**Michal Sedlaˇcík 1,2**

Received: 7 January 2021; Accepted: 10 January 2021; Published: 12 January 2021

Elastomer materials are characteristic for their high elongation and (entropy) elasticity, which makes them indispensable for widespread applications in various engineering areas, medical applications or consumer goods. Their application-oriented development has to go hand in hand with material resources, economic aspects as well as environmental issues. Not only are elastomer matrix properties of high importance when optimizing the utility properties of the product; the fillers, plasticizers and other compounds are other property-determining factors that need to be considered, as these can positively a ffect the stimuli-responsive character, novel functionality, biological application, or fracture behavior, among other things, for gaining advances in elastomers [1–4].

This Special Issue, which consists of seven articles written by research experts in their field of interest, reports on the most recent research on rubber mixtures composition with the emphasis on the final utility properties of the product. Several novel and entrancing methods related to the friction and abrasion, waste management, bio-based composition, as well as two comprehensive reviews on the field-responsive elastomer materials, are introduced.

The environmental issue aspects in terms of hazardous waste management and bio-based resources are the subjects of the first two publications [5,6]. Prochon et al. used bu ffing dust collagen (BDC) originating from a waste product of the chromium tanning process in the leather industry as a modern filler in styrene butadiene rubber (SBR) [5]. The e ffect of this biodegradable filler on the physicochemical properties, biodegradation and thermo-oxidative aging of the SBR vulcanizates was investigated. The rod-like shape together with the scleroprotein additives presented on the surface of such a nanofiller led not only to more favorable dispersion within the elastomer, but also increased the cross-link density of the SBR vulcanizates, resulting in enhanced mechanical strength. Another advantage of BDC came from its antioxidant properties stabilizing (through the incorporation of chromium ions) the whole vulcanizate against thermo-oxidative aging, and its intense black color enabling it to be used also as a coloring additive. Finally, the release of compact chromium presented in the BDC filler from the vulcanizate is reduced by the formation of stable interfacial bonds between BDC and SBR.

Continuous material development is essentially important not only in the rubber industry. Rahman et al. proved the advantageous e ffect of bio-based plasticizers not only from the material resources viewpoint, but also as a processing aid positively a ffecting the complete process chain [6]. They investigated the suitability of two bio-based plasticizers, namely epoxidized esters of glycerol formal from soybean and canola oil, as sustainable alternatives with lower health risks compared to conventional plasticizers. Acrylonitrile-butadiene rubber with di fferent ratios of monomers was used to observe the compatibility between the NBR and plasticizers for systems with di fferent polarities. The positive e ffect of the bio-based plasticizers used in this study on the complete process chain was found in the NBR cure-accelerating e ffect, and the mechanical and thermal properties, which all were better in comparison with the conventional plasticizers-based systems investigated simultaneously.

Pöschl and co-workers followed the trend of eliminating the undesirable mechanical vibrations by vibro-insulating materials [7]. They investigated the ability to damp the mechanical vibration of SBR vulcanizates filled with four types of carbon black. The vibro-insulation tests comprised the forced oscillation method based on the transfer damping function. It was observed that the first resonant frequency decreased with an increase in the carbon black particle size as a higher transformation of input mechanical energy into heat under dynamic loading occurred. Durability experiments on the basis of harmonic loading revealed a shift of the first resonance frequency peak to lower excitation frequencies. The damping of mechanical vibrations had also been correlated with the excitation frequency of the vibration, the sample's thickness and inertial mass.

Rubber-like materials are frequently working under such conditions as rubbing, abrading, chunking, and tearing, which lead easily to mechanical failure. Vaikuntam et al. contributed with the friction, abrasion, and crack growth behavior of tire tread compounds composed of solution SBR filled with in-situ generated alkoxide silica or commercial precipitated silica [8]. It was demonstrated that a masterbatch containing in-situ silica could be used, with benefits for the industrial production of car tires or technical rubber articles in general, as its vulcanizates possessed a lower friction coe fficient in comparison with classical precipitated silica-filled systems, which is promising for the low rolling resistance necessary, for example, for better fuel e fficiency. Furthermore, if the samples having similar crosslink densities are compared, a much better resistance to crack growth was again observed for in-situ silica-based system.

For their characteristic properties, elastomer materials are used also in various advanced applications. Smart external field-responsive systems such as these can reversibly change their properties under an external stimulus, represented by an electric or magnetic field, pH, and light, among other things [9]. Aziz and co-workers led the world not only in the characterization of magnetorheological elastomers (MREs) reacting with changes in the systems' sti ffness under the application of an external magnetic field, as is typical for such systems, but also included nanosized Ni–Mg cobalt ferrite particles into these MREs based on conventional carbonyl iron magnetic particles to make them suitable for use as actuators or flexible sensors [10]. Although the demanded electrical properties could be obtained with carbon-based particles, such as graphite or graphene, the necessary high concentration of the filler would negatively increase the sti ffness of the system, thus the presented study could solve this problem. The developed MRE alters the magnetic, rheological and electrical resistance behavior appropriately, even at small concentrations (1.0 wt. %) of Ni–Mg nanoparticles.

The development of MREs is described in this Special Issue in two review papers complementing each other [11,12]. A more general review is given by Kang et al., in which the authors concentrate not only on the material basis used in MREs and covering a broad range of polymeric elastomeric materials, including, e.g., waste tire rubber as well, but also on the particles' distribution within the elastomeric matrix and its e ffect on the MR performance described in various experimental techniques [11]. Finally, in their review Jamari et al. concentrated on magnetic particles' coating as an important task necessary in order to obtain a system with improved sedimentation and oxidation stability, and appropriate tribology properties [12]. The chemical methods for particle coating, such as atom transfer radical polymerization, chemical oxidative polymerization or dispersion polymerization, are thoroughly described together with the e ffect of the chemical nature of the coating on the MR performance.

**Funding:** This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic—project DKRVO (RP/CPS/2020/006).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** First of all, I would like to express my deep gratitude to *Materials*, especially to its Editorial office, particularly to Andy Zhan, for continuous guide, care, and help during all steps of the preparation and production of this Special Issue entitled "Advances in Elastomers".

**Conflicts of Interest:** The author declare no conflict of interest.


3.4.2. Promote and Disseminate Applied Research on Responsible Internet Use and Prevention

The second policy option mainly addresses support organizations, professionals, and practitioners. Applied research is present in almost all reviewed studies, as research seeks to find solutions to the problems in European community and clinical settings. Only a couple of studies described models of GIA [25] and Internet gaming addiction [24] to provide an understanding about which factors contribute to the problems, their phenomenology, and therapy components to clinically address them. Moreover, providing information and interventions seem to be the key public health strategies to prevent and address the problem in all settings. Early preventive actions can:

There is a need to improve this research field to diversify the methodologies used and translate them to the professional sector, and to promote joint clinical and educational research. It is also crucial for standardized measures to assess problems and compare them in order to support diagnosis and treatment success (e.g., cross-culturally and trans-diagnostically). These preventive actions can provide support for decision-makers to better understand the problems from a European public health perspective, and to promote responsible Internet use and media literacy.


**4. A multifractal theoretical approach for understanding the separation of particle flow during pulsed laser deposition of multicomponent alloys**

The details of the model have been previously reported in [14]. Let us consider that the evolution of the plasma components (plasma entities) is defined by continuous but non-differential curves, in specific rage of values. This premits us to corelate the properties of plasma plume in a multifractal matrix and thus reducing the dynamics of the individual entities by integrating them with their respective multifractal trajectories (geodesics). Therefore, at extreme times scales with respect to the inverse of the maxim Lyapunov exponent [23], the classical trajectories (deterministic) are replaced by fractal geodesics (families of potential trajectories and the notion of defined spatial coordinates is replaced by that of probability densities.

