**2. Methodology**

In practical applications, the computation of a global index to measure the importance to each node is a main task. If the system studied contains several types of relations between actors it is expected that the measures, in some way, consider the importance obtained from the different layers. A simple choice could be to combine the centrality of the nodes computed from the different layers independently according to some heuristic choice.

In this section, both the well-established methods and the proposed centrality for multiplex networks with data are described in detail.

### *2.1. The Adapted PageRank Algorithm (APA) Model*

Let us establish some notation that will be used in the following. Let G = ( N , E) be a graph where N = {1, 2, . . . , *n*} and *n* ∈ N. The link (*i*, *j*) belongs to the set E if and only if there exists a link connecting node *i* to *j*. The adjacency matrix of G is an *n* × *n* matrix *A* = *aij* , where

$$a\_{ij} = \begin{cases} 1 & \text{if } (i,j) \text{ is a link}, \\ 0 & \text{otherwise}. \end{cases}$$

The adapted PageRank algorithm (APA) proposed by Agryzkov et al. [25] provides us a model to establish a ranking of nodes in an urban network taking into account the data presented in it. This centrality was originally proposed for urban networks, although it may be generalized to spatial networks or networks with data. It constitutes a centrality measure for networks with the main characteristic being that it is able to consider the importance of data obtained from any source in the whole process of computing the centrality of the individual nodes. Starting from the basic idea of the PageRank vector concept, the construction of the matrix used for obtaining the classification of the nodes is modified.

In its original approach, PageRank was based on a model of a web surfer that probabilistically browses the web graph, starting at a node chosen at random according to a personalization vector whose components give us the probability of starting at node *v*. At each step, if the current node had outgoing links to other nodes, the surfer next browsed with probability *α* one of those nodes (chosen uniformly at random), and with probability 1 − *α* a node chosen at random according to the personalized vector. For the web graph, the most popular value of the dumping factor was 0.85. If the current node was a sink with no outgoing links, the surfer automatically chose the next node at random according to the personalized vector.

In the APA model, the data matrix was constructed following a similar reasoning from the original idea of the PageRank vector; a random walker can jump between connecting nodes following the local link given by the network or can jump between nodes (not directly connected) with the same probability, regardless the topological distance between them (number of nodes in the walk).

In the algorithm implemented to calculate the APA centrality (see [25], p. 2190), a new matrix *A*∗ = *pij* ∈ R*n*×*n* is constructed from the adjacency matrix *A*, as

$$p\_{ij} = \begin{cases} \frac{1}{c\_j} & \text{if } a\_{ij} \neq 0, \\\ 0 & \text{otherwise}, \end{cases} \quad 1 \le i, j \le n,\tag{1}$$

where *cj* represents the sum of the *j*-th column of the adjacency matrix.

Algebraically, *A*∗ may be obtained as

$$A^\* = A\Delta^{-1},\tag{2}$$

where Δ = *δij* ∈ R*n*×*n* is the degree matrix of the graph, that is, *δij* = *c*−1 *j* , for *i* = *j* and *δij* = 0, for *i* = *j*. We refer to *A*∗ as the transition matrix, and it represents, by columns, the probability to navigate from a page to other. In the literature related to this topic the matrix *A*∗ is also denoted as *P* or *PA*, so *A*∗, *P* or *PA* are the same matrix. Following the notation of Pedroche et al. [34] it will preferably be used *P*.

The transition matrix, *P* = *A*∗ has the following characteristics (see [25]):

The key point of the model is the construction of the so-called data matrix *D* of size *n* × *k*, with its *n* rows representing the *n* nodes of the network, and each of its *k* columns representing the attributes of the data object of the study. Specifically, an element *dij* ∈ *D* is the value we attach to the data class *kj* at node *i*.

However, not all the characteristics of data may have the same relevance or influence in the question object of the analysis. Therefore, a vector *v***0** ∈ R*k*×1 is constructed, where the element that occupies the row *i* is the multiplicative factor associated with the property or characteristic *ki*. With this vector *v***0** a weighting factor of the data is introduced, in order to work with the entire data set or a part of it.

Then, multiplying *D* and *v***0**, *v* may be obtained as

$$
\boldsymbol{v} = \boldsymbol{D} \cdot \boldsymbol{v}\_{0,\prime}
$$

with *v* ∈ R*n*×1.

The construction of vector *v* allows us to associate to each node a value that represents the amount of data assigned to it. Thus, two different values are associated with every node; on the one hand, its degree, related to the topology and, on the other hand, the value of the data associated to it. For a more detailed description of how the data are associated to the nodes, see [25,35].

After normalizing *v*, denoted as *v∗*, it is possible to define the matrix *MAPA* as

$$M\_{APA} = (1 - a)P + aV,\tag{3}$$

where *V* ∈ R*n*×*n* is a matrix in which all of its components in the *i*-th row are equal to *v∗i* . The parameter *α* is fixed and it is related to the teleportation idea. The value that is traditionally used is *α* = 0.15.

In practice, vector *v∗* is repeated (*n* times) in every column of the matrix *V*.

The matrix *MAPA* was used to compute the ranking vector for the network.

With these considerations, the APA algorithm proposed in [25] may be summarized by the Algorithm 1:

**Algorithm 1:** (Adapted PageRank algorithm (APA)). *Let G* = (*V*, *E*) *be a primary graph representing a network with n nodes*.

The main feature of this algorithm is the construction of the data matrix *D* and the weighted vector *v***0**. The matrix *D* allows us to represent numerically the dataset. Vector *v***0** determines the importance of each of the factors or characteristics that have been measured by means of *D*.

The Perron–Frobenius theorem is of great importance in this problem, since it constitutes the theoretical base that ensures that there exists an eigenvector *x* associated with the dominant eigenvalue *λ* = 1, so that all its components are positive, which allows establishing an order or classification of these elements. In our case, due to the way in which *P* and *V* have been constructed, it can be seen that *MAPA* is a stochastic matrix by columns, which assures us of the spectral properties necessary for the Perron–Frobenius theorem to be fulfilled. Therefore, the existence and uniqueness of a dominant eigenvector with all its components positive is guaranteed. See [36,37] for further study of spectral and algebraic properties of the models based on PageRank.

Vector *x* constitutes the adapted PageRank vector and provides a classification or ranking of the pages according to the connectivity criterion between them and the presence of data.

### *2.2. The Biplex Approach for Classic PageRank*

Pedroche et al. [34] propose a two-layer approach for the classic PageRank classification vector based on the idea that we now briefly expose. The two-layer approach is to consider the PageRank classification of the nodes as a process divided into two clearly differentiated parts. The first part is related to the topology of the network, where the connections of the nodes are basically taken into account by means of their adjacency matrix. There is a second part regarding to the teleportation from one node to another, following a criterion of equiprobability.

They affirm that the PageRank classification for a graph *G* with personalized vector *v* can be understood as the stationary distribution of a Markov chain that occurs in a network with two layers, which are:

*l*1**, physical layer** , it is the network *G*.

