Power-law Expression Research Articles

Fatigue properties of non-press-fitted part of full-scale induction-hardened axles of medium-carbon steel for high-speed railway vehicles

This study aimed to examine the stress–number of cycles (S–N) curve and fatigue limit of non-press-fitted parts to improve the sophistication of the design method of induction-hardened axles for medium-carbon steel high-speed railway cars. Macroscopic cracks were generated in the non-press-fitted parts of the axles by selecting appropriate fatigue test methods. Thus, the S–N curve was approximated, and the fatigue limit was obtained. The value of an index in the power-law expression of the S–N curve was 11, which was proposed to fatigue damage evaluation standard. Moreover, we constructed a prediction model for high-and very-high-cycle fatigue limits based on the local fatigue-limit approach and fatigue test results of cut-out specimens from several depth regions of induction-hardened axles. The fatigue limit predicted by the model agrees with the experimental high-cycle fatigue limit. The model estimated that the fatigue limit did not decrease in the very-high-cycle regime.

Discussion of “Water distribution characteristics of capillary absorption in internally cured concrete with superabsorbent polymers”

In March 2024 Construction and Building Materials published “Water distribution characteristics of capillary absorption in internally cured concrete with superabsorbent polymers”, which claims to present a water distribution model characterising the spatiotemporal moisture content evolution in internally cured concrete with superabsorbent polymers during capillary absorption. This discussion, considered a post-publication critique, establishes that the paper’s water distribution model conflicts with the paper’s capillary absorption tests. While the model is based on the premise of the square-root-of-time behaviour of capillary absorption, the tests do not demonstrate that square-root-of-time behaviour. This critique in addition questions the paper’s forthright application of the power-law diffusivity expression with exponent 4, given that its validity for the paper’s materials has not been verified. It is shown that different but equivalent diffusivity expressions lead to different moisture diffusivities at lower moisture contents.

Magnetic exchange interactions and non-Debye relaxation in spin-3/2 frustrated Kagomé magnet Co3V2O8

We report the experimental determination of the magnetic exchange parameter ( J/kB = 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co3V2O8 using the temperature dependence of dc-magnetic susceptibility χ(T) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strength Jex−NN∼ 2.45 K. Five different magnetic phase transitions (6.2–11.2 K) and spin-flip transitions (9.6–7.7 kOe) have been probed using the ∂ ( χT )/ ∂T vs. T, heat capacity (CP -T) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of the CP -T near TN (11.2 K) has been analyzed using the power-law expression CM = A|T — TN|−α resulting in the critical exponent α = 0.18 ± 0.01 (0.15 ± 0.003) for T < TN (T > TN ), respectively for the Co3V2O8. It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co3V2O8 and was evident from the Kohlrausch–Williams–Watts analysis of complex modulus and impedance spectra (0 ⩽β⩽ 1). Mott’s variable-range hopping of charge carriers process is evident through the resistivity analysis ( ρac -T −1/4 ) in the temperature range 275 ∘C–350 ∘C. Moreover, the frequency-dependent analysis of σac (ω) follows Jonscher’s power law yielding two distinct activation energies ( Ea∼ 0.37 and 2.29 eV) between the temperature range 39 ∘C–99 ∘C and 240 ∘C–321 ∘C.

Comparison of Polypentenamer and Polynorbornene Bottlebrushes in Dilute Solution.

Bottlebrush (BB) polymers were synthesized via grafting-from-atom transfer radical polymerization (ATRP) of styrene on polypentenamer and polynorbornene macroinitiators with matched grafting density (n g = 4) and backbone degrees of polymerization (122 ≥ N bb ≥ 61) to produce a comparative study on their respective dilute solution properties as a function of increasing side chain degree of polymerization (116 ≥ N sc ≥ 5). The grafting-from technique produced near quantitative grafting efficiency and narrow dispersity N sc as evidenced by spectroscopic analysis and ring closing metathesis depolymerization of the polypentenamer BBs. The versatility of this synthetic approach permitted a comprehensive survey of power law expressions that arise from monitoring intrinsic viscosity, hydrodynamic radius, and radius of gyration as a function of increasing the molar mass of the BBs by increasing N sc. These values were compared to a series of linear (nongrafted, N sc = 0) macroinitiators in addition to linear grafts. This unique study allowed elucidation of the onset of bottlebrush behavior for two different types of bottlebrush backbones with identical grafting density but inherently different flexibility. In addition, grafting-from ATRP of methyl acrylate on a polypentenamer macroinitiator allowed the observation of the effects of graft chemistry in comparison to polystyrene. Differences in the observed scaling relationships in dilute solution as a function of each of these synthetic variants are discussed.

