Power-law Exponent Research Articles

Ignition delays of two ADN/GAP mixtures irradiated by a CO2 laser: atmospheric experiments and numerical calculations

The ignition experiments of two ADN/GAP mixtures irradiated by a CO2 laser were conducted to investigate the dominant mechanism of ignition induced process. The power law exponents of experimental curves for ignition delay versus laser power density are all closed to -1. Two reduced numerical models were employed to calculate the ignition delay times against the experimental data. The analysis suggested that the ignition delays of ADN/GAP mixtures related to the corresponding burning rates and the ignition delay behaviours followed a fixed energy pattern approximately. The calculation results indicated that the measured ignition delay time might be mainly dominated by the formation of preheating layer for steady state burning.

An Unbiased CO Survey Toward the Northern Region of the Small Magellanic Cloud with the Atacama Compact Array. II. CO Cloud Catalog

The nature of molecular clouds and their statistical behavior in subsolar metallicity environments are not fully explored yet. We analyzed data from an unbiased CO (J = 2–1) survey at the spatial resolution of ∼2 pc in the northern region of the Small Magellanic Cloud with the Atacama Compact Array to characterize the CO cloud properties. A cloud-decomposition analysis identified 426 spatially/velocity-independent CO clouds and their substructures. Based on the cross-matching with known infrared catalogs by Spitzer and Herschel, more than 90% CO clouds show spatial correlations with point sources. We investigated the basic properties of the CO clouds and found that the radius–velocity linewidth (R–σ v ) relation follows the Milky Way-like power-law exponent, but the intercept is ∼1.5 times lower than that in the Milky Way. The mass functions (dN/dM) of the CO luminosity and virial mass are characterized by an exponent of ∼1.7, which is consistent with previously reported values in the Large Magellanic Cloud and in the Milky Way.

Optimizing surfactant removal from a soft-templated ordered mesoporous carbon precursor: an in situ SAXS study.

In situ small-angle X-ray scattering (SAXS) was employed to identify critical parameters during thermal treatment for template removal of an ordered mesoporous carbon precursor synthesized via a direct soft-templating route. The structural parameters obtained from the SAXS data as a function of time were the lattice parameter of the 2D hexagonal structure, the diameter of the cylindrical mesostructures and a power-law exponent characterizing the interface roughness. Moreover, detailed information on contrast changes and pore lattice order was obtained from analysis of the integrated SAXS intensity of the Bragg and diffuse scattering separately. Five characteristic regions during heat treatment were identified and discussed regarding the underlying dominant processes. The influence of temperature and O2/N2 ratio on the final structure was analyzed, and parameter ranges were identified for an optimized template removal without strongly affecting the matrix. The results indicate that the final structure and controllability of the process are optimum for temperatures between 260 and 300°C with a gas flow containing 2 mol% of O2.

Mechanism of enhanced oil recovery of ultra-dry CO2-in-water foams in porous media: Experiments and numerical simulation

The application of ultra-dry CO2 foam in enhanced oil recovery (EOR) accelerates recovery and enables CO2 utilization and sequestration. The flow characteristics of foam in porous media play a crucial role in the foam EOR process. Herein, ultra-dry CO2-in-water (C/W) foam with 10% water was prepared at 80 °C and 12 MPa using cocamidopropyl betaine (CAPB) and nonionic polyacrylamide (NPAM). Additionally, the constitutive equation for the foam fluid was determined by flow experiments using tubes with different diameters. The CO2 foam was a shear-thinning, non-Newtonian fluid and conformed to the Herschel–Bulkley (H–B) model. The core displacement experiment with the permeability of 470 mD showed that the oil recovery of foam flooding increased from 56.01% of water flooding to 76.01% at the same temperature and pressure. The maximum pressure difference rose sharply from 0.48 MPa of water flooding to 1.2 MPa of foam flooding, increasing by 2.5 times; the pressure difference finally stabilized at 0.64 MPa, which was approximately 4.3 times that of water flooding. Moreover, a two-dimensional (2D) model of the porous media was constructed using digital core technology. Using the validated model, sensitivity analysis based on the phase-field method (PFM) was performed to investigate the effect of different power-law exponents on displacement. The results indicate that increasing the power-law exponent of the foam fluid slowed down breakthrough and improved the sweep efficiency, resulting in higher oil recovery.

