**2.1 Characteristics of natural fibers**

Natural fibers are subdivided based on their origins, coming from plants, animals or minerals. All plant fibers are composed of cellulose while animal fibers consist of proteins (hair, silk and wool). Natural fibres can be classified according to which part of the plant they are obtained from, as shown in Fig. 5.

#### Fig. 5. Classification of natural fibres.

The strength characteristics of fiber depend on the properties of the individual constituents, the fibrillar structure and the lamellae matrix (Joseph et al., 2000).

Natural fibers exhibit considerable variation in diameter along with the length of individual filaments. Quality and other properties of fibers depend on factors such as size, maturity and processing methods adopted for the extraction of fiber (Mohanty et al., 2001). Properties such as density, electrical resistivity, ultimate tensile strength and initial modulus are related to the internal structure and chemical composition of fibers (Mohanty et al., 2001).

The structure, microfibrillar angle, cell dimensions, defects, and the chemical composition of fibres are the most important variables that determine the overall properties of the fibres.

Thermoplastic Matrix Reinforced with Natural Fibers: A Study on Interfacial Behavior 231

in thickness to the primary wall and consists of four to six lamellae which spiral in opposite directions around the longitudinal axis of the tracheid. The main bulk of the secondary wall is contained in the middle secondary cell wall (S2), and may be as little as 1 pm thick in early woods and up to 5 pm in summer wood. The microfibrils of this part of the wall spiral steeply about the axial direction at an angle of around 10 to 20°. The inner secondary wall (S3), sometimes also known as the tertiary wall, is not always well developed, and is of no great technological importance. The orientation of the microfibrils within the S2 layer has an important bearing on mechanical properties of the fibre such as its modulus of elasticity.

Mechanical properties are determined by the cellulose content and microfibril angle. A high cellulose content and low microfibril angle are desirable properties of a fiber to be used as

Selective removal of non-cellulosic compounds constitutes the main objective of fiber chemical treatment. Both the hemicellulosic and pectic materials play important roles in fiber bundle integration, fiber bundle strength and individual fiber strength as well as water absorbency, swelling, elasticity and wet strength. The production of individual fibers without the generation of kink bands will generate fibers with much higher intrinsic fiber

The reinforcing efficiency of natural fiber is related to the nature of cellulose and its crystallinity. Cellulose is a natural linear homopolymer (polysaccharide), in which D-glucopyranose rings are connected to each other with β- (1-4)-glycosidic linkages. The

It is thus a 1, 4-β-D-glucan. The cellobiose polymer chains are ordered in three-dimensional levels, which give the supramolecular structure of cellulose. The linear polymeric chains (one dimension) form sheets that are held together with hydrogen bonds (second

strength which is very useful for composite application (Mooney et al., 2001).

reinforcement in polymer composites (Williams & Wool, 2000).

**2.3 Composition of natural fibers**

structure of cellulose units is shown in Fig. 7.

Fig. 7. Molecular structure of cellulose (Raven et al., 1999).

**2.3.1 Cellulose**

Long term supply of resources is important point about natural fibers that can influence on natural fiber–thermoplastic composites production. The world consumption of natural fibers as illustrated in Table 1. The data presented in Table 1 suggests that wood with 68.5 % of the total world consumption, will continue to be a major source of bio-based fibers.

Table 1. Annual world production of natural fibers (Kandachar, 2000; Bolton, 1995).

#### **2.2 Structure of natural fibers**

The cell wall in a fiber is not a homogenous membrane. Each fibril has a complex, layered structure consisting of a thin primary wall that is the first layer deposited during cell growth encircling a secondary wall (Fig. 6).

Fig. 6. Positioning of the cellulose fibrils in wood fibres. M) Middle lamella; P) Primary wall; S) Secondary wall; S1) Secondary wall I ; S2) Secondary wall II; S3) Secondary wall III.

The secondary wall is made up of three layers and the thick middle layer determines the mechanical properties of the fiber. The middle layer consists of a series of helically wound cellular microfibrils formed from long chain cellulose molecules: the angle between the fiber axis and the microfibrils is called the microfibrillar angle. The characteristic value for this parameter varies from one fiber to another. The outer secondary cell wall (Sl) is comparable in thickness to the primary wall and consists of four to six lamellae which spiral in opposite directions around the longitudinal axis of the tracheid. The main bulk of the secondary wall is contained in the middle secondary cell wall (S2), and may be as little as 1 pm thick in early woods and up to 5 pm in summer wood. The microfibrils of this part of the wall spiral steeply about the axial direction at an angle of around 10 to 20°. The inner secondary wall (S3), sometimes also known as the tertiary wall, is not always well developed, and is of no great technological importance. The orientation of the microfibrils within the S2 layer has an important bearing on mechanical properties of the fibre such as its modulus of elasticity.

Mechanical properties are determined by the cellulose content and microfibril angle. A high cellulose content and low microfibril angle are desirable properties of a fiber to be used as reinforcement in polymer composites (Williams & Wool, 2000).

Selective removal of non-cellulosic compounds constitutes the main objective of fiber chemical treatment. Both the hemicellulosic and pectic materials play important roles in fiber bundle integration, fiber bundle strength and individual fiber strength as well as water absorbency, swelling, elasticity and wet strength. The production of individual fibers without the generation of kink bands will generate fibers with much higher intrinsic fiber strength which is very useful for composite application (Mooney et al., 2001).

#### **2.3 Composition of natural fibers**

#### **2.3.1 Cellulose**

230 Some Critical Issues for Injection Molding

Long term supply of resources is important point about natural fibers that can influence on natural fiber–thermoplastic composites production. The world consumption of natural fibers as illustrated in Table 1. The data presented in Table 1 suggests that wood with 68.5 % of the total world consumption, will continue to be a major source of bio-based fibers.

**Quantity(\*10 % of the total 3 Fiber tons)**

Wood fiber 1,750,000 68.5 Rice straw 700,000 27.4 Rice husks 70,000 2.8 Cotton 18,645 0.75 Bamboo 10,000 0.39 Jute 3,630 0.14 Kenaf 970 0.04 Flax 830 0.03 Sisal 380 0.01 Hemp 220 0.009 Ramie 110 0.004 Coir 100 0.0039

Table 1. Annual world production of natural fibers (Kandachar, 2000; Bolton, 1995).