Structural, and complex impedance studies of ruddlesden-popper Sr1.80Nd0.20MnO4 oxide

The solid-state reaction technique was employed to synthesize the Sr1.80Nd0.20MnO4 oxide. The resulting pure phase powder was obtained by quenching the mixture in air from 1400 °C to room temperature. The Rietveld refinement of XRD data confirmed the tetragonal K2NiF4-type structure and I4/mmm space group. Upon analysis of the complex impedance, it was observed that the Sr1.80Nd0.20MnO4 sample exhibited two electrical equivalent circuits, which were needed to explain the impedance results. To investigate the electrical conductive properties of composite materials under different temperate conditions, Jonscher's power law expression was utilized. The calculated activation energies from both the analysis of the electrical circuit equivalent and the conductivity data were found to be closely similar. This supports the conclusion that ion hopping mechanism plays a key role in the transport of charges within the investigated materials. Additionally, it was observed that thermal activation predominantly governs the conduction process.

Investigation of optical, dielectric, and conduction mechanism in lead-free perovskite CsMnBr3.

Metallic perovskites have advantageous optical and electrical properties, making them a valuable class of semiconductors for the manufacturing of solar cells. CsMnBr3 is notable among them due to its important optical characteristics. The electrical and dielectric characteristics as a semiconductor are examined in this study. Direct transitions with a 3.29 eV bandgap and an Urbach energy of 0.96 eV are revealed by the results. Through AC conductivity, it demonstrated semiconductor characteristics at 443 K. The dielectric loss varied with frequency and peaked at high frequencies. Furthermore, as temperature rose, a relaxation peak in the electrical modulus was seen to migrate to higher frequencies. Ac conductivity is described by the double power law expression. The conduction in our compound is governed by small polaron tunneling. Based on the optical results reported in the bibliography for this sample, we realize the importance of examining the electrical characteristics to comprehend the semiconductor behavior of CsMnBr3.

Hygrothermal Effects on Vibration Response of Porous FG Nanobeams Using Nonlocal Strain Gradient Theory Considering Thickness Effect

In this work, the thickness-dependent size effect on nonlinear free vibration response of a Porous Functionally Graded (PFG) nanobeam in a hygrothermal environment is examined via nonlocal strain gradient theory (NSGT). Through the depth of the beam, hygro-thermal loadings are uniformly distributed. The mechanical properties of the beam are assumed to vary continuously in the thickness direction according to the power law expression. The equations of motion are derived using Hamilton’s principle with consideration of von-Kármán nonlinearity. The nanobeam vibration responses are obtained with the aid of the Galerkin technique and the Hamiltonian approach. A vital point of this work is to explore the effects of power law index, slenderness ratio, porosity volume fraction, and hygrothermal changes on the vibration behavior of PFG nanobeams. The results indicate how the thickness effect and porosity volume fraction significantly change the size-dependent vibration response of the FG nanobeam under hygrothermal conditions. The paper findings can be applied to improve the mechanical performance of PFG nanobeams.