Re-examination and comparison of activation volume, strain rate sensitivity, and dislocation density for coarse grain and CGP-processed UFG materials

The frequently used metallurgical parameters such as activation volume, internal stress, strain rate sensitivity, and dislocation density are identified in ultrafine-grained (UFG) materials through erudite analytical relations. It is difficult to analyze such parameters optically since the material consists of highly distorted and inhomogeneous microstructure due to the large strain imposed during the constrained groove pressing (CGP) process. Hence, transient tests like stress relaxation tests are advantageous over the optical to use. Apart from the identification of parameters in low-carbon steel materials using uniaxial loading and stress relaxation tests, the relationship between the parameters is nobly investigated in as-received and UFG structure samples produced through the CGP process. In the relationship, the exponential-power law constitutive to describe the accurate stress–strain curves, identification of mobile and forest dislocation density during strain hardening, and exponential variation between grain size and activation volume are proposed. The replenishment or exhaustion of mobile and forest dislocation density significantly affects the metallurgical parameters during uniaxial tensile loading followed by stress relaxation testing. In this experimental and analytical work, the CGP process produces a UFG material that has lower activation volume and higher stress drop, mobile dislocation density, forest dislocations density, strain rate sensitivity, and internal stress.

Layer structure and intermolecular vibrations of water confined within graphite nanoslits

Molecular dynamics simulations were used to study layer structure and intermolecular vibrations of water confined within graphite nanoslits. The confinement effect was investigated by varying the slit width, with water density within the geometric slit space close to that of liquid water. The vibrational density of states (DOS) of nanoconfined water was dissected with the instantaneous-normal-mode (INM) analysis. The translational INM DOS of nanoconfined water shows a linear behavior at low frequencies; however, the components parallel and perpendicular to the confining wall display different behaviors, characterized with a power-law exponent less and larger than one, respectively.

Flow reversals of a non-Newtonian fluid in an expanding channel

The flow of an incompressible power-law fluid through convergent–divergent channels is considered where the choice of the viscosity is such that the zero-shear rate viscosity is neither zero nor infinity for any finite value of the power-law exponent. Rather than employing the classical similarity transformation employed by Jeffery and Hamel implying purely radial solutions for the velocity field, we instead consider flow in both the radial and angular directions, under three sets of boundary conditions. This work is in contrast to the earlier study by Mansutti and Rajagopal (1991). wherein the viscosity could be zero or infinity for certain values of the power-law exponent. While seeking solutions to nonlinear differential equations, when seeking similarity solutions, one ought to be cognizant that the equations might have solutions in addition to the similarity solution that is being sought. We observe that the tangential velocity does indeed play a role in the flow regime of the fluid, with flow reversal also present for certain values of α. In the case of traction boundary conditions, we also observe a change in the flow characteristics.

Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 – 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Origin of the Delayed Fluorescence by Triplet–Triplet Annihilation in Solids with a Power Law Exponent of between −1/2 and −1

Triplet–triplet annihilation (TTA) merges low electronic energies in two molecules to high electronic energy in one molecule, which, following triplet sensitization, allows us to achieve high-efficiency conversion using low-intensity light. Although efficient TTA up-conversion in solutions has been reported, the TTA up-conversion in solid matrixes is preferred for practical applications. However, the emission decay kinetics after pulsed-light excitation is more complex in solids than in liquids, and the process underlying the different TTA kinetics has not yet been elucidated. Herein, we report that the complexity in the TTA kinetics in solid matrixes can originate from processes such as slow mixing of triplet excitons by migration, strong dependence on the initial distribution of triplet excitons, and an anisotropic random walk of excitons. We show theoretically that power-law fluorescence with an exponent of between −1/2 and −1 can originate from the slow diffusional mixing of excitons in one and three dimensions, where the initial exciton generation is uniformly distributed. By analyzing experimental data, we show that rich fluorescence kinetics observed experimentally by varying the temperature in molecular solids can be deeply understood in terms of bulk and nonbulk TTA under dispersive as well as normal diffusion.

