**X-RAY CHARACTERIZATION OF NANOSTRUCTURED ENERGY MATERIALS BY SYNCHROTRON RADIATION**

Edited by **Mehdi Khodaei** and **Luca Petaccia**

#### **X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation**

http://dx.doi.org/10.5772/62715 Edited by Mehdi Khodaei and Luca Petaccia

#### **Contributors**

Marco Giorgetti, Lorenzo Stievano, Marcel Miglierini, Vit Prochazka, Dino Tonti, Massimo Innocenti, Roberto Felici, Andrea Giaccherini, Won-Sub Yoon, Hyunchul Kim, Shoaib Muhammad, Mehdi Khodaei

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X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation Edited by Mehdi Khodaei and Luca Petaccia p. cm. Print ISBN 978-953-51-3013-0 Online ISBN 978-953-51-3014-7 eBook (PDF) ISBN 978-953-51-4896-8


Engineering Measures for Isolation and Sequestration of Heavy Metals in Waste as Safe Final Sink

*Tomonori Ishigaki, Hiroyuki Ishimori, Hiroki Kitamura and Masato Yamada*

### **Abstract**

The long-term safety management of hazardous substances is essential to the development of an environmentally sound resource circulation society. To achieve this, engineering measures to attenuate environmental risks in the isolation and sequestration of hazardous heavy metals are reviewed. From the standpoint of the isolation and sequestration of heavy metals from resource circulation, we assess the challenges in implementing immobilization technologies, constructing updated isolation structures, and controlling environmental conditions. It is also focused intensively on the (bio) chemical transformation behavior of heavy metals and its effect on the migration of the transformed materials in the environment. The contributions of solubilized and gasified metal components to emission into the environment are considered. The obtained results underscore the necessity of multiple barriers to retard and attenuate the migration of hazardous heavy metals. Innovative schemes for the isolation and sequestration of heavy metals will lead to higher levels of safety and environmentally sound resource circulation.

**Keywords:** safe resource circulation, multi-barrier approach, final sink, heavy metals, immobilization, retarding migration, adsorption

#### **1. Introduction**

The world is facing several global and local problems caused by imbalanced resource utilization and inappropriate handling of waste. Climate change is threatening the lives of vulnerable people and regions by increasing extreme weather events. Marine plastic litter is widely recognized as a major risk to maritime activity, fisheries, and wildlife. Waste management practices, which are regarded as one of the major causes of these problems, must be updated to improve the situation.

Achieving environmentally sound resource circulation is a possible solution. The core concept of environmentally sound resource circulation is the harmonization of industrial (human) society with the earth's natural circulation system. It includes measures, such as (a) increased resource circulation to slow down and ultimately close the resource loop by reducing new resource inputs, (b) ethical production of goods

and services that generate hardly any waste to narrow and dematerialize the resource loop, and (c) removal of hazardous substances from the resource circulation loop for the safe loop of resources. Toxic-free resource circulation is essential for the sustainable operation of environmentally sound resource circulation. While it will be achieved, the amount of waste/residue generated can be minimized, and hazards will be removed from the loop of circulation. This minimized residue containing concentrated hazardous substances must be adequately managed to end the negative aspects of these resources.

This chapter describes an engineering approach to isolate and sequester hazardous substances concentrated in waste to remove them from the circulation loop, which will be essential to achieve environmentally sound resource circulation.


*2.2.2. N2 fixing bacteria*

fundamental mechanism for N2 fixation which is carried out by the nitrogenase enzyme

Nitrogenase contains two metalloprotein components: (i) the homodimeric Fe‐protein: acting as a reductase which has a high reducing power and is responsible for the providing of electrons and (ii) the heterotetrameric MoFe‐protein: a nitrogenase which utilizes the electrons

The rate‐determining step in the overall nitrogenase enzyme kinetics is built on the complex‐ ation of Fe‐protein and MoFe‐protein [46]. Although the definitive structural properties of the nitrogenase complex are unknown, some possible properties can be determined by the

In the overall reaction which explains the electron flow during the nitrogenase activity, electrons are introduced by Fe‐protein and leave the system as reduced products. Although the intermediate steps have not been experimentally validated, there is a "consensus" model which suggests the order of compounds that electrons follow. The suggested occurrence can

Degradation of substrate by nitrogenase is done via three elementary electron transfer reactions. In the first basic reaction Fe‐proteins are reduced by electron carries (i.e., flavodoxin, ferrodoxin, or dithionite). Second reaction is a MgATP‐dependent process where a single electron moves from Fe‐protein to MoFe‐protein. Third, the substrate, bound to the active site

When optimum requirements are provided, the overall stoichiometry for the reaction where

with an overall negative enthalpy of reaction which is ΔH0 = ‐45.2 kJ mol‐1 NH3 and a very high

Mainly nitrogenase is responsible for N2 reduction to NH3 while simultaneously catalyzing the reduction reactions of protons and other small unsaturated molecules (i.e., acetylene, cyanide) [48]. With this property, nitrogenase can be considered as a hydrogenase with an ATP‐ dependent evolution activity. Uptake hydrogenase can play an important role in energy saving via recycling H2 released by nitrogenase. Furthermore, uptake hydrogenase allows some organisms such as *A. lipoferum*, *Derxia gummosa*, and *P. diazotrophicus* to grow chemolithoau‐ totrophically even under N2‐fixing conditions. Electron donor limitation can improve expres‐ sion of the uptake hydrogenase. Like nitrogenase, hydrogenase activity is sensitive to oxygen.

system.

supplied to reduce N2 to NH3.

be found below:

N2 + 8H+ + 8e‐

characteristics of these individual metalloproteins.