*l*2**, teleportation layer** , it is an all-to-all network, with weights given by the personalized vector.

Under this perspective, it is easy to construct a block matrix *MA* based on these two layers where each of the diagonal blocks is associated to a given layer. Therefore, we can construct

$$M\_A = \left(\begin{array}{c|c} \alpha P\_A & (1-\alpha)I \\ \hline 2\alpha I & (1-\alpha)ev^T \end{array}\right) \quad \in \mathbb{R}^{2n \times 2n},\tag{4}$$

where *MA* defines a Markov chain in a network with two layers.

Due to the good spectral characteristics of *MA* (it is irreducible and primitive), they arrive to the conclusion that given a network with *n* nodes, whose adjacency matrix is *A*, the two-layer approach PageRank of *A* is the vector

$$
\mathfrak{H}\_A = \pi\_\mathfrak{u} + \pi\_\mathfrak{d} \in \mathbb{R}^n,
$$

where *πTu πTd T* ∈ R2*n* is the unique normalized and positive eigenvector of matrix *MA* given by the expression (4).

In [38], the authors propose a new centrality measure for complex networks with geo-located data based on the application of the two-layer PageRank approach to the APA centrality measure for spatial networks with data. They design an algorithm to evaluate this centrality and show the coherence of this measure regarding the original APA by calculating the correlation and the quantitative difference of both centralities using different network models. This coherence in the results obtained for the APA and the proposed centrality using the two-layer approach is absolutely mandatory in our objective to extend the two-layer approach for multiplex networks with data.

Therefore, the two-layer approach may be extended to the case of multiplex networks, where we have several networks with the same nodes and with different topologies and connections between nodes. Following the notation used by Pedroche et al. [34], let us consider a multiplex network M = (N , E, S) with layers S = (*l*1, *l*2, ... , *lk*). Given a multiplex network M with several layers, a multiplex PageRank centrality can be defined by associating to each layer *li* a two-layer random walker with one the physical layer and a teleportation layer. In addition, transition between these layers must be allowed. The idea behind this process is the application of the two-layer approach to each layer of the multiplex network.

For now, let us consider our problem restricted to biplex networks M = (N , E, S), with layers S = (*l*1, *l*2) whose adjacency matrices are *A*1, *A*2 ∈ *Rn*×*n*, respectively. For convenience in the notation we will write *PA*, *P*1 and *P*2 instead of *A*∗, *A*∗1and *A*∗2, respectively.

It is straightforward to check that all the spectral properties of *M*2 are essentially the same as the Google matrix in the PageRank model. Then, there exists an eigenvector

$$\mathfrak{H}\_2 = (\pi\_{\mathfrak{u}\_{1'}}, \pi\_{\mathfrak{u}\_{2'}}, \pi\_{\mathfrak{d}\_{1'}}, \pi\_{\mathfrak{d}\_2}) \in \mathbb{R}^{4n}$$

associated to the dominant eigenvalue *λ* = 1. This vector is the key to obtain the classification vector representing the nodes centrality.

Consequently, summarizing the main characteristic of the biplex PageRank approach, considering a biplex network M with *n* nodes, with two layers S = (*l*1, *l*2), and whose adjacency matrices are *A*1, *A*2 ∈ R*n*, it can be affirmed that the PageRank vector that classifies the nodes of this biplex network is the unique vector *π***2** such as

$$
\pi\_{\mathsf{T}} = \frac{1}{2} \left( \pi\_{\mathsf{u}\_{\mathsf{1}}} + \pi\_{\mathsf{u}\_{\mathsf{2}}} + \pi\_{\mathsf{d}\_{\mathsf{1}}} + \pi\_{\mathsf{d}\_{\mathsf{2}}} \right) \in \mathbb{R}^{n},
$$

with *π***2** normalized.

### *2.3. Constructing the APABI Centrality by Applying the Two-Layer Approach*

The idea of the treatment of the PageRank concept by means of two layers has a great sense within the idea of APA centrality, since the influence of the data in the network is measured separately in the original algorithm. Paying attention to the construction of *MAPA* given by (3), note that *V* is the matrix summarizing all the data information. But not only the application of this concept is interesting for our centrality, since may be also interesting to analyze the differences that occur between both techniques of calculating the importance of the nodes.

In this section, we describe how to adapt the APA centrality taking as a reference the two-layers technique, where a block matrix is used to distinguish the topology and the personalized vector.

The original APA centrality model, described in Section 2, presents some differences from the model described and implemented by Pedroche et al. [34], where the final matrix involved in the eigenvector computation is stochastic by rows. In our approach, the basis of the original APA model consists of the construction of a stochastic matrix by columns, where we reflect the topology of the network by the probability matrix *P* and the influence of the data, through the matrix *V*.

In order to build a 2 × 2 block matrix, the same approach used in [34] may be reproduced. The first upper diagonal block contains the information referring to the network topology, while the lower diagonal block is associated to the collected data in the network and assigned to each node of it.

Taking as a reference the APA algorithm, the matrix used to compute the eigenvector associated to the dominant eigenvalue *λ* = 1 is given by

$$\mathcal{M}\_{\text{APA}} = (1 - a)P + aV.$$

A new 2 × 2 block matrix is constructed as

$$M\_{APA2} = \left(\begin{array}{c|c} aP\_A & (1-a)I \\ aI & aV \end{array}\right) \quad \in \mathbb{R}^{2n \times 2n}.\tag{6}$$

The idea that underlies the construction of the matrix by blocks given by (6) is to maintain the spectral properties of the original matrix *MAPA*, with the aim that the numerical algorithms for *Symmetry* **2019**, *11*, 284

determining dominant eigenvalue and eigenvector are stable and fast. Note that we have doubled the size of the original matrix.

Following the same reasoning used in Section 3 to construct a model for biplex networks taking as a basis the classical PageRank vector, it is necessary to extend the two-layers APA approach given by the block matrix (6). Using the same notation, let us consider M = (N , E, S), with layers S = (*l*1, *l*2) be a biplex network.

Reordering the blocks in such a way that the physical layers appear in the first block, the final matrix is given by

$$M\_{BI} = \frac{1}{2} \left( \begin{array}{cc|cc} (1-a)P\_1 & I & 2(1-a)I & 0 \\ \hline I & (1-a)P\_2 & 0 & 2(1-a)I \\ \hline I & 0 & aV\_1 & aV\_2 \\ 0 & I & aV\_1 & aV\_2 \end{array} \right) \tag{7}$$

with *Pi*, for *i* = 1, 2 column stochastic matrices and *Vi*, for *i* = 1, 2, the matrices containing the data information.

Note the differences between matrices *M*2 (5) and *MBI* (7). The matrix *M*2 is stochastic by rows, however, in the APA centrality the basic matrix *MAPA* is stochastic by columns, so the definition of the matrix *MBI* is determined by the need to maintain the spectral properties suitable for obtaining the proper vector of the centrality. These desirable spectral properties are ensured by the way in which *MBI* has been built, being stochastic by columns, as well as irreducible.