The cell wall in a fiber is not a homogenous membrane. Each fibril has a complex, layered structure consisting of a thin primary wall that is the first layer deposited during cell growth

Fig. 6. Positioning of the cellulose fibrils in wood fibres. M) Middle lamella; P) Primary wall; S) Secondary wall; S1) Secondary wall I ; S2) Secondary wall II; S3) Secondary wall III.

The secondary wall is made up of three layers and the thick middle layer determines the mechanical properties of the fiber. The middle layer consists of a series of helically wound cellular microfibrils formed from long chain cellulose molecules: the angle between the fiber axis and the microfibrils is called the microfibrillar angle. The characteristic value for this parameter varies from one fiber to another. The outer secondary cell wall (Sl) is comparable

**2.2 Structure of natural fibers**

encircling a secondary wall (Fig. 6).

The reinforcing efficiency of natural fiber is related to the nature of cellulose and its crystallinity. Cellulose is a natural linear homopolymer (polysaccharide), in which D-glucopyranose rings are connected to each other with β- (1-4)-glycosidic linkages. The structure of cellulose units is shown in Fig. 7.

Fig. 7. Molecular structure of cellulose (Raven et al., 1999).

It is thus a 1, 4-β-D-glucan. The cellobiose polymer chains are ordered in three-dimensional levels, which give the supramolecular structure of cellulose. The linear polymeric chains (one dimension) form sheets that are held together with hydrogen bonds (second

Thermoplastic Matrix Reinforced with Natural Fibers: A Study on Interfacial Behavior 233

made up of phenyl propane (C9) units and it is the most complex polymer among naturally occurring high-molecular-weight materials. Due to its lipophilic character, lignindecreases the permeation of water across the cell walls, which consist of cellulose fibres and amorphous hemicelluloses, thus enabling the transport of aqueous solutions of nutrients and metabolites in the conducting xylem tissue. Secondly, lignin imparts rigidity to the cell walls and, in woody parts, together with hemicelluloses, functions as a binder between the cells generating a composite structure with outstanding strength and elasticity. Finally, lignified materials effectively resist attacks by micro organisms by impeding penetration of destructive enzymes into the cell walls. When incorporated in a plastic, lignin, due to its phenolic base structure, could improve the mechanical properties (Thielemans et al., 2002). Fig. 9 shows building blocks of lignin. There is a wide variation of structure within different plant species (Alder, 1977). Lignin is considered to be a thermoplastic polymer exhibiting a glasstransition temperature of around 90°C and melting temperature of around 170°C (Olesen & Plackett, 1999). It is not hydrolyzed by acids, but soluble in hot alkali, readily

oxidized, and easily condensable with phenol.

Fig. 9. Partial structure of a spruce lignin fragment (Alder, 1977).

**3. Natural fiber for use in injection molded composite**

Injection molding is a widely used technique for mass producing articles with a high degree of geometrical complexity. Injection molding has many advantages, such as short product cycle, excellent surface of the product and easily molded complicated shapes. The characteristics of the product are easily affected by the flow type of the melt, the heat transfer effect, the material properties and the specific geometry of the mold. Thus, different injection molding conditions will induce different fiber orientation. The degree of fiber orientation depends on the fiber characteristics, the variation of the cross-sectional area for flow, and the injection molding conditions. Composite materials for use in injection molding applications must be capable of fluid-like flow during processing and thus usually consist of

dimension). Then, these sheets are connected by Van der Waals bonds generating microfibril crystalline structures (third dimension). The crystal nature (monoclinic sphenodic) of naturally occurring cellulose is known as cellulose I. Cellulose is resistant to strong alkali (17.5 wt%) but is easily hydrolyzed by acid to water-soluble sugars. Cellulose is relatively resistant to oxidizing agents. Native cellulose (cellulose I) has two crystalline allomorphs, Iα and Iβ. The main difference between the two crystalline phases is the relative position of the chains to each other. These hydroxyl groups and their ability to hydrogen bond play a major role in directing the crystalline packing and also govern the physical properties of cellulose. Solid cellulose forms a microcrystalline structure with regions of high order, i.e. crystalline regions, and regions of low order, i.e. amorphous regions. Although the chemical structure of cellulose from different natural fibers is the same, the degree of polymerization (DP) varies. Its degree of polymerisation is typically between 10000 and 15000 glucose residues depending upon source and it is never found in a completely crystalline form, but occurs as a partly crystalline.

#### **2.3.2 Hemicellulose**

Hemicelluloses are another component of plant fibers. Hemicelluloses are polysaccharides and differ from cellulose in that they consist of several sugar moieties, are mostly branched, and have lower molecular mass with a degree of polymerization (DP) of 50 – 200. They are not, as the name seems to imply, biosynthetic precursors of cellulose. The two main types of hemicelluloses are xylans and glucomannans. Fig. 8 shows partial structure of hemicelluloses with a combination of 5-ring carbon ring sugars.

Fig. 8. Structure of softwood galacto-glucomannan (Bledzki & Gassan, 1999).

Hemicllulose differs from cellulose in three aspects. Firstly, they contain several different sugar units whereas cellulose contains only 1,4-b-D-glucopyranose units. Secondly, they exhibit a considerable degree of chain branching containing pendant side groups giving rise to its noncrystalline nature, whereas cellulose is a linear polymer. Thirdly, DP of hemicellulose is around 50–300, whereas that of native cellulose is 10–100 times higher than that of hemicellulose.