222 Soil Contamination - Current Consequences and Further Solutions

*2.2.1. ATP hydrolysis and electron transfer in the nitrogenase system*

Fe‐protein ➔ P‐cluster pair ➔ MoFe‐cofactor ➔ substrate

of the MoFe‐protein, is reduced by an electron transfer.

activation energy which is EA = 230–420 kJ mol‐1.

nitrogenase reduces the N2 to NH3 can be summarized as [47]:

 + 16MgATP ➔ 2NH3 + H2 + 16MgADP + 16Pi

Several bacteria fix nitrogen, a short list is given in **Table 6**. Rhizobium bacteria, listed as the first kind as "symbiotic bacteria," is typically linked to leguminous plants, frankia, or cyano‐ bacteria with nonlegume plants. The "nonsymbiotic" second kind (also referred as "free‐ living" bacteria), exist either in water or soil. Examples of the nonsymbiotic N2 fixing bacteria are cyanobacteria (blue‐green algae, *Anabaena*, and *Nostoc)* and genera such as *Azotobacter*, *Beijerinckia*, and *Clostridium*. The third kind typically is found around roots of the plant rhizosphere and stream the fixed nitrogen to the plant. This group is typically referred as "associative nitrogen fixation" bacteria and includes *Azospirillum*, *Klebsiella sp.*, *Azotobacter paspali*, and *Alcaligenes*. The fourth kind is "endophytic nitrogen fixation" linked with cereal grasses such as sugarcane and includes *Azoarcus sp.* and *Burkholderia sp.*

**Table 6.** Plant growth promoting rhizobacteria (PGPR) and their relationship to hosts [67].

The abundantly available PGPRs are diazotrophs and can fix N2 via the biological nitrogen fixation, this characteristic is not the main mechanism with which they promote growth to their host plant. The plant growth stimulations primarily occur due to bacteria's enzymatic activities such as nitrogenase.

#### **2.3. Phytase**

Phosphorus (P) is an essential element for plants to grow and develop. Although P is found in soil both as insoluble inorganic and organic forms, it is unavailable for plants [49]. In soil, there are phosphate‐solubilizing bacteria (PSB) which can turn the insoluble inorganic phosphates in organic acids, into an available form. Therefore, these microorganisms have been generally studied to improve the growth properties and yield of crops. Despite being the most abundant form of phosphates in soil (10–50% of total P) [50, 51], phytates should be hydrolyzed by phytases (myo‐inositol‐hexakisphosphate‐phosphohydrolases) to be con‐ sumed by the plants [52, 53].

Phytic acid (myo‐inositol hexa‐phosphate, IP6) has six phosphate groups. It is present mainly in plant‐based nutrients, particularly in cereals and legumes. Phytic acid is thought to be a major stock component for plant germination and growth [54]. IP6 forms a vigorous structure called "chelating agent" by its six P groups and this structure plays a role in binding minerals such as Ca2+, Mg2+, Fe3+, and Zn2+. Presence of phytates may also have a negative effect on digestion of protein [55, 56], starch [57], and lipids [58]. Endogenous phytases in most seeds of higher plants may degrade the IP6 partly to produce penta‐, tetra‐, or tri‐phosphate compounds through food processing and digestion [59].

Phytases are the enzymes which catalyze the degradation reaction of phytate which is the primary reserve form of P in plants. Phytases are a different type of phosphatases and they can hydrolyze phytate to a set of lower phosphate esters of myo‐inositol and phosphate. Phytates are present in wide range of living things including plants and microorganisms. In the last decade, the number of researches, which focuses on how to lower the phytate levels found in animal feed by improving the enzymatic reaction of phytases, has been increased [60– 62].

A great deal of phytases assumes broad specificity to substrates and can therefore hydrolyze different phosphorylated compounds, irrespective of their similarity to phytic acid, including phosphorylated sugars (e.g., G6P). In contrast, few phytases, e.g., the one from Bacillus sp. and few other bacteria and fungi, e.g., *Aspergillus* sp., are characterized to be highly specific to phytic acid and/or to the class of protein tyrosine phosphatase‐PTP‐like pyhtases.

### *2.3.1. Pathways of phytic acid dephosphorylation*

Pythase degrade phytic acid at various rates and order. The mechanism of hydrolysis is reported to be step‐wise, the product of each step is the substrate of the subsequent one. Depending on the mechanism, this enzyme is recognized having three subclasses: 3‐phytase (EC <IP_ADDRESS>), 4‐phytase (EC <IP_ADDRESS>), and 5‐phytase (EC<IP_ADDRESS>), each class depending on the position of the first phosphate hydrolyzed. Note that, phytases are mostly able to hydrolyze five out of six available phosphates.

#### *2.3.2. Phytase and plant growth promotion*

There are several microorganisms in rhizosphere which interact with plant roots and affect plant nutrition in different ways. Direct effects of these microorganisms are altering the uptake and availability of plant nutrition. Indirect effects include promoting plant growth. For instance, in a study phytate was used as the unique source of phosphate to grow *Trifolium subterraneum*, as a result secretion of phytase in a very low grade from plant roots was observed. Following *A. niger* phytase was added to the medium and liberation of sufficient phosphates was observed. This step enables *T. subterraneum* seedlings to grow and plants supplied with inorganic phosphorus.

**Table 7.** Microorganisms expressing (extracellularly) phytase and their affectees of the resulting enzyme [68].

Since fungi hydrolyze several organic phosphorus compounds efficiently, they are considered as sufficient utilizers of organic phosphorous which can beneficial to the plant growth. Therefore, fungi which produce phytase and phosphatases were applied to seeds as inoculant, for effective use of phytate phosphorus in soil [63]. For instance, *Chaetomium globosum* is a fungus which produces phosphatase and phytase was used as the inoculation agent for wheat and pearl millet crops [64]. As a result, a remarkable progress in plant biomass, root length, plant phosphate concentration, seed and straw yield, and seed P content was obtained after inoculation with the fungus. A brief summary of phytase sources and their host plants can be found on **Table 7**.

