Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
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This achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
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We are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
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Thank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
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\n'}],latestNews:[{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"},{slug:"introducing-intechopen-book-series-a-new-publishing-format-for-oa-books-20210915",title:"Introducing IntechOpen Book Series - A New Publishing Format for OA Books"}]},book:{item:{type:"book",id:"1354",leadTitle:null,fullTitle:"Soil Erosion Studies",title:"Soil Erosion",subtitle:"Studies",reviewType:"peer-reviewed",abstract:"Soil erosion affects a large part of the Earth surface, and accelerated soil erosion is recognized as one of the main soil threats, compromising soil productive and protective functions. The land management in areas affected by soil erosion is a relevant issue for landscape and ecosystems preservation. In this book we collected a series of papers on erosion, not focusing on agronomic implications, but on a variety of other relevant aspects of the erosion phenomena. \nThe book is divided into three sections: i) various implications of land management in arid and semiarid ecosystems, ii) erosion modeling and experimental studies; iii) other applications (e.g. geoscience, engineering). The book covers a wide range of erosion-related themes from a variety of points of view (assessment, modeling, mitigation, best practices etc.).",isbn:null,printIsbn:"978-953-307-710-9",pdfIsbn:"978-953-51-4927-9",doi:"10.5772/1820",price:139,priceEur:155,priceUsd:179,slug:"soil-erosion-studies",numberOfPages:334,isOpenForSubmission:!1,isInWos:null,isInBkci:!1,hash:"54b680a6a971eb10ae500071207ab86d",bookSignature:"Danilo Godone and Silvia Stanchi",publishedDate:"November 21st 2011",coverURL:"https://cdn.intechopen.com/books/images_new/1354.jpg",numberOfDownloads:65826,numberOfWosCitations:48,numberOfCrossrefCitations:22,numberOfCrossrefCitationsByBook:4,numberOfDimensionsCitations:55,numberOfDimensionsCitationsByBook:5,hasAltmetrics:1,numberOfTotalCitations:125,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 24th 2010",dateEndSecondStepPublish:"December 22nd 2010",dateEndThirdStepPublish:"April 28th 2011",dateEndFourthStepPublish:"May 28th 2011",dateEndFifthStepPublish:"July 27th 2011",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6,7",editedByType:"Edited by",kuFlag:!1,featuredMarkup:null,editors:[{id:"313983",title:"Dr.",name:"Danilo",middleName:null,surname:"Godone",slug:"danilo-godone",fullName:"Danilo Godone",profilePictureURL:"https://mts.intechopen.com/storage/users/53849/images/system/53849.jpg",biography:"Dr. Danilo Godone holds a Ph.D. in 'Agriculture, Forest and Food Sciences”, with his doctorate’s topic being the cryosphere’s phenomena monitoring by innovative geomatic methodologies. Currently he is a Research Scientist in the Geohazard Monitoring Group (CNR IRPI), studying geomatic contribution in natural hazard monitoring and analysis. His main research interests are landslides, glaciers and, more generally, natural disasters. During his activities, he has developed skills in GIS, R programming, and land surveying with UAVs, GNSS, and LiDAR. He was also involved in several scientific expeditions in the Alps, Nepal, Chilean Andes, and Patagonia. He is a member of NATRISK - Research Centre on Natural Risks in Mountain and Hilly Environments, in Turin University.",institutionString:null,position:null,outsideEditionCount:null,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"4",institution:{name:"National Research Council",institutionURL:null,country:{name:"Italy"}}}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:{id:"120871",title:"Dr.",name:"Silvia",middleName:null,surname:"Stanchi",slug:"silvia-stanchi",fullName:"Silvia Stanchi",profilePictureURL:"https://mts.intechopen.com/storage/users/120871/images/system/120871.jpg",biography:"Silvia Stanchi holds a PhD in “Agriculture, Forest and Food Sciences”, with a focus on fractal theory approaches for the study of soil aggregation and structure. Currently, she is a PostDoc at Turin University working on soil hazards and vulnerability in mountain areas. Silvia Stanchi is a member of NATRISK - Research Centre on Natural Risks in Mountain and Hilly Environments, in the same University. She is actively involved in outreach and soil awareness raising activities targeting kids and the large public, and in international training activities focusing on mountain development and management.",institutionString:null,position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:null},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"676",title:"Soil Degradation",slug:"soil-degradation"}],chapters:[{id:"23108",title:"Natural Potential for Erosion for Brazilian Territory",doi:"10.5772/23163",slug:"natural-potential-for-erosion-for-brazilian-territory",totalDownloads:3811,totalCrossrefCites:2,totalDimensionsCites:6,hasAltmetrics:0,abstract:null,signatures:"Alexandre Marco da Silva, Clayton Alcarde Alvares and Claudia Hitomi Watanabe",downloadPdfUrl:"/chapter/pdf-download/23108",previewPdfUrl:"/chapter/pdf-preview/23108",authors:[{id:"50872",title:"Dr.",name:"Alexandre Marco",surname:"Da Silva",slug:"alexandre-marco-da-silva",fullName:"Alexandre Marco Da Silva"},{id:"52326",title:"MSc.",name:"Clayton",surname:"Alcarde Alvares",slug:"clayton-alcarde-alvares",fullName:"Clayton Alcarde Alvares"},{id:"52332",title:"Ms.",name:"Claudia",surname:"Watanabe",slug:"claudia-watanabe",fullName:"Claudia Watanabe"}],corrections:null},{id:"23109",title:"Soil Erosion Processes in Semiarid Areas: The Importance of Native Vegetation",doi:"10.5772/23211",slug:"soil-erosion-processes-in-semiarid-areas-the-importance-of-native-vegetation",totalDownloads:4783,totalCrossrefCites:2,totalDimensionsCites:13,hasAltmetrics:0,abstract:null,signatures:"Rebeca Vásquez-Méndez, Eusebio Ventura-Ramos, Klavdia Oleschko, Luis Hernández-Sandoval and Miguel Angel Domínguez-Cortázar",downloadPdfUrl:"/chapter/pdf-download/23109",previewPdfUrl:"/chapter/pdf-preview/23109",authors:[{id:"51105",title:"Prof.",name:"Rebeca",surname:"Vasquez-Mendez",slug:"rebeca-vasquez-mendez",fullName:"Rebeca Vasquez-Mendez"},{id:"51117",title:"Dr.",name:"Eusebio",surname:"Ventura",slug:"eusebio-ventura",fullName:"Eusebio Ventura"},{id:"51118",title:"Dr.",name:"Luis G",surname:"Hernandez-Sandoval",slug:"luis-g-hernandez-sandoval",fullName:"Luis G Hernandez-Sandoval"},{id:"51119",title:"Prof.",name:"Klavdia",surname:"Oleschko",slug:"klavdia-oleschko",fullName:"Klavdia Oleschko"},{id:"51120",title:"Dr.",name:"Migue A",surname:"Dominguez-Cortazar",slug:"migue-a-dominguez-cortazar",fullName:"Migue A Dominguez-Cortazar"}],corrections:null},{id:"23110",title:"Deforestation / Reforestation in Mediterranean Europe: The Case of Greece",doi:"10.5772/23466",slug:"deforestation-reforestation-in-mediterranean-europe-the-case-of-greece",totalDownloads:3309,totalCrossrefCites:3,totalDimensionsCites:7,hasAltmetrics:1,abstract:null,signatures:"Olga G. 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1. Introduction
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.