Then, there exists an eigenvector

$$
\hat{\pi}\_{BI} = (\pi\_{u\_1}, \pi\_{u\_2}, \pi\_{d\_1}, \pi\_{d\_2}) \in \mathbb{R}^{4u} \tag{8}
$$

associated to the dominant eigenvalue *λ* = 1. This vector is the key to obtain the classification vector representing the nodes centrality. Therefore, it can be obtained a unique vector

$$\mathbf{x} = \frac{1}{2} \left( \pi\_{\mathfrak{u}\_1} + \pi\_{\mathfrak{u}\_2} + \pi\_{\mathfrak{d}\_1} + \pi\_{\mathfrak{d}\_2} \right) \in \mathbb{R}^n,\tag{9}$$

with *x* a normalized vector.

In Figure 1, a schematic representation of the extended APA model for biplex networks has been represented. All the graphs share the same *n* nodes, although the relationships between them in the two layers *l*1 and *l*2 are different, which produces two different adjacency matrices *A*1 and *A*2. Data are also different in each layer; consequently, two data matrices are constructed *D*1 and *D*2.

**Figure 1.** Scheme of the adapted PageRank algorithm (APA) extended model for biplex networks.

The existence of the weighted vectors *v*01 and *v*02 allows us to determine those data that are the object of our interest, being able to discard those that do not present real interest for the study that is carried out.

The model presented in this section may be summarized by the Algorithm 2.

**Algorithm 2:** (Adapted PageRank algorithm biplex (APABI)). *Let* M = (N , E, S)*, with layers* S = (*l*1, *l*2) *and adjacency matrices A*1, *A*2 *be a biplex network with n nodes.*

Algorithm 2 summarizes the steps necessary to calculate a centrality measure that will be denoted as the adapted PageRank algorithm biplex (APABI). This measure provides us with a vector for classifying the nodes of the network according to their importance within a biplex network. This classification is obtained from the importance of the nodes in two networks where what changes are the associations between the nodes and the data associated with them. This classification is obtained from the importance of the nodes in two layers where the nodes are the same and what changes are the associations (links) between the nodes and the data associated with them.

Note that the *MBI* matrix is built for biplex networks. However, it can be easily extended the same reasoning for a multiplex network with *k* layers {*l*1, *l*2,..., *lk*}, defining the adjacency matrices {*A*1, *A*2,... *Alk*} and a set of *k* data matrices {*D*1, *D*2,..., *Dk*}. The matrix *MBI* is extended to a multiplex network with *k* layers as

$$M\_{multi} = \frac{1}{k} \left( \begin{array}{c|c} M\_{1,1} & M\_{1,2} \\ \hline M\_{2,1} & M\_{2,2} \end{array} \right).$$

with

$$M\_{1,1} = \begin{pmatrix} (1-\alpha)P\_1 & I & \cdots & \cdots & I \\ & I & (1-\alpha)P\_2 & \cdots & \cdots & \cdots \\ & \cdots & \cdots & \cdots & \cdots & \cdots \\ & & I & & \cdots & (1-\alpha)P\_k \end{pmatrix},\tag{10}$$

$$M\_{2,2} = \begin{pmatrix} \begin{array}{cccc} aV\_1 & aV\_2 & \cdots & aV\_k \\ aV\_1 & aV\_2 & \cdots & aV\_k \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ & aV\_1 & aV\_2 & \cdots & aV\_k \end{pmatrix},\tag{11}$$

where *M*1,2, *M*2,1 are diagonal matrices.

In the approach made so far in this section, we have considered the same value for the parameter *α* in all the layers that make up the network. However, it could happen that the *α* value was different in the different layers, as a consequence of the need to differentiate the importance that must be assigned to the data in each of the layers. That leads us to consider various *αi*, for each layer *i*. Note that this

variant does not imply in any way modify the spectral properties of the matrices involved in the calculation of centrality. Consequently, matrix *MBI* should be written now as

$$M\_{BI} = \frac{1}{2} \left( \begin{array}{cc|cc} (1 - a\_1)P\_1 & I & \\ I & (1 - a\_2)P\_2 & 0 & 2(1 - a\_2)I \\ \hline I & 0 & a\_1V\_1 & a\_2V\_2 \\ 0 & I & a\_1V\_1 & a\_2V\_2 \end{array} \right) \tag{12}$$

The generalization of the matrix *MBI* to *k* layers with *k* parameters *αi* consists simply of replacing each *α* in the expressions (10) and (11) with its corresponding *αi* in the *i*-th row.

### *2.4. A Note About the Computational Cost*

We discuss certain general aspects of the computational cost of the proposed model. It should be noted that if we look closely at Algorithm 2, the most expensive algebraic operations that are carried out are the product of a scalar by a matrix, the matrix-vector product and the calculation of the dominant eigenpair (*λ*, **x**) of matrix *MBI*, given by the expression (8).

As it is well-known and can be seen in any linear algebra textbook, the product of a scalar by a square matrix of size *n* requires *n* × *n* multiplications, while the product of two square matrices of size *n* requires a computational cost of *O*(*n*2). In our case, we need to make the product *D* · *vi*, for *i* = 1, 2, where *D* is the data matrix of size *n* × *k* and *vi* is a column vector of size *n*. Therefore, the computational cost of *D* · *v*0 is of *O*(*nk*).

However, the most expensive part from the computational point of view is found in step 8 of the algorithm, in which, once the *MBI* matrix is constructed, it is necessary to obtain its dominant eigenpair (*λ*, **x**). The numerical problem of calculating the eigenvalues and eigenvectors of any matrix is very expensive, in general, if the matrix in question does not have a structure that simplifies its calculation in some way. In general, for matrices of low dimension (such as *N* < 150), there are efficient methods for finding all the eigenvalues and eigenvectors. For example, the Householder–QL–Wilkinson modification of the given method is built into the EISPACK routines and is routinely used. The computation time for any of these methods grows as *N*3 and the memory requirement grows as *N*2. For large matrices, a very commonly used algorithm is Lanczos, that is an adaptation of power methods to find the *m* most useful eigenvalues and eigenvectors of an *n* × *n* Hermitian matrix. For a more detailed description of the numerical matrix eigenvalue problems, see [39].

Due to the way we have built the *MBI* matrix following the original idea of the Google matrix used in the original PageRank combined with the two-layer PageRank approach, we have ensured that this matrix inherits the spectral properties of the original Google matrix in the original PageRank model. It is a stochastic matrix by columns of which we can affirm, using a variant of the Perron–Frobenius theorem, that its own dominant eigenvector associated to eigenvalue *λ* = 1 corresponds to the stationary distribution of the Markov chain by the column normalized matrix *MBI*. This stationary vector *π***ˆ** *BI* verifies that

$$M\_{BI}\dot{\pi}\_{BI} = \dot{\pi}\_{BI}$$

and may be obtained by using the well-known power iteration method, applying it until the convergence of the iterative process

$$\begin{array}{rcl} \mathfrak{star}\_{\mathbb{k}} &=& M\_{BI} \pi\_{\mathbb{k}-1} \\ \mathfrak{m}\_{\mathbb{k}} &=& \mathfrak{H}\_{\mathbb{k}} / \max(\mathfrak{H}\_{\mathbb{k}})\_{\mathbb{k}} \end{array}$$

for *k* = 1, 2, . . ..

