General Power Law Research Articles

Characterizing mechanical response of bio-modified bitumen at sub zero temperatures

Cracks associated with large temperature fluctuation especially in cold regions are among prevalent pavement distresses. Binder rheology is typically found to the key factor affecting low temperature cracking resistance. Recognizing the importance of binder properties, many road authorities are requiring the use of special additives to enhance low temperature properties of binder to alleviate low temperature cracking problems. However, most of these modifiers are petroleum-based products with unstable price and depleting resources. Therefore, the asphalt industry is looking for renewable alternatives for modifying bitumen and improving its low temperature performance. Accordingly, this paper incorporates laboratory experiments and modeling to study merits of modifying bitumen with several bio-binders to enhance low temperature properties of bitumen. To investigate rheological properties at low temperatures, an extended bending beam rheometer test was used incorporating a simple fractional viscoelastic model based on the general power law. The data collected during loading and unloading portion of the test was used to evaluate the effect of introduction of bio-modifiers on low temperature properties of bitumen. The experimental results showed that introduction of bio-modifiers to bitumen significantly enhanced bitumen behavior both during creep loading and relaxation. The results of finite element modeling based on the extended bending beam rheometer geometry and boundary conditions proved that the simple fractional viscoelastic model can accurately characterize low-temperature mechanical behavior of bio-modified bitumen.

Mathematical model of the polymeric composition melt flow in the middle layer extruder of the coextrusion equipment

The paper analyzes the urgency of using coextrusion technology while recycling the secondary polymeric raw material. The balance equation in the melt flow tensions is obtained. The connection between the tensor of tensions and tensor of deformation rates components is determined. The generalized power law is used as a rheological equation of state. The energy balance equation is worked out for the stable regime of the melt flow. The limiting conditions for the complete differential model of extrusion are determined. The equation for determining the effective output of the middle layer extruder is worked out based on the efficiency of the whole extrusion machinery which depends on the characteristics of the rest four extruders and the head’s characteristics.

Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

Compensation between radiative and Auger recombinations in III-nitrides: The scaling law of separated-wavefunction recombinations

The magnitude of radiative and Auger recombinations in polar InGaN quantum wells is studied. Lifetime measurements show that these two processes are related by a power law as the electron-hole wavefunction overlap varies, leading to a near-compensation of their relative contributions. Theoretical investigation reveals that, in systems with wavefunction separation, recombination rates are controlled by the spatial tails of decaying wavefunctions. Such recombinations observe a general power law whose exponent is determined only by the ratio of the carriers' effective masses. These findings explain why III-nitride emitters remain efficient despite significant wavefunction separation.

Non-linear flow through rockfill embankments

ABSTRACT This article considers experimental data from throughflow investigations conducted on rockfill dams and adds to the state of the art in the study discipline of non-linear flow through rockfill medium, which previously has been limited to permeameter studies. The experimental program consisted of throughflow tests conducted on three different rockfill dam model setups comprising of a large-scale test conducted on a 6 m high homogenous rockfill dam and 1:10 and 1:5 scale models of the same tested in laboratory settings. The test dams were composed of uniformly graded rockfill with median particle sizes ranging from 10.2 to 350 mm. Based on statistical analysis conducted on the experimental data sets, a general non-Darcy type power-law describing non-linear flow through homogenous rockfill dams is proposed. Also, some of the well-known power-law relationships from the available literature are validated employing the experimental data sets.

Numerical simulations of the pulsatile blood flow in narrowing small vessels using different rheological models

The study of the blood flow through the circulatory system vessels depends on the rheological properties of the blood, the pulsatile nature of the blood flow and the vessel diameter. Blood behaves as a non-Newtonian fluid in small vessels, in situations of complex geometry and in certain cardiovascular diseases such as hypertension, coronary artery diseases, etc.In this article, we present two-dimensional computational simulation of blood flow in an axisymmetric narrowed small vessels (stenosis artery) taking into consideration the non-Newtonian fluid properties. The study is based on the numerical solution of the Navier-Stokes equations for Pulsatile flow using three constitutive relations for modeling the rheological blood behavior, ie; the Cross law; the Generalized power law; Gpl, and the Herschel-Bulkley law. We examined the flow characteristics particularly the velocity, shear rate distribution, wall shear stress and time-dependent vortex structures with respect to critical flow conditions in small vessels. Results indicate that the instantaneous flow characteristics are significantly affected by the blood rheological models considered, especially, in zones of important shear rate.

