Power-law Approach Research Articles

A scaling law for predicting urban trees canopy cooling efficiency

Urban heat mitigation is a pressing concern for cities. Intense urban heat poses a threat to human health and urban sustainability. Tree planting is one of the most widely employed nature-based heat mitigation methods worldwide. Therefore, city policy makers require knowledge of how much temperature will be reduced by increasing urban tree canopy (UTC). Cooling efficiency (CE), which was been proposed to quantify the magnitude of temperature reduction associated with a 1% increase in UTC, has been primarily investigated at smaller scales previously. However, such small-scale results cannot be used to develop policy at the whole-city scale. This study developed a method that reveals the scaling relations of CE so as to predict its effects at the city scale. CE was found to follow the form of a power law as spatial scale increased from the small analytical units through intermediate size units up to the extent of a whole city. The power law form appeared consistently across cities with different climate backgrounds during summer daylight hours. Furthermore, the power law form was robust within cities under different summer weather conditions. The power-law scaling approach can thus be used to predict CE at the whole-city scale, providing a useful tool for managers to set UTC goals to mitigate extreme urban heat.

The Casimir, Van der Waals, and electrostatic forces’ effects on the response of magneto-electro-elastic nanosensor/switch beams under thermal environment

This study investigates the impact of Casimir, Van der Waals, and electrostatic forces on nanomechanical switches’ thermomechanical and free vibration behavior. The analysis is conducted using a novel higher-order beam theory and the nonlocal strain gradient elasticity. The motion equations of the nanosensor/switch beam are derived using Hamilton’s principle and solved using Navier’s method for general boundary conditions. The nanoswitch is composed of electroelastic barium-titanate (BaTiO3) and magnetostrictive cobalt-ferrite (CoFe2O4) materials, which are modeled using a power-law approach to account for functionally graded material property variations across the beam’s thickness. The impact of different parameters, such as Casimir, Vander Waals, electrostatic forces, and variations in material composition, size parameters, and gap distance, on a nanoswitch system’s bucking and free vibration is comprehensively examined. With the intermolecular and electrostatic forces, the temperature dependency of barium-titanate and cobalt-ferrite nanoswitch materials, which have not been extensively studied in any previous research, is considered in the modeling of free vibration, and the buckling behavior of a nanoswitch for the first time. This research represents the first comprehensive analysis of these factors. Considering the investigated parameters, the study’s findings can provide helpful insights into developing micro/nano-electromechanical systems, including switches, sensors, and actuators.

Near-critical behavior of the Zhong-Zhang model.

The Zhong-Zhang (ZZ) model is a one-degree-of-freedom dynamical system describing the motion of an insulating plate of length d floating on the upper surface of a convecting fluid, with locking at the boundaries. In the absence of noise, the system away from the boundaries is described by linear differential equationswith a delay time τ. The d,τ plane consists of two domains separated by a critical curve. For asymptotically long times, subcritical orbits approach a nontrivial periodic attractor, while the supercritical ones tend to a stationary state at the origin. We investigate near-critical behavior using a modified fourth-order Runge-Kutta integration scheme. We then construct a piecewise analytic decomposition of the periodic attractor, which makes possible a far higher level of accuracy. Our results provide solid evidence for an asymptotic power-law approach to criticality of several observables. The power laws are fed back to determine the piecewise-analytic structure deep into the near-critical regime. In an Appendix, we explore the effect of introducing noise using modified order-3/2 Kloeden-Platen-Schurz stochastic integration, following several observable quantities through the near-critical parameter domain.

Enhancement of the balanced total horizontal derivative of gravity data using the power law approach

Mapping the boundaries of subsurface geological structures constitutes a fundamental aspect of interpreting gravity data. Various methods relying on gravity derivatives have been introduced to delineate these boundaries. However, these approaches are not without their limitations, often leading to the generation of false edges or resulting in divergent outcomes. This article introduces a novel method that utilizes the power law approach and balanced total horizontal derivative for mapping gravity data edges. To assess the robustness of the proposed technique, we conducted tests on model examples and applied it to a real case study in northwest Vietnam. The results demonstrate that our method can accurately and clearly map edges in comparison to existing methodologies, while also preventing the generation of spurious edges in the output maps.

Experimental validation of the power law hemolysis model using a Couette shearing device.