In addition, it should be noted that the use of the power method for the calculation of the dominant eigenvector is especially useful when applied to sparse matrices.


**Author details**

In this study, for an equipment activity extending over a period of 7 years, the cost of acquisition and maintenance cost represent, respectively, 11.4% and 5.0% of

But when the activity of the same equipment is done over a period of 2 years, the cost of acquisition and maintenance cost represent, respectively, 31.0% and 3.9% of

Added to this, for the same annual rate, the minimum unit test cost is € 3.9 for a 7-year activity cycle, whereas it costs € 5 if the activity cycle is reduced to

Therefore, it should be noted that when operating conditions remain the same, amortization of equipment carried on shorter lead times significantly increases the

Even though this example only concerns electrophoresis capillary equipment, extrapolating conclusions on agarose gel equipment is possible for the following reasons: installation, operation, and maintenance are less demanding than for cap-

While sub-Saharan Africa is the most affected region in the world for sickle cell

At its 60th session held in Malabo from 30 August to 3 September 2010, the WHO was already raising the option of a strategy for its African region. Nine years

The management improvement of this pathology solicits several challenges, including the one concerning the technical platform necessary for diagnosis. The costs of acquiring and operating equipment often require significant fundraising, which is often lacking. The missing financial means are often one of the first

The study mentioned above proves that it is possible to optimize the available resources, however modest they may be, in order to obtain good and lasting results. In the case of biomedical equipment, it is sufficient to involve the right people to achieve the expected results. Policymakers in sub-Saharan African countries must therefore integrate the skills of biomedical engineers into the design and start-up of medical projects so that they, in turn, contribute effectively to improve the quality

the total life cycle cost.

the total life cycle cost.

cost of the test at the expense of patients.

*Human Blood Group Systems and Haemoglobinopathies*

disease, research and care are relatively slow.

obstacles to the launching of the relevant programs.

after the effects are hardly noticeable.

of medical care populations.

**196**

2 years [37].

illary technology.

Vincent Mulunda-a-Mulunda1 \*, Pierre Kouam2 and Taty Oke Ingwen3

1 Institut Supérieur de Techniques Appliquées (ISTA), Kinshasa, Democratic Republic of Congo

2 Groupe Hospitalier Nord Essonne, Lonjumeau, France

3 Wagenia Sarl, Kinshasa, Democratic Republic of Congo

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 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.


**4.1 The CSR strategy in** *Telefónica*

As already indicated, the CSR strategy in *Telefónica* is an integral part of the reputation strategy. For *Telefónica*'s Director of Corporate Responsibility, the importance of reputation is underlined by the collapse of the stock market in the 90s (twentieth century). The previous system was centered on the creation of value by keeping only two parties in check, namely the investors and the media, which proved insufficient. The different approach to CSR suggests that we must address the entire environment in which the company operates, taking care of its relationships with the community, its customers, employees, and society in general [53]. *Telefónica* launched its Proyecto de *Reputación Corporativa (PRC)* in November 2001, which outlined an operational plan that was then achieved over time and is described and discussed in the following paragraphs of which Andreu5 himself became the bearer.


*3.1.4. Hydrogenation of benzoic acid with 5%Pd-2%Re/C bimetallic catalyst*

The activity of bimetallic 5%Pd-2%Re/C catalyst was higher than that for monometallic 5% Pd/C and 5% Re/C catalysts in terms of benzoic acid conversion (98.5%). But the selectivity to benzyl alcohol, cyclohexane carboxylic acid, or cyclohexyl methanol was low as compared to the other catalysts such as 5% Re/C and 5% Pd/C. This is because hydrogenation of benzoic acid with 5%Pd-2%Re/C catalyst gives benzyl alcohol which undergoes hydrogenolysis. The reaction is thus both consecutive and parallel, which gives a series of products such as CCA, cyclohexyl methanol (CHM), toluene (TOL), and methyl cyclohexane (MCH).

**Scheme 2.** Reaction scheme for hydrogenation of benzoic acid using 5%Ru/C catalyst.

**Scheme 3.** Reaction scheme for hydrogenation of benzoic acid with 5% Re/C catalyst.

The selectivity for hydrogenation of BZA with 5%Pd-2%Re/C to CCA, CHM, TOL, and MCH is 19, 47, 3.3, and 30.6%, respectively (at 6 h). Such a difference in activity and selectivity for monometallic and bimetallic catalyst only confirms that Pd and Re form a synergistic combination [11].


**5. Physical activity as a public health intervention**

Public health covers both illness prevention and promotion of personal wellbeing. Today's public health requires an inter- and multi-disciplinary team of public health workers that can implement a variety of preventive and/or responsive interventions, including epidemiology, outreach, screening, health teaching, social marketing, and policy development. Due to physical activities ability to contribute to numerous spheres of public health, it has become an integral component of public health systems [36, 37].

Research in the physical activity adherence has resulted in the recognition of several methods to influence an uptake of physical activity at the individual level [38]. However, the considerable prevalence of inactivity across most sectors of the global population necessitates higher-level approaches to physical activity promotion that include environmental, organisational, and policy-level strategies.

Physical activity provides an ideal population-wide public health intervention due to it efficacy and its low-cost ideally suited to the limited resource environment public health decision makers frequently find themselves in [39]. In this regard, many physical activity interventions require little/no equipment, require minimal supervision (in those without high risk), and can be delivered in community settings. Further, many health professionals such as physiotherapists, Biokineticists, and exercise physiologists are already serving in communities and at a population level in many countries, including low- and middle-income countries (LMICs) [40]. Where communities and countries exist that do not have such professionals specifically trained in physical activity, there is opportunity for roles and training for physical activity awareness and prescription to be offered to other healthcare professionals, such as public health practitioners, and nurses, already well placed in communities, at schools, and at a population level.

It is important to understand how physical activity affects the whole ecology. In this regard, physical inactivity and its associated morbidity and mortality affects the home, school, and workplace. It is this pervasive importance that should ensure that physical activity considerations be utilised in local strategy, policy and planning and enhancements to the built or natural physical environment to improve public spaces, workplaces, and schools to boost and provide individuals of all sectors, ages, and abilities access to physical activity.

Physical activity is imperative at a local community level due to its significant impact on physical and mental wellbeing. Determining methods for individuals in communities to enjoy physical activity can encourage regular physical activity participation. This can be achieved by prioritising pedestrians, cyclists and individuals who utilise public transport, involving community members in creating and managing public spaces [41].