2. Complementary shapes in the cross section for different applications
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 (TE10) input-wave profile. These two different complementary shapes of the cross section are demonstrated for two different applications. The first example (Figure 1(a)) is useful in millimeter regimes where the circular dielectric material is located in the center of the cross section. The second example (Figure 1(b)) is useful in the millimeter regimes where the circular hollow core is located in the center of the cross section.
Figure 1.
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
Ex=Dx+α1M1M2−1Êx0−α2M1Êy0,E1
Ey=Dy+α1M3M4−1Êy0−α3M3Êx0,E2
Ez=Dz−1Êz0+12sGxEx0+GyEy0−12GxEx+GyEy,E3
where Ex0,Ey0,Ez0 are the initial values of the corresponding fields at z = 0, i.e., Ex0=Ex (x, y, z = 0), and Êx0,Êy0,Êz0 are the initial-value vectors.
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
Eyxyz=∑n∑m∫σ−j∞σ+j∞Eynmsexpjnkoxx+jmkoyy+szds,E7
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 wi and pi are the weights and zeros, respectively, of the orthogonal polynomials of order 15. The Laplace variable s is normalized by pi/ζ in the integration points, where Repi>0 and all the poles should be localized on their left side on the Laplace transform domain. This approach of a direct integral transform does not require as in other methods, to deal with each singularity separately.
The relation between the functions f (t) and F (p) is given by
ft=12πj∫σ−j∞σ+j∞eptFpdp.E9
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 (σ−j∞, σ+j∞). One may find f(t) numerically by using new quadrature formulas (analogous to those employing the zeros of the Laguerre polynomials in the direct Laplace transform). A suitable choice of pi yields an n-point quadrature formula that is exact when p2n is any arbitrary polynomial of the 2n(th) degree in x≡1/p, namely
12πj∫σ−j∞σ+j∞epρ1/pdp=∑i=1nAinρ2n1/pi.E10
In Eq. (10), xi≡1/pi are the zeros of the orthogonal polynomials pnx≡Πx−xi where
12πj∫σ−j∞σ+j∞ep1ppn1p1pidp=0,E11
i = 0,1,…,n − 1 and Ain correspond to the Christoffel numbers. The normalization Pn1/p≡4n−24n−6,…,6pn1/p, for n≥2, produces all integral coefficients. Pn1/p is proven to be −1ne−ppndnep/pn/dpn. The numerical table gives us the values of the reciprocals of the zeros of Pnx or pin, the zeros of Pnx, or 1/pin, and the corresponding Christoffel numbers Ain. By using these quantities in the quadrature formula that represents in Eq. (10), then the “Christoffel numbers” are given by
Ain≡12πj∫σ−j∞σ+j∞epLin+11pdp.E12
A sufficient condition for Eq. (12) to hold is obviously the “Orthogonality” of 1/ppn1/p with respect to any “arbitrary” ρ1/p (see Eq. (11)). The points 1/pi are denoted by 1/pin and they are the “zeros” of a certain set of “orthogonal polynomials” in the variable 1/p. By using these quantities in the “quadrature formula” we can obtain theoretically “exact accuracy” for “any polynomial” in 1/p up to the 16(th) degree.
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).
3. Calculation of the different inhomogeneous profiles
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).
3.1 Calculation for circular dielectric material in the center of the cross section
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 (0≤x≤a, and 0≤y≤b) to regions that are four-fold larger (−a≤x≤a, and −b≤y≤b). The elements of the matrix g(n,m) are calculated for an arbitrary profile in the cross section of the straight waveguide according to Figure 2(a) and (b).
Figure 2.
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 gxy is calculated according to εxy=ε01+gxy and according to Figure 2(a) and (b) where gxy=g0. The specific case of circular dielectric material in the center of the cross section is shown in Figure 2(b) by using the image method. We obtain
The radius of the circle is given by r=x−a/22+y−b/22, thus for the specific case of the cross section (Figure 1(a)) and according to the image method, we obtain.
y11x=b/2−r2−x−a/22,E15
y12x=b/2+r2−x−a/22E16
The dielectric profile for the cross section (Figure 1(a)) is given by.
The cyclic matrix G is given as follows. The Fourier transform is applied to the transverse dimension
g¯kxky=Fgxy=∫x∫ygxye−jkxx−jkyydxdy.E19
The components are organized in a vectorial notation as follows
E=E¯−N,−M⋮E¯−N,+M⋮E¯+n,+m⋮E¯+N,+M.E20
The Fourier components of the dielectric profile are calculated in the Fourier space. The convolution operation
g¯∗E¯=∑n′=−NN∑m′=−MMgn−n′,m−m′En′,m′E21
is written in a matrix form as GE where
g¯nmn′m′=gn−n′,m−m′E22
and the matrix order is (2 N + 1)(2 M + 1), where E is the electric field.