The study of blood trauma, such as hemolysis in blood-carrying devices, is crucial due to the high incidence of adverse events like alteration of blood function, bleeding, and multi-organ failure. The extent of flow-induced hemolysis, predominantly influenced by stress duration and intensity, is described by established model parameters based on the power law approach. In recent years, various parameters were determined using different Couette shearing devices and donor species. However, they have not been validated due to limited experimental data. This study provides hemolysis measurements in a Couette shearing device and evaluates the suitability of different power law parameters. The revised Couette shearing device generates well-defined dynamic stress loads that are repeatedly applied to blood samples at a defined temperature. Human blood samples with an adjusted hematocrit of 30%, were tested with varying repetitions (20 to 80 times). The half-sinusoidal stress loads had amplitudes of 73 to 140 Pa and exposure times of 24 msec per repetition. The parameters of five common power law hemolysis approaches were then compared with the experimental data. The prediction with the power law model parameters C = 3.458 × 10-6, α = 0.2777 and β = 2.0639 showed a good agreement with the experimental results. The effect of multiple short-time stresses on hemolysis was investigated to validate the power law hemolysis model with the Couette shearing device of this study.

Reaction kinetics of an emulsified acid using a mixed emulsifier and carbonate rocks

For successful emulsified acid treatment, it is imperative to have emulsified acid that can maintain a water-in-oil emulsion state for 24 h at room temperature and 4 h at high temperatures. As a result, a hybrid emulsified acid was developed by combining cationic and nonionic emulsifiers, guaranteeing stability at both room and high temperatures. We assessed its viscosity and explored the interaction dynamics of the emulsified acid with carbonate rock samples using rotating disk apparatus experiments. Viscosity measurements revealed a non-Newtonian shear-thinning behavior modeled using a power-law approach. We examined limestone, dolomite, and chalk disks to evaluate weight loss tendencies, dissolution rates, and diffusion coefficients when exposed to the emulsified acid and hydrochloric acid (HCl). Both the weight loss and dissolution rate demonstrated that the reactivity of HCl surpasses that of the emulsified acid by up to 2.4 times at the same rotating speed. This indicates that the emulsified acid in our study can significantly slow the rapid reaction between acid and rock due to the diffusion barrier created by the oil phase. The diffusion coefficient for the limestone sample with emulsified acid was 1.46 times greater than that of dolomite (limestone: 1.64 E–7 cm2/s, dolomite: 1.12 E–8 cm2/s, and chalk: 1.47 E–8 cm2/s). Consequently, understanding the rock/mineral composition of the targeted reservoir is crucial when designing matrix acidizing with emulsified acid in carbonates. In summary, it is vital to account for the impact of emulsified acid on acid-rock reaction kinetics when establishing injection parameters for carbonate acidizing.

Bioaccumulation of chemical elements at post-industrial freshwater sites varies predictably between habitats, elements and taxa: A power law approach

Elevated environmental levels of elements originating from anthropogenic activities threaten natural communities and public health, as these elements can persist and bioaccumulate in the environment. However, their environmental risks and bioaccumulation patterns are often habitat-, species- and element-specific. We studied the bioaccumulation patterns of 11 elements in seven freshwater taxa in post-mining habitats in the Czech Republic, ranging from less polluted mining ponds to highly polluted fly ash lagoons. We found nonlinear, power-law relationships between the environmental and tissue concentrations of the elements, which may explain differences in bioaccumulation factors (BAF) reported in the literature. Tissue concentrations were driven by the environmental concentrations in non-essential elements (Al, As, Co, Cr, Ni, Pb and V), but this dependence was limited in essential elements (Cu, Mn, Se and Zn). Tissue concentrations of most elements were also more closely related to substrate than to water concentrations. Bioaccumulation was habitat specific in eight elements: stronger in mining ponds for Al and Pb, and stronger in fly ash lagoons for As, Cu, Mn, Pb, Se, V and Zn, although the differences were often minor. Bioaccumulation of some elements further increased in mineral-rich localities. Proximity to substrate, rather than trophic level, drove increased bioaccumulation levels across taxa. This highlights the importance of substrate as a pollutant reservoir in standing freshwaters and suggests that benthic taxa, such as molluscs (e.g., Physella) and other macroinvertebrates (e.g., Nepa), constitute good bioindicators. Despite the higher environmental risks in fly ash lagoons than in mining ponds, the observed ability of freshwater biota to sustain pollution supports the conservation potential of post-industrial sites. The power law approach used here to quantify and disentangle the effects of various bioaccumulation drivers may be helpful in additional contexts, increasing our ability to predict the effects of other contaminants and environmental hazards on biota.