#### **2.3.3 Lignin**

After cellulose, lignin is the most abundant natural organic polymer. Its content is higher in softwoods (27–33 %) than in hardwoods (18–25 %) and grasses (17–24 %). Lignin is totally amorphous and hydrophobic in nature. It is the compound that gives rigidity to the plants. It is thought to be a complex, three-dimensional copolymer of aliphatic and aromatic constituents with very high molecular weight. Lignin is a randomly branched polyphenol,

dimension). Then, these sheets are connected by Van der Waals bonds generating microfibril crystalline structures (third dimension). The crystal nature (monoclinic sphenodic) of naturally occurring cellulose is known as cellulose I. Cellulose is resistant to strong alkali (17.5 wt%) but is easily hydrolyzed by acid to water-soluble sugars. Cellulose is relatively resistant to oxidizing agents. Native cellulose (cellulose I) has two crystalline allomorphs, Iα and Iβ. The main difference between the two crystalline phases is the relative position of the chains to each other. These hydroxyl groups and their ability to hydrogen bond play a major role in directing the crystalline packing and also govern the physical properties of cellulose. Solid cellulose forms a microcrystalline structure with regions of high order, i.e. crystalline regions, and regions of low order, i.e. amorphous regions. Although the chemical structure of cellulose from different natural fibers is the same, the degree of polymerization (DP) varies. Its degree of polymerisation is typically between 10000 and 15000 glucose residues depending upon source and it is never found in a completely crystalline form, but occurs as

Hemicelluloses are another component of plant fibers. Hemicelluloses are polysaccharides and differ from cellulose in that they consist of several sugar moieties, are mostly branched, and have lower molecular mass with a degree of polymerization (DP) of 50 – 200. They are not, as the name seems to imply, biosynthetic precursors of cellulose. The two main types of hemicelluloses are xylans and glucomannans. Fig. 8 shows partial structure of

hemicelluloses with a combination of 5-ring carbon ring sugars.

Fig. 8. Structure of softwood galacto-glucomannan (Bledzki & Gassan, 1999).

Hemicllulose differs from cellulose in three aspects. Firstly, they contain several different sugar units whereas cellulose contains only 1,4-b-D-glucopyranose units. Secondly, they exhibit a considerable degree of chain branching containing pendant side groups giving rise to its noncrystalline nature, whereas cellulose is a linear polymer. Thirdly, DP of hemicellulose is around 50–300, whereas that of native cellulose is 10–100 times higher than

After cellulose, lignin is the most abundant natural organic polymer. Its content is higher in softwoods (27–33 %) than in hardwoods (18–25 %) and grasses (17–24 %). Lignin is totally amorphous and hydrophobic in nature. It is the compound that gives rigidity to the plants. It is thought to be a complex, three-dimensional copolymer of aliphatic and aromatic constituents with very high molecular weight. Lignin is a randomly branched polyphenol,

a partly crystalline.

**2.3.2 Hemicellulose**

that of hemicellulose.

**2.3.3 Lignin**

made up of phenyl propane (C9) units and it is the most complex polymer among naturally occurring high-molecular-weight materials. Due to its lipophilic character, lignindecreases the permeation of water across the cell walls, which consist of cellulose fibres and amorphous hemicelluloses, thus enabling the transport of aqueous solutions of nutrients and metabolites in the conducting xylem tissue. Secondly, lignin imparts rigidity to the cell walls and, in woody parts, together with hemicelluloses, functions as a binder between the cells generating a composite structure with outstanding strength and elasticity. Finally, lignified materials effectively resist attacks by micro organisms by impeding penetration of destructive enzymes into the cell walls. When incorporated in a plastic, lignin, due to its phenolic base structure, could improve the mechanical properties (Thielemans et al., 2002).

Fig. 9 shows building blocks of lignin. There is a wide variation of structure within different plant species (Alder, 1977). Lignin is considered to be a thermoplastic polymer exhibiting a glasstransition temperature of around 90°C and melting temperature of around 170°C (Olesen & Plackett, 1999). It is not hydrolyzed by acids, but soluble in hot alkali, readily oxidized, and easily condensable with phenol.

Fig. 9. Partial structure of a spruce lignin fragment (Alder, 1977).

#### **3. Natural fiber for use in injection molded composite**

Injection molding is a widely used technique for mass producing articles with a high degree of geometrical complexity. Injection molding has many advantages, such as short product cycle, excellent surface of the product and easily molded complicated shapes. The characteristics of the product are easily affected by the flow type of the melt, the heat transfer effect, the material properties and the specific geometry of the mold. Thus, different injection molding conditions will induce different fiber orientation. The degree of fiber orientation depends on the fiber characteristics, the variation of the cross-sectional area for flow, and the injection molding conditions. Composite materials for use in injection molding applications must be capable of fluid-like flow during processing and thus usually consist of

Thermoplastic Matrix Reinforced with Natural Fibers: A Study on Interfacial Behavior 235

Many attempts have been done by researchers to increase mechanical properties of biocomposites by alkaline treatments. For example, the effect of alkali treatment on properties of hybrid fiber biocomposite was reported by John et al., (2008). It has been reported that alkali treatment leads to fiber fibrillation i.e. breaking down of fiber bundles into smaller fibers

Partial removal of lignin and hemicellulose on the alkali modification of cellulose fibers was reported by Sreekala et al., (1997). Mukherjee et al., (1993) reported that the removal of hemicellulose produces less dense and less rigid interfibrillar region. Kokot et al., (1995) also noted that as lignin is removed, the middle lamella joining the ultimate cells is expected to be more plastic as well as homogeneous, due to the gradual elimination of microvoids. Alkaline treatment increases the amount of crystalline cellulose and removes natural and

Silane is a chemical compound with chemical formula SiH4. Silanes are used as coupling agents to let glass fibers adhere to a polymer matrix, stabilizing the composite material. Silane coupling agents may reduce the number of cellulose hydroxyl groups in the natural fiber–matrix interface. Silanes undergo hydrolysis, condensation and the bond formation

Fig. 11. Hydrolysis of silane and hypothetical reaction of fibers and silane (Sreekala et al., 2000).

