Using a similar approach to that reported in Sect. 3.2 for X = 1 , first we analyse the flow of **power**-**law** **fluids** using the geometry obtained for a Newtonian fluid. Figure 4a shows the normalised average wall shear stress in each con- secutive generation of a network designed for a Newtonian fluid with X = 1.25. For the case of n = 1 , the CFD results are in very good agreement with the results presented by Emerson et al. (2006) and Barber and Emerson (2008) and with theory (Eq. 9), resulting in a maximum deviation of less than 0.5 %. When X = 1.25, the average wall shear stress increases at each consecutive generation, resulting in a positive gradient along the network as imposed by set- ting the branching parameter to a value greater than unity (X > 1 ) in the biomimetic rule. However, unlike the equiv- alent case for X = 1 , the use of the Newtonian geometry produces very different shear-stress distributions along the network for each **power**-**law** fluid tested (Fig. 4a). It is clear that for a branching parameter X = 1.25, the **power**- **law** **fluids** will not display the desired behaviour when flowing in the Newtonian-designed geometry. This is also highlighted from the deviations in the resistances shown in Fig. 4b.

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Most of the work described above concerns flow of a Newtonian fluid; there are somewhat fewer papers on surface-shear-stress-driven flow of a non-Newtonian **power**-**law** fluid. For exam- ple, Pascal [32] obtained analytical and numerical solutions for the spreading of a fixed volume of a **power**-**law** fluid over a slightly denser Newtonian fluid subject to a shear stress at the free surface. Recently, Pascal and D’Alessio [33] investigated the linear stability of the flow of Newtonian and **power**-**law** **fluids** down an inclined plane subject to a prescribed shear stress at the free surface; they found that a shear stress down the plane destabilizes the flow whereas a shear stress up the plane stabilizes it. Wilson et al. [34] obtained similarity solutions describing steady flow of non-uniform slender rivulets of Newtonian and **power**-**law** **fluids** on an inclined plane, driven by either gravity or a constant shear stress at its free surface; their solutions for the two different driving mechanisms are qualitatively similar.

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Mishra and Jayaraman [6] examined numerically and experimentally the asymmetric steady flow patterns of shear-thinning **fluids** through planar sudden expansions with a large expansion ratio, ER= 16. Manica and De Bortoli [7] studied numerically the flow of **power**-**law** **fluids** in a 1:3 planar sudden expansion for n = 0.5, 1 and 1.5. They presented the vortex characteristics for these values of n and for 30 ≤ Re ≤125, and observed that the flow bifurcation for shear-thinning **fluids** occurs at a critical Reynolds number higher than for Newtonian **fluids**, and that shear-thickening **fluids** exhibited the lowest critical Reynolds number. Considering again purely viscous **fluids** represented by the **power**-**law** and Casson models, Neofytou [8] analyzed the transition from symmetric to asymmetric flow of **power**-**law** **fluids** with **power**-**law** indices in the range 0.3 ≤ n ≤ 3 in a 1:2 planar sudden expansion and also studied the effect of Reynolds number on the flow patterns.

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The flow of boundary layer for non-Newtonian **fluids** over a moving surface has import engineering applications, for example metal or plastic extrusion, lubrication and heat exchangers etc. Yürüsoy [1] studied the similarity solution of a boundary layer on a stretched surface for a **Power**-**Law** fluid. By using a special similarity transformation, which was used also in this paper, he reduces the unsteady boundary layer equations to a non-linear ordinary differential equation system. Yürüsoy and Pakdemirli [2] treated the symmetry reductions of unsteady three dimensional boundary layer equations of non-Newtonian **fluids** by using Lie Group analysis. Acrivos et al.[3] examined the flow past a horizontal flat plate including heat transfer without dispersion term in the energy equation. Schowalter [4] investigated two and three dimensional boundary layer equation of **power**-**law** **fluids**. Chen [5] treated effect of suction-injection and magnetic field on convection heat transfer of **power**-**law** fluid over a stretching sheet. Ece [6] investigated free convection to **power**-**law** **fluids** from a vertical cone of variable surface temperature. Luna et al. [7] analyzed the case of conjugated heat transfer in circular ducts for a **power**-**law** fluid. Hassanien [8] considered the heat transfer in **power**-**law** fluid over a non-isothermal stretching sheet.