Influence of anisotropy of marine turbulence on the variance of optical wave AOA fluctuations.

The optical wave angle of arrival (AOA) fluctuations in marine turbulence severely degrade long-range imaging quality by introducing image distortion. Theoretical investigations of optical wave AOA fluctuations are critical to improve the performances of long-range imaging systems in marine turbulence conditions. In this work, analytic expressions for the variance of optical plane and spherical wave AOA fluctuations in anisotropic marine turbulence will be derived. Compared with the previous models that focus on the isotropic and Kolmogorov properties of marine turbulence, both the anisotropy and non-Kolmogorov features of marine turbulence are considered. The anisotropic factor, general spectral power law instead of constant value of 11/3, finite turbulence inner and outer scales, and variable wavelength are included in the models developed in this work. Also, comparative analyses are performed for the models derived separately in marine and terrestrial anisotropic turbulence conditions. It turns out the anisotropy of turbulence cells degrades the effects of marine turbulence on the optical wave AOA fluctuations. Also, the marine atmosphere humidity fluctuations increase the impacts of anisotropic marine turbulence on the final derived models.

Configuration of Late Archaean Chilimanzi and Razi Suites of Granites, South-Central Zimbabwe Craton, From Gravity Modelling: Geotectonic Implications

The subsurface geometry of five representative late Archaean ‘Chilimanzi and Razi’ suite plutons in the Zimbabwe craton (ZC) has been investigated by gravity modelling constrained in part by surface geology, density measurements and seismic information, to determine their 3D configuration and infer tectonic context of emplacement. The generally K-rich, massive, homogeneous monzogranites are characterised by large Bouguer gravity lows (up to − 30 mGal amplitude) whose gradients outline their spatial extent well. The southernmost plutons and their anomalies have general trends paralleling the North Marginal Zone (NMZ) of the Limpopo orogenic belt (LB). Predictive gravity models indicate that the density contrast of the Chivi batholith (CB) adjacent to the ‘volcanic arc-like’ Belingwe greenstone belt extends to a depth of about 13 km. The nearby Razi pluton (RP) which intrudes the ZC-LB boundary appears to have been emplaced at shallower depths/levels. The gravity model suggests a thickness of about 5–6 km, and a moderate to shallow dip to the southeast under the NMZ, compatible with syn-kinematic intrusion during overthrust of the LB over the ZC. The smallest Nalatale granite (Ng) is on average 2.5 km thick under the Fort Rixon greenstone belt but includes a root up to 4.5 km thick under the anomaly peak, and a steep contact with the tonalite/gneiss to the east. These granites follow the general power-law for pluton dimension and are similar in this respect to the classical wedge-shaped plutons, extending largely in one direction, with large aspect ratios (Length (L)/Thickness (T) > 7). However, the overall shape of the RP is typical of a diapir (Width (W) 5; L/T > 15). Overall, the CB and the ZG are interpreted as massive, deep-rooted batholithic intrusions (L/T ≅ 10), contrary to some geological interpretations of these late, post-kinematic intrusions as sheet-like bodies emplaced at relatively shallow levels in the crust. On the other hand, the ChB appears to be a tabular intrusion, probably fed by dykes; it exhibits a lateral extent much greater than the vertical one, outlining a sheeted geometry (W/T > 7; L/T > 18). The geophysical evidence, together with geological and fabric data, support and/or confirm the two main granite configurations: sheets and batholith; and thus also confirm the two main modes of emplacement: dyke and diapirism or ballooning plutonism. This is consistent with other known batholiths on the ZC but considered unusual for plutons of the same age and spatially close when compared to other Archaean cratons.