Bledzki et al., (1996) concluded that in the process of interaction between natural fibers and silanes, alkoxy silanes are able to form bonds with hydroxyl groups. In presence of moisture hydrolyzable alkoxy group of silans leads to the formation of silanols. Silanols can form

John et al., (2008) and Mathew et al., (2004) investigated the effect of silane treatment on the mechanical properties of biocomposites. They observed a marked improvement in the properties after chemical modification. Sreekala et al., (1997) also suggested that the silane treated cellulose fiber composite showed an increase in nucleation density compared the untreated fiber composite. The increased nucleation yielded smaller crystals that result in a transcrystalline interphase region, with improved bonding between the fiber and the matrix

polysiloxane structures by reaction with hydroxyl group of the fibers.

which increases the effective surface area available for contact with the matrix.

artificial impurities, producing a rough surface topography.

stage. The reaction scheme is given as follows:

**4.1.2 Silane treatment**

(Agrawal et al., 2000).

short fibers with a relatively low fiber fraction. Natural fiber compounds offer numerous advantages over other injection molding compounds, for instance, low wear of manufacturing tools, often reduced cycle time, and ease of recycling. The final properties of natural fiber thermoplastic composites manufactured by injection molding depend not only on the properties of raw materials used and their compositions, but also on processing methods. Injection molding is a very suitable procedure to process natural fiber reinforced polymers into sophisticated 3-dimensional parts. In this case, the use of granular material, which already includes natural fibers and coupling agent, proves a success. But the incorporation of natural fibers to thermoplastics leads to flow limitation, which are increased by the incompatibility of natural fibers and thermoplastics. A lot of methods have been used to solve this incompatibility problem, and natural fiber chemical modification and coupling agent have a better result that is explained below.


**6. Research support for floor time**

The Floor time approach examines the functional developmental capacities of children in the context of their unique biological profile and their family relationships and interactive pat‐ terns. A longitudinal study [15] was conducted to determine if children with ASD could overcome the core deficits in social behavior and become empathetic and reflective with floor time intervention. A follow-up study of 16 children diagnosed with (ASD) revealed that with the DIR/Floor time approach, a subgroup of children with ASD can become empa‐ thetic, creative, and reflective, with healthy peer relationships and solid academic skills. This suggests that some children with ASD can master the core deficits and reach levels of devel‐ opment formerly thought unattainable with a family-oriented approach that focuses on the building blocks of relating, communicating, and thinking [16].

In another study undertaken by Greenspan and Weider [15] where the progress of 200 chil‐ dren who had earlier received Floor time sessions, was reviewed showed that majority of the children learned to relate and engage with warmth, trust and intimacy; they were able to interact, read and respond to social signals; a subgroup of children developed the capacity for imaginative play, creative use of language and reflective thinking. This sub group was included in mainstream schools where the children developed meaningful relationships with peers.

Josefi and Ryan [17] conducted a case study on a 6 year old boy with severe autism. Video recordings of 16 sessions of play therapy with the child were analyzed qualitatively and quantitatively. The study concluded that this child was able to enter into a therapeutic rela‐ tionship and demonstrated attachment behavior towards the therapist. Key areas of im‐ provement were in the child's development of autonomy and pretend play, while ritualistic behaviors showed only mild improvement. Changes were also noted in the boy's behavior at home of increased independence and empathy. One implication of this preliminary re‐ search is that non-directive play therapy may enhance and accelerate emotional/social de‐ velopment of children with severe autism.

Children with ASD differ from one another—in the ways they engage, relate, and communi‐ cate and in the ways they respond to sensations, and plan and sequence their actions. These differences mean that each child requires an intervention approach tailored to his unique‐ ness, an intervention that must also consider the home setting. According to Costa and Wit‐ ten [18] the goals of such a program, regardless of the approach used, must be to strengthen the child's core deficits, namely: building the foundations for relating, communicating and thinking. The DIR/Floor time Model is especially beneficial to children with ASD and other developmental and/or emotional challenges.

Solomon et al [19] published an evaluation of The PLAY Project Home Consultation, a wide‐ ly disseminated program that trains parents of children with autism spectrum disorders in the DIR/Floor time model. Sixty- eight children, 2 to 6 years old (average 3.7 years) complet‐ ed an 8–12 month program where parents were encouraged to deliver 15 hours per week of 1:1 interaction. Pre/post ratings of videotapes by blind raters using the Functional Emotional Assessment Scale (FEAS) showed significant increases in child subscale scores. That is, 45.5 percent of children made good to very good functional developmental progress. Overall pa‐ rents' satisfaction with program was 90 percent.


**6.1 Drought hardening**

Drought hardening refers to an agronomic practice to improve the resistance of genotype to drought as a consequence of seed/seedling treatment. Pre-sowing and post sowing treatments improve drought hardening. In pre-sowing treatments, seed is soaked in water for 24 hr. and dried in sun before they are sown in the main field. In post sowing treatment, a slight moisture stress applied to young seedlings to recover their drought resistance during later stages of growth.


**5. Conclusions**

In this study, the performance of SM2RAIN-CCI and SM2RAIN-ASCAT were assessed extensively across Pakistan using the rain gauge (RGs) observations. The assessment was carried across four different climate regions of Pakistan, namely glacial, humid, arid and hyper-arid regions during the period 2000–2015 (for SM2RAIN-CCI) and 2007–2015 for (SM2RAIN-ASCAT) on a daily scale. Three statistical metrics, i.e., Bias (%), ubRMSE (mm/day), and Theil's U coefficient, and four categorical metrics, i.e., POD, FAR, CSI and Bias score, were used to assess the performance of SM2RAIN-based products. Moreover, the total mean square error was also decomposed to random and systematic error components, while KGE was also used to evaluate the performance of PPs. Finally, SM2RAIN-CCI and SM2RAIN-ASCAT were compared and evaluated against an extensively evaluated satellite precipitation product, i.e., TRMM TMPA 3B42 v7 (TMPA). Based on the results, following conclusions were drawn:

(9) Comparison of SM2RAIN-based products with TMPA revealed the better performance of TMPA across all climate regions in terms of all statistical metrics.

**Author Contributions:** K.U.R. and S.S. conceived the research topic and formulated the methods; K.U.R. and M.S. collected and arranged the data, K.U.R. and Y.W. performed data processing and analysis, K.U.R. and S.S. interpreted the results, K.U.R. wrote the paper, S.S., M.S. and Y.W. provided reviews and revised manuscript.

**Funding:** This research was partially supported by the National Natural Science Foundation of China (grant numbers 51779119 and 51839006).