In such a context, in agreement with the results from [21, 22] at a differentiable resolution scale the ablation plasma dynamics are driven by the specific fractal force:

$$\boldsymbol{F}\_{F}^{i} = \left[ \boldsymbol{u}\_{F}^{l} + \frac{\mathbf{1}}{\mathbf{4}} (d\boldsymbol{t})^{(2/D\_{F})-1} \boldsymbol{D}^{kl} \partial\_{\mathbf{k}} \right] \partial\_{\mathbf{l}} \boldsymbol{u}\_{F}^{i} \tag{8}$$

The introduction of this multifractal force in explicit manner is essential at and is responsible for the structuring of ablation plasma on each component, though a special velocity field. The functionality of our differential system of equations is given by:

$$F\_F^i = \left[ u\_F^l + \frac{1}{4} (dt)^{(2/D\_F)-1} D^{kl} \partial\_k \right] \partial\_l u\_F^i = 0 \tag{9}$$

$$
\partial\_l \boldsymbol{u}\_F^l = \mathbf{0} \tag{10}
$$

(9) represents that at a differential scale resolution the multifractal force becomes null, while (10) represents the state density conservation law at nondifferentiable scale resolution.

Generally speaking it is rather difficult to obtain an analytic solution for the system of equations considered here, taking into account its multifractal nature (through *ul F∂lui F* the multifractal convection and *Dkl∂l∂kui F* the multifractal type dissipation); also the fractalization type, introduced through multifractal type tensor *Dkl*, is left unknown purposefully in this particular representation of the model.

The continuous development of our multifractal model and its implementation for the simulation of *real* plasma like phenomena implies the definition of a threedimensional plasma like-fluid flow of a with a revolution symmetry around the *z* axis, and investigate its dynamics through a 2-dimensional projection of the plasma in the (x*,y*) plane.

Considering the symmetry plane (*x,y*), the (9) and (10) system becomes:

$$
\mu\_{F\_x} \frac{\partial \mathfrak{u}\_{F\_x}}{\partial \mathfrak{x}} + \mathfrak{u}\_{Fx} \frac{\partial \mathfrak{u}\_{F\_x}}{\partial \mathfrak{y}} = \frac{1}{4} (dt)^{(2/D\_F)-1} \, \mathcal{D}^{\mathcal{V}} \frac{\partial^2 \mathfrak{u}\_{F\_x}}{\partial \mathfrak{y}^2} \tag{11}
$$

*Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys DOI: http://dx.doi.org/10.5772/intechopen.94748*

$$\frac{\partial u\_{F\_x}}{\partial \mathbf{x}} + \frac{\partial u\_{F\_y}}{\partial \mathbf{y}} = \mathbf{0} \tag{12}$$

Let us solve the equation system (11) and (12) by imposing the following conditions

$$\lim\_{y \to 0} u\_{F\_y}(\mathbf{x}, y) = \mathbf{0}, \lim\_{y \to 0} \frac{\partial u\_{F\_x}}{\partial y} = \mathbf{0}, \lim\_{y \to \infty} u\_{F\_x}(\mathbf{x}, y) = \mathbf{0} \tag{13}$$

$$\Theta = \rho \int\_{-\infty}^{+\infty} u\_x \,^2 dy = \text{const.}$$

with:

strongly heterogenous and it aides particles with an elevated fractalization degree leading to a non-congruent transfer in case of PLD and the lighter elements are predominantly in the outer regions of the plume, while the heavier ones are mainly

**4. A multifractal theoretical approach for understanding the separation of particle flow during pulsed laser deposition of multicomponent**

The details of the model have been previously reported in [14]. Let us consider

continuous but non-differential curves, in specific rage of values. This premits us to corelate the properties of plasma plume in a multifractal matrix and thus reducing the

that the evolution of the plasma components (plasma entities) is defined by

dynamics of the individual entities by integrating them with their respective multifractal trajectories (geodesics). Therefore, at extreme times scales with respect to the inverse of the maxim Lyapunov exponent [23], the classical trajectories (deterministic) are replaced by fractal geodesics (families of potential trajectories and the notion of defined spatial coordinates is replaced by that of probability densities. In such a context, in agreement with the results from [21, 22] at a differentiable

resolution scale the ablation plasma dynamics are driven by the specific fractal

4 ð Þ *dt* ð Þ� 2*=DF* 1

The introduction of this multifractal force in explicit manner is essential at and is responsible for the structuring of ablation plasma on each component, though a special velocity field. The functionality of our differential system of equations is

4 ð Þ *dt* ð Þ� 2*=DF* 1

*∂lul*

(9) represents that at a differential scale resolution the multifractal force becomes null, while (10) represents the state density conservation law at non-

Generally speaking it is rather difficult to obtain an analytic solution for the system of equations considered here, taking into account its multifractal nature

dissipation); also the fractalization type, introduced through multifractal type tensor *Dkl*, is left unknown purposefully in this particular representation of the model.

Considering the symmetry plane (*x,y*), the (9) and (10) system becomes:

*∂uFx ∂y* ¼ 1

The continuous development of our multifractal model and its implementation for the simulation of *real* plasma like phenomena implies the definition of a threedimensional plasma like-fluid flow of a with a revolution symmetry around the *z* axis, and investigate its dynamics through a 2-dimensional projection of the plasma

4 ð Þ *dt* ð Þ� 2*=DF* 1 D*yy ∂*2

*F* the multifractal convection and *Dkl∂l∂kui*

*Dkl∂k*

*Dkl∂k*

*∂lui*

*F* ¼ 0 (10)

*uFx*

*∂y*2 (11)

*∂lui*

*F* (8)

*F* ¼ 0 (9)

*F* the multifractal type

*F* þ 1

*F* þ 1

*Fi F* ¼ *ul*

*Fi F* ¼ *ul*

*uFx ∂uFx ∂x*

þ *uFx*

differentiable scale resolution.

*F∂lui*

part of the core.

*Practical Applications of Laser Ablation*

**alloys**

force:

given by:

(through *ul*

in the (x*,y*) plane.

**128**

$$D^{\mathcal{Y}} = \mathfrak{a} \exp\left(i\theta\right) \tag{14}$$

Let us highlight that existence of a complex phase can be the pathway to a hidden temporal evolution of the system. The variation of a complex phase defines a time-dependence in an implicit manner. This means that for multifractal system can describe both spatial and temporal evolutions. Thus, the choice for Dyy gives the possibility of a both spatial and temporal investigations on the LPP plasma dynamics.

The solution of (11) and (12), in their general form in normalized quantities can be written as:

$$X = \frac{\boldsymbol{\varkappa}}{\boldsymbol{\varkappa}\_{0}}, \mathbf{Y} = \frac{\boldsymbol{y}}{\boldsymbol{y}\_{0}}, \mathbf{U} = \boldsymbol{u}\_{F\_{x}} \frac{4\boldsymbol{y}\_{0}^{2}}{\boldsymbol{\varkappa}\_{0}d}, \boldsymbol{V} = \boldsymbol{u}\_{F\_{y}} \frac{4\boldsymbol{y}\_{0}^{2}}{\boldsymbol{\varkappa}\_{0}d}, \frac{\left(\frac{\boldsymbol{\Phi}\_{0}}{\boldsymbol{\Phi}\boldsymbol{\rho}}\right)^{1/3}}{\left(\boldsymbol{\varkappa}\_{4}\right)^{2/3}} = \frac{\boldsymbol{\varkappa}\_{0}^{2/3}}{\boldsymbol{\varkappa}\_{0}}, \boldsymbol{\mu} = \left(\mathbf{d}\mathbf{t}\right)^{\left(D\_{\mathbb{E}\_{2}}\right)-1} \tag{15}$$

is given according to the method from [21, 22]:

$$U(\mathbf{X}, Y) = \frac{3\slash\_2}{[\mu \mathbf{X}]^{\natural\_3} \exp\left(\frac{i\theta}{3}\right)} \cdot \text{sech}^2\left\{\frac{\omega \llcorner\_2 Y}{[\mu \mathbf{X}]^{\natural\_3} \exp\left(\frac{2i\theta}{3}\right)}\right\} \tag{16}$$

$$V(X,Y) = \frac{{\langle \gamma'\_{\gamma} \rangle}^{2\gamma\_{\beta}}}{[\mu X]^{\dot{\gamma}\_{\dot{\gamma}}} \exp\left(\frac{i\theta}{3}\right)} \left\{ \left[\frac{Y}{\mu X^{\dot{\gamma}\_{\dot{\gamma}}} \exp\left(\frac{2i\theta}{3}\right)}\right] \cdot \text{sech}\, h^2 \left[\frac{\nu\_{\dot{\gamma}} Y}{[\mu X]^{\dot{\gamma}\_{\dot{\gamma}}} \exp\left(\frac{2i\theta}{3}\right)}\right] - \tanh\left[\frac{\nu\_{\dot{\gamma}} Y}{[\mu X]^{\dot{\gamma}\_{\dot{\gamma}}} \exp\left(\frac{2i\theta}{3}\right)}\right] \right\} \tag{17}$$