Limited evidence exists to demonstrate the most appropriate methods to enhance physical activity in young children, especially considering declining school participation in sports and removal of physical education programmes [42]. However, the inclusion of parents in public health initiatives to perform parental goal setting with their children regarding physical activity have been found to be successful. Further,

parental monitoring, having physical activity training providers, and encouraging healthy role-modelling in schools could increase children's levels of physical activity and could lead to healthier familial and school environments. This increase in physical activity is especially important in that being active in childhood has unequivocally been shown to encourage physical activity participation into adulthood [41].

The workplace presents an ideal setting to promote and deliver physical activity initiatives. This is because physical activity in the workplace provides the opportunity to overcome one of the most common barriers to regular physical activity namely a 'lack of time'. Workplace physical activity programmes also provide access to physical activity to a large portion of society [43]. Apart from the long-term physical and mental health benefits associated with physical activity, when physical activity is promoted in the workplace it has been shown to decrease conditions that contribute to absenteeism associated with illness, improve productivity and staff retention, decrease the costs for employers, and increase loyalty [41].


*Edited by Jose C. Jimenez-Lopez*

*and Alfonso Clemente*

Legumes have nutraceutical qualities that impart beneficial effects on human health. They are an alternative protein source with great potential for use in producing novel foods with improved nutritional properties. This book presents a comprehensive overview of legume proteins, including information on their nutritional and nutraceutical profiles, the health benefits of their compounds, and their underlying bioactivities such as anti-diabetic, hepatoprotective, anti-inflammatory, antioxidant, and anti-cancer properties.

ISBN 978-1-80356-914-7

Legumes Research - Volume 2

Published in London, UK © 2022 IntechOpen © Olga Kaya / iStock


**4. Coupled mathematical model in macroscopic-scale shale matrix**

In this section, the experimental results of full-scale pore size distributions of real shale samples from a gas field are combined with the coupled flow model in nanopores to realize the upscaling transformation of the flow model into that in macroscopic-scale shale matrix by integration.

In the unitary model which is widely used for the flow estimation on a macroscopic scale [12, 18–22], indirect averaging methods are applied, e.g., the pore space of shale is assumed to be composed of a certain number of isodiametric pores, regardless of the pore size distributions. Some research [15, 47] used specific functions to characterize the probability density function of shale pore size distributions, with, however, assumed parameters for the purpose of conducting parameter sensitivity analysis. Here, the fitting parameters needed for the macroscopic form of the derived coupled flow model in nanopores are obtained by performing the experiments of pore size distributions of real shale samples from a gas field.

Michel et al. [15] and Xiong et al. [47] described the probability density function of shale pore size distributions as logarithmic normal distribution. Enlightened by their studies, the following expression is used to fit the experimental data of full-scale shale pore size distributions:

$$f(r\_{in}) = \frac{1}{r\_{in}\sigma\sqrt{2\pi}}e^{-0.5\left(\frac{\text{lw}\_{in} - \eta}{\sigma}\right)^2} \tag{6}$$

*Mechanism, Model, and Upscaling of the Gas Flow in Shale Matrix: Revisit DOI: http://dx.doi.org/10.5772/intechopen.91821*

#### **Table 2.**

*Fitting results of η and σ.*

where *η* = normal mean, dimensionless.

*σ* = variance, dimensionless.

Three kinds of experiments, i.e., the high-pressure mercury intrusion experiment, the liquid nitrogen adsorption experiment, and the low-temperature carbon dioxide adsorption experiment, were performed, and the full-scale pore size distribution data of the three shale samples from the Well "Ning 203", Longmaxi formation of Changning-Weiyuan district, Sichuan Basin of China, were obtained by stitching the three results together according to the effective range of each experiment, where the total volume of pores greater than 100 nm is attributed to the pore whose radius is closest to 100 nm in the experiments allowing for the difficulty of curve fitting caused by the severe fluctuations of the pore size data [42]. The values of *η* and *σ* are listed in **Table 2**. Because the samples "Ning 203-219", "Ning 203-240", and "Ning 203-250" are all taken from a depth interval of 2300-2400 m, the three groups of data in **Table 2** are averaged, i.e., *η* = 0.8055 and *σ* = 0.9060, to represent the typical shale pore size distribution in this depth range.

The number of single pipes in shale with the radius range of *rin* to *rin* + d*rin* is expressed in Eq. (7). By integrating in the entire pore size range, the flow rate in shale is obtained as Eq. (8):

$$\frac{10^{18} \phi\_{co} V\_{co}}{\pi r\_{in}^2 L\_{co}} f(r\_{in}) \mathrm{d}r\_{in} \tag{7}$$

$$Q = \int\_{r\_{in,\min}}^{r\_{in,\max}} \frac{10^{18} N \phi\_{co} V\_{co}}{\pi r\_{in}^2 L\_{co}} f(r\_{in}) \mathrm{d}r\_{in} \tag{8}$$

where *Vco* = apparent volume of a core sample, m3 .

*Lco* = length of a core sample, m.

*rin,*min = lower limit of integration, which should be larger than 0.19 nm because the diameter of methane molecules is 0.38 nm [48].

*rin,*max = upper limit of integration.

The macroscopic-scale mathematical model of shale gas flow can be obtained by substituting Eqs. (5) and (6) into Eq. (8) as:

$$Q = \int\_{r\_{\rm in,in}}^{r\_{\rm in,max}} \frac{10^{\rm lb/8} \left[ \varepsilon^{-\rm K\rm in} N\_D + \left( \frac{1}{1+\rm K\alpha} - \varepsilon^{-\rm K\rm in} \right) N\_b + \varepsilon^{-1.8/\rm K\alpha} N\_K + \left( \frac{\rm K\alpha}{1+\rm K\alpha} - \varepsilon^{-1.8/\rm I\alpha} \right) N\_i \right] \phi\_{\alpha} V\_{\alpha}}{\pi r\_{\rm in} r\_{\rm in}^3 \sigma \sqrt{2\pi}} \epsilon^{-0.9 \left( \frac{\rm I\alpha}{\rm or} \right)^2} d\tau\_{\rm in} \tag{9}$$

Literature survey shows that there are several main upscaling methods of flow models from microscopic to macroscopic scale, i.e.:

Method (1): the commonly used unitary model [12, 18–22] as already mentioned. Method (2): the sum method of calculating the permeability of every straight capillary tube [27].

**Method Description/equation Advantages Shortcomings** porous medium is considered, in which a microscopic unit cell is periodically repeated Pore network model [54, 55] Generate pore network models by extracting pore structure information from real images or generate porous media by simulating the sedimentation and diagenesis processes and then incorporate relevant flow mechanisms into the Pore size distribution, anisotropy and low connectivity of the pore structure, etc. can be taken into account Substantial work for model establishment; representativeness and verisimilitude of pore network models to the real pore structures remain a challenge

*Mechanism, Model, and Upscaling of the Gas Flow in Shale Matrix: Revisit DOI: http://dx.doi.org/10.5772/intechopen.91821*

#### **Table 3.**

*Comparison of upscaling methods from microscopic to macroscopic scale.*

gas flow models

Method (3): the statistical sum method of the individual permeability from each shape type [49, 50].