Kinetics of CO2 absorption in N-Methyldiethanolamine solution promoted by potassium sarcosine

Potassium sarcosine (KSar) shows promise as an effective co-promoter of N-methyldiethanolamine (MDEA), a tertiary amine known for its high CO2 absorption capacity but relatively slow kinetics. This study investigated the CO2 absorption kinetics in a KSar + MDEA + H2O solution using the pressure-decay technique in a stirred cell reactor. The experiments were performed at temperatures ranging from 303.15 K to 333.15 K, with varying concentrations of KSar (ranging from 3% to 15% by weight), while keeping the MDEA concentration constant at 20% by weight. Furthermore, the study involved assessing the physicochemical and mass transfer properties and comparing them to those of a solution containing MDEA (30 wt%) + H2O solution. Properties like density, viscosity, Henry's constant (HN2O), and the physical mass-transfer coefficient of the liquid phase (kl) were measured and applied to analyze CO2 absorption kinetics. The overall reaction rate constant (kOV) was assessed using both termolecular and zwitterion mechanisms within a pseudo-first-order reaction regime. Additionally, kOV was estimated via correlated Arrhenius power law expression of the individual rate contributions of CO2−MDEA, CO2–H2O, and CO2−KSar. The calculated kOV values were found to closely match the experimental data, with absolute average relative deviations (AARD) of 4.53% and 3.03% for the termolecular and zwitterion models, respectively. The experimental results clearly showed that the rate of CO2 absorption, represented by kOV, can be significantly enhanced by adding a small amount of KSar into the MDEA + H2O solution.

Wave spectrum characterization in turbulent stratified air-water flows in a large diameter pipe

This study presents an analysis of interfacial waves in turbulent stratified air-water pipe flow in a 10 cm diameter pipe at atmospheric conditions. Interface elevation measurements are performed by means of conductance probes at a high sampling rate. In particular, the frequency spectra are characterized and the wave structure is assessed through the analysis of the power spectral density (PSD) and its important features, such as dominant frequencies, peak densities and dissipation region. The influence of both gas and liquid superficial velocities is assessed. For the range of superficial velocities investigated (USL = 0.08-0.15 m/s, USG = 1.0-4.5 m/s), dominant frequencies of approximately 7-8 and 3-4 Hz are observed in the wave growth and saturation regimes, respectively, defined by Ayati & Carneiro (2018). A transition from wave growth to wave saturation regime was observed to occur in the range of USG = 1.0-2.0 m/s, for the current conditions studied. In the saturation regime, a secondary peak is observed in the frequency spectra at approximately 7-8 Hz. A scaling analysis is performed to support the interpretation of results and parameterization of spectral parameters, as an indication of the wave structures. In the saturation regime, the high frequency region of the frequency spectra (spectral tail) displays a nearly monotonic decay, and the data supports in general a power law of the form F−n, n ∼ 4-4.5, as evidenced by the non-dimensional analysis covering the full range of conditions tested in this work. This is in accordance with the power law expression derived by Phillips (1985) and supports recent interpretation of air-flow separation and micro-breaking as wave dissipation mechanisms (Ayati, 2018). Power-laws of the form S(F0) ∼(F0) -5 for the peak densities in the PSDs are also found to represent well the current data set for the envelope curve of the spectral peaks. Particularly for the wave saturation regime. For the waves analyzed in the current work, a direct relation between the dominant frequencies and the mean liquid depth is shown to hold.

A non-iterative solution for frost growth on flat surfaces

An algebraic, first-principles solution for frost growth on horizontal flat surfaces is derived. To avoid dependence on the frost surface temperature, the proposed solution uses a generic, power-law frost density expression. This yields a new class of non-iterative, fully-algebraic solutions to the problem of frost growth and densification on flat surfaces that are based explicitly on time and heat transfer characteristics. Closure of the derived solution is reached via semi-empirical frost property expressions. With three frost density expressions selected from literature, the predictive accuracy of the proposed frost thickness solution for each density expression is compared to flat plate and parallel plate frost thickness databases. The proposed solution is shown to accurately predict frost thickness, with 73.2% and 81.5% of the predictions falling within ±20% proportional error bands for the flat and parallel plate geometries respectively. Moreover, the proposed solution is shown to be comparably accurate to other predictive methods. The proposed approach is particularly useful in applications that require a non-iterative implementation, or those interested in decreasing computational effort in frost predictions.