To verify the validity of such unusual approach we obtained 3D (**Figure 5**) representations of the transient plasma flow developed based on the solution given by our multifractal system of equations. The transient plasma is *generated* in the framework of our multifractal model as a mixture of various particles with different physical properties (electron, ions, atoms, nanopatricles). This implies that the some multifractal parameters such as the complex phase, fractal dimension or specific length (*x0, y0*) will include within their values the properties of each individual component. In **Figure 5** we represented the angular separation of the plasma low for different values of the complex phase leading to the appearance of preferential *expansion directions for various elements of the plasma* for *Θ > 1.5*.

In **Figure 6** we have represented the 2D distribution portraying various plasma flow scenarios with respect to the structure of the laser ablation plasma, starting form a pure, single ionized plasma (only atoms, ions and electrons) towards a multi-component flow (including nanoparticles, molecules or clusters). There is a separation into multiple structures in the two expansion directions (across *X* and *Y*).

**Figure 5.**

*3D representation of the total fractal velocity field of a multi-fractal plasma flow for various complex phases (0.5 – (a) 1 – (b) 1.5 – (c)).*

different flow velocities as the distance between the maxima of the three structures does not remain constant during expansion. Supplementary investigations were performed by implementing similar data treatment for the Y direction. For the cross section on the Y axis (at X = 0) we can report a more fuzzy separation. This result can be explained as the structuring phenomena of the plasma is not limited to a unique flow axis, being observed in all directions. Moreover, the fractality of the our multifractal system, defined here through ξ and *μ*, is directly related to the trajectory of the plasma *particles*. As such, for a more complex plasma model (multielement, multi-structured) the intrinsic dynamic within the plasma structures will

*Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys*

This rather complex multifractal theoretical approach manages to simulate the structuring of a multielement (complex) plasma flow. Nevertheless, this is remains an abstracted view to a real dynamics in various technological application. For the validation of the conceptual and mathematical approach we chose to perfume comparisons with our experimental investigations of laser produced plasmas in quasi-identical conditions to those generally used for pulse laser deposition. Our model is suitable for the description of PLD physical phenomena as in past years various groups have shown [26–29] that in the case of multi-element plasmas there is axial and lateral segregation of the plasma particles during expansion based on their physical properties (mass, melting temperature), which damages the quality

The dynamics of a complex multi element plasma was investigated in the framework on a non-differential, multifractal theoretical model. Structuring into multiple plasma fragments were observed for the multi-fractal fluid like system containing structural units with various physical properties. The formation of complex plasma structures during expansion is corelated to the interaction between the transient plasma structural units and it is defined here by the complex phase of the velocity field and the fractalization of the particle geodesics. The multifractal system of equations was simplified by analyzing only two main directions. The plasma

The multifractal theoretical model was compared with empirical investigations of transient plasmas generated by laser ablation of a multielement metallic targets. The expansion of the plasma plume was monitored by means of ICCD fast camera photography and optical emission spectroscopy. The ICCD fast camera imaging showcased the formation of two or three main plasma structures in the main expansion direction, coupled with a similar phenomenon in the transversal

splits in multiple structures symmetrically to the main expansion axis.

induce to a separation on the main expansion axis (at X = 0).

*Transversal cross section for ξ = 0.3 (a), ξ = 1 (b) and ξ = 5 (c).*

*DOI: http://dx.doi.org/10.5772/intechopen.94748*

and properties of the deposited film.

**5. Conclusion**

**131**

**Figure 7.**

**Figure 6.**

*Total fractal velocity field evolution on the two main directions (X,Y) for a multi fractal system with ξ values of 0.1 (a), 0.4 (b), 0.7 (c).*

For small values of the fractalization degree, which from here on further will be considered as *control* parameter, we define a plasma flow containing only one type of particles thus on plasma component. In **Figure 6(a)**, there can be seen only one plasma structure along the main expansion axis. The increase of this fractalization degree, control parameter, subsequently leads to changes in the homogeneity of the structural units of the plasma (i.e. our model of plasma becomes more heterogeneous in term of plasma particle mass and energy). It is also noticeable the formation of two symmetrically positioned secondary structures (lateral with respect to the main expansion axis). We conclude that those volume of plasma contain mainly components defined by a small physical volume and low kinetic energy. A subsequent increase in the fractalization degree and thus of the heterogeneity of the plasma leads to the formation of lateral-symmetrically situated plasma *structures* each defining different families of particles with physical properties.

An important conclusion extracted from our simulation is that the plasma structuring process is gradual one. For values of ξ = 0.3 1, we can obtain three main lateral structures which are also followed by a continuous internal structuring visible for fractalization degrees ξ > 1. Within the framework of our multifractal model this is reversible transition as the distribution often returns to the threestructure system. Another approach of understating this novel phenomenon is to assimilated then with *breathing modes of the fractal system* (oscillatory behavior). The evolution of our plasma model in a multifractal framework attempts a complete transition towards a completely separate flow but the interactions of the multifractal forces between the individual plasma structures are then in charge for the unification of the plasma structures.

The multi-structuring of the laser produced plasma was highlighted by executing cross sections in X direction (see **Figure 7**). In X direction the separation is more obvious first moments of expansion. Each of the new plasma structure is defined by *Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys DOI: http://dx.doi.org/10.5772/intechopen.94748*

**Figure 7.** *Transversal cross section for ξ = 0.3 (a), ξ = 1 (b) and ξ = 5 (c).*

different flow velocities as the distance between the maxima of the three structures does not remain constant during expansion. Supplementary investigations were performed by implementing similar data treatment for the Y direction. For the cross section on the Y axis (at X = 0) we can report a more fuzzy separation. This result can be explained as the structuring phenomena of the plasma is not limited to a unique flow axis, being observed in all directions. Moreover, the fractality of the our multifractal system, defined here through ξ and *μ*, is directly related to the trajectory of the plasma *particles*. As such, for a more complex plasma model (multielement, multi-structured) the intrinsic dynamic within the plasma structures will induce to a separation on the main expansion axis (at X = 0).

This rather complex multifractal theoretical approach manages to simulate the structuring of a multielement (complex) plasma flow. Nevertheless, this is remains an abstracted view to a real dynamics in various technological application. For the validation of the conceptual and mathematical approach we chose to perfume comparisons with our experimental investigations of laser produced plasmas in quasi-identical conditions to those generally used for pulse laser deposition. Our model is suitable for the description of PLD physical phenomena as in past years various groups have shown [26–29] that in the case of multi-element plasmas there is axial and lateral segregation of the plasma particles during expansion based on their physical properties (mass, melting temperature), which damages the quality and properties of the deposited film.