### **3. Conclusion**

hydrolyzed by phytases (myo‐inositol‐hexakisphosphate‐phosphohydrolases) to be con‐

Phytic acid (myo‐inositol hexa‐phosphate, IP6) has six phosphate groups. It is present mainly in plant‐based nutrients, particularly in cereals and legumes. Phytic acid is thought to be a major stock component for plant germination and growth [54]. IP6 forms a vigorous structure called "chelating agent" by its six P groups and this structure plays a role in binding minerals such as Ca2+, Mg2+, Fe3+, and Zn2+. Presence of phytates may also have a negative effect on digestion of protein [55, 56], starch [57], and lipids [58]. Endogenous phytases in most seeds of higher plants may degrade the IP6 partly to produce penta‐, tetra‐, or tri‐phosphate

Phytases are the enzymes which catalyze the degradation reaction of phytate which is the primary reserve form of P in plants. Phytases are a different type of phosphatases and they can hydrolyze phytate to a set of lower phosphate esters of myo‐inositol and phosphate. Phytates are present in wide range of living things including plants and microorganisms. In the last decade, the number of researches, which focuses on how to lower the phytate levels found in animal feed by improving the enzymatic reaction of phytases, has been increased [60–

A great deal of phytases assumes broad specificity to substrates and can therefore hydrolyze different phosphorylated compounds, irrespective of their similarity to phytic acid, including phosphorylated sugars (e.g., G6P). In contrast, few phytases, e.g., the one from Bacillus sp. and few other bacteria and fungi, e.g., *Aspergillus* sp., are characterized to be highly specific to

Pythase degrade phytic acid at various rates and order. The mechanism of hydrolysis is reported to be step‐wise, the product of each step is the substrate of the subsequent one. Depending on the mechanism, this enzyme is recognized having three subclasses: 3‐phytase (EC <IP_ADDRESS>), 4‐phytase (EC <IP_ADDRESS>), and 5‐phytase (EC<IP_ADDRESS>), each class depending on the position of the first phosphate hydrolyzed. Note that, phytases are mostly able to hydrolyze

There are several microorganisms in rhizosphere which interact with plant roots and affect plant nutrition in different ways. Direct effects of these microorganisms are altering the uptake and availability of plant nutrition. Indirect effects include promoting plant growth. For instance, in a study phytate was used as the unique source of phosphate to grow *Trifolium subterraneum*, as a result secretion of phytase in a very low grade from plant roots was observed. Following *A. niger* phytase was added to the medium and liberation of sufficient phosphates was observed. This step enables *T. subterraneum* seedlings to grow and plants supplied with

phytic acid and/or to the class of protein tyrosine phosphatase‐PTP‐like pyhtases.

sumed by the plants [52, 53].

224 Soil Contamination - Current Consequences and Further Solutions

62].

compounds through food processing and digestion [59].

*2.3.1. Pathways of phytic acid dephosphorylation*

five out of six available phosphates.

inorganic phosphorus.

*2.3.2. Phytase and plant growth promotion*

Soil pollution is an important problem affecting millions of individuals, and surely this effect is not restricted to humans. Therefore, sustainable methods that are suitable for large‐scale methods, to remediate soil, become increasingly interesting for both fundamental and applied research. In particular, using biological systems (microbes and enzymes produced by these plants) has shown considerable progress. This needs to be applied in different agro climatic zones of the world.

A key element in these remediation methods is the fundamental (underlying principles) and executive (application principles) understanding of the microbe‐plant interaction, that may be physical, chemical, and biological. This will further draw attention to generating engineered agro‐lands, as mass production of these organisms and enzymes also economically interesting.

Despite important progress made in, particularly for PGPRs, growth conditions, enzyme portfolio vis‐a‐vis to soil remediation, and other (symbiotic) interaction with plants, the research is still at its infancy, especially about the interaction with plant roots and other bacteria.

A still unexplored aspect is the molecular engineering of these microbes and/or plants that would enhance the efficiency of these organisms for soil remediation. This has a large potential, as some PGPR can increase plant tolerance to degraded soil and other extreme conditions such as heavy metal contamination and increased salinity.


**1.6 Field of ecotoxicological study**

The increase in usage of pesticides on agricultural farms has led to ecosystems disturbance. As a result of this incident, the need for research on how pesticides should be applied to increase agricultural productivity without compromising the ecological standard became necessary over the years. The study of the effect of chemicals/pesticides on biological species is known as ecotoxicology. The science of ecotoxicology and environmental toxicology [102] includes:

Due to the involvement of different disciplines, they are different aims of ecotoxicology research [102] which include the following:

*Effect of Biodegradable Multiple Pesticides on Aquatic Biospecies DOI: http://dx.doi.org/10.5772/intechopen.104626*