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Consider the evolution of a thin layer of non-Newtonian fluid. I model the case of a nonlinear viscosity that depends only upon the shear-rate; **power** **law** **fluids** are an important example, but the analy- sis is for general nonlinear dependence upon the shear-rate. The mod- elling allows for large changes in film thickness provided the changes occur over a large enough lateral length scale. The modelling is based on two macroscopic modes by fudging the spectrum: here fiddle the surface boundary condition for tangential stress so that, as well as a mode representing conservation of fluid, the lateral shear flow u ∝ y is a neutral critical mode. Thus the resultant model describes the dy- namics of gravity currents of non-Newtonian **fluids** when their flow is not very slow. For an introduction I first report on an analogous case of nonlinear diffusive dissipation.

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For the case of Newtonian **fluids** (n = 1), the CFD results are in very good agreement with theory. When X = 1.25, the average wall shear-stresses are increasing at each con- secutive generation, while for X = 0.75 they are decreasing as imposed by the biomimetic rule. However, unlike in the case of X = 1, the use of the Newtonian geometry produces very different shear-stress distributions along the network for each **power**-**law** fluid (Figs. 3a and 3b). It is clear that for branching pa- rameters different from unity, the **power**-**law** **fluids** will not display the desired behaviour when flowing in the Newtonian-designed ge- ometry.

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Different authors proposed models to explain the behavior of a reservoir, depending on its properties, for example, Odehand Yang (1979), and Ikokuand Ramey (1979a, 1979b) were the first ones who developed models for when there are non-Newtonian **fluids** inside infinite reservoirs; also, Chang and Yortsos (1990) characterized a fracture network in a reservoir using fractal geometry. They introduced the concepts of Df which represents the fractal dimension of a fractal network of fractures, and which characterizes the geometry and transport properties in the fracture network.

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evolution of fluid mechanics and heat transfer for non- Newtonian pseudo plastic and dilatant **power** **law** **fluids** undergoing inward annular solidification processes between two concentric thick walled horizontal cylinders. External inner and outer forced convection originates the transient motion of a binary alloy by natural convection inside a cylindrical mold in which conduction in the walls is included. The liquid to solid phase transformation is described by a liquid phase fraction that varies linearly with temperature. The effects of Rayleigh number Ra and radii ratio R on the time evolution of velocity and temperature distributions are investigated for pseudo plastic and dilatant **fluids** in comparison with the results corresponding to the Newtonian fluid assumption for the alloy in the mushy zone and in the liquid phase.

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There is already substantial literature on primes adopting the statistical physics pers- pective. In line with our finding, the histograms in the distribution of gaps between primes divided into “congruence families” are shown to be scale invariant [3]. A theory to explain the origin of the unexpected periodic behavior of gaps between primes has been linked to the k -tuple conjecture, the statistical mechanics of spin systems and the Sierpinski fractal [4]. Higher-order gaps between the primes have been analyzed by Fourier decomposition to show patterns in the resulting **power** spectra [5]. The gaps between primes have been shown to exhibit a period six oscillation [6]. The histogram of the increments (the difference between two consecutive gaps between primes) has been shown to follow an exponential distribution with superposed periodic behavior of period three [7]. Rather than prime gaps, for the distribution of primes themselves there have been claims of self-similarity [8], small world networks [9] and even chaos [10].