## **5. Conclusion**

For small values of the fractalization degree, which from here on further will be considered as *control* parameter, we define a plasma flow containing only one type of particles thus on plasma component. In **Figure 6(a)**, there can be seen only one plasma structure along the main expansion axis. The increase of this fractalization degree, control parameter, subsequently leads to changes in the homogeneity of the structural units of the plasma (i.e. our model of plasma becomes more heterogeneous in term of plasma particle mass and energy). It is also noticeable the formation of two symmetrically positioned secondary structures (lateral with respect to the main expansion axis). We conclude that those volume of plasma contain mainly components defined by a small physical volume and low kinetic energy. A subsequent increase in the fractalization degree and thus of the heterogeneity of the plasma leads to the formation of lateral-symmetrically situated plasma *structures*

*Total fractal velocity field evolution on the two main directions (X,Y) for a multi fractal system with ξ values of*

*3D representation of the total fractal velocity field of a multi-fractal plasma flow for various complex phases*

each defining different families of particles with physical properties.

transition towards a completely separate flow but the interactions of the

the unification of the plasma structures.

**Figure 5.**

**Figure 6.**

**130**

*0.1 (a), 0.4 (b), 0.7 (c).*

*(0.5 – (a) 1 – (b) 1.5 – (c)).*

*Practical Applications of Laser Ablation*

multifractal forces between the individual plasma structures are then in charge for

The multi-structuring of the laser produced plasma was highlighted by executing cross sections in X direction (see **Figure 7**). In X direction the separation is more obvious first moments of expansion. Each of the new plasma structure is defined by

An important conclusion extracted from our simulation is that the plasma structuring process is gradual one. For values of ξ = 0.3 1, we can obtain three main lateral structures which are also followed by a continuous internal structuring visible for fractalization degrees ξ > 1. Within the framework of our multifractal model this is reversible transition as the distribution often returns to the threestructure system. Another approach of understating this novel phenomenon is to assimilated then with *breathing modes of the fractal system* (oscillatory behavior). The evolution of our plasma model in a multifractal framework attempts a complete

The dynamics of a complex multi element plasma was investigated in the framework on a non-differential, multifractal theoretical model. Structuring into multiple plasma fragments were observed for the multi-fractal fluid like system containing structural units with various physical properties. The formation of complex plasma structures during expansion is corelated to the interaction between the transient plasma structural units and it is defined here by the complex phase of the velocity field and the fractalization of the particle geodesics. The multifractal system of equations was simplified by analyzing only two main directions. The plasma splits in multiple structures symmetrically to the main expansion axis.

The multifractal theoretical model was compared with empirical investigations of transient plasmas generated by laser ablation of a multielement metallic targets. The expansion of the plasma plume was monitored by means of ICCD fast camera photography and optical emission spectroscopy. The ICCD fast camera imaging showcased the formation of two or three main plasma structures in the main expansion direction, coupled with a similar phenomenon in the transversal


*4.4. Assessment of local Nusselt Number*

In Table 1, one can see that a good agreement is found between the present results and previous literature. A very good agreement is found in RK-45 results; however, the results of HAM are a little different but the variation trend is similar in all the cases. Table 2 presents the significance of physical parameters through local Nusselt number *Nu* for axisymmetric Marangoni convective flow of Casson liquid over an infinite disk with the impact of an inclined MHD. Near the wall or boundary, Nusselt number has a dominant role, for the computation of thermal profile variations. The numerical quantities of Nusselt number is supportive to convey the cumulative tendency of temperature gradient in flow domain. It is observed in the table that rises in the Marangoni convective fluid parameter, *Ma*, Marangoni ratio, *Ra*, and *N*2 monotonically decrease the Nusselt number *Nu* by keeping other fluid parameters fixed. On the other hand, the parameters *N*1, Pr, *B*1 and *Le* manifest rises in heat flux behavior *Nu*. The small increase on average Nusselt number indicates that greater heat exchange rate occurs near boundary of the disk due to these parameters.

**Table 1.** Comparison table of current results with previously published literature setting the additional parameters equals to zero.

**Table 2.** Numeric values of local Nusselt parameter *Nu* for distinct values of sundry parameter where *β*1 = 1.5, *M*1 = 1.0, *Ec* = 0.8 and *α*1 = *π*/5.


**3. Optical vortices in turbulent atmosphere and the problem of adaptive correction**

In early investigations [12] it was shown that the presence of optical vortices is a distinctive property of the so called speckled fields, which form when the laser beam propagates in the scattering media. Experimental evidence of the existence of screw dislocations in the laser beam, passed through a random phase plate, were obtained in [55, 56, 57] where topological limitations were also noted of adaptive control of the laser beams propagating in inhomoge‐ neous media.

Turbulent atmosphere can be represented as the consequence of random phase screens. Un‐ der propagation in the turbulent atmosphere the regular optical field acquires rising aberra‐ tions. These aberrations manifest themselves in the broadening and random wandering of laser beams; the intensity distribution becomes non-regular and the wavefront deviates from initially set surface. These deformations of the wavefront can be corrected using adap‐ tive optics. To this end, effective sensors and correctors of wavefront were designed [1-6]. The problem becomes more complicated when the laser beam passes a relatively long dis‐ tance in a weak turbulent medium or if the turbulence becomes too strong. In this case opti‐ cal vortices develop in the beam; the shape of the wavefront changes qualitatively and singularities appear.

The influence of the scintillation effects are determined (see, for example, [2, 4]) by the close‐ ness to unity of the Rytov variance

$$\left\| \sigma\_{\chi}^{2} \approx 0.56k \stackrel{7/6}{\int\_{0}^{L} \mathbf{C}\_{n}^{2}(\mathbf{z}) \mathbf{z}^{5/6} \text{( $\mathbf{z} / L$ )}^{5/6} d\mathbf{z} \right\| \tag{6}$$

where *Cn* 2 (*z*) describes the dependence of structure constant of the refractive index fluctua‐ tions over the propagation path and *L* is the path length. The regime of strong scintillations is not realized when *σχ* 2 <<1.

Figure 4 demonstrates the results of numerical simulation of propagation of a Gaussian laser beam (*λ*=1 µ) in turbulent atmosphere in a model case of invariable structure constant *Cn* 2 =10-14 cm-2/3 for the distance of 1 km when the regime of strong scintillations is realized ac‐ cording to (6). The steady-state equation for the slowly-varying complex field amplitude *A* differs from the equation (2) by the presence of the inhomogeneous term:

$$\frac{\partial A}{\partial z} - \frac{i}{2k} \frac{\partial^2 A}{\partial r^2} + \frac{ik}{2} (\tilde{\varepsilon} - 1) A = 0,\tag{7}$$

where *ε*˜ is the fluctuating dielectric permittivity of the turbulent atmosphere. In numerical simulations we use the finite-difference algorithm of numerical solving of parabolic equa‐ tion (7) described in [58]. It is characterized by an accuracy, which considerably exceeds the accuracy of the widespread spectral methods [59]. The amplitude error of an elementary harmonic solution of the homogeneous equation is equal to zero, whereas the phase error is significantly reduced and proportional to the transverse integration step to the power of six. To take into account the inhomogeneous term of the equation, the splitting by physical proc‐ esses is employed. The effect of randomly inhomogeneous distribution of dielectric permit‐ tivity is allowed for using a model of random phase screens, which is commonly used in calculations of radiation propagation in optically inhomogeneous stochastic media [60]. The spatial spectrum of dielectric permittivity fluctuations is described taking into account the Tatarsky and von Karman modifications of the Kolmogorov model [61].

cordance with the law of topologic charge conservation. The predicted effects have been

**3. Optical vortices in turbulent atmosphere and the problem of adaptive**

In early investigations [12] it was shown that the presence of optical vortices is a distinctive property of the so called speckled fields, which form when the laser beam propagates in the scattering media. Experimental evidence of the existence of screw dislocations in the laser beam, passed through a random phase plate, were obtained in [55, 56, 57] where topological limitations were also noted of adaptive control of the laser beams propagating in inhomoge‐

Turbulent atmosphere can be represented as the consequence of random phase screens. Un‐ der propagation in the turbulent atmosphere the regular optical field acquires rising aberra‐ tions. These aberrations manifest themselves in the broadening and random wandering of laser beams; the intensity distribution becomes non-regular and the wavefront deviates from initially set surface. These deformations of the wavefront can be corrected using adap‐ tive optics. To this end, effective sensors and correctors of wavefront were designed [1-6]. The problem becomes more complicated when the laser beam passes a relatively long dis‐ tance in a weak turbulent medium or if the turbulence becomes too strong. In this case opti‐ cal vortices develop in the beam; the shape of the wavefront changes qualitatively and

The influence of the scintillation effects are determined (see, for example, [2, 4]) by the close‐

tions over the propagation path and *L* is the path length. The regime of strong scintillations

Figure 4 demonstrates the results of numerical simulation of propagation of a Gaussian laser beam (*λ*=1 µ) in turbulent atmosphere in a model case of invariable structure constant *Cn*

=10-14 cm-2/3 for the distance of 1 km when the regime of strong scintillations is realized ac‐ cording to (6). The steady-state equation for the slowly-varying complex field amplitude *A*

(*z* / *L* ) 5/6

(*z*) describes the dependence of structure constant of the refractive index fluctua‐

*dz*, (6)

2

completely confirmed experimentally [52, 53, 54].