Cassava Diversity and Its Microbiome

**3**

**Chapter 1**

**Abstract**

1990 to 2020

*Luis Augusto Becerra Lopez-Lavalle,*

*Adriana Bohorquez-Chaux and Xiaofei Zhang*

Identification of Cassava Varieties

in Ex-Situ Collections and Global

Farmer's Fields: An Update from

The identification of cassava cultivars is important for understanding the crop's production system, enabling crop improvement practitioners to design and deliver tailored solutions with which farmers can secure high yields and sustainable production. Across the lowland tropics today, a large number improved varieties and landraces of cassava are under cultivation, making it inefficient for breeders and geneticists to set improvement goals for the crop. The identification and characterization of cassava genotypes is currently based on either morphological characters or molecular features. The major aim of cultivar identification is to catalog the crop's genetic diversity, but a consensus approach has still not been established. Of the two approaches to the identification of variety, morphological characters seem to account for most of the genetic variability reported in cassava. However, these characters must be treated with caution, as phenotypic changes can be due to environmental and climatic conditions as well as to the segregation of new highly heterozygous populations, thus, making the accurate identification of varieties difficult. The use of molecular markers has allowed researchers to establish accurate relationships between genotypes, and to measure and track their heterozygous status. Since the early 1990's, molecular geneticists working with cassava have been developing and deploying DNA-based tools for the identification and characterization of landraces or improved varieties. Hence, in the last five years, economists and social scientists have adopted DNA-based variety identification to measure the adoption rates of varieties, and to support the legal protection of breeder's rights. Despite the advances made in the deployment of molecular markers for cassava, multiple platform adoption, as well as their costs and variable throughput, has limited their use by practitioners of crop improvement of cassava. The postgenomic era has produced a large number of genome and transcriptome sequencing tools, and has increased our capacity to develop and deploy genome-based tools to account for the crop's genetic variability by accurately measuring and tracking allele diversity. These technologies allow the creation of haplotype catalogs that can be widely shared across the cassava crop improvement community. Low-density genome-wide SNP markers might be the solution for the wide adoption of molecular tools for the identification of cultivars or varieties of cassava. In this review we survey the efforts made in the past 30 years to establish the tools for cultivar

#### **Chapter 1**


**Abstract**

Titanium dioxide (TiO2) is a versatile material used in a variety of applications, including photocatalysis, photovoltaics, sensing, and environmental remediation. The properties of TiO2 are influenced by its defect disorder, with oxygen vacancy (V0) being a prominent defect that has been widely studied. Defective TiO2 materials, particularly those containing V0 defects, are of interest for the development of next-generation semiconducting nanomaterials. Several methods, including high-temperature calcination, ion implantation, and chemical doping, are used to produce defective TiO2 with varying degrees of V0 defects. The properties of defective TiO2, including optical, electronic, and structural characteristics, are essential for determining the material's suitability for various applications. Modification of the defect structure of TiO2 through doping with impurities can enhance the photocatalytic activity of the material. Researchers continue to investigate the impact of factors such as crystal structure and the presence of other defects on the properties of TiO2-based materials, further enhancing their potential for various applications. Overall, a deeper understanding of defect disorder and the development of production methods for defective TiO2 will play a crucial role in the design and production of next-generation semiconducting nanomaterials.

**Keywords:** TiO2, defects, oxygen vacancies, structural, electronic, optical properties


4. Periodic γ-Hamiltonian systems

Once the linear Hamiltonian systems become periodic, i.e., the matrix H tð Þ of the system in Eq. (18) possesses a periodically time-varying H tðÞ¼ H tð Þ þ Ω , the underlying monodromy matrix becomes μ-symplectic and γ-Hamiltonian.

Definition 28 Any linear periodic system that can be written as

$$
\dot{\mathbf{x}} = J[H(\mathbf{t}) + \mathbf{y}I] \mathbf{x} \tag{33}
$$

with H tðÞ¼ H tð Þ þ Ω will be named linear periodic γ-Hamiltonian system, where x∈ R2n and HTðÞ¼ t H tð Þ are a 2n � 2n matrix and γ ≥ 0.

Remark 29 According to Lemma 18, the state transition matrix Φð Þ t; t0 of Eq. (33) is μ-symplectic, in particular, the state transition matrix evaluated over one period Ω.

Corollary 30 The monodromy matrix M ¼ eRΩ and the matrix R of the periodic system in Eq. (33) are μ-symplectic and γ-Hamiltonian matrices, respectively, with μ ¼ e�2γΩ.

Proof 31 From the definition of a μ-symplectic matrix MTJM ¼ eRΩ � �T J eRΩ � � ¼ μJ, we obtain eRTΩ ¼ μJe�RΩJ �1 ¼ μJ I2n � RΩ þ RRΩ2 2 � RRRΩ3 3! þ … þ RkΩ4 k! þ … n oJ �1 ¼ μe�JRJ�1 Ω ¼ e�2γΩe�JRJ�1Ω thus eRTΩ ¼ e�2γΩ�JRJ�1 Ω ) RTJ þ JR ¼ �2γJ.

This corollary states the main relation in our analysis. The symmetry of the μ-symplectic matrix will be utilized for obtaining the stability conditions of the system in Eq. (33). Furthermore, by applying the Lyapunov transformation

$$z(t) = P(t)\mathbf{x}(t)\tag{34}$$

we conclude that any linear periodic γ-Hamiltonian system can be reduced to a linear time-invariant γ-Hamiltonian system

$$
\dot{z}(t) = Rz(t). \tag{35}
$$

The next two subsections are based on [12] and are adapted for characteristic polynomials of μ-symplectic matrices.

#### 4.1 Stability of a system with one degree of freedom

For n ¼ 1, the characteristic polynomial of the monodromy matrix M associated with the system in Eq. (33) becomes PMð Þ¼ λ λ2 þ aλ þ μ with a ¼ �trð Þ M . According to the Lemma 18, M is μ-symplectic. Then, there are two multipliers symmetric to the circle of radius r and the real axis. Therefore, the multipliers only can leave the unit circle at the coordinates 1ð Þ ; 0 or ð Þ �1; 0 (see Figure 2). Note that the term �a is equal to the transformation in Eq. (13):

$$\delta = \lambda + \frac{\mu}{\lambda} = \text{tr}(\mathcal{M}) = -a$$

Theorem 32 For n ¼ 1, the system in Eq. (33) is asymptotically stable if and only if the inequality

$$|a| < (1+\mu)$$

is satisfied.

Proof 33 Since the multipliers only leave the unit circle on the points λ ¼ 1 or λ ¼ �1, the stability boundaries are given by

$$P\_M(\mathbf{1}) = \left(\mathbf{1}\right)^2 + a(\mathbf{1}) + \mu = a + (\mu + \mathbf{1})$$

$$P\_M(-\mathbf{1}) = \left(-\mathbf{1}\right)^2 + a(-\mathbf{1}) + \mu = -a + (\mu + \mathbf{1})$$

This means that a þ ð Þ μ þ 1 . 0 and �a þ ð Þ μ þ 1 . 0 must be fulfilled; thus, j j a , ð Þ 1 þ μ .