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Structure metrics include the number of nodes, edges and average path length or diameter of. the schemas[r]

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In some ways, coercive control creep, the increasingly present use of this concept as a point of uncontested reference, emulates this policy process. Throughout this process, little thought has apparently been given to alternatives to criminalisation; Goodmark (2017) outlines some of the possible reasons for this. At the same time, there is sufficient evidence pointing to the unintended consequences of harnessing the **law** in this way—particularly for those whom it is believed might be protected by the **law** (see, e.g., Douglas 2018; Tolmie 2018)—with protection from the **law** being additionally problematic for Indigenous women (Blagg 2016), women with disabilities (Thiara, Hague and Mullender 2011) and those from ethnic minorities (Gill and Harrison 2017). This evidence is multifaceted and multilayered, ranging from the specific consequences associated with particular legal strategies to the more general question of what response women (in violent relationships) might want from a criminal justice system and what they might receive in reality. The criminalisation of coercive control has drawn comment along all these dimensions.

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From the very start of the well-known essay, first published as a newspaper editorial, Butler separates modalities of **power** and **law**. Governmentality and sovereignty are read from the start as forces that act upon jurisdiction, the ‘territory’ 3 of **law**. At first blush, the proposition (and its consequences) creates an aporia, at least to those who are familiar with Foucault’s modalities of **power**, the very modalities that Butler is invoking in this essay. In Discipline and Punish (1991a), Foucault hardly differentiates between the sovereign and the **law**: both fall under the category of juridical **power**. Nevertheless, I want to emphasise that Foucault does not equate the sovereign with the **law**; rather, he vests the sovereign with the ‘force of **law**’. Foucault recognises that there is a jurisdiction that is legal. This jurisdiction, through the instrument of the trial, decides upon the ‘truth’ of the alleged event, and through the instrument of punishment, publicises the ‘truth’. In this context, Foucault writes, ‘[t]he body, several times tortured, provides the synthesis of the reality of the deeds and the truth of the investigation, of the documents of the case and the statements of the criminal, of the crime and the punishment’ (1991a: 47). For Foucault, the juridical order entertains itself with the trying of the accused (1991a: 44-8), but the king or prince, engages in a distinct practices with distinct effects. In the sovereign is vested the **power** of deciding life or death

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The paper analyzes the spreading of population in Indonesia. The spreading of population in Indonesia is clustered in two regional terms, i.e.: kabupaten and kotamadya. It is interestingly found that the rank in all kabupaten respect to the population does not have fat tail properties, while in the other hand; there exists **power**-**law** signature in kotamadya. We analyzed that this fact could be caused by the equal or similar infrastructural development in all regions; nevertheless, we also note that the first 20 kabupatens are dominated in Java and Sumatera. Furthermore, the fat tail character in the rank of kotamadya could be caused by the big gap between big cities one another, e.g.: Jakarta, Surabaya, and others. The paper ends with some suggestions of more attention to infrastructural development in eastern regional cities.

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It has now established itself in a number of locations just within the Greater Brisbane catchment, with two university campuses located at Springfield and Ipswich. It also has a Queensland College of Wine Tourism at Stanthorpe. It offers courses in **law**, health, engineering, surveying, sciences, business, education, and the arts. The institution was established in 1967 as the Darling Downs campus of the Queensland Institute of Technology. In 1970, the institution had provided studying programs for rural Queensland and international communities. In 1971, it became the Darling Downs Institute of Advanced Education, then the University College of Southern Queensland in 1990 and finally the University of Southern Queensland in 1992. USQ is ranked No.1 in Australia for Engineering Graduates in full-time work and graduate salary (Good Universities Guide, 2018/2019).