The convolution operation is expressed by the cyclic matrix G which consists of Fourier components of the dielectric profile g¯nm. Thus, the cyclic matrix G is given by the form
where y11 and y12 are given according to Eqs (15) and (16). Similarly, we can calculate the value of gynm, where gyxy=1/εxydεxy/dy.
3.2 Calculation for the circular hollow core in the center of the cross section
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.
Figure 3.
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)).
4. Numerical results
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 (TE10) input-wave profile.
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:
Figure 4.
(a) A dielectric slab in a rectangular metallic waveguide. (b) A comparison between the theoretical model (Eq. (2)) and the transcendental equation (Eqs (25)–(27)) according to Ref. [20], where a = 2b = 2 cm, d = 3.3 mm, εr= 9, and λ= 6.9 cm. (c) The convergence of our theoretical results.
Ey1=jkzε0sinνx0<x<tE25
Ey2=jkzε0sinνtcosμt−a/2cosμx−a/2t<x<t+dE26
Ey3=jkzε0sinνa−xt+d<x<a,E27
where ν≡ko2−kz2 and μ≡εrko2−kz2 result from the transcendental equation
a−dddμ2tandμ2−tνcottν=0.E28
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 (N = 1, 3, 5, 7, and 9). The order N determines the accuracy of the solution. The convergence of the solution is verified by the criterion for the Ey component of the fields.
The convergence of the solution is verified by the criterion
CN≡logmaxEyN+2−EyN∣maxEyN+2−minEyN∣,N≥1.E29
where the number of the modes is equal to 2N+12. The order N determines the accuracy of the solution.
If the value of the criterion (Eq. (29)) is less than −2, then the numerical solution is well converged. When N increases, then EyN approaches Ey. The value of the criterion between N = 7 and N = 9 is equal to −2.38 ≃ −2, namely a hundredth part. Comparison between the theoretical mode-model (Eq. (2)) and the known model [20] shows good agreement.
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, εr = 3, 5, 7, 9, for r = 2.5 mm, where r is the radius of the circular dielectric material. The output field in the same cross section of the results Figure 5(a)–(d) are shown in Figure 5(e) for the x-axis and where y = b/2 = 10 mm, for the values of εr = 3, 5, 7, and 9, respectively. Figure 6(a)–(e) demonstrates the output fields by changing only the parameter of the radius of the circular dielectric material from r = 2.5 to r = 2. The other parameters are a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m.
Figure 5.
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) εr = 3, for (b) εr = 5, for (c) εr = 7, and for (d) εr = 9. (e) The output field in the same cross section of the results (a)–(d) for x-axis and where y = b/2 = 10 mm, for the values of εr = 3, 5, 7, and 9, respectively. The other parameters are a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β =58 1/m.
Figure 6.
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) εr = 3, for (b) εr = 5, for (c) εr = 7, and for (d) εr = 9. (e) The output field in the same cross section of the results (a)–(d) for x-axis and where y = b/2 = 10 mm, for the values of εr = 3, 5, 7, and 9, respectively. The other parameters are a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m.
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, εr = 1.5, 1.6, 1.7, 1.8, for r = 2.5 mm, where r is the radius of the circular hollow core. The output field in the same cross section of the results Figure 7(a)–(d) are shown in Figure 7(e) for x-axis and where y = b/2 = 10 mm, for the values of εr = 1.5, 1.6, 1.7, and 1.8, respectively. Figure 8(a)–(e) demonstrates the output fields by changing only the parameter of the radius of the circular hollow core from r = 2.5 to r = 2. The other parameters are a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m.
Figure 7.
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) εr = 1.5, for (b) εr = 1.6, for (c) εr = 1.7, and for (d) εr = 1.8. (e) The output field in the same cross section of the results (a)–(d) for x-axis and where y = b/2 = 10 mm, for the values of εr = 1.5, 1.6, 1.7, and 1.8, respectively. The other parameters are a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m.
Figure 8.
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) εr = 1.5, for (b) εr = 1.6, for (c) εr = 1.7, and for (d) εr = 1.8. (e) The output field in the same cross section of the results (a)–(d) for x-axis and where y = b/2 = 10 mm, for the values of εr = 1.5, 1.6, 1.7, and 1.8, respectively. The other parameters are a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β =58 1/m.
By increasing only the dielectric constant from εr = 3 to εr = 9, according to Figures 5(a)–(e) and 6(a)–(e), and from εr = 1.5 to εr = 1.8, according to Figures 7(a)–(e) and 8(a)–(e), the Gaussian shape of the output transverse profile of the field increased, the TE10 wave profile decreased, and the relative amplitude of the output field decreased.
We can predict the waveguide parameters (εr and r) for obtaining the Gaussian behavior of the output field in all case. The cross section in the first interesting case consists of circular dielectric material in the center of the cross section (Figure 1(a)). The cross section in the second interesting case consists of a circular hollow core in the center of the cross section (Figure 1(b)). The output results refer to the same parameters a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m. According to the results of the first case, in order to obtain the Gaussian behavior, the values of εr = 3, 5, 7, 9 and r = 2 or r = 2.5 are needed. In the second case, in order to obtain the Gaussian behavior, the values of εr = 1.5, 1.6, 1.7, and 1.8 and r = 2 or r = 2.5 are needed.
These results are strongly affected by the different parameters εr and r, and for the same other parameters of k0 = 167 1/m, λ = 3.75 cm, β = 58 1/m, and the dimensions of the rectangular cross section.
5. Conclusions
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, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m.
By increasing only the dielectric constant from εr = 3 to εr = 9, according to Figures 5(a)–(e) and 6(a)–(e), and from εr = 1.5 to εr = 1.8, according to Figures 7(a)–(e) and 8(a)–(e), the Gaussian shape of the output transverse profile of the field increased, the TE10 wave profile decreased, and the relative amplitude of the output field decreased.