**Acknowledgments:** The authors would like to thank the Pakistan Meteorological Department (PMD) and Water and Power Development Authority (WAPDA) for providing the gauge based precipitation records and grateful to the developers of SM2RAIN-based precipitation products. The authors are thankful to editor and anonymous reviewers for their insightful comments and constructive suggestions, which have substantially improved the quality of the paper.

**Conflicts of Interest:** The authors declare no conflicts of interest.


**4. Classification of POCA Schemes in Wireless Mesh Networks**

Partially overlapping channel assignment (POCA) schemes can be classified based on different criteria and approaches. The criteria that we have used for classification is the *interference model*, which is defined as the technique for capturing interference of radios belonging to nodes operating on partially overlapping channels in a WMN. Figure 10 presents the classification on which the rest of the section is based. Note that our classification based on interference model may not create disjoint categories and thus, a particular scheme may have significant overlaps with another scheme belonging to a different category.

Partially Overlapping Channel Assignments in Wireless Mesh Networks 115

of intersection between a transmitter's signal spectrum and receiver's band-pass filter, we can calculate how much overlap there is between these signals; this is defined as the interference factor (I-factor). Since, IEEE 802.11 standards operate on a set of discrete channels,

The authors of [5] have also revised two existing channel assignment algorithms in the context of WLANs and WMNs and have applied the I-factor model to these algorithms. First, an existing algorithm [22] was modified which is a centralized greedy-style approach for CA in WLANs using only orthogonal channels with the objective of increasing overall spectrum utilization. The algorithm employs an indicator variable to model the interference in WLANs and the authors have modified this indicator variable to capture not only the orthogonal channels (which was previously the case) but also channels with partial overlap (using their I-factor model). The actual channel assignment problem is formulated as a conflict set coloring problem where a conflict is present when clients belonging to a particular AP experience interference from neighboring clients (which are attached to their respective APs). The objective function is a min-max formulation to capture the total interference experienced by each client. The algorithm starts with a random permutation on how channels are assigned to APs; this is followed by the computation of the objective function. The best channel with minimum interference among the available channels is chosen and the process repeats for each AP. The modification lies in the interference calculation function to incorporate POCs into the algorithm. Interferences among channels with partial overlaps are calculated based on the I-factor interference model either empirically or analytically; this enables the possibility of assigning

Still in [5], another CA algorithm which was designed for wireless mesh networks using only orthogonal channels [21] was modified to include POCs. It is a joint channel assignment, routing and link scheduling approach and a mathematical formulation in the form of a linear program (LP) is presented. The formulation also includes an indicator variable to model interference in the network. The authors have modified the link scheduling part of the joint mathematical formulation to change the conflict links' constraints to include the Ifactor model (partial interference). They have evaluated the performance of this modified LP to show improved throughput in WMNs. The revised algorithms demonstrate that careful use of POCs can lead to significant improvements in spectrum utilization and application performance. They have performed extensive simulations to show that the use of POCs can improve network throughput (the extent of which depends on the nodal density of the net-

*4.1.2. Channel Assignment Exploiting Partially Overlapping Channels (CAEPO)*

The authors in [12] have proposed a POC channel assignment scheme called CAEPO. The main contribution of their work is the design of a traffic-aware metric that captures the degree of overlap among the channels when measuring interference. It is a hybrid distributed channel assignment protocol, where each node collects information locally and hence performs the channel assignment locally. The proposed I-factor based metric captures

the continuous variable *δ* can be discretized as follows: *δ = 5|i-j|* (in MHz).

all available channels to the WLAN.

work).

**Figure 10.** Classification of partially overlapping channel assignment algorithms based on the interference model employed.

#### **4.1. Interference factor model (I-Factor)**

#### *4.1.1. Revised Channel Assignment Schemes for Wireless Networks*

One of the first models to capture partial interference in wireless networks was presented by A. Mishra, et al. in [5]. They have extensively studied the practicality of using POCs in WLANs and WMNs. Through analytical formulation they have shown the benefits of POCs in terms of how they increase network capacity and improve channel-reuse. In order to model the interference generated by nodes operating on channels with partial overlaps, they have proposed a novel concept called interference factor (I-factor) capturing the extent of overlap between two communicating nodes. They define I-factor as:

$$IF\_{\left(t,r\right)}\left(\delta\right) = \int\_{-\infty}^{+\infty} \mathcal{S}\_t\left(f\right)B\_r\left(f-\delta\right)df$$

where *t* and *r* are indices of the transmitting and receiving nodes, and *δ* denotes the difference of the frequencies of the transmitting and receiving nodes. In other words, parameter *δ* represents the amount of overlap between the two frequencies and is defined as a continuous variable*. St(f)* is the transmitter's signal's power distribution and *Br(f)* denotes the frequency response of the receiver's band pass filter. In lay man terms: if we measure the area of intersection between a transmitter's signal spectrum and receiver's band-pass filter, we can calculate how much overlap there is between these signals; this is defined as the interference factor (I-factor). Since, IEEE 802.11 standards operate on a set of discrete channels, the continuous variable *δ* can be discretized as follows: *δ = 5|i-j|* (in MHz).

114 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

Partially overlapping channel assignment (POCA) schemes can be classified based on different criteria and approaches. The criteria that we have used for classification is the *interference model*, which is defined as the technique for capturing interference of radios belonging to nodes operating on partially overlapping channels in a WMN. Figure 10 presents the classification on which the rest of the section is based. Note that our classification based on interference model may not create disjoint categories and thus, a particular scheme may have

**Figure 10.** Classification of partially overlapping channel assignment algorithms based on the interfer-

One of the first models to capture partial interference in wireless networks was presented by A. Mishra, et al. in [5]. They have extensively studied the practicality of using POCs in WLANs and WMNs. Through analytical formulation they have shown the benefits of POCs in terms of how they increase network capacity and improve channel-reuse. In order to model the interference generated by nodes operating on channels with partial overlaps, they have proposed a novel concept called interference factor (I-factor) capturing the extent of

> ��(���)(�) ��� ��(�)��(� � �)�� ��

�� where *t* and *r* are indices of the transmitting and receiving nodes, and *δ* denotes the difference of the frequencies of the transmitting and receiving nodes. In other words, parameter *δ* represents the amount of overlap between the two frequencies and is defined as a continuous variable*. St(f)* is the transmitter's signal's power distribution and *Br(f)* denotes the frequency response of the receiver's band pass filter. In lay man terms: if we measure the area

ence model employed.