#### 4.2 Stability of a system with two degrees of freedom

For n ¼ 2, the characteristic polynomial of the monodromy matrix M associated with the system in Eq. (33) reads

$$P\_M(\lambda) = \lambda^4 + a\lambda^3 + b\lambda^2 + a\mu\lambda + \mu^2 \tag{36}$$

where a ¼ �trð Þ M and 2b ¼ ð Þ trð Þ M 2 � tr M2 . There are four multipliers, and due to the symmetry with respect to the μ-circle, they can be categorized in the position configurations depicted in Figure 2.

Respecting that the characteristic polynomial is associated with a μ-symplectic matrix, we can use the transformation

$$
\delta = \lambda + \frac{\mu}{\lambda} \tag{37}
$$

to obtain the auxiliary polynomial

$$Q\_M(\delta) = \delta^2 + a\delta + b - 2\mu. \tag{38}$$

The symmetry of the eigenvalues yield

$$a = -\text{tr}(\mathcal{M}) = \lambda\_1 + \frac{\mu}{\lambda\_1} + \lambda\_3 + \frac{\mu}{\lambda\_3} = \delta\_1 + \delta\_2.1$$

The transition boundaries are characterized by having at least one eigenvalue at j j λ ¼ 1. The simplest cases are if λ ¼ 1 (δ ¼ 1 þ μ) or λ ¼ �1 (δ ¼ �1 � μ). These points overlay if a real-valued multiplier leaves the unit circle at the point 1ð Þ ; 0 or ð Þ 0; �1 (see the cases c, d, e, f, or g in Figure 2). Substituting these two values into Eq. (36) gives

$$b = -a(\mathbf{1} + \mu) - \left(\mathbf{1} + \mu^2\right) \tag{39}$$

and

$$b = a(\mathbf{1} + \boldsymbol{\mu}) - (\mathbf{1} + \boldsymbol{\mu}^2). \tag{40}$$

Considering the case λ∈ C, we search the transition boundary line when two complex multipliers leave the unit circle at points different to 1ð Þ ; 0 and 0ð Þ ; �1 (see cases a or b in Figure 2). Then the transition boundary line can be obtained by considering the symmetry of the multipliers with respect to the real axis and the circle of the radius r ¼ ffiffiffi μ p . Here, λ1 ¼ x þ iy, λ2 ¼ μ λ1 , λ3 ¼ x � iy, and λ4 ¼ μ λ3 . At j j λ ¼ 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 p ¼ 1 � �, it follows that

$$
\lambda\_1 = \infty + i\mathfrak{y}, \quad \lambda\_2 = \mu(\infty - i\mathfrak{y}), \quad \lambda\_3 = \mathfrak{y} - i\mathfrak{y}, \quad \lambda\_4 = \mu(\infty + i\mathfrak{y}).
$$

Hence, the transformation in Eq. (13) follows:

$$\begin{aligned} \delta\_1 &= \lambda\_1 + \frac{\mu}{\lambda\_1} = \varkappa(\mathbf{1} + \mu) + i\wp(\mathbf{1} - \mu) \\ \delta\_2 &= \lambda\_3 + \frac{\mu}{\lambda\_3} = \varkappa(\mathbf{1} + \mu) - i\wp(\mathbf{1} - \mu) \end{aligned}$$

Adding δ1 and δ2 gives

$$
\delta\_1 + \delta\_2 = 2\mathfrak{x}(\mathbf{1} + \mu). \tag{41}
$$

From Eq. (38) we obtain

$$\delta\_{1,2} = \frac{-a}{2} \pm \frac{\sqrt{a^2 + 8\mu - 4b}}{2}. \tag{42}$$

Note that for δ1 and δ2 to become complex, the inequality

$$4b \ge a^2 + 8\mu$$

must be fulfilled. Adding δ1 and δ2, one obtains

$$
\delta\_1 + \delta\_2 = -\mathfrak{a} \tag{43}
$$

Equating Eqs. (41) and (43) yields

$$2\mathfrak{x}(1+\mu) = -\mathfrak{a}.\tag{44}$$

Coupled Mathieu Equations: γ-Hamiltonian and μ-Symplectic DOI: http://dx.doi.org/10.5772/intechopen.88635

The real part x of the eigenvalues results from Eq. (37)

$$
\lambda^2 - \lambda \delta + \mu = 0
$$

and

$$
\lambda = \frac{\delta \pm \sqrt{\delta^2 - 4\mu}}{2}. \tag{45}
$$

Substituting Eq. (42) into Eq. (45) and choosing only the positive signs gives

$$\lambda\_1 = \frac{1}{4}\left(-a + \sqrt{w - 4\mu - 2b + a^2}\right) + \frac{i}{4}\left(\sqrt{w + 4\mu + 2b - a^2} + \sqrt{-(a^2 + 8\mu) + 4b}\right)$$

with the abbreviation w ¼ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi �4a2μ þ ð Þ b þ 2μ 2 q . Consequently, the real part of λ is

$$\infty = \frac{1}{4} \left( -a + \sqrt{w - 4\mu - 2b + a^2} \right),$$

and substituting into Eq. (44) results in

$$\frac{1}{2}\left(-a+\sqrt{w-4\mu-2b+a^2}\right)(1+\mu)=-a$$

which can be solved for b to obtain the transition boundary curve

$$b = \frac{\mu^4 + 2\mu^3 + 2\mu^2 + 2\mu + a^2\mu + 1}{\left(1 + \mu\right)^2}. \tag{46}$$

Two intersection points exist on each line in Eqs. (39) and (40) with the curve defined by Eq. (46). These points are

$$b = \frac{1}{\mu} \left( \mu^4 + \mu^3 + 2\mu^2 + \mu + 1 \right) \tag{47}$$

$$b = \mu^2 + 4\mu + \mathbf{1} \tag{48}$$

and are highlighted in Figure 3. The line in Eq. (47), dashed line in the figure, is a necessary condition for stability.