**correction**

154 Adaptive Optics Progress

neous media.

singularities appear.

where *Cn*

2

is not realized when *σχ*

ness to unity of the Rytov variance

*σχ*

2 <<1.

2 ≈0.56*k* 7/6

*∫* 0

differs from the equation (2) by the presence of the inhomogeneous term:

*L Cn* 2 (*z*)*z* 5/6 The fragment of speckled distribution of optical field intensity after the propagation is shown in Figure 4. Dark spots are seen where the intensity vanishes. As it has been noted before, the presence of optical vortices in the beam is easily detected, based on the picture of its interference with an obliquely incident plane wave. The correspondent picture is shown in Figure 4 as well. In the centers of screw dislocations the fringe branching is observed, i.e. the birth or disappearance of the fringes takes place with formation of typical "forks" in the interferogram (compare with Figure 2). There are also zones of edge dislocations (compare with Figure 3). The number, allocation and helicity of the vortices in the beam are random in nature but the vortices are born as well as annihilated in pairs. If the initial beam is regular (vortex-free), then the total topological charge of the vortices in the beam will be equal to zero in each transverse section of the beam along the propagation path in accordance with the conservation law of topological charge (or orbital angular moment) [7-9].

**Figure 4.** Optical vortices in the laser beam after atmospheric propagation: the speckled intensity distribution and the picture of interference of the beam with the obliquely incident plane wave including "forks" denoted by light circles.

One of the first papers dealing with the appearance of optical vortices in laser beams propa‐ gating in randomly inhomogeneous medium was published by Fried and Vaughn in 1992 [62]. They pointed out that the presence of dislocations makes registration of the wavefront more difficult and they considered methods for solving the problem. In 1995 the authors of Ref. [63] encountered this problem in experimental investigations of laser beam propagation in the atmosphere. It was shown that the existence of light vortices is an obstacle for atmos‐ pheric adaptive optical systems. After that it was theoretically shown that screw dislocations give rise to errors in the procedure of wavefront registration by the Shack-Hartmann sensor [64, 65]. Due to zero amplitude of the signal in singular points, the information carried by the beam becomes less reliable and the compensation for turbulent aberrations is less effec‐ tive [66]. Along with [63], the experimental investigation [67] can be taken here as an exam‐ ple where the results of adaptive correction are presented for distortions of beams propagating in the atmosphere.

The problem of a wavefront corrector (adaptive mirror) suitable for controlling a singular phase surface is also topical. In the adaptive optical systems [77, 78] the wavefront correctors were based on the micro-electromechanical system (MEMS) spatial light modulators with the large number of actuators. The results of [77, 78] shown that continuous MEMS mirrors with high dynamic response bandwidth, combined with the interferometric wavefront sen‐ sor, can ensure a noticeable correction of scintillation. However, the MEMS mirrors are char‐ acterized by low laser damage resistance that can considerably limit applications. The bimorph or pusher-type piezoceramics-based flexible mirrors with the modal response func‐ tions of control elements have a much higher laser damage threshold [3-5]. Recently [88] a complicated cascaded imaging adaptive optical system with a number of bimorph piezocer‐ amic mirrors was used to mitigate turbulence effect basing, in particular, on conventional Hartmann-Shack wavefront sensor data. Conventional adaptive compensation was obtained in [88] which proved to be very poor at deep turbulence. The scintillation and vortices may

Adaptive Optics and Optical Vortices http://dx.doi.org/10.5772/53328 157

In the investigations, the results of which are described in this chapter, the development of an algorithm of the Hartmann-Shack reconstruction of vortex wavefront of the laser beam plays a substantial role. The creation of efficient algorithms for the wavefront sensor of vor‐ tex beams implies the experiments under modeling conditions when the optical vortices are artificially generated by special laboratory means. Moreover, as long as the matter concerns the creation of a new algorithm of wavefront reconstruction, it is possible to estimate its ac‐ curacy only under operation with the beam, the singular phase structure of which is known in detail beforehand. The formation of optical beams with the given configuration of phase singularities and their transformations is one of main trends in the novel advanced optical

Thus, the first stage of the research sees the generation of a vortex laser beam with the given topological charge. In our case the role of this beam is played by the single optical vortex, namely, the Laguerre-Gaussian mode. Further, at the second stage, with the help of the Hartmann-Shack wavefront sensor, the task of registration of the vortex beam phase surface is solved using the new algorithm of singular wavefront reconstruction. Finally, at the third stage, the correction of the singular wavefront is undertaken in a closed-loop adaptive opti‐ cal system, including the Hartmann-Shack wavefront sensor and the wavefront corrector in

As it has been indicated above, to examine the accuracy of the wavefront reconstruction al‐ gorithm and its efficiency in the experiment itself a "reference" vortex beam has to be formed with a predetermined phase surface. This is important as, otherwise, it would be im‐ possible to make sure that the algorithm recovers the true phase surface under conditions when robust alternative methods of its reconstruction are missing or unavailable. The La‐

*m* can play the role of such "reference" optical vortices.

be one of the causes of this.

branch – singular optics [7-9].

the form of a piezoelectric-based bimorph mirror.

**4. Generation of optical vortex**

guerre-Gaussian vortex modes *LGn*

Since one of the key elements of an adaptive optical system is the wavefront sensor of laser radiation, there is a pressing need to create sensors that are capable of ensuring the required spatial resolution and maximal accuracy of the measurements. In this connection there is necessity need to develop algorithms for measurement of wavefront with screw disloca‐ tions, which are sufficiently precise, efficient and economical given the computing resour‐ ces, and resistant to measurement noises. The traditional methods of wave front measurements [1-6] in the event of the above-mentioned conditions are in fact of no help. The wavefront sensors have been not able to restore the phase under the conditions of strong scintillations [68]. The experimental determination of the location of phase discontinuities itself already generates serious difficulties [69]. In spite of the fact that the construction features of algo‐ rithms of wavefront recovery in the presence of screw dislocations were set forth in a num‐ ber of theoretical papers [68, 69, 70, 71, 72, 73, 74, 75], there were not many published experimental works in this direction. Thus, phase distribution has been investigated in different diffrac‐ tion orders for a laser beam passed through a specially synthesized hologram, designed for generating higher-order Laguerre-Gaussian modes [76]. An interferometer with high spatial resolution was used to measure transverse phase distribution and localization of phase singu‐ larities. The interferometric wavefront sensor was applied also in a high-speed adaptive optical system to compensate phase distortions under conditions of strong scintillations of the coher‐ ent radiation in the turbulent atmosphere [77] as well as when modelling the turbulent path under laboratory conditions [78]. In [77, 78] the local phase was measured, without reconstruct‐ ing the global wavefront that is much less sensitive to the presence of phase residues. The interferometric methods of phase determination are rather complicated and require that several interferograms are obtained at various phase shifts between a plane reference wave and a signal wave. It is noteworthy, however, that in the adaptive optical systems [1-6] the Hartmann-Shack wavefront sensor [79, 80] has a wider application compared with the interferometric sensors including the lateral shearing interferometers [81, 82], the curvature sensor [83, 84, 85], and the pyramidal sensor [86, 87]. The cause of this is just in a simpler and more reliable arrangement and construction of the Hartmann-Shack sensor. However, there have been practically no publications of the results of experimental investigations connected with appli‐ cations of this sensor for measurements of singular phase distributions.