We can predict the waveguide parameters (εr and r) for obtaining the Gaussian behavior of the output field in all cases. The output results refer to the same parameters a = b = 20 mm, k0 = 167 1/m, λ = 3.75 cm, and β = 58 1/m. According to the results of the first case, in order to obtain the Gaussian behavior, the values of εr = 3, 5, 7, 9 and r = 2 or r = 2.5 are needed. In the second case, in order to obtain the Gaussian behavior, the values of εr = 1.5, 1.6, 1.7, and 1.8 and r = 2 or r = 2.5 are needed.
The results are strongly affected by the different parameters εr and r, and for the same other parameters of k0 = 167 1/m, λ = 3.75 cm, β = 58 1/m, and the dimensions of the rectangular cross section.
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
a∼s=Laζ=∫ζ=0∞aζe−sζdζ,E30
is applied on the z-dimension, where az represents any z-dependent variables of the wave equations.
A Fourier transform is applied on the transverse dimension
g¯kxky=Fgxy=∫x∫ygxye−jkxx−jkyydxdy,E31
and the differential equations are transformed to an algebraic form in the (ω,s,kx,ky) space.
The method of images is applied to satisfy the conditions n̂×E=0 and n̂⋅∇×E=0 on the surface of the ideal metallic waveguide walls, where n̂ is a unit vector perpendicular to the surface. The dielectric profile, gxy, is defined inside the waveguide boundaries, 0≤x≤a and 0≤y≤b. In order to maintain the boundary conditions without physical metallic walls, a substitute physical problem is constructed with infinite transverse extent. The periodicity and the symmetry properties are chosen to force the boundary conditions at the location of the walls in the real problem. This is done by extending the waveguide region 0≤x≤a,0≤y≤b to a four-fold larger region. Hence, the following relations are yielded
g−xy=gx−y=gxy=g−x−y,E32
Exx−y=−Exxy,Ex−xy=Exxy.E33
The region −a≤x≤a,−b≤y≤b is then further extended to infinity by periodic replication, gx+2ℓay+2kb=gxy, where −∞<ℓ,k<∞. The field components are periodically, namely, Exx+2ℓay+2kb=Exxy for −∞<ℓ,k<∞. The substitution of the physical problem is equivalent to the original problem in the region 0≤x≤a, 0≤y≤b, and satisfies the same boundary conditions on the boundary of this region. The discrete Fourier transform series is given with kx=nπ/a and ky=mπ/b, and the transverse wavenumbers are given by kox=π/a, and koy=π/b, where a and b are the transverse dimensions of the rectangular boundaries. We substitute kx=nkox and ky=mkoy, where the integers n and m are truncated by −N≤n≤N and −M≤m≤M, respectively. The orders N and M determine the accuracy of the solution.
The output transverse field profiles are given by the inverse Laplace and Fourier transforms, as follows
Eyxyz=∑n∑m∫σ−j∞σ+j∞Eynmsexpjnkoxx+jmkoyy+szds,E34
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.
\n',keywords:"wave propagation, dielectric profiles, rectangular waveguide, circular dielectric material, circular hollow core",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/82335.pdf",chapterXML:"https://mts.intechopen.com/source/xml/82335.xml",downloadPdfUrl:"/chapter/pdf-download/82335",previewPdfUrl:"/chapter/pdf-preview/82335",totalDownloads:5,totalViews:0,totalCrossrefCites:0,dateSubmitted:null,dateReviewed:"April 5th 2022",datePrePublished:"June 22nd 2022",datePublished:null,dateFinished:"June 22nd 2022",readingETA:"0",abstract:"This chapter presents wave propagation along a straight rectangular waveguide for practical applications where there are two complementary shapes of the dielectric profile in the cross section. 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 consists of a circular hollow core 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 for all cases. The method is based on Laplace and Fourier transforms and inverse Laplace and Fourier transform. In order to solve any inhomogeneous problem in the cross section, more than one technique can be proposed for the same mode-model method. We will explain in detail how and where the technique can be integrated into the proposed mode-model. The image method and periodic replication are needed for fulfilling the boundary condition of the metallic waveguide. 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.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/82335",risUrl:"/chapter/ris/82335",signatures:"Zion Menachem",book:{id:"11150",type:"book",title:"Recent Advances of Wavelet Transform and Their Applications",subtitle:null,fullTitle:"Recent Advances of Wavelet Transform and Their Applications",slug:null,publishedDate:null,bookSignature:"Dr. Francisco Bulnes",coverURL:"https://cdn.intechopen.com/books/images_new/11150.jpg",licenceType:"CC BY 3.0",editedByType:null,isbn:"978-1-80355-739-7",printIsbn:"978-1-80355-738-0",pdfIsbn:"978-1-80355-740-3",isAvailableForWebshopOrdering:!0,editors:[{id:"92918",title:"Dr.",name:"Francisco",middleName:null,surname:"Bulnes",slug:"francisco-bulnes",fullName:"Francisco Bulnes"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Complementary shapes in the cross section for different applications",level:"1"},{id:"sec_3",title:"3. Calculation of the different inhomogeneous profiles",level:"1"},{id:"sec_3_2",title:"3.1 Calculation for circular dielectric material in the center of the cross section",level:"2"},{id:"sec_4_2",title:"3.2 Calculation for the circular hollow core in the center of the cross section",level:"2"},{id:"sec_6",title:"4. Numerical results",level:"1"},{id:"sec_7",title:"5. Conclusions",level:"1"},{id:"sec_9",title:"",level:"1"}],chapterReferences:[{id:"B1",body:'Chiang KS. Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides. Optical and Quantum Electronics. 1994;26:S113-S134'},{id:"B2",body:'Wagner RL, Otto GP, Chew WC. Fast waveguide mode computation using wavelet-like basis functions. IEEE Microwave and Guided Wave Letters. 1993;3:208-210'},{id:"B3",body:'Goswami JC, Chan AK, Chui CK. 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TE-wave propagation in graded waveguide structures. Osa Continuum. 2020;3:67-76'},{id:"B14",body:'Srikanth KH. Studying the characteristics of a rectangular waveguide using HFSS. International Journal of Computer Applications (0975–8887). 