Theorem 34 The Eq. (33) when n ¼ 2 is asymptotically stable if and only if the inequalities are fulfilled:

$$b \ge -a(\mathbf{1} + \mu) - \left(\mathbf{1} + \mu^2\right),\tag{49}$$

$$b \ge a(\mathbf{1} + \boldsymbol{\mu}) - (\mathbf{1} + \boldsymbol{\mu}^2),\tag{50}$$

$$b \le \frac{\mu^4 + 2\mu^3 + 2\mu^2 + a^2\mu + 2\mu + \mathbf{1}}{\left(1 + \mu\right)^2}. \tag{51}$$

From this analysis, the multipliers position in relation to the unit circle and μcircle are defined by inequalities. These split the complex plane into four regions as it is shown in the Figure 3.

#### Figure 3.

Multiplier map in the case of n ¼ 2: Horizontal and vertical axes are the coefficients a and b of the characteristic polynomial of the monodromy matrix M in Eq. (36). The solid lines represent the borders of the inequalities in Theorem 34, Eqs. (49), (50), and (51). The dots indicate the position of multipliers and the unit circle, in solid line, associated with the system in Eq. (33) in the case of n ¼ 2. The dashed circle depicts the μ-circle.

## 5. Coupled Mathieu equations

Consider two coupled and damped Mathieu equations of the following form:

$$
\begin{bmatrix} \ddot{\boldsymbol{z}}\_1 \\ \ddot{\boldsymbol{z}}\_2 \end{bmatrix} + \begin{bmatrix} \Theta\_{11} & \Theta\_{12} \\ \Theta\_{21} & \Theta\_{22} \end{bmatrix} \begin{bmatrix} \dot{\boldsymbol{z}}\_1 \\ \dot{\boldsymbol{z}}\_2 \end{bmatrix} + \left( \begin{bmatrix} \boldsymbol{a}\_1^2 & \mathbf{0} \\ \mathbf{0} & \boldsymbol{a}\_2^2 \end{bmatrix} + \beta \begin{bmatrix} \mathbf{Q}\_{11} & \mathbf{Q}\_{12} \\ \mathbf{Q}\_{21} & \mathbf{Q}\_{22} \end{bmatrix} \begin{bmatrix} \boldsymbol{z}\_1 \\ \boldsymbol{z}\_2 \end{bmatrix} \cos\left(\boldsymbol{\nu}t\right) \right) \begin{bmatrix} \mathbf{z}\_1 \\ \mathbf{z}\_2 \end{bmatrix} = \mathbf{0}.\tag{52}
$$

Following the procedure presented in Section 3.1, the system in Eq. (52) can be cast into the γ-Hamiltonian form in Eq. (33) if Θ12 ¼ Θ21 and Q12 ¼ Q21, i.e., the coefficient matrices Θ and Q are symmetric. In this case, the coupled Mathieu equations present all the properties of the periodic γ-Hamiltonian system defined in Eq. (33) for n ¼ 2 and Ω ¼ 2π=ν. Hence, all the above analysis on Hamiltonian systems can be applied. The monodromy matrix is computed by numerical methods, and the stability chart is obtained by applying the Theorem 34.

The following numerical values are chosen for the analysis of a specific system ω2 1 ¼ 8, ω2 2 ¼ 26, Q11 ¼ Q22 ¼ 2, Q12 ¼ Q21 ¼ �2. Figure 4a depicts the multiplier chart similar to Figure 3. The unstable regions are colored and the stable regions are kept white. Each color depicts a specific configuration of the multiplier positions within the unit circle and the μ-circle according to the inequalities stated in Theorem 34 and visualized in Figures 3 and 4a. The description of each color is relevant because each color describes the parametric resonance phenomenon. Thus, yellow, magenta, and cyan colors refer to the configuration of four real-valued multipliers, two of them inside and two outside of the unit circle. These multipliers are either all negative (magenta region), all positive (yellow region), or two positive and two negative (cyan region). The blue and red regions indicate two complex conjugate multipliers on the μ-circle, while the other two are real with j j λ . 1. The two real multipliers are either positive (blue) or negative (red). Then, all four multipliers are complex conjugate within the green region. In this case, two multipliers lie inside and two outside of the unit circle.

Coupled Mathieu Equations: γ-Hamiltonian and μ-Symplectic DOI: http://dx.doi.org/10.5772/intechopen.88635

#### Figure 4.

Multiplier map and stability charts, for example, systems in Eq. (52). Multiplier map corresponds to Figure 3 but now with colored regions for the different unstable multiplier configurations. Stability charts are given for different values of damping. (a) Multiplier map: a and b are the coefficients of the corresponding characteristic polynomial of the monodromy matrix. All colored zones correspond to unstable positions multipliers configurations. (b) Stability chart of coupled Mathieu equations, Eq. (52), with small damping: Θ12 ¼ Θ21 ¼ 0 and Θ11 ¼ Θ22 ¼ 0:1: Each color code is according to the position of the multipliers as in Figure 4a. (c) Stability chart of coupled Mathieu equations, Eq. (52), with damping: Θ12 ¼ Θ21 ¼ 0 and Θ11 ¼ Θ22 ¼ 0:3.

Additionally, parametric primary resonances occur at parametric excitation frequencies ν ¼ 2ωi=k, with k∈ℕþ, and parametric combination resonances of summation type occur at ν ¼ ð Þ ω1 þ ω2 =k [7, 10]. These frequencies are also observed for the example system in Figure 4. The green regions mark parametric combination resonances. The blue and red regions correspond to parametric primary resonances. The presented calculation technique can be categorized as a semi-analytical method. After rewriting the original system into the form in Eq. (33), the monodromy matrix is constructed by integrating the equations of motion using numerical methods.