A fractal power-law approach for investigating the interactions between reservoir microstructure and gas migration

As one of the most significant clean energy sources, the migration characteristics and extraction processes of coalbed methane (CBM) have been extensively studied. The structural distribution and evolutionary characteristics of reservoir fractures, as the main conduit for gas migration, significantly affect the permeability and gas production. However, few models have been able to quantitatively and accurately explore reservoir micro–macro interactions under coupled thermal-fluid–solid effects. This work develops a new highly coupled model based on the widely adopted power-law function to quantify reservoir thermal conduction effect, gas pressure evolution, reservoir deformation, in situ stress, the adsorption–desorption effect, and reservoir microstructure evolution. Three parameters are adopted to quantitatively characterize the reservoir structure: (1) fracture power index αf (to characterize the fracture density), (2) fracture length ratio rf (to characterize the fracture size), and (3) the maximum fracture length l. The results demonstrate that the fractal network is a special kind of network in the power-law length distribution. The proposed power-law seepage model is able to accurately characterize the evolution of reservoir microstructure and the impact of microevolution on extraction under multi-field coupling effects, compared to the traditional power-law model. The proposed model can provide a good theoretical and practical support for the study of CBM migration and extraction.

Free vibration analysis of functionally graded porous circular and annular plates using differential quadrature method

The research aims to find the fundamental frequencies of functionally graded (FG) porous circular and annular plates while accounting for three alternative porosity distributions in the thickness direction: uniform, O-shape, and X-shape. In the thickness direction, the material characteristics of FG plates are considered to vary constantly. The material characteristics are determined using Voigt's micromechanical model, which uses the power-law distribution approach with an arbitrary power index. The first-order shear deformation theory (FSDT) is used to derive the mathematical formulation of functionally graded plates. The equilibrium equation is determined using Hamilton's energy principle, and the problem is solved using the differential quadrature method (DQM). The established solution approach for non-dimensional frequencies of FG circular/annular plates is validated using convergence studies concerning the number of nodes. The FG circular/annular plate's non-dimensional frequency is determined and compared to current literature results. The natural frequency of FG porous circular/annular plates is studied in-depth in terms of thickness to radius ratio, material properties, porosity distribution, and boundary conditions.

Investigate the bending and free vibration responses of multi-directional functionally graded plates with variable thickness based on isogeometric analysis

This study investigates the static bending and free vibration behaviour of Multi-directional Functionally Graded (MFGM) plates having a variable thickness. With this regard, the third-order shear deformation plate theory is used to describe the kinematic relation. Material properties of MFGM are assumed to be graded in spatial direction within the plate’s volume and the effective material properties are calculated based on the power-law approach. The governing equations are derived based on Hamilton’s principle and the Isogeometric Analysis (IGA) is employed as a discretization tool to develop system equations. Several numerical examples are conducted to verify the accuracy of the proposed approach and investigate the influence of different geometrical and material parameters on the behaviour of MFGM plates

Finite element analysis for thermal enhancement in power law hybrid nanofluid

Ethylene glycol with nanoparticles behaves as a non-Newtonian fluid and its rheology can be best predicted by the power-law rheological approach. Further nanoparticles (molybdenum disulfide and silicon dioxide) are responsible for anti-oxidation, anti-evaporation, and anti-aging. Therefore, their dispersion in ethylene glycol is considered as these properties make the nanofluid stable. This article examines the impact of molybdenum disulfide and silicon dioxide on the thermal enhancement of ethylene glycol as it is a worldwide used coolant. Moreover, simultaneous effects of temperature and concentration gradients, Joule heating, viscous dissipation, thermal radiations, and buoyancy forces are modeled and developed, and investigations are computed by the finite element method. An increase in temperature due to the composition gradient and an increase in concentration due to the temperature gradient are observed. A significant increase in the Ohmic phenomenon with an increase in the intensity of the magnetic field is observed. Numerical experiments are performed by considering single-type nanoparticles (MoS2) and hybrid-type nanoparticles (simultaneous dispersion of SiO2 andMoS2is considered). During the visualization of simulations, the effective thermal conductivity of MoS2-SiO2-ethylene glycol is observed.