Exploring spatio-temporal changes of city inbound tourism flow: The case of Shanghai, China

Knowledge on spatio-temporal changes of inbound tourism flow is important for destination economy, cultural communication and city image. This paper proposes a novel research framework for the spatio-temporal distribution and changes of inbound tourism flow by, first, using R-HDBSCAN clustering algorithm to extract tourism area of interest (AOI), second, by utilizing several key indicators adopted from the complex network theory literature to study the structure of inbound tourism flow with a case study example from Shanghai, China. The results show, first, that tourism in Shanghai is highly concentrated on the most popular AOI clustered in the city center relatively close to each other and, second, that, the inbound tourism flow network of Shanghai has small-world characteristics, while the distribution of its AOI (nodes) and tourist routes (edges) has general power law features, which has been influenced by the World Expo.

The Beneficial Role of Piles on the Seismic Loading of Structures

We examine the kinematic response of fixed-head vertical floating piles embedded in continuously nonhomogeneous soils and subjected to upward propagating seismic waves. The problem is explored numerically by means of a rigorous finite element (FE) model of the soil-pile system to quantify the kinematically induced reduction of the horizontal free-field spectral acceleration. Soil stiffness varies continuously with depth according to a generalized power law function. We show that kinematic pile response in the harmonic regime is controlled by a unique dimensionless frequency parameter involving the active pile length in a generalized nonhomogeneous soil. A new, simplified expression for the horizontal kinematic interaction factor Iuis proposed for practical time-domain applications while a novel physical interpretation of the filtering action of piles is reported by introducing the role of pile stiffness in averaging soil motion over an effective pile length. Following a parametric study under transient motion, we propose a set of novel, ready-to-use formulae for a rapid assessment of the pile-induced filtering action. An application of the proposed formulae to clayey soils is finally presented, leading to useful indications for the selection of the pile diameter associated with the maximum filtering potential.

Neural Computing Strategy for Predicting Deactivation of Fischer–Tropsch Synthesis With Different Nickel Loadings

Direct determination of the process deactivation model relates to catalyst stability and plays a crucial role in the process control. The present study aims at investigating the influence of nickel loading (10–20 wt%) on the deactivation model parameters of Ni/Al2O3 catalyst prepared by incipient wetness impregnation. Artificial neural network (ANN) predicts a steady-state activity of the catalyst for the ultimate purpose of a deactivation model selection. The results obtained from an ANN demonstrated that the first-order general power law expressions (GPLE1 model) could adequately predict the catalytic activity during long reaction time. Considering various loadings of nickel on an alumina support, better stability of 20Ni/Al2O3 catalyst was confirmed. Model parameters affirmed that a decrease in the loading of the nickel-made active phase increases the deactivation rate of the catalyst.

SEEPAGE PROPERTIES OF ROCK FRACTURES WITH POWER LAW LENGTH DISTRIBUTIONS

Fractures with power law length distributions abound in nature such as carbonate oil and gas reservoirs, sandstone, hot dry rocks, etc. The fluid transport properties and morphology characterization of fracture networks have fascinated numerous researchers to investigate for several decades. In this work, the analytical models for fracture density and permeability are extended from fractal fracture network to general fracture network with power law length distributions. It is found that the fracture density is related to the power law exponents [Formula: see text] and the area porosity [Formula: see text] of fracture network. Then, a permeability model for the fracture length distribution with general power law exponent [Formula: see text] and the power law exponent [Formula: see text] for fracture length versus aperture is proposed based on the well-known cubic law in individual fracture. The analytical expression for permeability of fractured networks is found to be a function of power law exponents [Formula: see text], area porosity [Formula: see text] of fracture network, and the micro-structural parameters (maximum fracture length [Formula: see text], fracture azimuth [Formula: see text] and fracture dip angle [Formula: see text]). The present model may shed light on the mechanism of seepage in fracture networks with power law length distributions.