2015;118(21):5-8'},{id:"B15",body:'Islamov IJ, Shukurov NM, Abdullayev RS, Hashimov KK, Khalilov AI. Diffraction of electromagnetic waves of rectangular waveguides with a longitudinal. IEEE. 2020;1–7'},{id:"B16",body:'Menachem Z, Jerby E. Transfer matrix function (TMF) for propagation in dielectric waveguides with arbitrary transverse profiles. IEEE Transactions on Microwave Theory and Techniques. 1998;46:975-982'},{id:"B17",body:'Salzer HE. Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms. Mathematical Tables and Other Aids to Computation. 1955;9:164-177'},{id:"B18",body:'Salzer HE. Additional formulas and tables for orthogonal polynomials originating from inversion integrals. Journal of Mathematical Physics. 1961;39:72-86'},{id:"B19",body:'The Numerical Algorithms Group (NAG) Ltd, Wilkinson House, Oxford, UK. 1999'},{id:"B20",body:'Collin RE. Foundation for Microwave Engineering. New York: McGraw-Hill; 1996'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Zion Menachem",address:"zionme@sce.ac.il;, zionmm@gmail.com",affiliation:'
Department of Electrical Engineering, Shamoon College of Engineering, Beer Sheva, Israel
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Since 1983, he has been a faculty member of the RO Perelman Department of Dermatology, NYU School of Medicine, where he is codirector of a training grant in cutaneous biology. Dr. Blumenberg’s research is focused on the epidermis, expression of keratin genes, transcription profiling, keratinocyte differentiation, inflammatory diseases and cancers, and most recently the effects of the microbiome on the skin. 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Dr. Madfa also regularly attends international conferences and holds administrative positions (Deputy Dean of the Faculty for Students’ & Academic Affairs and Deputy Head of Research Unit).",institutionString:"Thamar University",institution:null},{id:"210472",title:"Dr.",name:"Nermin",middleName:"Mohammed Ahmed",surname:"Yussif",slug:"nermin-yussif",fullName:"Nermin Yussif",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/210472/images/system/210472.jpg",biography:"Dr. Nermin Mohammed Ahmed Yussif is working at the Faculty of dentistry, University for October university for modern sciences and arts (MSA). Her areas of expertise include: periodontology, dental laserology, oral implantology, periodontal plastic surgeries, oral mesotherapy, nutrition, dental pharmacology. She is an editor and reviewer in numerous international journals.",institutionString:"MSA University",institution:null},{id:"204606",title:"Dr.",name:"Serdar",middleName:null,surname:"Gözler",slug:"serdar-gozler",fullName:"Serdar Gözler",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/204606/images/system/204606.jpeg",biography:"Dr. Serdar Gözler has completed his undergraduate studies at the Marmara University Faculty of Dentistry in 1978, followed by an assistantship in the Prosthesis Department of Dicle University Faculty of Dentistry. Starting his PhD work on non-resilient overdentures with Assoc. Prof. Hüsnü Yavuzyılmaz, he continued his studies with Prof. Dr. Gürbüz Öztürk of Istanbul University Faculty of Dentistry Department of Prosthodontics, this time on Gnatology. He attended training programs on occlusion, neurology, neurophysiology, EMG, radiology and biostatistics. In 1982, he presented his PhD thesis \\Gerber and Lauritzen Occlusion Analysis Techniques: Diagnosis Values,\\ at Istanbul University School of Dentistry, Department of Prosthodontics. As he was also working with Prof. Senih Çalıkkocaoğlu on The Physiology of Chewing at the same time, Gözler has written a chapter in Çalıkkocaoğlu\\'s book \\Complete Prostheses\\ entitled \\The Place of Neuromuscular Mechanism in Prosthetic Dentistry.\\ The book was published five times since by the Istanbul University Publications. Having presented in various conferences about occlusion analysis until 1998, Dr. Gözler has also decided to use the T-Scan II occlusion analysis method. Having been personally trained by Dr. Robert Kerstein on this method, Dr. Gözler has been lecturing on the T-Scan Occlusion Analysis Method in conferences both in Turkey and abroad. Dr. Gözler has various articles and presentations on Digital Occlusion Analysis methods. He is now Head of the TMD Clinic at Prosthodontic Department of Faculty of Dentistry , Istanbul Aydın University , Turkey.",institutionString:"Istanbul Aydin University",institution:{name:"Istanbul Aydın University",country:{name:"Turkey"}}},{id:"240870",title:"Ph.D.",name:"Alaa Eddin Omar",middleName:null,surname:"Al Ostwani",slug:"alaa-eddin-omar-al-ostwani",fullName:"Alaa Eddin Omar Al Ostwani",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/240870/images/system/240870.jpeg",biography:"Dr. Al Ostwani Alaa Eddin Omar received his Master in dentistry from Damascus University in 2010, and his Ph.D. in Pediatric Dentistry from Damascus University in 2014. Dr. Al Ostwani is an assistant professor and faculty member at IUST University since 2014. \nDuring his academic experience, he has received several awards including the scientific research award from the Union of Arab Universities, the Syrian gold medal and the international gold medal for invention and creativity. Dr. Al Ostwani is a Member of the International Association of Dental Traumatology and the Syrian Society for Research and Preventive Dentistry since 2017. He is also a Member of the Reviewer Board of International Journal of Dental Medicine (IJDM), and the Indian Journal of Conservative and Endodontics since 2016.",institutionString:"International University for Science and Technology.",institution:{name:"Islamic University of Science and Technology",country:{name:"India"}}},{id:"42847",title:"Dr.",name:"Belma",middleName:null,surname:"Işik Aslan",slug:"belma-isik-aslan",fullName:"Belma Işik Aslan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/42847/images/system/42847.jpg",biography:"Dr. Belma IşIk Aslan was born in 1976 in Ankara-TURKEY. After graduating from TED Ankara College in 