Method (4): the 3D fractal model with variable pore sizes [51].

Method (5): the homogenization method to upscale gas flow through two distinct constituents, a mineral matrix and organic matter [52, 53].

Method (6): the pore network model including pore size distribution, anisotropy, and low connectivity of the pore structure, etc. in shale [54, 55].

The comparison among them is summarized in **Table 3**.

After reviewing the upscaling methods in **Table 3**, it is obvious that the method used in this work is not a bad compromise when compared to method (1) which is too simple and coarse, methods (2) and (3) where it is impractical and daunting to count the size/shape of every single pore with huge computational efforts, method (5) where complex processing for the model establishment and solution is needed, and methods (4) and (6) where redundant parameters/information about pore structure need to be assumed or obtained from multiple ways. Therefore, on the one hand, only the pore size distribution experiment is needed for the determination of the upscaling parameters in this chapter to make the consideration of various pore sizes happen. On the other hand, the derived model in this chapter is practical to operate, and the results can thus be readily obtained. However, it does not necessarily mean that there is no drawback for the upscaling method used. For example, although SEM images of the shale samples show that the pores in the organic matter are mostly circular [56], various types of pore shapes, e.g., cylindrical, triangular, rectangular shaped, etc., can be detected in shale samples [50, 57]. Singh et al. [50] concluded that the geometry of pores significantly influences apparent permeability of shale and diffusive flux. The study of effective liquid permeability in a shale system by Afsharpoor and Javadpour [58] confirmed that the assumption of simplified circular pore causes apparent permeability to be significantly overestimated and the discrepancy between the realistic multi-geometry pore model and the simplified circular pore model becomes more pronounced when pore sizes reduce and liquid slip on the inner pore wall is taken into account. Xu et al. [59] developed a model for gas transport in tapered noncircular nanopores of shale rocks and found the following: (1) pore proximity induces faster gas transport, and omitting pore proximity leads to the enlargement of the adsorbed gas-dominated region; (2) increasing taper ratio (ratio of inlet size to outlet size) and aspect ratio weakens real gas effect and lowers free gas transport; (3) moreover, it lowers the total transport capacity of the nanopore, and the tapered circular nanopore owns the greatest

transport capacity, followed by tapered square, elliptical, and rectangular nanopores. To conclude, there is still much room for improvement of the upscaling method in this work in multiple aspects in future research.


4. The model of the plasma-dynamical filter for micro-droplets eliminations

Now the vacuum-plasma technologies are widely used in erosion plasma sources, such as cathodic arc and laser-produced plasma, for thin films synthesis, and coatings with control properties. However, the micro-droplets present in the formed ion plasma flow restrict the applicability of this method of film synthesis. The micro-droplets component of erosion for the majority of metals is an essential part of general losses of the cathode material in a vacuum-arc, comparable with ion component. Therefore, for prevention of effect of micro-droplets on a substrate, it is necessary to eliminate droplets. The formation and propagation of microdroplets, and also the mechanisms of decreasing of their effects on quality and rate deposition films and coatings were investigated in detail in works [22–26]. It is known from several approaches micro-droplets density reduction in ion plasma flows. Therefore, proposed methods do not provide the complete solution of the problem of micro-droplets elimination.

In paper Anders [26], the conclusion has been formulated that micro-droplets cannot be evaporated in the arc plasma flow without additional energy source. A new approach to the elimination or reduction of micro-droplets from the dense metal plasma flow based on the use of a cylindrical electrostatic PL configuration to generate an energetic radial electron beam within the low-energy ion plasma flow has been proposed and described in [27, 28]. The pumping of energy into arc plasma flow by the self-consistently formed radial beam of highenergy electrons for evaporation of micro-droplets could serve as additional energy source. The beam is formed by double layer, appeared in a cylindrical channel of the novel plasmaoptical system in crossed radial electrical and longitudinal magnetic fields. Here we detailed describe the model of device for filtering dense plasma flow from micro-droplets.

### 4.1. Model approach

where R(r,rj

z-axis in both direction.

3.3. Conclusion remarks

(left) and 340(right).

) – usual standard PIC – core, that characterizes particle size and shape and charges

distribution in it. After that, the Poisson equation was solved, and new electric field distribution was found. Since electrons are magnetized we consider their movement in radial plane only, thus can solve for electrons one-dimensional hydrodynamic equations on each layer at z separately. Solve it we find electron density, calculate electric field on each layer and correct particle trajectories. After that, the procedure was repeated again. Modeling time is large enough for establish of ion multiplication process. The formation of the sufficient number of ions is possible due to magnetic field presence, which isolates anode from the cathode. Ions practically do not feel the magnetic field action and move from anode to the axis, where create a space charge, first in the center of the system. Electrons move along the magnetic field strength line, but due to collisions with neutrals, they start moving across the magnetic field. An internal electric field is formed, which slow down the ions and pushes out them from the volume along system axis. Figure 13 shows results of modeling high-current mode (Ua = 1.2 kV, pressure 0.15 Pa, and magnetic field at the axis is 0.03 T). Figure 13a shows how the ions number to axis increases when ionization process is steady-state. One can see that number of ions increase not only to axis but also along axis from center to edge too. Figure 13b shows ion space charge distribution for different time step. One can see that ions create space charge in center of the system first, but then under electric field action they leave center and move along

282 Plasma Science and Technology - Basic Fundamentals and Modern Applications

First, the original approach to use plasma accelerators with closed electron drift and open walls for creation cost-effective low-maintenance plasma device for production converging toward axis accelerating ion beam was described. Based on the idea of continuity of current transferring in the system are found exact analytical solutions describing electric potential distribution along acceleration gap. It was shown that potential distribution is parabolic for different operation modes as in low-current mode as well as in high-current quasi-neutral plasma mode and cannot depend on electron temperature. It is found under conditions that everything electrons originated within the gap by impact ionization only, and go out at the anode due to mobility in transverse magnetic field, the condition full potential drop in the accelerating gap corresponds to equality gap length to the anode layer thickness. In case when the gap length less than anode layer thickness potential drop is not completed. For case when the gap length more than anode

Figure 13. (a) Ions number dependence on r and z (r = 0,z = 0–center of the system); (b) ion space charge for time step 70

We will consider electrostatic PL configuration through which a low-energy arc ion plasma flow passes. Figure 14 shows experimental device (left) and simplified model (right). A dense arc plasma flow with micro-droplets is propagated from the cathodic arc source and passes

Figure 14. (a) Schema of the experimental set-up, (b) simplify model (Δ–spatial layer in which the strong radial electrical field is supported).

process and electrons multiplication. The potential distribution is found by solving Poisson

density we can use expression: ne = ne0� exp.(eφ/Te), where ne0 – electron density of quasineutral plasma. For simplicity, we did not take into account the plasma heating and used finite Te and Ti at the first stage. For all particles in the calculation box, the motion equations solve and find new positions and velocities. Part of the ions reaches the cathode and knocks out γelectrons from it. We took them into account for Poisson equation solving too. We also take into account their ability to ionize when acquiring energy exceed the ionization energy. Very soon (in real time it corresponds to 1.6–2.5 μs) the potential jump near cathode is formed (see