Ultrasonic evaluation of elastic properties in laser powder bed fusion manufactured AlSi10Mg components

The complete stiffness matrices of different zones in laser powder bed fusion manufactured parts out of the aluminium alloy AlSi10Mg were analysed using Ultrasonic Phase Spectroscopy (UPS). With micro-computed tomography (μCT), the complex pore architecture resulting from the layer-wise additive manufacturing was studied for two cases: a sample taken from the bulk as built hatching zone of a part and a sample representing the interface between the perimeter scan and hatching zone of a part. Five independent elastic constants describing transverse isotropic elastic anisotropy with respect to the building direction were determined by UPS and then correlated to the porosity description analysed via μCT. Anisotropy was found especially for longitudinal wave propagation. In all cases, consistent and reproducible results are obtained. Finally, the influence of porosity on the elastic properties was described with a power-law approach and a good agreement is obtained.

Deepwater soil investigation using a free fall penetrometer

Free fall penetrometers (FFP) can improve the efficiency of deepwater geotechnical site investigations. This study investigates the derivation of geotechnical properties from piezocone FFP measurements in the upper 4 m of the seabed at a clayey site with water depths of ∼1500 m. Data analysis methods as commonly applied in cone penetration test (CPT) analysis were tested with strain rate normalization methods previously suggested for FFP analysis. The logarithmic, inverse hyperbolic sine, and power law approaches were applied for strain rate normalization. Strain rate effects appeared small for FFP cone resistance (with μ = 0.1 for the logarithmic and β = 0.06 for the power law approach), but were apparent. Undrained shear strength derived from FFP data matched overall the CPT results, using an N factor Nkt = 12. Undrained shear strength derived from excess pore pressure measured at the u1 position also yielded favorable results using N∆u _FFP = 6. Two soil behavior type classifications showed acceptable agreement between strain rate normalized FFP and CPT results.

Scaling behaviour of braided active channels: a Taylor’s power law approach

At a channel (reach) scale, braided channels are fluvial, geomorphological, complex systems that are characterized by a shift of bars during flood events. In such events water flows are channeled in multiple and mobile channels across a gravel floodplain that remain in unmodified conditions. From a geometrical point of view, braided patterns of the active hydraulic channels are characterized by multicursal nature with structures that are spatially developed by either simple- and multi-scaling behavior. Since current studies do not take into account a general procedure concerning scale measurements, the latter behavior is still not well understood. The aim of our investigation is to analyze directly, through a general procedure, the scaling behavior of hydraulically active channels per transect and per reach analyzed. Our generalized stochastic approach is based on Taylor’s law, and the theory of exponential dispersion distributions. In particular, we make use of a power law, based on the variance and mean of the active channel fluctuations. In this way we demonstrate that the number of such fluctuations with respect to the unicursal behavior of the braided rivers, follows a jump-process of Poisson and compound Poisson–Gamma distributions. Furthermore, a correlation is also provided between the scaling fractal exponents obtained by Taylor’s law and the Hurst exponents.

Sensitivity Analysis and Cost Estimation of a CO2 Capture Plant in Aspen HYSYS

A standard CO2 capture process is implemented in Aspen HYSYS, simulated, and evaluated based on available data from Fortum’s waste burning facility at Klemetsrud in Norway. Since amine-based CO2 removal has high costs, the main aim is cost-optimizing. A simplified carbon-capture unit with a 20-m absorber packing height, 90% CO2 removal efficiency, and a minimum approach temperature for the lean/rich amine heat exchanger (ΔTmin) of 10 °C was considered the base case simulation model. A sensitivity analysis was performed to optimize these parameters. For the base case study, CO2 captured cost was calculated as 37.5 EUR/t. When the sensitivity analysis changes the size, the Power Law method adjusts the equipment cost. A comparison of the Enhanced Detailed Factor (EDF) and the Power Law approach was performed for all simulations to evaluate the uncertainties in the findings from the Power Law method. The optimums calculated for ΔTmin and CO2 capture rate were 15 °C and 87% for both methods, with CO2 removal costs of 37 EUR/t CO2 and 36.7 EUR/t CO2, respectively. With 19 m of packing height to absorber, the minimum CO2 capture cost was calculated as 37.3 EUR/t and 37.1 EUR/t for the EDF and Power Law methods, respectively. Since there was a difference between the Power Law method and the EDF method, a size factor exponent derivation was performed. The derivation resulted in the following exponents: for the lean heat exchanger 0.74, for the lean/rich heat exchanger 1.03, for the condenser 0.68, for the reboiler 0.92, for the pump 0.88, and for the fan 0.23.