1994, she attended to Gazi University, Faculty of Dentistry in Ankara. She completed her PhD in orthodontic education at Gazi University between 1999-2005. Dr. Işık Aslan stayed at the Providence Hospital Craniofacial Institude and Reconstructive Surgery in Michigan, USA for three months as an observer. She worked as a specialist doctor at Gazi University, Dentistry Faculty, Department of Orthodontics between 2005-2014. She was appointed as associate professor in January, 2014 and as professor in 2021. Dr. Işık Aslan still works as an instructor at the same faculty. She has published a total of 35 articles, 10 book chapters, 39 conference proceedings both internationally and nationally. Also she was the academic editor of the international book 'Current Advances in Orthodontics'. She is a member of the Turkish Orthodontic Society and Turkish Cleft Lip and Palate Society. She is married and has 2 children. Her knowledge of English is at an advanced level.",institutionString:"Gazi University Dentistry Faculty Department of Orthodontics",institution:null},{id:"178412",title:"Associate Prof.",name:"Guhan",middleName:null,surname:"Dergin",slug:"guhan-dergin",fullName:"Guhan Dergin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/178412/images/6954_n.jpg",biography:"Assoc. Prof. Dr. Gühan Dergin was born in 1973 in Izmit. He graduated from Marmara University Faculty of Dentistry in 1999. He completed his specialty of OMFS surgery in Marmara University Faculty of Dentistry and obtained his PhD degree in 2006. In 2005, he was invited as a visiting doctor in the Oral and Maxillofacial Surgery Department of the University of North Carolina, USA, where he went on a scholarship. Dr. Dergin still continues his academic career as an associate professor in Marmara University Faculty of Dentistry. He has many articles in international and national scientific journals and chapters in books.",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"178414",title:"Prof.",name:"Yusuf",middleName:null,surname:"Emes",slug:"yusuf-emes",fullName:"Yusuf Emes",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/178414/images/6953_n.jpg",biography:"Born in Istanbul in 1974, Dr. Emes graduated from Istanbul University Faculty of Dentistry in 1997 and completed his PhD degree in Istanbul University faculty of Dentistry Department of Oral and Maxillofacial Surgery in 2005. He has papers published in international and national scientific journals, including research articles on implantology, oroantral fistulas, odontogenic cysts, and temporomandibular disorders. Dr. Emes is currently working as a full-time academic staff in Istanbul University faculty of Dentistry Department of Oral and Maxillofacial Surgery.",institutionString:null,institution:{name:"Istanbul University",country:{name:"Turkey"}}},{id:"192229",title:"Ph.D.",name:"Ana Luiza",middleName:null,surname:"De Carvalho Felippini",slug:"ana-luiza-de-carvalho-felippini",fullName:"Ana Luiza De Carvalho Felippini",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/192229/images/system/192229.jpg",biography:null,institutionString:"University of São Paulo",institution:{name:"University of Sao Paulo",country:{name:"Brazil"}}},{id:"256851",title:"Prof.",name:"Ayşe",middleName:null,surname:"Gülşen",slug:"ayse-gulsen",fullName:"Ayşe Gülşen",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/256851/images/9696_n.jpg",biography:"Dr. Ayşe Gülşen graduated in 1990 from Faculty of Dentistry, University of Ankara and did a postgraduate program at University of Gazi. \nShe worked as an observer and research assistant in Craniofacial Surgery Departments in New York, Providence Hospital in Michigan and Chang Gung Memorial Hospital in Taiwan. \nShe works as Craniofacial Orthodontist in Department of Aesthetic, Plastic and Reconstructive Surgery, Faculty of Medicine, University of Gazi, Ankara Turkey since 2004.",institutionString:"Univeristy of Gazi",institution:null},{id:"255366",title:"Prof.",name:"Tosun",middleName:null,surname:"Tosun",slug:"tosun-tosun",fullName:"Tosun Tosun",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/255366/images/7347_n.jpg",biography:"Graduated at the Faculty of Dentistry, University of Istanbul, Turkey in 1989;\nVisitor Assistant at the University of Padua, Italy and Branemark Osseointegration Center of Treviso, Italy between 1993-94;\nPhD thesis on oral implantology in University of Istanbul and was awarded the academic title “Dr.med.dent.”, 1997;\nHe was awarded the academic title “Doç.Dr.” (Associated Professor) in 2003;\nProficiency in Botulinum Toxin Applications, Reading-UK in 2009;\nMastership, RWTH Certificate in Laser Therapy in Dentistry, AALZ-Aachen University, Germany 2009-11;\nMaster of Science (MSc) in Laser Dentistry, University of Genoa, Italy 2013-14.\n\nDr.Tosun worked as Research Assistant in the Department of Oral Implantology, Faculty of Dentistry, University of Istanbul between 1990-2002. \nHe worked part-time as Consultant surgeon in Harvard Medical International Hospitals and John Hopkins Medicine, Istanbul between years 2007-09.\u2028He was contract Professor in the Department of Surgical and Diagnostic Sciences (DI.S.C.), Medical School, University of Genova, Italy between years 2011-16. \nSince 2015 he is visiting Professor at Medical School, University of Plovdiv, Bulgaria. \nCurrently he is Associated Prof.Dr. at the Dental School, Oral Surgery Dept., Istanbul Aydin University and since 2003 he works in his own private clinic in Istanbul, Turkey.