One can see that size of the potential jump layer is very small (about 5�10�7 cm, so it is <<rLe), thus electric field formed in the layer is large enough to accelerate the electrons to high-energy in the layer and force them to move toward the axis. We assumed the initial energy of emitted electron is 5 eV. Initial electrons move along magnetic field line as it shown in Figure 16a. However, due to appearance strong electric field in the layer, the average electron energy increases. It begins to exceed 10 eV at field strength is about 100 V/cm, and when electric field strength reaches about 500 V/cm it exceeds 100 eV. At such energies, the secondary electrons acquire the ability to ionize neutrals with the new secondary electrons appearance. As results, an avalanche-like ionization begins. Electrons move toward the axis and can accumulate there (see Figure 16b)). Note that application of the plasma lens to the transport of low-energy

¼ 0. For electron

Modeling of Novel Plasma-Optical Systems http://dx.doi.org/10.5772/intechopen.77512 285

equation (see Eq.(7)). Ion density we find from the continuity equation: div ji

Figure 15. (a) Initial copper plasma flows, (b) potential distribution for time step 50.

Figure 16. Trajectories of the emission electrons depends on time (a) Nt = 40, (b) Nt = 80.

Figure 15b).

through diaphragm into the plasma-optical system. A part of the micro-droplets settles on the diaphragm, which is at the beginning of plasma-optical system, and remaining ones along with the flow propagate through the system.

The system consists of a cylinder (central electrode) of length L and diameter D on which the negative voltage U 1–3 kV is applied, and a pair of external ring grounded electrodes arranged symmetrically to the central electrode. The system is in the magnetic field of a short coil or permanent magnets. When arc plasma flow reaches the zone of the magnetic field action, it penetrates into the flow. The magnetic field must satisfy to the condition: rLe << D << rLi, where rLe, rLi – are the electron and ion Larmour radiuses. In such a magnetic field the electrons are magnetized, and ions are not magnetized. A dense plasma flow propagating inside the cylinder creates a thin wall layer Δ with a large radial electric field Er. The magnetic field lines are equipotential inside flow, and electrical field, which created is similar to magnetic field lines. Because of the electrons of the flow are magnetized, they in the magnetic field are displaced to axis and prevent radial expansion of the flow. The density of flow increases with increasing of the magnetic field near axis, so control by magnetic field we can control by flow, keeping it from expansion.

High-energy electrons appear near the inner cylindrical surface by secondary ion-electron emission at this surface bombardment by peripheral flow ions. In result, the fast electrons beam created with current density jeb = γjis in near-wall layer (γ – secondary ion-electron emission coefficient).This electron beam injected from near-wall layer to plasma flow axis can serve as additional effective energy source for micro-droplet elimination.

#### 4.2. Modeling and results

The modeling of high-energy radial electron beam formation was the first task of our consideration. For simulation, we used PIC-method with Boris scheme, analogically to previous section. The copper plasma flows transport through the plasma lens with applied potential 3 kV on the central electrode and magnetic field about 300–400 E was considered. Figure 15a shows initial plasma flow. The peripheral ions of flow collide with the inner wall of the central electrode and emitted electrons. The Monte-Carlo method was used for modeling emission

Figure 15. (a) Initial copper plasma flows, (b) potential distribution for time step 50.

through diaphragm into the plasma-optical system. A part of the micro-droplets settles on the diaphragm, which is at the beginning of plasma-optical system, and remaining ones along

Figure 14. (a) Schema of the experimental set-up, (b) simplify model (Δ–spatial layer in which the strong radial electrical

The system consists of a cylinder (central electrode) of length L and diameter D on which the negative voltage U 1–3 kV is applied, and a pair of external ring grounded electrodes arranged symmetrically to the central electrode. The system is in the magnetic field of a short coil or permanent magnets. When arc plasma flow reaches the zone of the magnetic field action, it penetrates into the flow. The magnetic field must satisfy to the condition: rLe << D << rLi, where rLe, rLi – are the electron and ion Larmour radiuses. In such a magnetic field the electrons are magnetized, and ions are not magnetized. A dense plasma flow propagating inside the cylinder creates a thin wall layer Δ with a large radial electric field Er. The magnetic field lines are equipotential inside flow, and electrical field, which created is similar to magnetic field lines. Because of the electrons of the flow are magnetized, they in the magnetic field are displaced to axis and prevent radial expansion of the flow. The density of flow increases with increasing of the magnetic field near axis, so control by magnetic field we can control by

High-energy electrons appear near the inner cylindrical surface by secondary ion-electron emission at this surface bombardment by peripheral flow ions. In result, the fast electrons beam created with current density jeb = γjis in near-wall layer (γ – secondary ion-electron emission coefficient).This electron beam injected from near-wall layer to plasma flow axis can

The modeling of high-energy radial electron beam formation was the first task of our consideration. For simulation, we used PIC-method with Boris scheme, analogically to previous section. The copper plasma flows transport through the plasma lens with applied potential 3 kV on the central electrode and magnetic field about 300–400 E was considered. Figure 15a shows initial plasma flow. The peripheral ions of flow collide with the inner wall of the central electrode and emitted electrons. The Monte-Carlo method was used for modeling emission

serve as additional effective energy source for micro-droplet elimination.

with the flow propagate through the system.

284 Plasma Science and Technology - Basic Fundamentals and Modern Applications

field is supported).

flow, keeping it from expansion.

4.2. Modeling and results

process and electrons multiplication. The potential distribution is found by solving Poisson equation (see Eq.(7)). Ion density we find from the continuity equation: div ji ¼ 0. For electron density we can use expression: ne = ne0� exp.(eφ/Te), where ne0 – electron density of quasineutral plasma. For simplicity, we did not take into account the plasma heating and used finite Te and Ti at the first stage. For all particles in the calculation box, the motion equations solve and find new positions and velocities. Part of the ions reaches the cathode and knocks out γelectrons from it. We took them into account for Poisson equation solving too. We also take into account their ability to ionize when acquiring energy exceed the ionization energy. Very soon (in real time it corresponds to 1.6–2.5 μs) the potential jump near cathode is formed (see Figure 15b).

