Power-law Theory Research Articles

Contextualizing macroecological laws: A big data analysis on electrofishing and allometric scalings in Ohio, USA

We investigated the influence of different electrofishing methods on allometric scaling features of fish assemblages in lotic environments. The ultimate aim was to elucidate to which extent the structure of fish assemblages is predictable by the three-quarter power law theory. Water bodies across the state of Ohio, USA, provided a suitable data set to analyze the size–biomass spectra of 2051 fish assemblages. For the first time, 41,070 allometric field observations were screened according to sampling methods (i.e., longline, tote barge, boat) adopted for sampling collection. Allometric patterns varied considerably in relation with the sampling method, in turn imposed by the local hydrology and morphology of the investigated water courses, as shown by the lowering of scalings from boatable to wadeable systems. There are several lines of evidence indicating that the chosen type of electrofishing acts as a pitfall for size spectra. Using individually weighted body-mass values as independent predictor of spectra we show that the specific sampling methodology required by the physical characteristics of different lotic habitats influence the allometric outcomes, a novel result that makes universality of community power laws not as straightforward as supposed until now.

Studies on temperature induced creep in high strength Q460 steel

Significant levels of creep deformation in structural steel members exposed to high temperatures have been widely observed in experiments; however inclusion of creep effects in numerical simulations has been limited due to lack of reliable experimental data and corresponding constitutive creep models for structural steel, especially for high strength steel. This paper presents an experimental investigation into temperature induced creep in high strength Q460 steel which is commonly used in structural member. A set of creep tests is carried out at various stress levels in 300–900 °C temperature range. Data from these creep tests indicate that temperature has significant influence on the level of creep deformations in Q460 steel, especially when the temperature in steel exceeds 400 °C. The creep strain at a given temperature increases with stress level and the creep strain at a given stress level increases with temperature. Results from creep tests are utilized to develop relations for expressing creep as a function of temperature and stress. These relations, which are based on creep power law and unified theory on plasticity and creep phenomenon, can be utilized in modeling the response of steel structures made of Q460 steel exposed to fire.

Building and Analyzing of Enterprise Network

Social business moves beyond linear, process-driven organizations to create new, dynamic, networked businesses that focus on customer value. Enterprise network (EN) is used to support social business by maximizing current and future opportunities and facilitate network-enabled processes, which can lead to value co-creation. EN is a multi-level hypergraph model with enterprises, employees, products and other related entities. In this paper the authors refine the EN model and present the foundation of EN to support social businesses. Then they introduce a case study on China automobile supply network (CASN). For the similarity with social networks, they verify power-law and small world theories in EN with statistical results on this data set. These theories are fitful in EN, but some new characteristics exist. The structure of EN consists of star-shaped clusters and the authors extract ego networks taking suppliers and manufacturers as the ego respectively. With the structure and distribution features of EN, they present the enterprise business similarity analysis method based on common-neighbors. And they also introduce the tentative work to detect Dunbar circles in EN. To analyze the data in a more intuitional and effective way, the authors use some data visualization tools to process the data in EN.

On the Quantification of the Constraint Effect Along a Three-Dimensional Crack Front

Elbows with a shallow surface cracks in nuclear pressure pipes have been recognized as a major origin of potential catastrophic failures. Crack assessment is normally performed by using the J-integral approach. Although this one-parameter-based approach is useful to predict the ductile crack onset, it depends strongly on specimen geometry or constraint level. When a shallow crack exists (depth crack-to-thickness wall ratio less than 0.2) and/or a fully plastic condition develops around the crack, the J-integral alone does not describe completely the crack tip stress field. In this paper, we report on the use of a three-term asymptotic expansion, referred to as the J-A 2 methodology, for modeling the elastic-plastic stress field around a three-dimensional shallow surface crack in an elbow subject to internal pressure and out-of-plane bending. The material, an A 516 Gr. 70 steel, used in the nuclear industry, was modeled with a Ramberg-Osgood power law and flow theory of plasticity. A finite deformation theory was included to account for the highly nonlinear behavior around the crack tip. Numerical finite element results were used to calculate a second fracture parameter A 2 for the J-A 2 methodology. We found that the used three-term asymptotic expansion accurately describes the stress field around the considered three-dimensional shallow surface crack.

Extrudate expansion model in a twin-screw extrusion cooking process considering melt rheological property

A new extrudate bulk density model framework was developed, which is taking into account the melt rheological effects based on mixing principle and non-Newtonian power law theory for a twin-screw extrusion cooking process. The main ingredients in the extrusion process investigation were wheat, fish meal and soybean protein. The average absolute deviation (AAD) of the model prediction for extrudate bulk density is 5.3 % for the investigated process. The prediction results demonstrate that the proposed equation can be used to model the extrudate bulk density in the twin-screw extruder extrusion cooking process.