Generalized Modeling and Propagation Characterization of THz Wireless Links in Computer Desktop Environment

AbstractIn this paper presents terahertz (THz) channel propagation characterization and generalized channel model for a desktop environment. Path loss and power delay profiles (PDPs) measured on the motherboard in both free space and desktop‐like metal cavity are compared. To characterize the large scale fading of the channel, a mean path loss model as a function of antenna height is proposed by treating the motherboard desktop environment as a partially dielectric filled resonant cavity. The measured and modeled mean path loss achieve 98.5% R‐squared goodness of fit. For the shadowing, a Gamma‐mixture model is applied to characterize the oscillations of in‐cavity measured path loss. Results show that with proper choice of the number of mixed Gamma distributions k, the goodness of fit between the model and the probability density function (PDF) can be greater than 97%. Multipath components are characterized by cluster‐based channel modeling. Modifications were made on the conventional Saleh‐Valenzuela (S‐V) model to accurately characterize the channel by rewriting the cluster power decay with step‐wise functions and each sub‐function is expressed exponentially in dB, and the ray power decay with power law approach. It is shown that measured and simulated multipath components match well with each other with at least 98.2% goodness of fit.

On the Prediction of Boundary Layer Quantities at High Reynolds Numbers

In the current paper, a new formula for calculating boundary layer quantities—such as the boundary layer thickness, friction coefficients, and the boundary layer profile—for a flat plate is presented. The formula is based on the power-law approach and represents a generalisation of the 1/7 power-law to a more extensive Reynolds number range. In addition to the derivation and the theoretical background, the main focus is on the comparison with various experimental data from the literature. The good agreement of the data shows that this approach allows for precise predictions of boundary layer quantities for a flat plate with zero-pressure gradients. Especially for estimating boundary layers along with large vehicles such as trains, ships, or aeroplanes, the formula offers added value in terms of accuracy compared to previously existing approaches, such as the 1/7 power-law.

Comparative Study on Mechanistic Kinetic Modeling of the Enzymatic Synthesis of Galacto‐Oligosaccharides

AbstractThe galacto‐oligosaccharide synthesis by β‐galactosidase from Bacillus circulans is described mathematically using three kinetic models of different complexity – a simple power law approach, an extended Michaelis Menten kinetics and, in particular, an advanced, innovative mechanistic kinetic model for biocatalysis. Based on a detailed experimental study, a comprehensive reaction network is identified, and a reliable database provided. The evaluation of the kinetic models studied is performed by the Akaike information criterion, which allows the assessment of the model accuracy taking into account complexity and transferability.

A Review on the Modeling of the Elastic Modulus and Yield Stress of Polymers and Polymer Nanocomposites: Effect of Temperature, Loading Rate and Porosity.

Porous polymer-based nanocomposites have been used for various applications due to their advantages, including multi-functionalities, easy and known manufacturability, and low cost. Understanding of their mechanical properties has become essential to expand the nanocomposites’ applications and efficiency, including service-life, resistance to different loads, and reliability. In this review paper, the focus is on the modeling of the mechanical properties of porous polymer-based nanocomposites, including the effects of loading rates, operational temperatures, and the material’s porosity. First, modeling of the elastic modulus and yield stress for glassy polymers and polymer reinforced by nanofillers are addressed. Then, modeling of porosity effects on these properties for polymers are reviewed, especially via the use of the well-known power-law approach linking porosity to elastic modulus and/or stress. Studies related to extending the mechanical modeling to account for porosity effects on the elastic modulus and yield stress of polymers and polymer-nanocomposites are discussed. Finally, a brief review of the implementation of this modeling into 3D computational methods to predict the large elastic-viscoplastic deformation response of glassy polymers is presented. In addition to the modeling part, the experimental techniques to measure the elastic modulus and the yield stress are discussed, and applications of polymers and polymer composites as membranes for water treatment and scaffolds for bone tissue engineering are addressed. Some modeling results and validation from different studies are presented as well.

Relationships between size and abundance in beach plastics: A power-law approach

Sandy beaches are one of the most relevant coastal environments in terms of socio-ecological and economical value. So, the presence and accumulation of plastic litter determines a degradation of these values, and calls for management actions for cleaning are required. In this research, we investigated the features of plastic litter distribution on a Mediterranean beach in relation to size and abundance of the sampled items. Simple allometric models were applied with the aim to provide a parsimonious tool for estimating the amount and sizes of the beach plastic litter. The results show effective relations between size and abundance of plastic items according to the power-law distribution. This relationship could support decision-makers to estimate the total amount of beach plastics through the application of a simple model instead of more complex models requiring the estimation of many parameters and the availability of large datasets.