The problem of a wavefront corrector (adaptive mirror) suitable for controlling a singular phase surface is also topical. In the adaptive optical systems [77, 78] the wavefront correctors were based on the micro-electromechanical system (MEMS) spatial light modulators with the large number of actuators. The results of [77, 78] shown that continuous MEMS mirrors with high dynamic response bandwidth, combined with the interferometric wavefront sen‐ sor, can ensure a noticeable correction of scintillation. However, the MEMS mirrors are char‐ acterized by low laser damage resistance that can considerably limit applications. The bimorph or pusher-type piezoceramics-based flexible mirrors with the modal response func‐ tions of control elements have a much higher laser damage threshold [3-5]. Recently [88] a complicated cascaded imaging adaptive optical system with a number of bimorph piezocer‐ amic mirrors was used to mitigate turbulence effect basing, in particular, on conventional Hartmann-Shack wavefront sensor data. Conventional adaptive compensation was obtained in [88] which proved to be very poor at deep turbulence. The scintillation and vortices may be one of the causes of this.

In the investigations, the results of which are described in this chapter, the development of an algorithm of the Hartmann-Shack reconstruction of vortex wavefront of the laser beam plays a substantial role. The creation of efficient algorithms for the wavefront sensor of vor‐ tex beams implies the experiments under modeling conditions when the optical vortices are artificially generated by special laboratory means. Moreover, as long as the matter concerns the creation of a new algorithm of wavefront reconstruction, it is possible to estimate its ac‐ curacy only under operation with the beam, the singular phase structure of which is known in detail beforehand. The formation of optical beams with the given configuration of phase singularities and their transformations is one of main trends in the novel advanced optical branch – singular optics [7-9].

Thus, the first stage of the research sees the generation of a vortex laser beam with the given topological charge. In our case the role of this beam is played by the single optical vortex, namely, the Laguerre-Gaussian mode. Further, at the second stage, with the help of the Hartmann-Shack wavefront sensor, the task of registration of the vortex beam phase surface is solved using the new algorithm of singular wavefront reconstruction. Finally, at the third stage, the correction of the singular wavefront is undertaken in a closed-loop adaptive opti‐ cal system, including the Hartmann-Shack wavefront sensor and the wavefront corrector in the form of a piezoelectric-based bimorph mirror.


**3. Proposed model**

This Section discusses the proposed model addressing all proposed model components. First will address basic concepts of the model. Section 3.1 addresses the QoC metric and Section 4 addresses the QoE metric used in this work. In our work, it is proposed that the QoE is considered a utility function determined from QoC correctness parameter.

The model proposed in this work approaches QoE based on the concepts of resource utility when an application is submitted to a distributed system. The concepts of QoE applied, and the relationship between QoE and utility, are explained in Section 4. Is important to mention that application classes have a strong relationship with the concept of utility since each class has different needs regarding which resources they use on a larger scale. In this sense, the main information that a user describes refers to the application class. The classes referring to the application features are presented as follows: serial applications; parallel applications; network-oriented applications; CPUoriented applications; I/O and storage-oriented applications.

### **3.1 QoC parameters**

### *3.1.1 Correctness*

In our work, the QoC is used to verify how much a given context is in accordance with what is being demanded by the application. As mentioned earlier in the introductory section of this chapter, the model proposed in this thesis meets different classes (or categories) of applications, each class is characterized by a different need for resources. Therefore, the parameter *correctness*, or correctness, provides a quantitative reference to determine if the current context of a particular resource is suitable to serve an application taking into account its category.

To obtain the value of QoC, an approach based on Bayesian probability theory is proposed. This approach is inspired and adapted from the solution proposed by [10]. The Bayesian probability combines information in a way that relates observed events to hypotheses. In other words, Bayes' theorem is used to calculate the probability conditional that a given event occurs given an observation. For example, calculation of the probability of overhead in allocating an amount *cpi* of processes in a given node of a computational grid, in which an amount *cpj* of processes available in that node was observed.

Proposed approach, aims to calculate the QoC using conditional probability from the contextual information specified in each submission of *job*, and from the status system update. A *job* is understood as a set of specifications for the execution of a certain task, these specifications being conditional on each other. For example, if context information reveals that the system has processes available in order to provide a processing rate *x* to execute a *job1*, it is also necessary to know the exact number of processes available to meet the application's execution flow. In other words, if the context manager determines the availability of a certain CPU rate for processing, it is also necessary to know if there are processes available to fulfill the request of *job1*.

In addition to the application demand, the approach proposed in this work aims to manage the workload exerted on the system. Therefore, one of the main functions delegated to the context manager is to collaborate for context-driven load balancing. Eq. (1) determines the probability that a given demand for a resource will be met without generating overload. Eq. (1) expresses the probability that a given demand *cpi* for a resource *i* will overload a capacity node *cpj* . Thus, the probability of the resource executing properly is determined by the completeness of Eq. (1). Therefore, the QoC for the resource *i* considering the available capacity *cpj* is given by Eq. (2). The QoC defined in Eq. (2) is actually the partial correctness, considering only an amount of resource of type *i* on a single node *j*, named as *QoCi*∣*j* just to facilitate understanding. For partial correctness, calculation *QoCi*∣*j* is not considered the application class; therefore, the context for all resources described in *job* are calculated in the same way.

$$P\left(cp\_i|cp\_j\right) = \frac{P\left(cp\_j|cp\_i\right) \* P(cp\_i)}{P\left(cp\_j\right)}\tag{1}$$

$$QoE\_{(i|j)} = 1 - P\left(cp\_i|cp\_j\right) \tag{2}$$

#### *3.1.2 Probability for each required resource*

The probability for each required resource *CPi* is given in Eq. (3), where *ENVresource* is the total capacity of the environment to provide the required resource. The *ENVresource* is given by Eq. (4), where *n* is the number of provider nodes in distributed resource facilities.

$$P(cp\_i) = \frac{cp\_i}{ENV\_{response}}\tag{3}$$

$$ENV\_{reoun\epsilon} = \sum\_{j=0}^{n} CP\_j \tag{4}$$

*A Resource Allocation Model Driven through QoC for Distributed Systems DOI: http://dx.doi.org/10.5772/intechopen.106458*

The probability for each resource *CPj* is given in Eq. (5), where *AVRresource* is the average of total capacity of the environment to provides the required resource. The *AVRresource* is given by Eq. (6), where *n* is the number of provider nodes in distributed resource facilities.

$$P\left(cp\_j\right) = \frac{cp\_j}{\text{AVR}\_{\text{resources}}}\tag{5}$$

$$\text{AVR}\_{\text{resource}} = \frac{\sum\_{j=0}^{n} \text{CP}\_{j}}{n} \tag{6}$$

#### *3.1.3 Conditional probability*

The conditional probability that associates the required and the available amount of resource is defined in Eq. (7). The probability of a required resource *cpi* given an amount *cpj* is defined by the magnitude correlation between what was requested and what is available.

$$P\left(cp\_j|cp\_i\right) = \frac{cp\_i}{cp\_j} \tag{7}$$

#### *3.1.4 Conditional context parameter*

Eq. (1) determines context evaluation from Dependent Context Parameters (DCP) set. Thus, is possible to achieve Eq. (8), where *n* is the applications context parameters (*cpi* ). The set *CCP* Conditional Context Parameters resulting from the Eq. (8).

$$\text{CCP}(cp\_i) = \left\{ P\{cp\_i|cp\_j\}; j = \mathbf{1}..n \cap cp\_j \varepsilon \text{PDC}\_i \right\} \tag{8}$$

