**3.2 Governing equations**

*Computational Fluid Dynamics Simulations*

**3. Computational fluid dynamics**

procedures.

**3.1 CFD methodology**

*3.1.1 Preprocessing*

*3.1.2 Processing*

algebraic equations.

*3.1.3 Postprocessing*

operations. It is necessary to identify the characteristics of the chemical reaction and the main features that the reactor should provide and from there define the next steps. Once these are identified, the appropriate physical and chemical con-

Computational fluid dynamics (CFD) is the analysis of systems involving fluid flow, heat transfer, and associated phenomena such as chemical reactions by means of computer-based simulation. This methodology is very powerful and may be used in a wide range of industrial and nonindustrial application areas. For hydrodynamic simulations, CFD is the proper methodology that may be used during reactor design

CFD codes may be considered a series of numerical algorithms that can resolve fluid flow problems. Commercial CFD packages include sophisticated user interfaces to facilitate the process of input problem parameters and to examine the results, and our interest within this chapter is the code ANSYS® [6, 7]. Most codes contain three main elements: (a) a preprocessor, (b) a solver, and (c) a postprocessor. There are external functions that can be coded as additional or complementary functions that can add up to the calculations and results; for ANSYS Fluent® these functions are known as user-defined functions (UDFs) [8]. Briefly, the function of

Preprocessing consists of the input of a flow problem to a CFD program by means of an interface and the subsequent transformation of this input into a data ready to use by the solver. The user activities at the preprocessing stage involve geometry definition (domain), grid generation (mesh), physical and chemical

There are three different schemes for numerical solution techniques: finite difference, finite element, and spectral methods. In this work only finite volume method will be considered, a special finite difference formulation that is central to the most well-established CFD codes including the program used in our case of study ANSYS Fluent®. The numerical algorithm to resolve the problem at hand consists of the following steps: governing equations, discretization, and solution of

In this step, results are available, and thanks to the visualization code tools, the data may be presented in different ways to facilitate the results analysis. The leading CFD packages are equipped with versatile data visualization tools. These may include domain geometry and grid display, vector plots, line and shaded contour plots, 2D and 3D surface plots, particle tracking, and view in perspective (translation, rotation, scaling, etc.), and more recently, animation has been included.

phenomena to be modeled, fluid properties, and boundary conditions.

cepts are applied to describe the selected reactor operation [1–5].

each of these elements within a CFD code is mentioned [1–5].

**88**

The governing equations of fluid flow represent mathematical statements of the conservation laws of physics: (a) mass conservation, (b) momentum conservation, and (c) energy conservation.

The fluid will be subject to the theory of the continuum. For the analysis of fluid flows at macroscopic length scales (around 1 μm and larger), the molecular structure of matter and molecular motions may be ignored. The behavior of the fluid is described in terms of macroscopic properties, such as velocity, pressure, density and temperature, and their space and time derivatives. These may be thought of as averages over a suitable large number of molecules. We will save the mathematical development because it is beyond the scope of this chapter and recommend the reader to consult CFD textbooks for such purpose.


**Meet the editor**

Vu Dang Hoang completed his doctorate in pharmaceutics at the University of Strathclyde, UK, in 2005 and conducted a postdoctoral research at the Ecole Nationale d'Ingénieurs des Techniques des Industries Agricoles et Alimentaires, France, in 2006. He has been lecturing at the Department of Analytical Chemistry and Toxicology, Hanoi University of Pharmacy, Vietnam, since 2007. He

became an associate professor in the field of drug quality control in 2015. His research interests include chemico-physical characterization of topical drug delivery systems and chemometrics-based methods for the analysis of drugs in pharmaceutical dosage forms and biological fluids. So far, he has authored more than 30 publications in pharmaceutical research and analytical chemistry in leading national and international peer-reviewed journals.


**9. Early Childhood Caries (ECC)**

Dental caries is a complex, multi-factorial disease and is a significant health and social problem which affects people of all ages and is responsible for a vast amount of pain, misery and economic loss. It is a major problem in young children. Caries of the primary teeth "Early Childhood Caries" or ECC is one of the most prevalent health problems in infants and toddlers (Mayanagi et al, 1995). It can be considered an epidemic in lower-income families and in under developed parts of the world (Ismail & Sohn 1999). ECC is one of the major causes of hospitalization in young children, who often need to receive general anaesthesia for extraction or tooth restoration (Sheller et al, 1996).