**4.1. Interference factor model (I-Factor)**

*4.1.1. Revised Channel Assignment Schemes for Wireless Networks*

overlap between two communicating nodes. They define I-factor as:

**4. Classification of POCA Schemes in Wireless Mesh Networks**

significant overlaps with another scheme belonging to a different category.

The authors of [5] have also revised two existing channel assignment algorithms in the context of WLANs and WMNs and have applied the I-factor model to these algorithms. First, an existing algorithm [22] was modified which is a centralized greedy-style approach for CA in WLANs using only orthogonal channels with the objective of increasing overall spectrum utilization. The algorithm employs an indicator variable to model the interference in WLANs and the authors have modified this indicator variable to capture not only the orthogonal channels (which was previously the case) but also channels with partial overlap (using their I-factor model). The actual channel assignment problem is formulated as a conflict set coloring problem where a conflict is present when clients belonging to a particular AP experience interference from neighboring clients (which are attached to their respective APs). The objective function is a min-max formulation to capture the total interference experienced by each client. The algorithm starts with a random permutation on how channels are assigned to APs; this is followed by the computation of the objective function. The best channel with minimum interference among the available channels is chosen and the process repeats for each AP. The modification lies in the interference calculation function to incorporate POCs into the algorithm. Interferences among channels with partial overlaps are calculated based on the I-factor interference model either empirically or analytically; this enables the possibility of assigning all available channels to the WLAN.

Still in [5], another CA algorithm which was designed for wireless mesh networks using only orthogonal channels [21] was modified to include POCs. It is a joint channel assignment, routing and link scheduling approach and a mathematical formulation in the form of a linear program (LP) is presented. The formulation also includes an indicator variable to model interference in the network. The authors have modified the link scheduling part of the joint mathematical formulation to change the conflict links' constraints to include the Ifactor model (partial interference). They have evaluated the performance of this modified LP to show improved throughput in WMNs. The revised algorithms demonstrate that careful use of POCs can lead to significant improvements in spectrum utilization and application performance. They have performed extensive simulations to show that the use of POCs can improve network throughput (the extent of which depends on the nodal density of the network).

#### *4.1.2. Channel Assignment Exploiting Partially Overlapping Channels (CAEPO)*

The authors in [12] have proposed a POC channel assignment scheme called CAEPO. The main contribution of their work is the design of a traffic-aware metric that captures the degree of overlap among the channels when measuring interference. It is a hybrid distributed channel assignment protocol, where each node collects information locally and hence performs the channel assignment locally. The proposed I-factor based metric captures

the interference experienced by nodes operating on channels with partial interference. Each node measures the interference according to the degree of overlap between channels and scales it to the traffic load experienced by its neighboring node (this information is maintained by each node). Each node does this for all of its neighbors and combines the results to determine the total interference it is "suffering" due to its neighboring nodes. Thus, the interference metric at node *i* is calculated as:

Partially Overlapping Channel Assignments in Wireless Mesh Networks 117

group leader who if agrees relays the information onwards to the other members in the group. Because of the addition of a new grouping algorithm and the load-aware feature,

In [10], the authors have introduced the concept of *node orthogonality:* two nodes, operating over adjacent and partially overlapping channels, are considered orthogonal if they are sufficiently physically apart. A novel interference model is proposed that captures the adjacent channel interference and also takes into account the physical distance of the two nodes

��(�� �) =1− ���������� ��(��� ��)}

where *Di(ci,cj)* is the adjacent channel interference range between channels *i* and *j,* extracted from the physical model of the I-factor described in [3-6]. *Di(ci,cj)* captures both the channel separation and physical distance among the nodes to model the interference due to POCs. The proposed interference factor *Ic(i,j)* can be used to define *node orthogonality* by stating that

Given a particular channel assignment, a weighted interference graph can be constructed with weights on the edges measured by the interference factor *Ic(i,j)*; Figure 11 shows an example. Here, it is assumed that the data rate and the transmit power for all the APs are the

Using the weighted interference graph model, a minimum weighted interference optimization problem is formulated with the objective of minimizing the sum of weights in the interference graph. A centralized heuristic is proposed called minimum interference for channel allocation (MICA) to obtain a near-optimal solution which relaxes the formulated minimum interference problem in order to find fractional interference in polynomial time and eventually to assign POCs to APs (after rounding off the fractional solution to the

��(��� ��)

load-aware CAEPO-G achieves much better performance than the original CAEPO.

configured on POCs. The proposed interference factor *Ic(i,j)* is defined as follows:

two nodes are orthogonal if and only if their interference factor value is equal to 0.

*4.1.4. Minimum Interference for Channel Allocation (MICA)*

**Figure 11.** Construction of a weighted interference graph

same.

nearest integer).

$$Interference[i] = \sum\_{j \in N(l)} f[i][j] \* B(j)$$

where *B(j)* is the proportion of the busy time of a neighboring node *j*, and *N(i)* is the set of neighbors of node *i*; *f[i][j]* captures the extent of overlap a node operating on a particular channel has from its neighboring nodes configured on another channel. This is based on the extent of the channel separation between the channels used by the two nodes (taken from [23]).

More precisely, CAEPO works as follows: each node in the network is equipped with two interfaces; the first interface is configured to a fixed channel while the other interface can be dynamically switched between channels. The algorithm starts with each node assigning a fixed channel to its fixed interface and a default channel to its switchable interface using the interference estimation metric with the initial value of *B(j)*=1. Then, this channel assignment information, together with the interference measurements are relayed to all neighbors. After this initial channel assignment, each node periodically calculates the interference using the interference metric described above and if the fixed interface channel needs to be changed, then that information is relayed on the default channel of the switchable interface. Similarly, when a node has data to send, it switches its dynamic interface to the fixed channel of the receiver node's interface. Performance evaluations of CAEPO show improved network performance when all 11 channels of IEEE 802.11b are used.