\u2028\nDr.Tosun is reviewer in journal ‘Laser in Medical Sciences’, reviewer in journal ‘Folia Medica\\', a Fellow of the International Team for Implantology, Clinical Lecturer of DGZI German Association of Oral Implantology, Expert Lecturer of Laser&Health Academy, Country Representative of World Federation for Laser Dentistry, member of European Federation of Periodontology, member of Academy of Laser Dentistry. Dr.Tosun presents papers in international and national congresses and has scientific publications in international and national journals. He speaks english, spanish, italian and french.",institutionString:null,institution:{name:"Istanbul Aydın University",country:{name:"Turkey"}}},{id:"171887",title:"Prof.",name:"Zühre",middleName:null,surname:"Akarslan",slug:"zuhre-akarslan",fullName:"Zühre Akarslan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/171887/images/system/171887.jpg",biography:"Zühre Akarslan was born in 1977 in Cyprus. She graduated from Gazi University Faculty of Dentistry, Ankara, Turkey in 2000. \r\nLater she received her Ph.D. degree from the Oral Diagnosis and Radiology Department; which was recently renamed as Oral and Dentomaxillofacial Radiology, from the same university. \r\nShe is working as a full-time Associate Professor and is a lecturer and an academic researcher. \r\nHer expertise areas are dental caries, cancer, dental fear and anxiety, gag reflex in dentistry, oral medicine, and dentomaxillofacial radiology.",institutionString:"Gazi University",institution:{name:"Gazi University",country:{name:"Turkey"}}},{id:"256417",title:"Associate Prof.",name:"Sanaz",middleName:null,surname:"Sadry",slug:"sanaz-sadry",fullName:"Sanaz Sadry",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/256417/images/8106_n.jpg",biography:null,institutionString:null,institution:null},{id:"272237",title:"Dr.",name:"Pinar",middleName:"Kiymet",surname:"Karataban",slug:"pinar-karataban",fullName:"Pinar Karataban",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/272237/images/8911_n.png",biography:"Assist.Prof.Dr.Pınar Kıymet Karataban, DDS PhD \n\nDr.Pınar Kıymet Karataban was born in Istanbul in 1975. After her graduation from Marmara University Faculty of Dentistry in 1998 she started her PhD in Paediatric Dentistry focused on children with special needs; mainly children with Cerebral Palsy. She finished her pHD thesis entitled \\'Investigation of occlusion via cast analysis and evaluation of dental caries prevalance, periodontal status and muscle dysfunctions in children with cerebral palsy” in 2008. She got her Assist. Proffessor degree in Istanbul Aydın University Paediatric Dentistry Department in 2015-2018. ın 2019 she started her new career in Bahcesehir University, Istanbul as Head of Department of Pediatric Dentistry. In 2020 she was accepted to BAU International University, Batumi as Professor of Pediatric Dentistry. She’s a lecturer in the same university meanwhile working part-time in private practice in Ege Dental Studio (https://www.egedisklinigi.com/) a multidisciplinary dental clinic in Istanbul. Her main interests are paleodontology, ancient and contemporary dentistry, oral microbiology, cerebral palsy and special care dentistry. She has national and international publications, scientific reports and is a member of IAPO (International Association for Paleodontology), IADH (International Association of Disability and Oral Health) and EAPD (European Association of Pediatric Dentistry).",institutionString:null,institution:null},{id:"202198",title:"Dr.",name:"Buket",middleName:null,surname:"Aybar",slug:"buket-aybar",fullName:"Buket Aybar",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/202198/images/6955_n.jpg",biography:"Buket Aybar, DDS, PhD, was born in 1971. She graduated from Istanbul University, Faculty of Dentistry, in 1992 and completed her PhD degree on Oral and Maxillofacial Surgery in Istanbul University in 1997.\nDr. Aybar is currently a full-time professor in Istanbul University, Faculty of Dentistry Department of Oral and Maxillofacial Surgery. She has teaching responsibilities in graduate and postgraduate programs. Her clinical practice includes mainly dentoalveolar surgery.\nHer topics of interest are biomaterials science and cell culture studies. She has many articles in international and national scientific journals and chapters in books; she also has participated in several scientific projects supported by Istanbul University Research fund.",institutionString:null,institution:null},{id:"260116",title:"Dr.",name:"Mehmet",middleName:null,surname:"Yaltirik",slug:"mehmet-yaltirik",fullName:"Mehmet Yaltirik",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/260116/images/7413_n.jpg",biography:"Birth Date 25.09.1965\r\nBirth Place Adana- Turkey\r\nSex Male\r\nMarrial Status Bachelor\r\nDriving License Acquired\r\nMother Tongue Turkish\r\n\r\nAddress:\r\nWork:University of Istanbul,Faculty of Dentistry, Department of Oral Surgery and Oral Medicine 34093 Capa,Istanbul- TURKIYE",institutionString:null,institution:null},{id:"172009",title:"Dr.",name:"Fatma Deniz",middleName:null,surname:"Uzuner",slug:"fatma-deniz-uzuner",fullName:"Fatma Deniz Uzuner",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/172009/images/7122_n.jpg",biography:"Dr. Deniz Uzuner was born in 1969 in Kocaeli-TURKEY. After graduating from TED Ankara College in 1986, she attended the Hacettepe University, Faculty of Dentistry in Ankara. \nIn 1993 she attended the Gazi University, Faculty of Dentistry, Department of Orthodontics for her PhD education. After finishing the PhD education, she worked as orthodontist in Ankara Dental Hospital under the Turkish Government, Ministry of Health and in a special Orthodontic Clinic till 2011. Between 2011 and 2016, Dr. Deniz Uzuner worked as a specialist in the Department of Orthodontics, Faculty of Dentistry, Gazi University in Ankara/Turkey. In 2016, she was appointed associate professor. Dr. Deniz Uzuner has authored 23 Journal Papers, 3 Book Chapters and has had 39 oral/poster presentations. She is a member of the Turkish Orthodontic Society. Her knowledge of English is at an advanced level.",institutionString:null,institution:null},{id:"332914",title:"Dr.",name:"Muhammad Saad",middleName:null,surname:"Shaikh",slug:"muhammad-saad-shaikh",fullName:"Muhammad Saad Shaikh",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Jinnah Sindh Medical University",country:{name:"Pakistan"}}},{id:"315775",title:"Dr.",name:"Feng",middleName:null,surname:"Luo",slug:"feng-luo",fullName:"Feng Luo",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Sichuan University",country:{name:"China"}}},{id:"423519",title:"Dr.",name:"Sizakele",middleName:null,surname:"Ngwenya",slug:"sizakele-ngwenya",fullName:"Sizakele