The correctness is calculated correlating *CPj*, *CPi*, and *n* for all context parameters that characterize *cpi* . The *QoC cpi* � � *k* is context association that characterizes *cpi* for kth CP. The Eq. (1) relates the application requirements with resources available resulting in Eq. (9) resulting in Eq. (15).

$$\text{QoE}\_{(ij)} = \mathbf{1} - \frac{P\left(cp\_j|cp\_i\right) \* P(cp\_i)}{P\left(cp\_j\right)}\tag{9}$$

The resulting correctines, Eq. (10), is obtained from resulting QoC.

$$\text{Correctimes} = \text{QoC}\_{(X|Y)} \tag{10}$$

$$\mathcal{Q}\rho \mathcal{C}\_{(X|Y)} = \mathbf{1} - \frac{P(X|Y) \* P(X)}{P(Y)} \tag{11}$$

$$\text{QoC}\_{(X|Y)} = \mathbf{1} - \frac{\frac{X^\*}{Y}\frac{X}{Z}}{P(Y)}\tag{12}$$

$$Q\mathcal{C}\_{(X|Y)} = \mathbf{1} - \frac{\frac{X^2}{Y^\*Z}}{\frac{Y}{\tilde{\pi}}} \tag{13}$$

*Ubiquitous and Pervasive Computing - New Trends and Opportunities*

$$Q\rho C\_{(X|Y)} = 1 - \frac{X^{2^\*}}{Y^2} \left. \frac{1}{N} \right. \tag{14}$$

Thus, the correctiness parameter for X amount of computation requested is defined by Eq. (15).

$$Correctness = 1 - \left(\frac{1}{N}\right) \* \left(\frac{X}{Y}\right)^2\tag{15}$$

The resulting QoC is given by Eq. (16), for all *CPj* potential associated with *CPi*, and from the number of all *n* possible CPs, where *m* is the number of parameters considered QoC resource *CPi*. The expression *QoC cpi* � � *k* is the k-th conditional element that characterizes the *job Ji*.

$$QoE(I\_i) = \frac{1}{m} \left(\sum\_{k=1}^{m} QoE(I\_i)\_k\right) \tag{16}$$

From the QoC, obtained in our model, it is possible to quantitatively predict the user's experience. The relationship between QoE and QoC proposed in our work is presented in the following section.


*4.1. Carbon Steels*

Directly connected to the effect of ultrafast heating on grain size refinement, the mechanical properties of carbon steels subjected to the UFH process showed a clear improvement. Specifically, the evolution of mechanical characteristics was reported for low/medium carbon steel in the case of conventional annealing + soaking (10 ◦C/s + soak.), conventional annealing (10 ◦C/s) and ultrafast annealing (500–1000 ◦C/s) prior to quenching and partitioning (Q and P) heat treatment [40]. Results showed that the Ultimate Tensile Strength (UTS)increased for a higher HR (Figure 8); from conventional annealing (HR of CA = 10 ◦C/s) to ultrafast heating (HR of UFH = 1000 ◦C/s), the UTS shifted from 1097 to 1318 MPa (an increase of ~20%). The yield stress (YS), in the same range of heating rate, decreased from 837 to 811 MPa (−3.2%), and uniform elongation εc increased from 2.6% to 12.8%.

A comparison of CA (5 ◦C/s) and UFH (500 ◦C/s) on dual-phase steel [39] showed the following results: the UTS improved from 625.0 ± 3.6 MPa to 666.0 ± 2.6 MPa (~6.5%), the YS increased from 277.0 ± 8.1 MPa to 372.0 ± 3.0 MPa (~34%), and the uniform elongation and total elongation increased from 16.5 ± 0.2% to 18 ± 0.5% and from 23.3 ± 0.8% to 26.6 ± 0.5%, respectively (Figures 9 and 10).

**Figure 8.** Effect of HR increase on UTS and Vicker hardness value of a low/medium carbon steel undergone the UFH process compared to CA + soaking process (steel chemical composition 0.25% C + 1.5% Si + 3.0% Mn)). Peak temperature of 850 ◦C, and cooling rate of 20 ◦C/s (data from [40]).

**Figure 9.** YS and UTS increase with increase in heating rate between CA (5 ◦C/s) and UFH (500 ◦C/s), on dual-phase steel (data from [41]).

**Figure 10.** Uniform and total elongation variation with increasing heating rate between CA (5 ◦C/s) and UFH (500 ◦C/s) on dual-phase steel (data from [41]).

#### *4.2. Stainless Steels*

Regarding the mechanical properties in ferritic stainless steels [60]:

Instead, from data reported in [45]:

In austenitic stainless steels, data from [44] show that:


**Potentials of Selected Tropical Crops and Manure as Sources of Biofuels**

Babajide A. Adelekan *Federal College of Agriculture Ibadan, Institute of Agricultural Research & Training, Ibadan, Nigeria*


**3.3.1 The pros and cons for simple direct comparison transfer**

The above analyses based on the method illustrated in Fig. 2 are the simple direct comparison transfer calibration method. It is the most basic microwave power transfer technique. The system setup is fast, easy and simple.

But it is only for relatively rough measurement, since the reflection coefficient of a generator *ΓG*, is more difficult to measure than that of a passive load. *ΓG* varies with time and frequency. Many signal generators and amplifiers have non-linear output impedance. There are several developments on the measurement methods for *ΓG* (Shimaoka et al., 2006; Torok et al., 2001) which is beyond the discussion of this chapter.


**1. Introduction**

Cultivated rice is grouped in to the genus *Oryza* taxonomically. The genus *Oryza* (*O*.) contains 23 species of which two are cultivated while the rest are wild [1]. The two cultivated species, are *Oryza glaberrima*, commonly referred to as African rice, and *Oryza sativa* L*.*, commonly referred to as Asian rice [2]. *O. glaberrima* is indigenous to sub-Saharan Africa and its domestication is believed to have been from *Oryza barthii* (which used to be referred to as *Oryza brevilugata*). On the other hand, *O. sativa* was domesticated independently probably in China [3]. Cultivated rice is not limited to the two *Oryza* species, other inter-specifics for example the New Rice for Africa marketed as NERICA'S that arose due to crossing of *O. sativa,* and *O. glaberrima* are also cultivated [2].

Rice is an essential food crop that provides for most of world's population. It is also the second most consumed among cereal crops that include maize, wheat, barley, sorghum and millet. Rice is a major cereal crop with high economic and nutritional importance [4, 5]. Worldwide the leading producers of rice are Indonesia, India and China who together account for 50% world production [6]. Africa accounts for only 3% of the world's total production, with biggest producing countries being found in West Africa and they include Cote d'Ivoire, Nigeria and Mali. Mozambique and Malawi are the leading producers in Southern Africa. Madagascar and Egypt are also other substantial producers. In East Africa Tanzania ranks top in production followed by Kenya then Uganda [6].

In Kenya rice is mainly consumed as food with byproducts having other roles, for example rice hull is used as animal feeds, rice straw is also used as animal feed and substrate for growing mushrooms, while rice husks are used as cooking fuel [7]. In Kenya rice consumption has increased tremendously at an annual rate of 12% in comparison to wheat and maize that have increased at about 4% and 1% respectively. This is credited to changes in eating habits mostly among people living in urban centers [8]. Therefore, demand for rice is expected to increase further. In 2019 the annual rice consumption in Kenya was approximated to be 800,000 metric tons compared 130,000 metric tons produced the same year (**Figure 1**), the deficit was met through imports [6]. Current rice imports are estimated to be about \$87.5 million consequently stretching other parts of the economy [6].

Irrigated rice production land potential is about 540,000 ha while the production land potential for rain-fed ecology is 1.0 million ha [7, 9] currently area under production is estimated to be 30,000 ha. This indicates that if rain fed ecology potential is fully explored it will contribute to towards bridging production and consumption gap. Rice yield for irrigated rice is approximated at 4–6 t ha−1 while for rain fed is 1 t ha−1 which are below optimal production capability of about 10 t ha −1 and 7 t ha −1 respectively [7].

