}},subscriptionForm:{success:null,errors:{}},aboutIntechopen:{},privacyPolicy:{},peerReviewing:{},howOpenAccessPublishingWithIntechopenWorks:{},sponsorshipBooks:{sponsorshipBooks:[],offset:8,limit:8,total:0},allSeries:{pteSeriesList:[{id:"14",title:"Artificial Intelligence",numberOfPublishedBooks:9,numberOfPublishedChapters:90,numberOfOpenTopics:6,numberOfUpcomingTopics:0,issn:"2633-1403",doi:"10.5772/intechopen.79920",isOpenForSubmission:!0},{id:"7",title:"Biomedical Engineering",numberOfPublishedBooks:12,numberOfPublishedChapters:107,numberOfOpenTopics:3,numberOfUpcomingTopics:0,issn:"2631-5343",doi:"10.5772/intechopen.71985",isOpenForSubmission:!0}],lsSeriesList:[{id:"11",title:"Biochemistry",numberOfPublishedBooks:33,numberOfPublishedChapters:330,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2632-0983",doi:"10.5772/intechopen.72877",isOpenForSubmission:!0},{id:"25",title:"Environmental Sciences",numberOfPublishedBooks:1,numberOfPublishedChapters:19,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2754-6713",doi:"10.5772/intechopen.100362",isOpenForSubmission:!0},{id:"10",title:"Physiology",numberOfPublishedBooks:14,numberOfPublishedChapters:145,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2631-8261",doi:"10.5772/intechopen.72796",isOpenForSubmission:!0}],hsSeriesList:[{id:"3",title:"Dentistry",numberOfPublishedBooks:9,numberOfPublishedChapters:139,numberOfOpenTopics:2,numberOfUpcomingTopics:0,issn:"2631-6218",doi:"10.5772/intechopen.71199",isOpenForSubmission:!0},{id:"6",title:"Infectious Diseases",numberOfPublishedBooks:13,numberOfPublishedChapters:122,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2631-6188",doi:"10.5772/intechopen.71852",isOpenForSubmission:!0},{id:"13",title:"Veterinary Medicine and Science",numberOfPublishedBooks:11,numberOfPublishedChapters:112,numberOfOpenTopics:3,numberOfUpcomingTopics:0,issn:"2632-0517",doi:"10.5772/intechopen.73681",isOpenForSubmission:!0}],sshSeriesList:[{id:"22",title:"Business, Management and Economics",numberOfPublishedBooks:1,numberOfPublishedChapters:21,numberOfOpenTopics:3,numberOfUpcomingTopics:0,issn:"2753-894X",doi:"10.5772/intechopen.100359",isOpenForSubmission:!0},{id:"23",title:"Education and Human Development",numberOfPublishedBooks:0,numberOfPublishedChapters:10,numberOfOpenTopics:1,numberOfUpcomingTopics:1,issn:null,doi:"10.5772/intechopen.100360",isOpenForSubmission:!0},{id:"24",title:"Sustainable Development",numberOfPublishedBooks:1,numberOfPublishedChapters:19,numberOfOpenTopics:5,numberOfUpcomingTopics:0,issn:"2753-6580",doi:"10.5772/intechopen.100361",isOpenForSubmission:!0}],testimonialsList:[{id:"13",text:"The collaboration with and support of the technical staff of IntechOpen is fantastic. The whole process of submitting an article and editing of the submitted article goes extremely smooth and fast, the number of reads and downloads of chapters is high, and the contributions are also frequently cited.",author:{id:"55578",name:"Antonio",surname:"Jurado-Navas",institutionString:null,profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRisIQAS/Profile_Picture_1626166543950",slug:"antonio-jurado-navas",institution:{id:"720",name:"University of Malaga",country:{id:null,name:"Spain"}}}},{id:"6",text:"It is great to work with the IntechOpen to produce a worthwhile collection of research that also becomes a great educational resource and guide for future research endeavors.",author:{id:"259298",name:"Edward",surname:"Narayan",institutionString:null,profilePictureURL:"https://mts.intechopen.com/storage/users/259298/images/system/259298.jpeg",slug:"edward-narayan",institution:{id:"3",name:"University of Queensland",country:{id:null,name:"Australia"}}}}]},series:{item:{id:"25",title:"Environmental Sciences",doi:"10.5772/intechopen.100362",issn:"2754-6713",scope:"\r\n\tScientists have long researched to understand the environment and man’s place in it. 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