Natural Oil Polyol from High-Oleic Palm Oil─Reaction Kinetics and Monitoring Using Near-Infrared Spectroscopy

Natural oil polyols are widely used biobased monomers for the manufacture of polymers and resins. They are mainly produced via hydroxylation of epoxidized vegetable oils. This work studied the kinetics of hydroxylation of epoxidized high-oleic palm oil via oxirane ring cleavage with ethylene glycol (EG). Experiments were performed at different temperatures (65–95 °C), hydroxyl-to-oxirane mol ratios (1.75–14), and catalyst loadings (H2SO4, 0.5–4% wt). The reaction was monitored by measuring the hydroxyl value and oxirane oxygen content in samples using near-infrared absorbance. Different power-law kinetic expressions were evaluated, and the lower average error (3.25%) resulted in first order with respect to epoxide, second order with respect to EG, and considering oligomers formation. The corresponding frequency factor and energy of activation for hydroxylation were 3.58 × 104 and 51.9 kJ/mol, and those for oligomerization were 3.32 × 105 and 67.2 kJ/mol, respectively. The obtained model is suitable for further process design and scale up.

Cerofolini’s Model and the Fractal Adsorption Isotherms

The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal behavior concerning both energetic and geometric surface heterogeneities described by the power-law expressions and fractal dimensions, the paper will develop some fractal adsorption isotherms. Using our theoretical approach, fractal isotherms will provide insights not only into the fractal behavior of the surface geometry but also into the fractal energetic heterogeneities, implying that a sorbent does not need to be porous to apply a fractal isotherm: adsorption on “flat” surfaces can also be described by fractal isotherms and fractal dimensions related to energetic disorders. For example, the theory will be applied to computing the energetic fractal dimensions of some nanoparticle catalysts, Rh/Al2O3, Rh/TiO2, and Rh/WO3.

Stress analysis of rotating thick-walled nonhomogeneous sphere under thermomechanical loadings

In this work, a rotating thick-walled spherical vessel made of nonhomogeneous materials subjected to internal and/or external pressure under thermal loading was analyzed within the context of three-dimensional elasticity theory. An analytical formulation was established for computing the displacement and stress fields. It has been assumed that the mechanical and thermal properties are varying through thickness of the functionally graded material (FGM) according to a power-law nonlinear expression, while Poisson's ratio is considered as constant. Based on equilibrium equation, Hooke's law, stress-strain relationship in the spheres and other theories from mechanics a second-order ordinary differential equation well-known as Navier equation is obtained that represents the thermoelastic field in hollow FGM sphere. Navier equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Different results of thermoelastic field are presented across the thickness of the sphere. The analysis of the different results reveals that stress and strain in the FGM sphere are significantly depend upon variation made in temperature profile, rotation and inhomogeneity parameter on the thermoelastic field. Thus, the inhomogeneity in material properties can be exploited to optimize the distribution of displacement and stress fields.

Probing power laws in multifrequency AFM

Quantification of conservative forces in multifrequency atomic force microscopy requires solving the general equations of the theory expressed in terms of the virials of interaction. Power law expressions are commonly utilized when dealing with electrostatic, ferroelectric, magnetic, or long range (van der Waals) forces. Here, we discuss long range forces modeled in terms of power laws (n), where the exponent n covers the range n = 2–5, and employ the multifrequency theory to explore the relevant parameter space. Numerical integration of the equations of motion suggest that only a narrow range of operational parameters are available when imaging where the approximations are valid. Albeit these conditions exist, and the corresponding errors can be as low as 10% throughout for all exponents explored.

Exergy loss analysis on heat transfer characteristics of twisted petaloid spirally wound tube with the convection boundary condition