In Kenya like in many other sub-Sahara Africa counties rainfed rice farming has not been given priority [10]. With a potential of over 1 million ha about only 250, 000 ha are under rainfed rice crop [11]. Increasing Rain fed rice production is likely to increase the national rice production thus decreasing the rice import bill. This

*Rice production, imports and consumption in Kenya between 2015 and 2019.*

chapter aims at reviewing rainfed rice farming in Kenya by highlighting ecological conditions, ecological systems, the constraints faced by rainfed rice farming and discussing their potential solutions which if adopted can increase rice production in Kenya.


**Skeletal Muscle Regeneration for Clinical Application**

Fahd Azzabi Zouraq, Meline Stölting and Daniel Eberli

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55739

### **1. Introduction**

Comprising nearly 50% of the human body [1] skeletal muscles compose the machinery that sets the body in movement. When well-trained, muscles have the capability to protect joints and bones from daily waste and trauma [2]. They hold an intrinsic protective mechanism against cancer formation and metastasis settling [3] and are at the same time the main energy reservoir of the body storing more than 80% of our glycogen reserve [4]. Hence, muscle tissue is associated to several functions and networks with different parts of the body. It is composed of muscle fibers, the contractile units, which are bound together by connective tissue. Most importantly, skeletal muscles display an astonishing regenerative capacity [5]. Due to resident stem cells, one week after severe trauma new myotubes are already being formed, and within 28 days after trauma muscle regeneration is almost complete [6]. These intrinsic features turn the skeletal muscle into a very interesting topic of study in regenerative medicine. Taking advantage of the regenerative potential of stem and precursor cells, skeletal muscle is con‐ stantly renewed in response to injury, damage or aging. It is this natural process that research‐ ers are about to harness in order to help patients with many muscle diseases and diseases that causes weakness or destruction of the muscle - for instance stress urinary incontinence (SUI), muscular dystrophy. In this chapter, the focus will be on the regeneration of the skeletal muscle and especially in the case of incontinence. Urinary incontinence is the involuntary loss of urine and is a major medical problem affecting millions of people worldwide. It impairs the quality of life of patients and involves high healthcare costs. The main reason provoking SUI is the damage of the sphincter muscle due to childbirth, surgical treatments (as prostatectomy) or as an effect of aging. Current treatment encompasses behavioral training, pelvic floor exercising, drugs, medical devices and surgery. Unfortunately, all these options permit only limited recovery: short-term relief and are often accompanied with complications. The ultimate goal will be to prevent disease progression and to restore the tissue and its functions.

© 2013 Azzabi Zouraq et al.; licensee InTech. This is an open access article 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. © 2013 The Author(s). Licensee InTech. 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.

Stem cell therapy as a treatment for skeletal muscle diseases is becoming a reality and it represents a promising alternative for muscle regeneration and for treating SUI in a more complete and definitive manner.

In this chapter, the homeostasis and maintenance of skeletal muscle is explained in order to understand the basis behind muscle regeneration. As different types of stem cells have been demonstrated to form fibers and to develop into skeletal muscle, cell sources for a muscle cell therapy is discussed. Some of them have also been applied successfully in preclinical and clinical studies that are going to be described. Finally, we are going to highlight the parts important for the translational effort into clinics including biomaterials, cell delivery, imaging, regulatory affairs, and manufacturing.


**2.1.3 Yeasts associated with the gut of some pests**

In the gut of some maize' pests (*Diabrotica virgifera*, *Helicoverpa armigera* and *Ostrina nubialalis*), Molnar et al. (2008) isolated 97 yeast strains; furthermore they detected yeasts as well as other fungi of the genera: *Acremonium*, *Aspergillus*, *Cladosporium* and *Fusarium* by means of cloning and denaturing gradient gel electrophoresis (DGGE). The occurence of clones was given in percents. All methods reveald that *Metschnikowia* spp., closely related to *Metschnikowia pulcherrima*, *Cryptococcus* spp. (*Cr. luteolus, Cr. zeae* and *Cr. flavescens*) as well as *Candida* spp., bearing close similarity to *C. xestobii* or *C. sake,* and *Pseudozyma* spp. were the most frequently identified yeasts. *Pichia guiliermondii* and *Rhodotorula* species were less common. Some of occassionaly found yeasts e.g. *Aureobasidium pullulans, Candida quercitrusa, Hanseniaspora uvarum, Sprobolomyces coprosmae, Tilletiopsis washingtonensis* were detected however only via culturing. There are some publications reporting presence of the yeasts in the gut of mosquitos (*Diptera*: *Culicidae*), which are known to be vectors of many diseases in humans. Gusmão et al. (2007; 2010) identified *Pichia caribbica, Pichia guilliermondii, Pichia* (syn. *Kodamaea*) *ohmeri, Candida fermentati* and *Candida nodaensis* in the diverticulum of *Aedes aegypti*. Ricci et al. (2011a) investigated yeasts in the gut of *Anopheles stephensi* using molecular and cultivation-dependent methods. Forty six clones that expressed fragments of the 18S rRNA gene retrieved from the gut samples of 6 adults were sequenced. Eleven clones were identified as *Wickerhamomyces anomalus*, known also as *Pichia anomala*, while others could be assigned either to genus *Candida* or *Pichia* or to unidentified fungus. Moreover, 100 colonies were cultured from 10 insect speciemens, classified based on their morphology and identified as *Candida intermedia*, *Hanseniaspora uvarum* and *W. anomalus* (77%, 15% and 8% respectively) by sequencing analysis of 18S and 26S rRNA genes and ITS fragments. *W. anomalus* was detectable using both approaches. Furthermore, Ricci et al. (2011a; 2011b) observed the presence of *W. anomalus* in the midgut of different mosquitos species *Anopheles stephensi, Anopheles gambiae, Aedes albopictus* and *Aedes aegypti*  of both sexes as well as on larvae, pupae and gonads, thereby supposed close relationship between this yeast species and mosquitos.

Biodiversity of Yeasts in the Gastrointestinal

huge variety of yeasts (Suh et al., 2005a).

*Arxula Candida Cryptococcus Debaryomyces Dipodascus Endomyces Galactomyces Geotrichum Hanseniaspora Kluyveromyces Lodderomyces Metschnikowia Pichia Saccharomyces Saturnispora Stephanoascus Williopsis Zygoascusa*

insects during the study of Suh et al. (2005a).

midgut.

Ecosystem with Emphasis on Its Importance for the Host 287

*ernobii* and the strains related to the one *Candida* sp. were prevalent in all parts of gut and frass and *P. guilliermondii* and *C. ernobii* were cultured most frequently from the posterior

In relation to high number of the yeast isolates (richness) described above, comparatively low yeast diversity was found in the assemblage of *Dendroctonus* beetles. It thereby underlined the impact of the host and/or environmental factors on the yeasts diversity. Nevertheless, examination of yeasts harbouring the GIT of beetles from 27 families reviled a

Fungi

Dikarya

Ascomycota Basidiomycota

Fig. 1. Schematic representation of the different yeast taxa belonging to the two phyla *Ascomycota* and *Basidiomycota* of the Dikarya subkingdom isolated from the intestinal tract of

yeasts isolated from the gut of insects corroborates this supposition.

During three-years-period, Suh et al. (2005a) isolated about 650 yeasts from the gut of diverse beetles collected from the south-eastern USA and Panama. Sequence analyses of the D1&D2 domains of LSU rRNA gene revealed 290 single species belonging to at least 27 taxa (Fig. 1.); the great majority of which were ascomycetous and some basidiomycetous yeasts. It is noteworthy that nearly 200 yeasts determined throughout the study were considered by the authors to represent new, not yet described species. In the meantime, some of them (table 1) were characterized by Suh, Nguyen, Blackwell and their co-workers. Based on their observation Suh et al. (2005a) suggested that almost each beetle species may be a host for at least one unknown yeast species. In the last decades, describing of many novel species of

*Fellomyces Filobasidiella Leucosporidium Rhodosporidium Sporidiobolus Tilletia Tremella Trichosporon Ustilago*