One can see that size of the potential jump layer is very small (about 5�10�7 cm, so it is <<rLe), thus electric field formed in the layer is large enough to accelerate the electrons to high-energy in the layer and force them to move toward the axis. We assumed the initial energy of emitted electron is 5 eV. Initial electrons move along magnetic field line as it shown in Figure 16a. However, due to appearance strong electric field in the layer, the average electron energy increases. It begins to exceed 10 eV at field strength is about 100 V/cm, and when electric field strength reaches about 500 V/cm it exceeds 100 eV. At such energies, the secondary electrons acquire the ability to ionize neutrals with the new secondary electrons appearance. As results, an avalanche-like ionization begins. Electrons move toward the axis and can accumulate there (see Figure 16b)). Note that application of the plasma lens to the transport of low-energy

Figure 16. Trajectories of the emission electrons depends on time (a) Nt = 40, (b) Nt = 80.

discharge at low-pressure. Use of plasma lens configuration in this way was elaborated, explored and developed some cost efficiency, low-maintenance plasma devices for ion treatment, and deposition of exotic coatings with given functional properties. These devices make using permanent magnets and possess considerable flexibility with respect to spatial configuration. They can be operated as a stand-alone tool for ion treatment of substrates, or as part of integrated processing system together with cylindrical magnetron sputtering system, for coat-

Modeling of Novel Plasma-Optical Systems http://dx.doi.org/10.5772/intechopen.77512 287

The research described has shown a principal possibility of a positive space charge cloud creation for negative charged particle beam focusing. It was demonstrated that possible create a positive space charge due to the magnetic electron insulation and reach strong focusing electric field, which sufficient for creation of short-focus elements to be used in systems for manipulating intense beams of negative ions and electrons. The further development of focusing properties of these devices demands study of intense negatively charged particle beams

The simulations and experimental results demonstrate the high-efficiency of the electrostatic PL for focusing and manipulating wide aperture, high-current, low-energy, heavy metal ion plasma flow. These results open up new attractive way for further development and application erosion plasma sources for synthesis of exotic films and coatings with given functional properties. Some preliminary theoretical and experimental studies [27–29] have been carried out, providing confidence and optimism that the proposed idea for micro-droplet elimination

[1] Morozov A. Focusing of cold quasi-neutral beams in electromagnetic fields. Doklady of

This work was support by Grant NASU No PL-18 and No P-13\_18.

\* and Alexey Goncharov2

2 Institute of Physics NAS of Ukraine, Kiev, Ukraine

1 Institute for Nuclear Research NAS of Ukraine, Kiev, Ukraine

the Academy of Sciences of the U.S.S.R. 1965;163(6):1363

\*Address all correspondence to<EMAIL_ADDRESS>
ing deposition.

passing through the systems.

has good potential for success.

Acknowledgements

Author details

Iryna Litovko1

References

Figure 17. Influence radial electron beam on beam focusing: (a) trajectories of cu + beam; (b) space charge density in the beam.

high-current ion beam can improve the delivery of plasma flow to a substrate, as well as providing micro-droplet removal via the fast electrons within the lens region.

We considered the transport aspect and effect of fast electrons on transport characteristics lowenergy ion plasma beam. Figure 17 shows results of modeling transport copper ion beam with current 100A through plasma lens with presence of fast electrons in the volume. One can see that accumulation high-energy electrons on the axis and their space charge can provide additional compensation and focusing of the high-current ion beam.

#### 4.3. Conclusion remarks

A new approach was proposed for the elimination of micro-droplets from the dense metal plasma, based on evaporation and thus removal of micro-droplets from the arc plasma by energetic electrons within the electrostatic PL. These electrons are generated self-consistently by secondary emission in the near-wall plasma layer from the internal surface of the lens central electrode and serves to evaporate, and thus remove micro-droplets from the plasma flow. The experiments [29] demonstrate the effectiveness of the electrostatic PL for focusing and manipulating wide-aperture, high-current, low-energy, streaming metal ion plasma flows. In these experiments, the self-sustained focusing of high-density, wide-aperture, low-energy ion plasma flow was observed. It has been shown that the presence of fast electrons in the volume of the plasma lens both improves the propagating ion plasma flow toward the substrate and introduces additional energy for effective evaporation and elimination of micro-droplets from the plasma flow.


**2.3 Methodology**

To assess and analyze the effect of different variables on a single area, the weighted overlay method was conducted on the RUSLE variables (**Figure 5**).

## **Digital Image processing**

Digital image processing involves numerous procedures including formatting and correcting of the data, digital enhancement to facilitate better visual interpretation, had been carried out [32]. The common image processing functions available in image analyses like radiometric correction, geometric correction, image mosaic, subsetting, and image enhancement had been made accordingly.

### **Image Classification**

Image classification is defined as the process of sorting pixels into a finite number of individual classes, or categories of data, based on their data file values [32]. If a pixel satisfies a certain set of criteria, the pixel is assigned to the class that corresponds to those criteria. This process is also referred to as image segmentation. Depending on the type of information you want to extract from the original

*Remote Sensing and GIS-Based Soil Loss Estimation Using RUSLE in Bahir Dar Zuria District… DOI: http://dx.doi.org/10.5772/intechopen.95393*

data, classes may be associated with known features on the ground or may simply represent areas that look different to the computer. An example of a classified image is a land cover map, showing vegetation, bare land, pasture, etc. [33].

To classify the images, ground truth points were collected from different land use land cover types, and hence supervised image classification technique was applied. Supervised training is closely controlled by the analyst. The sample ground truth points taken during the field time help a lot to identify the land use/land cover on the image by using supervised classification and hence the computer can automatically classify the image based on the given sample ground truth points.


**Juganta K. Roy** †**, Supratik Kar \*,**† **and Jerzy Leszczynski \***

Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS 39217, USA

**\*** Correspondence<EMAIL_ADDRESS>(S.K<EMAIL_ADDRESS>(J.L.);

Received: 24 June 2019; Accepted: 12 July 2019; Published: 16 July 2019

**Abstract:** Ten novel fullerene-derivatives (FDs) of C60 and C70 had been designed as acceptor for polymer solar cell (PSC) by employing the quantitative structure-property relationship (QSPR) model, which was developed strategically with a reasonably big pool of experimental power conversion efficiency (PCE) data. The QSPR model was checked and validated with stringent parameter and reliability of predicted PCE values of all designed FDs. They were assessed by the applicability domain (AD) and process randomization test. The predicted PCE of FDs range from 7.96 to 23.01. The obtained encouraging results led us to the additional theoretical analysis of the energetics and UV-Vis spectra of isolated dyes employing Density functional theory (DFT) and Time-dependent-DFT (TD-DFT) calculations using PBE/6-31G(d,p) and CAM-B3LYP/6-311G(d,p) level calculations, respectively. The FD4 is the best C60-derivatives candidates for PSCs as it has the lowest exciton binding energy, up-shifted lowest unoccupied molecular orbital (LUMO) energy level to increase open-circuit voltage (VOC) and strong absorption in the UV region. In case of C70-derivatives, FD7 is potential candidate for future PSCs due to its strong absorption in UV-Vis region and lower exciton binding energy with higher VOC. Our optoelectronic results strongly support the developed QSPR model equation. Analyzing QSPR model and optoelectronic parameters, we concluded that the FD1, FD2, FD4, and FD10 are the most potential candidates for acceptor fragment of fullerene-based PSC. The outcomes of tactical molecular design followed by the investigation of optoelectronic features are suggested to be employed as a significant resource for the synthesis of FDs as an acceptor of PSCs.

**Keywords:** DFT; fullerene derivative; P3HT; polymer solar cell; QSPR; TD-DFT