• 1. Heat transfer characteristics of the twisted petaloid spiral wound tube (TPSWT) are investigated. • 2. Expression of heat transfer exergy loss number (HTELN) is derived. • 3. Characteristics of the HTELN is studied. • 4. Correlation of the HTELN for the TPSWT is formulated. The spiral flow motivates an extra centrifugal force inducing the secondary flow to effectively enhance the heat transfer performance of spirally wound tubes (SWTs). In this research, the flow and heat transfer characteristics of twisted petaloid spirally wound tube (TPSWT) basis of exergy theory was numerically analyzed, which integrates the technologies of spiral coil, petaloid section and twisted channel. Firstly, the flow and heat transfer characteristics of the TPSWT are numerically investigated. Secondly, the heat transfer exergy loss number (HTELN, ζ HT ) is proposed. Furthermore, the relationship between η (heat transfer effectiveness) and ζ HT is investigated. Finally, the correlations for Nu petal , η and ζ HT in the form of classical power–law expression are calculated. The results show that, the secondary flow induced by the integration of the centrifugal force and the torsional force destroying the steady flow state, which enhances the heat transfer performance; ζ HT can describe the heat transfer performance in 2 aspects, one is for the heat transfer irreversible loss, the other one is for the heat transfer efficiency; the predicted values of the regression functions are well aligned with the numerical calculated data (6.73% for Nu petal ; 1.68% for η; 0.38% for ζ HT ).

A comprehensive experimental and kinetic modeling study of di-isobutylene isomers: Part 2

A wide variety of high temperature experimental data obtained in this study complement the data on the oxidation of the two di-isobutylene isomers presented in Part I and offers a basis for an extensive validation of the kinetic model developed in this study. Due to the increasing importance of unimolecular decomposition reactions in high-temperature combustion, we have investigated the di-isobutylene isomers in high dilution utilizing a pyrolysis microflow reactor and detected radical intermediates and stable products using vacuum ultraviolet (VUV) synchrotron radiation and photoelectron photoion coincidence (PEPICO) spectroscopy. Additional speciation data at oxidative conditions were also recorded utilizing a plug flow reactor at atmospheric pressure in the temperature range 725–1150 K at equivalence ratios of 1.0 and 3.0 and at residence times of 0.35 s and 0.22 s, respectively. Combustion products were analyzed using gas chromatography (GC) and mass spectrometry (MS). Ignition delay time measurements for di-isobutylene were performed at pressures of 15 and 30 bar at equivalence ratios of 0.5, 1.0, and 2.0 diluted in ‘air’ in the temperature range 900–1400 K using a high-pressure shock-tube facility. New measurements of the laminar burning velocities of di-isobutylene/air flames are also presented. The experiments were performed using the heat flux method at atmospheric pressure and initial temperatures of 298–358 K. Moreover, data consistency was assessed with the help of analysis of the temperature and pressure dependencies of laminar burning velocity measurements, which was interpreted using an empirical power-law expression. Electronic structure calculations were performed to compute the energy barriers to the formation of many of the product species formed. The predictions of the present mechanism were found to be in adequate agreement with the wide variety of experimental measurements performed.

Logistic-Regression-Based Meta-Analysis of Factors Affecting Flame Stability in a Shock Tube

ABSTRACT This work describes a meta-analysis performed in an effort to better understand the parameters controlling flame stability in shock-tube flame experiments. The data set used in the analysis was aggregated from multiple prior studies employing the shock-tube flame speed method, as well as previously unreported results. Flames are first qualitatively classified as being smooth, distorted, or wrinkled based on end-wall images. A subset of trials capturing the stability transition from stable to unstable flames are then selected from each set of experiments. Across all data sets, the transition between stable and unstable flames is analyzed as a binary classification problem using logistic regression. The resulting classification model, cast in terms of a multivariate power-law expression for the critical temperature ( T crit ) at which flames become unstable, is found to be highly predictive of the stability transition. Consideration of the trained model coefficients allows the effects of different experimental parameters on T crit to be identified. Model parameters provide significant new insight into the selection of diluents in experiments; the use of a test gas with a high heat capacity ratio is found to have the most beneficial effect toward increasing T crit , while the effects of Lewis number and molecular weight are determined to be negligible. Ignition-location and pressure effects are less well quantified due to limited available data and are identified as key areas of further study.