Considerations for readdressing theoretical descriptions of particle-reinforced composite food gels.

The aim of this work was to address the ability of established theoretical models to describe the small deformation mechanical properties of particle-filled food protein gels. To this end, the effect of incorporating glass microspheres on the elastic modulus of heat-set whey protein isolate/xanthan gum gels is reported. Filler size and polydispersity strongly influenced the observed reinforcement with increasing filler content; however, these effects were also strongly correlated to the ionic strength of the gelator phase (0-200 mM NaCl). Fillers with greater polydispersity provided less reinforcement at high filler content, which was associated with improved packing efficiency. Increasing ionic strength reduced the extent of filler/matrix binding, drastically reducing the impact of the smaller glass microspheres (4 μm, 7-10 μm). Larger particles increased the elastic modulus at high salt content due to interfacial stress concentration and particle-particle contacts. Theoretical fits could not satisfactorily describe the general trend in reinforcement observed with increasing filler content, despite employing various methods to account for the effects of filler self-crowding. Using an empirical approach, we propose an alternative functional form which provides improved fits over the entire range of filler content investigated. This general power law (GPL) model provided physically reasonable values for the maximum packing fraction through an empirically-derived expression for the scaling exponent. A weighted average approach was also proposed to incorporate effects of imperfect filler/matrix adhesion. This method incorporates contributions of both bound and unbound fillers, providing a means to model the effect of increasing ionic strength.

Dynamic analysis of the anomalous diffusion in catalyst particles considering chemical reactions with non-linear kinetics

In this work, a generalized reaction-diffusion model useful to study the interactions between anomalous diffusion and chemical reactions in catalyst particles is presented. The fractional reaction-diffusion model considers the linearization of the non-linear reaction kinetic terms, which allows the solution of the mathematical model through the Fourier transform. The proposed methodology can be used for the dynamic analysis of the concentration profiles in the catalytic pellets, including internal and external mass transfer resistances, as well as for the estimation of effectiveness factor (EF). These findings revealed that the analysis of dynamic reaction-diffusion linearized models where the mass transfer is described by the anomalous transport can be analysed in the frequency domain. Two kinetic models, a general power-law and Langmuir-Hinshelwood, were considered. The results demonstrated the effect of use the traditional Fick’s law and the anomalous transport (i.e., subdiffusion or superdiffusion phenomena) in a porous media system, particularly on the space-time concentration profile predictions and the influence on the effectiveness factor of the catalytic particle.

Accurate Semantic Segmentation in Turbulence Media

Accurate image semantic segmentation in atmosphere turbulence conditions is challenging due to the severe degradation effects introduced by the random refractive-index fluctuations of atmosphere. In this paper, we present an end-to-end trainable methodology for turbulence-degraded image semantic segmentation that is capable of digging the physical imaging mechanism in atmosphere turbulence conditions, in order to improve semantic estimates. First, we investigate the physical imaging mechanism in kinds of turbulence conditions, including the isotropic turbulence and the anisotropic turbulence. Physical turbulence parameters are considered, such as the anisotropic factor, turbulence inner and outer scales, refractive-index structure constant, general spectral power law and imaging distance. Second, based on the physical imaging model in various turbulence conditions and image processing algorithms, we construct the turbulence-degraded image datasets, including the turbulence-degraded Pascal VOC 2012 and ADE20K. The new datasets cover a wide range of turbulence scenes. Third, in order to obtain more accurate boundary information, we propose the Boundary-aware DeepLabv3+ network that is trained on the constructed turbulence-degraded image datasets for semantic segmentation in turbulence media. The proposed model extends DeepLabv3+ by adding simple yet effective Edge Aware Loss and Border Auxiliary Supervision Module, which is helpful to acquire precise boundary segmentation effect while confining the target in this boundary region. Finally, without any pre-processing, the semantic segmentation accuracy reached a performance of 87.95% mIoU on the Turbulence-degraded Pascal VOC 2012 Dataset.