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dents were recorded although one had no data (40 injured, 1 severely harmed, 200 evacuations). One fluorocarbon leak was noted (1 injured, 1 death). Since the data originated from an organisation with an explicit interest in promoting fluorocarbons against LTS **fluids**, a selection of the links to the original data sites were checked and found to be correct. Using the search terms ‘ ammonia + accident ’ an Internet search generated additional, more recent examples of ammonia releases causing problems. ‘ hydrocarbon + accident + refrigerant ’ generated a recent report by the London Fire Brigade concerning the fire hazard of domestic freezers related especially the flammable cyclo-pentane blowing agent. EU and American legislation restricts the hydrocarbon charges in appliances with heat exchangers in rooms to a max- imum of 150 g. This information reinforces what was already known, that is ammonia and hydrocarbons are potentially hazard- ous, especially when used on the large scale without adequate

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Fortunately, a developing area of leadership research provides useful insights into **law** firm leadership. In recent years there has been growing interest among leadership scholars in what has variously been termed ‘collective’, ‘distributed’ or ‘shared’ leadership. In this plural conceptualisation of leadership, leadership roles are shared among multiple actors, and authority relationships are ambiguous and potentially contested. Unlike most conventional leadership research, a plural model of leadership views leadership as a collective process, unfolding over time and arising from the actions and interactions of a group of individuals. Leadership, in this sense, is not something that is done by people but something that happens between people seeking to influence each other. As a result, it can be more temporary, more insecure and more subject to negotiation than traditional individualised

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CONCLUSION : Fluid-mechanics is an “ancient science” that is incredibly alive today. The modern technologies require a deeper understanding of the behavior of real ﬂuids; on the other hand new discoveries often pose new challenging mathematical problems.The basic characteristic of the fluid is that it can flow. **Fluids** are divided in two categories, incompressible **fluids** (**fluids** that move at far subsonic speeds and do not change their density) and compressible **fluids** The aim of this paper is to furnish some results in very different areas that are linked by the common scope of giving new insight in the field of fluid dynamics. The aim of this paper is to furnish some results in very different areas that are linked by the common scope of giving new insight in the ﬁeld of ﬂuid dynamics. The study of these ﬂows has been attached with a wide range of mathematical techniques and, today, this is a stimulating part of both pure an applied mathematics.

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At least ten different models have been proposed for extrapo- lating the OAR. They cover a broad theoretical spectrum and levels of complexity (see Azaele, Cornell, & Kunin, 2012; Barwell, Azaele, Kunin, & Isaac, 2014) (Supporting Information Table S3). The simplest model proposed is the Poisson model which assumes that individuals are distributed independently according to a binomial distribution (Wright, 1991). Three models are variations assuming fractal distri- bution patterns, the **power** **law** (Kunin, 1998), Nachman (Nachman, 1981) and logistic (Hanski & Gyllenberg, 1997) models. Four mod- els are based on the negative binomial distribution and incorporate a measure of over-dispersion: the negative binomial (He & Gaston, 2000), generalised negative binomial (He, Gaston, & Wu, 2002), im- proved negative binomial (He & Gaston, 2003) and finite negative binomial (Zillio & He, 2010). The Thomas model incorporates spatial point processes in order to more flexibly account for species aggre- gations (Azaele et al., 2012). The only spatially-explicit model is the Hui model, which differs from the others in that it only requires data at a single grain size (Hui, 2009; Hui, McGeoch, & Warren, 2006; Hui et al., 2009). It is based on the conditional probability that a ran- domly chosen adjacent cell is occupied when the cell in question is also occupied. This has the advantage of giving some information on the likelihood of adjacent calls being occupied in the finer grid. A related model, which we do not consider here, accounts for the percolation effect on occupancy at coarse grains, this is the so-called “droopy-tail” model (Hui & McGeoch, 2007).

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Till now, we have seen that some of the largest networks such as Internet topologies, WWW, Social Network follows **power** laws. Faloutsos et al. [2] derived **power** laws related to computer networks considering three instance of inter-domain graphs. After a decade, they reviewed similar results using Oregon routeviews project [3] that span across 1600 days containing 1253 daily instances. They compared an instance from Oregon (of a previous year) and more complete topology Multi (a complete graph after some years Oregon was taken) to confirm whether behavior of Oregon predicts as Multi. Also, they modified probability distribution function with cumulative distribution function to get more realistic graphs. These graph uses the phenomena of “rich-gets-richer [9] ” and as a result

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