Ionizing feedback from an O star formed in a shock-compressed layer

ABSTRACT We develop a simple analytical model for what happens when an O star (or compact cluster of OB stars) forms in a shock-compressed layer and carves out an approximately circular hole in the layer, at the waist of a bipolar H ii region (H iiR). The model is characterized by three parameters: the half-thickness of the undisturbed layer, $Z_{_{\rm LAYER}}$, the mean number density of hydrogen molecules in the undisturbed layer, $n_{_{\rm LAYER}}$, and the (collective) ionizing output of the star(s), $\dot{\cal N}_{_{\rm LyC}}$. The radius of the circular hole is given by $W_{_{\rm IF}}(t)\sim 3.8\, {\rm pc}\, [Z_{_{\rm LAYER}}/0.1\,{\rm pc}]^{-1/6}[n_{_{\rm LAYER}}/10^4\,{\rm cm^{-3}}]^{-1/3}[\dot{\cal N}_{_{\rm LyC}}/10^{49}\,{\rm s^{-1}}]^{1/6}[t/{\rm Myr}]^{2/3}$. Similar power-law expressions are obtained for the rate at which ionized gas is fed into the bipolar lobes, the rate at which molecular gas is swept up into a dense ring by the shock front that precedes the ionization front, and the density in this dense ring. We suggest that our model might be a useful zeroth-order representation of many observed H iiRs. From viewing directions close to the mid-plane of the layer, the H iiR will appear bipolar. From viewing directions approximately normal to the layer, it will appear to be a limb-brightened shell but too faint through the centre to be a spherically symmetric bubble. From intermediate viewing angles, more complicated morphologies can be expected.

Non-Darcy flows in layered porous media (LPMs) with contrasting pore space structures

Compared to single layer porous media, fluid flow through layered porous media (LPMs) with contrasting pore space structures is more complex. This study constructed three-dimensional (3-D) pore-scale LPMs with different grain size ratios of 1.20, 1.47, and 1.76. The flow behavior in the constructed LPMs and single layer porous media was numerically investigated. A total of 178 numerical experimental data were collected in LPMs and single layer porous media. In all cases, two different flow regimes (i.e., Darcy and Non-Darcy) were observed. The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data. It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs, especially for LPM with large grain size ratio. The effective permeability, which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs. The inertial pressure loss in LPMs, which determines the onset of the Non-Darcy flow, was underestimated when using a power law expression of mean grain size. The constant B, an empirical value in the classical Ergun equation, typically equals 1.75. The inertial pressure loss in LPMs can be significantly different from it in single lager porous media. For Non-Darcy flow in LPMs, it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.

Inter- to intra-layer resistivity anisotropy of NdFeAs(O,H) with various hydrogen concentrations

With molecular beam epitaxy and a topotactic chemical reaction, we prepared NdFeAs(O,H) epitaxial thin films with various hydrogen concentrations on 5\ifmmode^\circ\else\textdegree\fi{} vicinal-cut MgO substrates. By measuring the resistivities along the longitudinal and transversal directions, the $ab$-plane and the $c$-axis resistivities (${\ensuremath{\rho}}_{ab}$ and ${\ensuremath{\rho}}_{c}$) were obtained. The resistivity anisotropy ${\ensuremath{\gamma}}_{\ensuremath{\rho}}\ensuremath{\equiv}{\ensuremath{\rho}}_{c}/{\ensuremath{\rho}}_{ab}$ of NdFeAs(O,H) with various hydrogen concentrations was compared with that of NdFeAs(O,F). At the H concentrations which led to superconducting transition temperatures ${T}_{\mathrm{c}}$ over 40 K, ${\ensuremath{\gamma}}_{\ensuremath{\rho}}$ recorded $\ensuremath{\sim}100--150$ at 50 K. On the other hand, a low ${\ensuremath{\gamma}}_{\ensuremath{\rho}}$ value of 9 was observed with the highest-doped sample. The exponent \ensuremath{\beta} of the $ab$-plane resistivity obtained by fitting a power-law expression ${\ensuremath{\rho}}_{ab}(T)={\ensuremath{\rho}}_{0}+A{T}^{\ensuremath{\beta}}$ to the data was close to unity down to a low temperature in the vicinity where the second antiferromagnetic phase locates, which may be related to the quantum critical point discussed at the overdoped side of the phase diagram.