Ngwenya",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of the Witwatersrand",country:{name:"South Africa"}}},{id:"419270",title:"Dr.",name:"Ann",middleName:null,surname:"Chianchitlert",slug:"ann-chianchitlert",fullName:"Ann Chianchitlert",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Walailak University",country:{name:"Thailand"}}},{id:"419271",title:"Dr.",name:"Diane",middleName:null,surname:"Selvido",slug:"diane-selvido",fullName:"Diane Selvido",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Walailak University",country:{name:"Thailand"}}},{id:"419272",title:"Dr.",name:"Irin",middleName:null,surname:"Sirisoontorn",slug:"irin-sirisoontorn",fullName:"Irin Sirisoontorn",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Walailak University",country:{name:"Thailand"}}},{id:"355660",title:"Dr.",name:"Anitha",middleName:null,surname:"Mani",slug:"anitha-mani",fullName:"Anitha Mani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"SRM Dental College",country:{name:"India"}}},{id:"355612",title:"Dr.",name:"Janani",middleName:null,surname:"Karthikeyan",slug:"janani-karthikeyan",fullName:"Janani Karthikeyan",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"SRM Dental College",country:{name:"India"}}},{id:"334400",title:"Dr.",name:"Suvetha",middleName:null,surname:"Siva",slug:"suvetha-siva",fullName:"Suvetha Siva",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"SRM Dental College",country:{name:"India"}}}]}},subseries:{item:{id:"10",type:"subseries",title:"Animal Physiology",keywords:"Physiology, Comparative, Evolution, Biomolecules, Organ, Homeostasis, Anatomy, Pathology, Medical, Cell Division, Cell Signaling, Cell Growth, Cell Metabolism, Endocrine, Neuroscience, Cardiovascular, Development, Aging, Development",scope:"Physiology, the scientific study of functions and mechanisms of living systems, is an essential area of research in its own right, but also in relation to medicine and health sciences. The scope of this topic will range from molecular, biochemical, cellular, and physiological processes in all animal species. Work pertaining to the whole organism, organ systems, individual organs and tissues, cells, and biomolecules will be included. Medical, animal, cell, and comparative physiology and allied fields such as anatomy, histology, and pathology with physiology links will be covered in this topic. Physiology research may be linked to development, aging, environment, regular and pathological processes, adaptation and evolution, exercise, or several other factors affecting, or involved with, animal physiology.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/10.jpg",hasOnlineFirst:!1,hasPublishedBooks:!1,annualVolume:11406,editor:{id:"202192",title:"Dr.",name:"Catrin",middleName:null,surname:"Rutland",slug:"catrin-rutland",fullName:"Catrin Rutland",profilePictureURL:"https://mts.intechopen.com/storage/users/202192/images/system/202192.png",biography:"Catrin Rutland is an Associate Professor of Anatomy and Developmental Genetics at the University of Nottingham, UK. She obtained a BSc from the University of Derby, England, a master’s degree from Technische Universität München, Germany, and a Ph.D. from the University of Nottingham. She undertook a post-doctoral research fellowship in the School of Medicine before accepting tenure in Veterinary Medicine and Science. Dr. Rutland also obtained an MMedSci (Medical Education) and a Postgraduate Certificate in Higher Education (PGCHE). She is the author of more than sixty peer-reviewed journal articles, twelve books/book chapters, and more than 100 research abstracts in cardiovascular biology and oncology. She is a board member of the European Association of Veterinary Anatomists, Fellow of the Anatomical Society, and Senior Fellow of the Higher Education Academy. Dr. Rutland has also written popular science books for the public. https://orcid.org/0000-0002-2009-4898. www.nottingham.ac.uk/vet/people/catrin.rutland",institutionString:null,institution:{name:"University of Nottingham",institutionURL:null,country:{name:"United Kingdom"}}},editorTwo:null,editorThree:null,series:{id:"10",title:"Physiology",doi:"10.5772/intechopen.72796",issn:"2631-8261"},editorialBoard:[{id:"306970",title:"Mr.",name:"Amin",middleName:null,surname:"Tamadon",slug:"amin-tamadon",fullName:"Amin Tamadon",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002oHR5wQAG/Profile_Picture_1623910304139",institutionString:null,institution:{name:"Bushehr University of Medical Sciences",institutionURL:null,country:{name:"Iran"}}},{id:"251314",title:"Dr.",name:"Juan Carlos",middleName:null,surname:"Gardón",slug:"juan-carlos-gardon",fullName:"Juan Carlos Gardón",profilePictureURL:"https://mts.intechopen.com/storage/users/251314/images/system/251314.jpeg",institutionString:"Catholic University of Valencia San Vicente Mártir, Spain",institution:null},{id:"245306",title:"Dr.",name:"María Luz",middleName:null,surname:"Garcia Pardo",slug:"maria-luz-garcia-pardo",fullName:"María Luz Garcia Pardo",profilePictureURL:"https://mts.intechopen.com/storage/users/245306/images/system/245306.png",institutionString:null,institution:{name:"Miguel Hernandez University",institutionURL:null,country:{name:"Spain"}}},{id:"283315",title:"Prof.",name:"Samir",middleName:null,surname:"El-Gendy",slug:"samir-el-gendy",fullName:"Samir El-Gendy",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRduYQAS/Profile_Picture_1606215849748",institutionString:null,institution:{name:"Alexandria University",institutionURL:null,country:{name:"Egypt"}}},{id:"178366",title:"Dr.",name:"Volkan",middleName:null,surname:"Gelen",slug:"volkan-gelen",fullName:"Volkan Gelen",profilePictureURL:"https://mts.intechopen.com/storage/users/178366/images/system/178366.jpg",institutionString:"Kafkas University",institution:{name:"Kafkas University",institutionURL:null,country:{name:"Turkey"}}}]},onlineFirstChapters:{paginationCount:7,paginationItems:[{id:"82405",title:"Does Board Structure Matter in CSR Spending of Commercial Banks? 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