**4. Bridging the bio-electro interface: Redox signaling and electrogenetic systems**

In addition to quorum sensing, bacteria use numerous other small chemical molecules to build up conversations between themselves and with the environment. It is well known that redox reactions and redox based signaling pervade living cells and are extremely crucial to both anabolic and catabolic metabolism. Redox-based molecular systems, however, are also leveraged by bacteria for communication. Cells must detect a variety of oxidative stressors and quickly respond so as to avoid oxidative damage and maintain redox balance in order to survive. In this section, several redox signaling pathways will be introduced, yet emphasis will be on how redox signaling and electrochemistry help connect communication and information transfer between biological systems and electronic devices. In this way, redox molecules can serve as exogenous and electronically-programmed controllers of biological function.


**5. Conclusions**

In this paper, we assessed soil organic carbon stocks and its particle-size fractionation across different cropping systems. The fallow lands, Ab10YF and 5YF, exhibited the highest C stocks 17.74 and 22.20 mg C·ha−1 , while cultivated land under tillage MCRC depicted the lowest C stocks. The three organic carbon fractions showed significant variation across the cropping systems, with the NOM fraction holding the largest contributions to total soil organic carbon for all the cropping systems. The cPOM and fPOM were most influenced by the cropping systems with the highest concentration observed in Ab10YF and 5YF. The hypotheses established at the beginning of the study, stating that fallow land and teak plantations store more carbon than cultivated lands and that the POM fraction is more sensitive to cropping system characteristics than NOM is partially confirmed since the teak plantation recorded a lower C stock. The implementation of sustainable soil fertility management practices, including efficient restitution of crop residues, mulching, legume intercropping, long rotation cycles, use of dual-purpose crops and avoiding seasonal fires are necessary to improve soil organic storage in agricultural soil in the watershed. Moreover, agricultural extension officers, policy-makers and officials of the ministry in charge of agriculture have the significant role in supporting farmers in the sustainable intensification of cropping systems and the regulation and enforcement for the respect of pastoral transhumance corridors.

**Author Contributions:** Conceptualization: A.M.A.A., F.K.A. and T.M.A.; data curation: A.M.A.A. and T.M.A.; formal analysis: A.M.A.A. and F.K.A.; finding acquisition and investigation: F.K.A. and T.M.A.; methodology: A.M.A.A., F.K.A. and T.M.A.; project administration: F.K.A., H.A.A. and P.H.; supervision: F.K.A.; validation: H.A.A. and P.H.; visualization: F.K.A., T.M.A.; writing—original draft: A.M.A.A. and T.M.A.; writing—review and editing: A.M.A.A., F.K.A., T.M.A., H.A.A. and P.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available upon request from the corresponding author.

**Acknowledgments:** We are grateful to the International Atomic Energy Agency (IAEA), which provided the equipment used for laboratory analysis, through the Regional Project RAF5075.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could appear to influence the work reported in this paper. The funders had no role in the design of the study; in the collection, analysis, or interpretation of the data; in the writing of the manuscript, or in the decision to publish the results.


**Author details**

Yüksel Atay1 , Oktay Pamuk2 , Bekir Boyaci3 , Esra Zeynep Yildiz4 \*, Tuncay Göksel1 , Dilek Yeşim Metin1 , Servet Gül3 , Gökberk Devrim3 and Özlem Topbaş3

1 Faculty of Medicine, Ege University, Izmir, Turkey

2 Textile Engineering Department, Ege University, Izmir, Turkey

3 Sun Tekstil, R&D Center, Izmir, Turkey

4 Emel Akın Vocational Training School, Ege University, Izmir, Turkey

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


*Article* **Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution**

### **Barry C. Arnold 1, Héctor W. Gómez 2, Héctor Varela 2,\* and Ignacio Vidal 3**

Received: 8 May 2019; Accepted: 10 June 2019; Published: 14 June 2019

**Abstract:** In this paper, we consider a stochastic representation of the epsilon–skew–Cauchy distribution, viewed as a member of the family of skewed distributions discussed in Arellano-Valle et al. (2005). The stochastic representation facilitates derivation of distributional properties of the model. In addition, we introduce symmetric and asymmetric extensions of the Cauchy distribution, together with an extension of the epsilon–skew–Cauchy distribution. Multivariate versions of these distributions can be envisioned. Bivariate examples are discussed in some detail.

**Keywords:** Epsilon-skew-Normal; Epsilon-skew-Cauchy; bivariate densities; generalized Cauchy distributions