Subsequently, the coefficients of the characteristic polynomial of the monodromy matrix can be computed as a ¼ �trð Þ M and 2b ¼ ð Þ trð Þ M 2 � tr M2 . This technique avoids the computation of the eigenvalues itself. This has the main advantage that numerical problems on the computation of the eigenvalues are avoided, e.g., numerical sensitivity of multipliers [21].

The definitions of μ-symplectic and γ-Hamiltonian matrices allow the analysis of a linear periodic Hamiltonian system with a particular dissipation. The main result of the proposed theory lies in Corollary 30 which states that the state transition matrix of any γ-Hamiltonian system is μ-symplectic. The symmetry properties of the eigenvalues of μ-symplectic matrices lead to an efficient calculation of the stability boundaries of this type of system. The general framework is applied for the example analysis of two damped and coupled Mathieu equations confirming the faster and robust computation of the stability chart. The procedure can be extended to a higher number of coupled Mathieu equations as outlined above.


**Progress in Experimental Research of Turbine Aeroacoustics**

Andreas Marn, Christian Faustmann and Thorsten Selic

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62431

#### **Abstract**

Modifications on the intermediate turbine duct in order to reduce noise emissions by changing interaction frequencies and/or modes capable to propagate are presented. Also different turbine exit casings are described that are optimised to reduce interaction noise that is propagating through the engine and is one of the major noise sources during landing (operating point approach). The most promising modifica‐ tions to reduce sound power levels are described. Depending on different modifica‐ tions at specific operating points, the reduction of sound power level is between 5 dB and 10 dB, which is a significant reduction. However, some of these measures show an increase in aerodynamic losses. Therefore, a compromise has to be found between higher losses during a short duration (e.g. landing) and significant noise reduction. The chapter focuses on experimental results obtained in the test facilities of the Institute for Thermal Turbomachinery and Machine Dynamics at Graz University of Technol‐ ogy.

**Keywords:** aeroacoustics, low pressure turbine, high pressure turbine, turbine exit casing, intermediate turbine duct


**2. Definition and classification of Parkinsonism and PD**

PD is a progressive parkinsonism of undetermined cause without features suggestive of an alternative diagnosis. It responds to dopaminergic treatment and is associated with depletion of dopaminergic neurons and the presence of Lewy body inclusions in some of the remaining nerve cells [13-15].

The diagnosis of PD is based on clinical criteria as there is no definitive laboratory test to diagnose the disorder. Pathological confirmation of Lewy bodies on autopsy, a hallmark of PD, has historically been considered the standard criterion for diagnosis [13]. In clinical practice, diagnosis is usually based on the presence of a number of cardinal motor features, response to levodopa, associated symptoms, and the exclusion of other disorders [15]. When patients have a classical presentation, diagnosis of PD is relatively simple. However, differ‐ entiating PD from other forms of parkinsonism in the early stages of the disease, when signs and symptoms overlap with other syndromes, can be difficult [16]. Criteria for diagnosis of PD were developed by the UK Parkinson's Disease Society Brain Bank (Table 1) and the National Institute of Neurological Disorders and Stroke (NINDS) [7,14]. When standard clinical criteria such as the UK Parkinson's disease brain bank criteria are used, significantly more accurate clinical diagnosis of the disease is possible; however, as many as 10% of patients diagnosed with the disease in life will still need to be reclassified at post-mortem examination [17]. These criteria have been estimated to have a diagnostic specificity and sensitivity of 98.6% and 91.1%, respectively [18].

Parkinsonian disorders can be classified into four categories: primary (idiopathic) parkinson‐ ism, secondary (acquired, symptomatic) parkinsonism, heredodegenerative parkinsonism, and multiple system degeneration (parkinsonism plus syndromes). A number of features, including tremor, early gait abnormality (e.g., freezing), postural instability, pyramidal tract signs, and response to levodopa, can be used to distinguish PD from other parkinsonian disorders. While differences in the density of postsynaptic dopamine receptors in PD patients or patients with atypical parkinsonian disorders have been used to account for the poor response to levodopa therapy in the latter group, other explanations may also be possible [19].

**Table 1.** Diagnostic criteria for Parkinson's disease (PD) [7,14]

five patients being affected. The prevalence of dysphagia in four studies was between 72% and 87%, with a pooled prevalence estimate of 82% (95% CI 77%–87%), suggesting that while the condition is common in PD, patients do not always report swallowing difficulties unless asked. This under-reporting calls for a proactive clinical approach to dysphagia, particularly in light

The aim of this chapter is to show dysphagia as a symptom/sign and an important cause of

PD is a progressive parkinsonism of undetermined cause without features suggestive of an alternative diagnosis. It responds to dopaminergic treatment and is associated with depletion of dopaminergic neurons and the presence of Lewy body inclusions in some of the remaining

The diagnosis of PD is based on clinical criteria as there is no definitive laboratory test to diagnose the disorder. Pathological confirmation of Lewy bodies on autopsy, a hallmark of PD, has historically been considered the standard criterion for diagnosis [13]. In clinical practice, diagnosis is usually based on the presence of a number of cardinal motor features, response to levodopa, associated symptoms, and the exclusion of other disorders [15]. When patients have a classical presentation, diagnosis of PD is relatively simple. However, differ‐ entiating PD from other forms of parkinsonism in the early stages of the disease, when signs and symptoms overlap with other syndromes, can be difficult [16]. Criteria for diagnosis of PD were developed by the UK Parkinson's Disease Society Brain Bank (Table 1) and the National Institute of Neurological Disorders and Stroke (NINDS) [7,14]. When standard clinical criteria such as the UK Parkinson's disease brain bank criteria are used, significantly more accurate clinical diagnosis of the disease is possible; however, as many as 10% of patients diagnosed with the disease in life will still need to be reclassified at post-mortem examination [17]. These criteria have been estimated to have a diagnostic specificity and sensitivity of 98.6%

Parkinsonian disorders can be classified into four categories: primary (idiopathic) parkinson‐ ism, secondary (acquired, symptomatic) parkinsonism, heredodegenerative parkinsonism, and multiple system degeneration (parkinsonism plus syndromes). A number of features, including tremor, early gait abnormality (e.g., freezing), postural instability, pyramidal tract signs, and response to levodopa, can be used to distinguish PD from other parkinsonian disorders. While differences in the density of postsynaptic dopamine receptors in PD patients or patients with atypical parkinsonian disorders have been used to account for the poor response to levodopa therapy in the latter group, other explanations may also be possible [19].

of the serious clinical consequences of the condition [12].