Assessment and influence of internal rigid core on the contact parameters for soft hemispherical fingertips

Abstract The main purpose of the present work is to develop an artificial fingertip comprised of a soft layer and an inner rigid core, which emulates a human one with skin and bone. The influences of introducing the core and the effects of variations in thickness of the soft layer over the contact parameters are investigated. From the results, it is evident that the power law theory proposed by (Xydas N, Kao I. Int. J. Rob. Res. 1999, 18, 941–950) becomes invalid in this criterion; by contrast, if the power law theory acts for finger tips with internal cores, the conclusion may be redefined in such a way that the soft material behaves more softly in the presence of internal cores and the dimensionless number, core-soft layer coefficient Fcs≈0.5, is the critical parameter which produces the change of behavior. Moreover, soft finger tips with an inner core are preferable to entirely soft ones, as a higher grasping stability is achieved with the same area of contact, and the conforming nature of the fingers is maintained.

Studies on the rheological properties of aluminium oxihydroxide (boehmite) colloidal suspension

This paper presents both experimental and theoretical aspects of the rheological properties and gelling behavior of boehmite suspensions over a range of pH, temperature and concentration. Boehmite sol–gel behaved as a non-Newtonian shear thinning fluid with the increase in consistency index k at lower pH. The flow behavior index (n) representing the relative degree of shear thinning was influenced by pH. The power law theory was used to explain the k and n for gelling behavior and the limit of pseudoplasticity of the boehmite suspensions. It was also found that the variation of activation energy with pH had an appreciable effect on the viscosity of the suspensions. Further it was observed that the density of the suspensions was strongly pH-dependent, with a maximum density at pH 1. Hence, it can be concluded that the rheological properties of colloidal aluminium oxihydroxide (boehmite) suspensions are predominantly affected by the physico-chemical parameters.

A New View of Financial Risk: What Officers Should Know to Minimize Risk?

This is an introductory highlight of the fractal theory and power law theory of investment analysis and with the findings of a research on using the above theory to predict crash and trough in Hang Seng Index.

A highly optimised tolerance-based approach for multi-stage, multi-product supply chain network design

In this paper we propose an algorithm called Highly Optimised Tolerance (HOT) for solving a multi-stage, multi-product supply chain network design problem. HOT is based on power law and control theory. The proposed approach takes its traits from the local incremental algorithm (LIA), which was initially employed to maximise the design parameter (i.e. yield), particularly in the percolation model. The LIA is somewhat analogous to the evolution by natural selection schema. The proposed methodology explores a wide search space and is computationally viable. The HOT algorithm tries to make the system more robust at each step of the optimisation. The objective of this paper is to reduce the total cost of supply chain distribution by selecting the optimum number of facilities in the network. To examine the effectiveness of the HOT algorithm we compare the results with those obtained by applying simulated annealing on a supply chain network design problem with different problem sizes and the same data sets.

Refinement of the 3/2 power law and radial drift theory of the ion current to a small probe or a dust particle in a rarified plasma

The ion current to a probe or a dust particle in a rarified plasma is considered in terms of the plasma sheath theory and the radial drift theory. The effect of the initial directed velocity of ions entering the sheath in accordance with the Bohm criterion on the current-voltage characteristic of the space charge sheath is studied. Computations based on both theories are performed for the extended range of the relative values of probes (0.0001–20.0) rp/λD, where rp is the size of the probe and λD is the electron Debye radius. The two theories are compared in the entire design range of the sizes of probes. Analytical approximations are given for practical application of the results.

Comparison of mean flow similarity laws in zero pressure gradient turbulent boundary layers

The paper presents an in depth assessment of different similarity laws for the mean velocity profile in zero pressure gradient (ZPG) turbulent boundary layers (TBL's) in comparison with mostly experimental and few computational data. The emphasis is on the descriptions which are complete in the sense that a full representation of the mean velocity profile, its streamwise evolution and all integral parameters, including the friction factor and the shape factor, are provided as a function of Reynolds number. The first such complete description is the classical two-layer theory with its characteristic logarithmic mean velocity profile in the region where the two layers overlap, henceforth referred to as the “log law.” The main alternative scalings which have been proposed over the last decade have led to power law descriptions of the turbulent mean velocity profile. Since the different descriptions were calibrated with different data sets, the controversy over the relative merits of the different approaches has lingered on. The purpose of the present paper is to measure the principal competing theories against the same vast data set of more than 300 mean velocity profiles from more than twenty different sources. The results confirm the conclusions of numerous authors that the log law provides a fully self-consistent and accurate description of all the mean quantities and demonstrates conclusively that the same cannot be achieved by the competing power law theories. Along the way, it is also argued that the traditional description of the outer velocity profile in terms of a wall-normal coordinate normalized to unity at a hypothetical boundary layer “edge” δ and a “wake parameter” Π is not robust with respect to the fit of the outer velicity profile and should therefore not be used in theoretical arguments.