**1. Introduction**

*1.1. Standardization of Clinical Procedures and Services for Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) in Europe: The Origins*

Initially designed by a group of ME/CFS researchers and health professionals, the European Network on Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (EUROMENE) has received funding from the European Cooperation in Science and Technology (COST)— COST action 15111 [1] —from 2016 to 2020. The main goal of the Cost Action was to assess the existing knowledge and experience on health care delivery for people with Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) in European countries and to enhance coordinated research and health care provision in this field.

One of the aims of the network was to *define a standardised clinical diagnosis for ME/CFS for clinical and research use.* With the paucity and lack of integration of clinical guidelines in European countries [1], a high need has been identified for addressing the uncertainties around diagnosis and treatment, and to support the development of health services and standard clinical practices for people with ME/CFS across the continent. We report here on the recommendations for clinical diagnosis and management of ME/CFS in Europe, as prepared by the group of clinicians and researchers from 22 countries participating in the network activities (including on Near Neighbour Country–Belarus), and 55 European researchers and health professionals, who have been informed by people with ME/CFS. The participating countries are Austria, Belarus, Belgium, Bulgaria, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovenia, Spain, Sweden, United Kingdom. The researchers' names and affiliations are listed in the COST Action website [1].

#### *1.2. The Population Burden of the Disease and the Need for Better Recognition*

ME/CF is characterised by intolerance to efforts expressed by profound or pathological fatigue, malaise, and other symptoms aggravated by physical or cognitive efforts at intensities previously well tolerated by the individual. Intolerance to efforts may be experienced immediately or typically be delayed for hours or a day or more after exertion and is

associated with slow recovery. This marked and prolonged exacerbation of symptoms of ME/CFS, which follows physical activity and, in some cases, cognitive activity, is termed post-exertional malaise (PEM) and may last several days.

Other key symptoms include unrefreshing sleep, cognitive impairment, orthostatic intolerance, and pain, including muscle and joint pain and headaches. The symptoms are persistent or recurrent over long periods of time and lead to a significant reduction in previous levels of functioning. Diagnosis is clinical, owing to the absence of biomarkers, and based on detailed clinical history and physical examination by a competent clinician [2–5]. There is no causal treatment for the disease. With symptom-oriented support, there can be improvement with time, or patients may learn to manage their illness. There is little evidence on long term prognosis. However, full recovery is not the norm, particularly in adults [2–7], and in addition, there has been a small number of studies reviewing mortality among people with ME/CFS. These are consistent in demonstrating increases in mortality from suicide, in the UK [8] and in the US [9,10]. One American study demonstrated increased cardiovascular and cancer mortality [11], but this has not been confirmed by other studies.

Prevalence rates have been estimated as between 0.1 and 0.7%, and the incidence rate as 0.015 new cases/1000-year [12]. This could represent between 1 million and over 5 million people, probably around 3 million, in the European continent living with ME/CFS. However, there are no European-wide estimates of disease burden [13]. A much larger number of people will have chronic fatigue for other reasons, and many of them will also be significantly incapacitated. At least 2/3 of the cases are in women [12,13], with young people in their most productive phases of life being preferentially affected. However, ME/CFS has been reported in all age groups [14,15]. Quality of life of those with ME/CFS is on average lower than with other chronic or disabling diseases, such as multiple sclerosis [16], cancer, rheumatoid arthritis, depression [17], diabetes, epilepsy, or cystic fibrosis [18]. Economic costs are considerable [19–23] with repercussions for the individuals affected, their families and society, as well as to educational and occupational services.

Many will be unable to work or do so only on a part-time basis; with some in the milder spectrum of the disease able to work full time, however, often at the cost of enduring significant symptoms and sacrificing their social life and other interests due to the need to rest when not working [24,25]. In the absence of economic analysis on the costs of the disease in Europe, we estimate, based on data from the UK, ME/CFS may cost some 40 billion Euros per year to health services and society [22]. There is, however, a large degree of imprecision in these estimates, due to variation in coverage and costs of health services provision and living costs across the Continent, as well as in many cases failure to recognize or diagnose the disease, which not only contributes to this imprecision but also may result in patients being treated inappropriately through their being misdiagnosed as having a psychiatric illness.

Despite the substantial disease burden, the health needs of people with ME/CFS remain largely unmet in Europe, as in many other parts of the world. Clinical services for people with the disease are in small numbers and sparse. A large proportion of the population with the disease has very limited access to health services, including in the public, mixed, and private sectors, because of either geographical inaccessibility, disability, or unsympathetic responses from healthcare professionals. The still limited knowledge of health professionals about the disease, including those in primary care, who are often the first port of call for those with ME/CFS, means diagnosis is often missed or delayed, and not infrequently patients remain undiagnosed and do not receive appropriate care for long periods of time. While waiting for diagnosis, patients often encounter difficulties in getting help from the health and other services, and their suffering and needs are not fully recognised, not only by health professionals but also by employers and educators. On the other hand, on some occasions, patients are over-investigated, with inherent risks and unnecessary costs to individuals and society. People with ME/CFS may easily get trapped into a situation where, while unable to carry on or start meaningful work- or school-related

activities, they receive very little guidance from the health sector or support from social services—where they feel disbelieved and neglected and are often failed by the welfare system [24]. Their disability contributes to social isolation, which adds to their burden, and limits their chances of recovery or re-integration in society, by restricting access to healthcare and social support.


*2.10. ROS Detection*

Detection of ROS was performed, as described previously [18]. Cells were treated with 1 µmol/L 20 ,70dichlorodihydrofluorescein diacetate (DCF-DA; Invitrogen, MA, USA) for 30 min, followed by a 1× PBS wash for 2 times. The reduced DCF-DA was oxidized by intracellular ROS and converted into fluorescent 20 , 70 -dichlorofluorescein (DCF). Fluorescent signals were detected by the *FACSCanto*™ flow cytometer (BD). A total of 10,000 cells were analyzed per sample.