**2. Definition and classification of Parkinsonism and PD**

disability in patients with PD.

180 Seminars in Dysphagia

nerve cells [13-15].

and 91.1%, respectively [18].

### **3. Non-motor symptoms in Parkinson's disease**

In his "Essay on the Shaking Palsy," James Parkinson did not consider PD to be just a motor disorder, and in 1817 he described the presence of sleep disturbance, constipation, dysarthria, dysphonia, dysphagia, sialorrhea, urinary incontinence, and constant sleepiness with slight delirium [20]. What has been well established is that in PD patients, non-motor symptoms (NMS) occur in more than 90% of individuals in all stages of the disorder and include a variety of symptoms from neuropsychiatric and autonomic dysfunction to sleep disturbances and little-understood and little-reported sensory symptoms such as pain and impaired vision [21]. These NMS frequently occur throughout the course of PD and may occur concurrently with motor symptoms or precede their onset by several years [22]. In advanced PD, NMS have been recognized as important factors associated with impaired quality of life [23] and impose a considerable economic burden on patients' families and society [24].

In contrast to the motor symptoms of PD, NMS are often under-recognized during routine clinical visits and poorly managed in clinical practice [21,25]. Indeed, they have only recently been considered sufficiently important to warrant study by clinicians and researchers. In a prospective study of 101 PD patients, neurologists failed to identify the presence of depression, anxiety, and fatigue in over 50% of patients and the presence of sleep disturbance in 40% [26].


**Author details**

Ravi Mohan Srivastava and Sneha Joshih Department of Entomology, College of Agriculture, G.B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, India

\*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.


3.3.3. Comparison between Overweight and Underweight Adolescents

The network comparison test revealed no statistically significant difference between the networks for overweight and underweight adolescents regarding the structural invariance (M = 0.118, *p* = 0.967) and the global network strength (S = 0.470, *p* = 0.159).


**4. Conclusions**

This work proposes the sampling of gunshot residues on shooters' hands using dry cotton swabs followed by vortex-assisted extraction with water over a short time (20 s). Aqueous samples were directly processed in the miniaturized IT-SPME-CapLC-DAD system for on-line clean-up and preconcentration of the sample and for quantization of the amount of diphenylamine as targeted organic residue. It is worth mentioning that non-toxic solvents and low-cost materials were employed. The efficiencies of the IT-SPME were tested for several compositions and lengths of the extractive phase, as well as sample volume processed in order to improve the sensitivity. The highest analytical responses were obtained for the longest TRB-35 capillaries (90 cm) were more likely due to π–π interactions and 1.8 mL of processed volume. The proposed approach is a rapid, green, and cost-effective option for detecting DPA on the hands of shooters. The sustainability of an analytical method is governed by minimization of toxic solvents, reduction of wastes, and employment of energy-efficient and cost-effective methodologies, but also on maintaining the reliability of the performance parameters, such as sensitivity, precision, and accuracy [25,26]. In two previous papers [27,28] our group demonstrated that IT-SPME-CapLC-DAD achieves the minimization of the sample pre-treatment step, analysis time, and wastes, the reduction of the analysis costs, and thus, improvement of the analytical and environmental performance. Satisfactory LOD (0.3 ng) and precision (RSD intra-day = 9%, RSD inter-day = 14%) were achieved.

In order to test the utility of the method for real cases, several shooters' hands were sampled by dry cotton swabs and processed by IT-SPME-CapLC-DAD. The results showed that DPA was found and quantified in 81% of samples. Additionally, IGSRs inspection of swab samples was carried out by optical microscopy in order to confirm the presence of gunshot residues on shooters' hands, which were analyzed by SEM-EDS after DPA extraction. Furthermore, some shooters' hands were sampled by a tape lift kit, which is the typical police sampler, but DPA extraction was fourteen times lesser than that achieved by the dry cotton swab sampler. Morphology, elemental composition, and distribution of the IGSRs particles were also studied. Then, improved results were obtained by the proposed sampling method as indicated above. If organic compounds are detected in combination with inorganic compounds, higher probative value can be achieved, and false positives/negatives can also be reduced for discriminating shooters' hands. In this work, a sensitive chromatographic method to detect the organic compound DPA can be combined with IGSR analysis by SEM-EDS in order to obtain valuable evidence of GSRs deposited on hands of a suspected shooter. Therefore, the proposed method is helpful to determine whether a person has fired a gun in a forensic investigation.

**Author Contributions:** All authors designed and performed part of the experiments, analyzed the data, and wrote the paper.

**Acknowledgments:** The authors are grateful to the EU-FEDER/MINCIU-AEI of Spain (project CTQ2017-90082-P) and Generalitat Valenciana (PROMETEO 2016/109) for the financial support received and to Police Headquarters of Valencian Community (Valencia, Spain) for the sampling.

**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.


*4.5. Electron Transport and JO2*

The electron transport rate was determined using the pulse amplitude modulated fluorometer (OSP1 Fluorometer), according to Guralnick et al. [20]. Samples were taken over the course of the light period beginning at 6:00 in the greenhouse. Intact leaf tissue of well-watered and water-stressed cotyledons were measured [20]. The true rate of O2 evolution (JO2) from Photosystem II activity was calculated, according to the method of Lal and Edwards [35].