Power Law Velocity Profile in the Turbulent Boundary Layer on Transitional Rough Surfaces

A new approach to scaling of transitional wall roughness in turbulent flow is introduced by a new nondimensional roughness scale ϕ. This scale gives rise to an inner viscous length scale ϕν∕uτ, inner wall transitional variable, roughness friction Reynolds number, and roughness Reynolds number. The velocity distribution, just above the roughness level, turns out to be a universal relationship for all kinds of roughness (transitional, fully smooth, and fully rough surfaces), but depends implicitly on roughness scale. The open turbulent boundary layer equations, without any closure model, have been analyzed in the inner wall and outer wake layers, and matching by the Izakson-Millikan-Kolmogorov hypothesis leads to an open functional equation. An alternate open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation of Izakson and Millikan, which admits two functional solutions: the power law velocity profile and the log law velocity profile. The envelope of the skin friction power law gives the log law, as well as the power law index and prefactor as the functions of roughness friction Reynolds number or skin friction coefficient as appropriate. All the results for power law and log law velocity and skin friction distributions, as well as power law constants are explicitly independent of the transitional wall roughness. The universality of these relations is supported very well by extensive experimental data from transitional rough walls for various different types of roughnesses. On the other hand, there are no universal scalings in traditional variables, and different expressions are needed for various types of roughness, such as inflectional roughness, monotonic roughness, and others. To the lowest order, the outer layer flow is governed by the nonlinear turbulent wake equations that match with the power law theory as well as log law theory, in the overlap region. These outer equations are in equilibrium for constant value of m, the pressure gradient parameter, and under constant eddy viscosity closure model, the analytical and numerical solutions are presented.

Three-term Asymptotic Stress Field Expansion for Analysis of Surface Cracked Elbows in Nuclear Pressure Vessels

Elbows with a shallow surface cracks in nuclear pressure pipes have been recognized as a major origin of potential catastrophic failures. Crack assessment is normally performed by using the J-integral approach. Although this one-parameter-based approach is useful to predict the ductile crack onset, it depends strongly on specimen geometry or constraint level. When a shallow crack exists (depth crack-to-thickness wall ratio less than 0.2) and/or a fully plastic condition develops around the crack, the J-integral alone does not describe completely the crack-tip stress field. In this paper, we report on the use of a three-term asymptotic expansion, referred to as the J–A2 methodology, for modeling the elastic-plastic stress field around a three-dimensional shallow surface crack in an elbow subjected to internal pressure and out-of-plane bending. The material, an A 516 Gr. 70 steel, used in the nuclear industry, was modeled with a Ramberg–Osgood power law and flow theory of plasticity. A finite deformation theory was included to account for the highly nonlinear behavior around the crack tip. Numerical finite element results were used to calculate a second fracture parameter A2 for the J–A2 methodology. We found that the used three-term asymptotic expansion accurately describes the stress field around the considered three-dimensional shallow surface crack.

Densities and viscosities of aqueous solutions of 1-propanol and 2-propanol at temperatures from 293.15 K to 333.15 K

Densities and viscosities of the binary aqueous solutions of 1-propanol and 2-propanol have been measured over the whole composition range at temperatures between 293.15 K and 333.15 K. The energies of activation for viscous flow for aqueous solutions of 1-propanol and 2-propanol were calculated and found to be 17.94 and 22.16 kJ mol − 1 , respectively. A polynomial equation and an equation based on the Power Law and Erying's absolute rate theory were used to correlate the viscosity data of the aqueous solutions of 1-propanol and 2-propanol. The average absolute deviations (AAD) for density correlations of aqueous solutions of 1-propanol and 2-propanol are less than 0.07%.

Is there a universal log law for turbulent wall-bounded flows?

The history and theory supporting the idea of a universal log law for turbulent wall-bounded flows are briefly reviewed. The original idea of justifying a log law from a constant Reynolds stress layer argument is found to be deficient. By contrast, it is argued that the logarithmic friction law and velocity profiles derived from matching inner and outer profiles for a pipe or channel flow are well-founded and consistent with the data. But for a boundary layer developing along a flat plate it is not, and in fact it is a power law theory that seems logically consistent. Even so, there is evidence for at least an empirical logarithmic fit to the boundary-friction data, which is indistinguishable from the power law solution. The value of kappa approximately 0.38 obtained from a logarithmic curve fit to the boundary-layer velocity data, however, does not appear to be the same as for pipe flow for which 0.43 appears to be the best estimate. Thus, the idea of a universal log law for wall-bounded flows is not supported by either the theory or the data.