Strongly nonlinear perturbation theory for solitary waves and bions

Strongly nonlinear perturbation theory would seem to be an oxymoron, that is, a contradiction of terms. Nonetheless, we here describe perturbation methods for wave categories that are intrinsically nonlinear including solitons (solitary waves), bound states of solitons (bions) and spatially periodic traveling waves (cnoidal waves). Examples include the Kortweg-deVries and Benjamin-Ono equations with general power law nonlinearity and the Fifth Order KdV equation. The perturbation strategies include (ⅰ) the Gorshkov-Ostrovsky-Papko near-equal-amplitude soliton interaction theory (ⅱ) perturbation series in the Newton-homotopy parameter and (ⅲ) approximations for large values of the nonlinearity exponent. A long section places strongly nonlinear perturbation theory for waves in a larger context as a subset of unconventional perturbation expansions including phase transition theory in \begin{document}$ 4 - \epsilon $\end{document} dimensions, the \begin{document}$ \epsilon = 1/D $\end{document} expansion where \begin{document}$ D $\end{document} is the dimension in quantum chemistry, the renormalized quantum anharmonic oscillator, the Yakhot-Orszag expansion in the exponent of the energy spectrum in hydrodynamic turbulence, and the Newton homotopy expansion.

Normal depth and wetted perimeter in general power-law channels

Open channel cross section is an important element in water structures engineering. A general power-law section allows simulation and modeling of natural rivers and man-made open channels. Given simple forms and superior properties, the power-law sections are of interest to water resources engineers. The power-law exponent, m, is a parameter for which the open channel takes different shapes. The range of practical interest for the parameter m is 1 <m< ∞. Normal flow depth is of high importance and used for design and computation of water surface profiles in open channels with different shapes. The calculation of wetted perimeter and normal flow depth in power-law channels, ends up the hypergeometric functions and thus has been the main challenge over the years. Direct and simple solutions for these key quantities are not available in technical literature over the entire practical range of m> 1. Some studies are only valid over m> 2.5 while the others are applicable in the range of 1 <m< 2. This study presents direct and simple solutions for the normal flow depth and wetted perimeter in power-law channels over the wide practical range of 1.05 <m< 50. The maximum relative error of the proposed approximations for the normal flow depth and wetted perimeter are less than 1.2% and 0.3%, respectively. The proposed superior approximations can be used for channel section construction and optimization.

On power law scaling dynamics for time-fractional phase field models during coarsening

In this paper, the energy scaling behavior of the time-fractional phase field models is investigated. We report a seminal observation that the effective free energy of the time-fractional phase field models obeys a general power-law scaling dynamics during coarsening. Mainly, the effective free energy and roughness in the time-fractional phase field models scale by following a similar power law as the integer phase field models, where the power is linearly proportional to the fractional order. This general scaling law is verified numerically against several classes of phase field models, including the Cahn–Hilliard equation with different types of variable mobilities and the molecular beam epitaxy models. This new finding opens potential paths of applying time-fractional phase field models in studying anomalous coarsening dynamics.

Confining massless Dirac particles in two-dimensional curved space

Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.

Generalized power law for predicting the air flow resistivity of thermocompressed fibrous materials and open cell foams

The compression of sound absorbing materials can change significantly their acoustical properties. It is commonly admitted that the air flow resistivity is the main parameter governing the acoustical efficiency. Several authors propose empirical laws to predict the resistivity as function of the compression rate. The models are based on a power function with a power related to the kind of material. In this paper, we propose a generalized power law to calculate the air flow resistivity of compressed porous materials with high porosity (⩾0.9). The power is here related to the material initial porosity. The influence of fibres orientation distribution is also addressed. The proposed formula shows a good agreement with the measurements performed on several types of porous materials (four fibrous materials and two open cell foams).