Multidisciplinary Design Optimization

*Hypersonic Vehicles - Past, Present and Future Developments*

[47] Iuspa L, Scaramuzzino F. A bitmasking oriented data structure for evolutionary operators implementation in genetic algorithms. Soft Computing.

[48] D'Amato E, Notaro I, Mattei M. Optimal flight paths over essential visibility graphs. In: Luque A, Hegedus S, editors. Handbook of Photovoltaic Science and Engineering. 2nd ed. Chichester: Wiley; 2011. pp. 169-217. DOI: 10.1002/978047974704.ch5

2002;**5**:58-68. ISSN: 1432-7643

**12**

Chapter 2

Abstract

1. Introduction

15

Parametric Integral Soft Objects-

based Procedure for Thermal

Andrea Aprovitola, Luigi Iuspa and Antonio Viviani

The present paper deals with a modeling procedure of a thermal protection system (TPS) designed for a conceptual reusable launch vehicle (RLV). A novel parametric model based on a scalar field created by a set of soft object primitives is used to assign an almost arbitrary seamless distribution of insulating materials over the vehicle surface. Macroaggregates of soft objects are created using suitable geometric supports allowing a distribution of coating materials using a limited number of parameters. Applications to different conceptual vehicle configurations of an assigned thickness map and materials layout show the flexibility of the model.

Keywords: reusable launch vehicles, reentry aerodynamics, integral soft objects,

Currently a number of projects related to the development of reusable launch vehicles (RLV) both single-stage-to-orbit (SSTO) and two-stage-to-orbit (TSTO) are ongoing. This trend relates to objectives of future space missions that demand to improve vehicle operability, reducing at the same time flight costs of putting payload into orbit. Several preliminary studies/experiments related to this design sce-

demonstrators, the EXPERT (European eXPErimental Re-entry Test-bed) program and the Intermediate eXperimental Vehicle (IXV), which performed an atmospheric lifting reentry from orbital speed [1]. Besides, an unmanned lifting body developed by Boeing X-37B has been put in orbit by an Atlas-5 rocket and

performed a successful lifting-guided reentry. Furthermore, a growing demand for space tourism has emerged also in recent years [2]; therefore, a great deal of research effort has been put to design RLV as blended wing bodies also allowing a conventional and more comfortable landing on runways. The main requirements currently considered for RLV design are (i) to perform very low-g (nearly 1.5 g) reentry; (ii) to adopt a lightweight (passive), fully reusable thermal protection system (TPS) to withstand several flights without any replacement; and

(iii) to provide vehicle autonomy to land at a predefined location for crew rescue

nario have been carried on. The European Space Agency developed two

Reusable Launch Vehicle

hypersonic flow, thermal protection system

Protection System Modeling of


Percentage of Hydrogen Peroxide

#### **Figure 2.**

*Fluctuations in H2O2 Concentration. Adapted from Hultman et al. [33] the concentration of hydrogen peroxide changes throughout different states of matter. When vapor condenses onto a surface the peroxide is more likely to enter the liquid state than the water vapor. This results in surface concentrations significantly higher than the original solution concentration. Concentrations exceeding 45% H2O2 are higher than the recommended maximum concentration for suitable interaction with other materials. In this manner a 35% solution that has been vaporized and condensed out on surfaces can reach concentrations of 77.8% H2O2 [33].*


**5. Functional properties of anthocyanins**

The stability of anthocyanins in processed products has been studied, demonstrating that some acid anthocyanins are stable after extraction. These compounds have antioxidant properties and play an important role in reducing the risk of developing several human degenerative diseases [27].

The interest in anthocyanin pigments is not only due to a potential replacement of artificial food colorings, but is also due to their pharmacological and therapeutic properties. **Table 2** shows different investigations on the biological properties of anthocyanins from several substrates.

#### **Table 2.**

*Functional properties attributed to anthocyanins.*


**3. The most common natural hazards in the world**

In the twenty-first century, reporting natural hazards and their types has become more advanced and comprehensive on a global scale (**Figure 1**) [5, 6]. **Figure 2** and **Table 1** provide statistical analysis of natural hazards. The data from the top ten countries indicate that 6358 significant natural hazards (excluding biological and extraterrestrial disasters) occurred between 1900 and 2022.

Of all hazards, 2410 were caused by storms, representing the highest frequency at 38% of the total. 1840 were caused by floods, accounting for 29%. 894 were caused by earthquakes, accounting for 14%. 410 were caused by landslides, accounting for 7%. 270 were caused by wildfires, accounting for 4%. 255 were caused by extreme temperatures, accounting for 4%. 192 were caused by volcanic activities, accounting for 3%. And 87 were caused by drought, accounting for 1% (**Table 1**, **Figure 2a**).


**Preface**

Differential equations naturally arise when modeling a large number of phenomena in optics, radiophysics, biology, medicine, economics, and sociology.

It is well known that, for the adequate mathematical modeling of the dynamics of many processes in various areas of science, it is crucial to take into account the influence of lags. That is why delay differential equations play an important role in mathematical modeling. For example, they are able to model gene networks, information transmission systems, population size, and infectious diseases.

Qualitative properties of solutions to equations with delay are also of great interest.

The present book contains the 11 articles accepted for publication out of the 31 manuscripts submitted to the Special Issue "Advances in Delay Differential Equations" of the MDPI journal *Mathematics*.

The 11 articles cover a wide range of topics connected to the theory of differential equations with delay. These topics include, among others, the construction of solutions and analytical and numerical methods for; dynamical properties of; and applications of DDE to the mathematical modeling of various phenomena and processes in physics, biology, ecology, and medicine.

It is hoped that the book will be interesting and useful for those working in the area of differential equations with delays and nonlinear dynamics, as well as for those with the proper mathematical background who are willing to become familiar with recent advances in mathematical modelling.

As the Guest Editor of the Special Issue, I am grateful to the authors of the papers for their quality contributions, to the reviewers for their valuable comments towards the improvement of the submitted manuscripts, and to the administrative staff of MDPI for the support needed to complete this project. Special thanks are due to the Managing Editor of the Special Issue, Dr. Syna Mu, for excellent collaboration and valuable assistance.

> **Alexandra Kashchenko** *Editor*