Turbulent boundary layers: reality and myth

In this paper, we discuss several recent theoretical approaches to wall-bounded flows such as turbulent boundary layers and pipe flows. Specifically, the power law theories by Barenblatt and George and a higher-order approach proposed by Buschmann and Gad-el-Hak are discussed. By employing probably the best data sets currently available worldwide, we uncover the qualities of these approaches. The outcome shows that the mean-velocity profile of turbulent wall-bounded flows is much more complex than the classical logarithmic law or a simple power law. A Reynolds number dependence of the mean profile persisting for arbitrarily high but finite Reynolds numbers seems to be highly likely. Both experimental and theoretical efforts are needed to solve the currently open questions.

Unified theory of reversible target reactions

We discuss two fundamental reversible diffusion influenced reactions: (i) A+B⇌C and (ii) A+B⇌C+D. In the pseudo-unimolecular case, we prove that reaction (i) is a special case of (ii), which thus constitutes a unified reversible problem of multiparticle kinetics. For static A and C (the “target” limit), we suggest to treat this problem as follows. First we generalize the Smoluchowski theory to reaction (ii). In Laplace space, we combine this with a power-law theory, determining the combination coefficient so that the unified theory reduces correctly in all known limits. We also show how to rewrite it in the time domain, with the generalized Smoluchowski theory as the leading term. Comparison with Brownian simulations shows near perfect agreement for both versions of our theory under all conditions.

Interfacial effects in the spreading kinetics of liquid droplets on solid substrates

Several theories deal with the spreading kinetics of liquids on solid substrate, most of which relate the rate of spreading to the surface tension and the viscosity of the liquid. Measurements of the spreading of a number of liquids exhibiting a wide range of surface tension and viscosity on dry soda-lime glass have been carried out to validate the proposed models. The measurements used a small droplet of constant volume to minimize gravitational effects. The contact radius was acquired as a function of time by an image analysis system. It was noted that power law theories describe the spreading rate for silicone oil on glass. However, significant departures were noted in the case of other liquids. Mechanistic considerations of our data suggest that equal volume droplets of similar surface tension and of diverse viscosity spread to the same area but at different rates. On the other hand, the spreading rate of glycerine, which exhibits incomplete spreading on glass, and that of silicone oil, with comparable viscosity behave similarly. These observations seemingly support the view that surface tension acts to retain the spherical shape of the droplet, whereas the difference between the solid–liquid and solid–vapor interfacial energies acts to enlarge the contact area. In the meantime, viscous dissipation acts to retard the spreading rate, past a constant rate regime.

Experimental investigation of Richtmyer–Meshkov instability in shock tube

An experimental investigation of the Richtmyer–Meshkov instability is carried out in a shock tube. The purpose of this study is to obtain information on the growth in the thickness of the turbulent mixing zone, which is induced by the impulsive acceleration of the interface between two gases of different densities. The turbulent phase of the evolution of this instability is of interest here. The thickness of the turbulent mixing zone is inferred from two different diagnostic techniques: measurements of infrared emission of CO2 and black-and-white or color schlieren photographs. Following an assessment of the diagnostic techniques, discussions of the main experimental difficulties as the presence of membrane fragments and the disturbances induced by the wall boundary layers, are given. Comparisons of the thickness and the thickness growth rate of the turbulent mixing zones obtained in the present experiments, with both experimental and theoretical results, are made. A tentative picture of the evolution in time of the turbulent mixing zone thickness has been developed. Results fall between the predictions of the linear and the t2/3 power law theories, with a tendency toward the latter one.

Flow of a Magnetic Fluid between Concentric Annuli. Rheological Property of Water-based Magnetic Fluid.

The authors experimentally studied a shear flow of a water-based magnetic fluid between concentric annuli. The experiment was carried out by changing the roll accerelation of the outer cylinder, and the moment acting on the inner cylinder was measured. Experimental results were discussed in the following three ways. At first the magnetic fluid was treated as a Newtonian fluid, and a small difference in the flow curves was found. Next the power law theory was applied in order to explain these differences. Finally the authors examined this flow problem using the micropolar theory, which gives the theoretical relation between the moment acting on the inner cylinder and the roll accerelation of the outer one. In this relation, a coefficient denotes the micropolar effect. The authors measured this value and showed the effect of the substructure on the fluid.