Formation of silver particles in [PVA:CS:PEG]-AgNO3 based biopolymer electrolyte membranes: Structural and electric transport properties study

[Chitosan (CS)-poly(vinyl) alcohol (PVA)-polyethylene glycol (PEG-200)]+xwt% silver nitrate (AgNO3) (x = 0, 10, 20, 30, 40) based biopolymer blend electrolytes (BPBEs) were prepared using solution casting method. FTIR results show the interaction of Ag+/NO3− with the constituents of polymers CS/PVA. XRD results reveal that the amorphousness increases with increasing AgNO3 concentration. Optical morphological (OM) images show that the silver, Ag(o) particles are agglomerated on the surface of the membrane. Temperature dependent dc conductivity (σdc) and dielectric relaxation frequency (fr) for BPBEs follow the Arrhenius type behavior and the sample containing 30 wt% salt has optimum dc conductivity, σdc∼1.7×10−4 S/cm at 30oC with lowest activation energy∼ 0.16 eV. The ac conductivity spectra follow the Jonscher's power law (JPL) with power law exponent, s > 1. The scaling of AC conductivity and loss tangent (tanδ) spectra were performed with respect to temperatures/concentrations of salt. The dielectric permittivity study reveals that the electrode polarization effect predominates at low frequencies. The Ionic Transference Number (ITN) measurement was used to determine the nature species of charge carrier, either ionic or electronic. The linear sweep voltammetry (LSV), result shows that 30% AgNO3containing sample has the electrochemical stability window (ESW) ∼+1.5 to -1.5 V.

Significance of skewness and kurtosis on the solute dispersion in pulsatile Carreau–Yasuda fluid flow in a tube with wall absorption

Solute dispersion in Carreau–Yasuda fluid flow in a tube presented in Rana & Murthy (Proc. R. Soc. Lond.A, vol. 472, 2016, p. 20160294) was limited to a steady-state velocity profile due to the nonlinearity associated with the Yasuda parameter$a$with power-law exponent$n$. This limitation is overcome and the velocity profile is obtained for all values of the Yasuda parameter by using the Lagrange inversion theorem, which admits power series solution for the flow field. An analytical solution for the concentration distribution in the circular tube is obtained for the unsteady and pulsatile flow with$n\leq 1$and$\alpha <<1$and the numerical solution is presented for all values of$\alpha$and$n$. The solute dispersion is analysed analytically using the Sankarasubramanian–Gill generalized dispersion method and also using the Aris–Barton method of moments considering up to fourth-order moments. The solute dispersion is also simulated numerically by using a new class of computationally explicit Runge–Kutta method. The axial mean concentration of the solute is estimated by the exchange, convective and dispersion coefficients. The third- and fourth-order moments give rise to skewness and kurtosis revealing the deviation from the Gaussianity and reduction in the peak of the mean concentration profile at a small time of the solute injection. All time variations of these five moments against flow governing parameters are thoroughly investigated. The flow and dispersion regimes that are derived here for moments provide a good understanding of the solute dispersion in the tube. The increase in the Womersley frequency parameter led to a phase lag at each period. This work is the initiation of estimating the skewness and kurtosis in a non-yield stress fluid flow in a tube.

Vertically neutral collapse of a pulsating bubble at the corner of a free surface and a rigid wall

Vertically neutral collapse of a pulsating bubble occurs when the boundaries above or below the bubble balance the buoyancy effect over a pulsation. In this study, the vertically neutral collapse of a bubble near a vertical rigid wall below the free surface is investigated. The boundary integral method (BIM) is employed to model the bubble dynamics with an open-domain free surface. Moreover, this method is validated against several buoyant bubble experiments. Bubble dynamics in such conditions are associated with three dimensionless parameters: the bubble-free surface distance $\gamma _{{f}}$ , bubble–wall distance $\gamma _{{w}}$ and buoyancy parameter $\delta$ . We derive the Kelvin impulse of a spherical bubble and the algebraic relationship for vertically neutral collapse, which proves to be accurate for predicting vertically neutral collapse when the bubble is relatively far from the boundaries. Four patterns of the vertically neutral collapse of the bubble for different $\gamma _{{w}}$ and $\gamma _{{f}}$ are identified: (i) formally downward jet; (ii) annular collapse; (iii) horizontal jet; and (iv) weak jet. Despite the downward jet shape, the ‘formally downward jet’ is in the vertically neutral collapse state in terms of the profile of toroidal bubbles and the orientation of local high-pressure zones around the bubble at jet impact. A bulge with a high curvature above the bubble in the ‘annular collapse’ pattern is formed during bubble collapse under two local high-pressure zones at the left and right extremities of the bubble. The ‘horizontal jet’ pattern has the greatest potential to attack the wall, and the power laws of the moment of the jet impact, jet velocity and bubble displacement with respect to the theoretical Kelvin impulse are discussed. In particular, we quantitatively illustrate the role of the free surface on bubble migration towards the wall through the variational power-law exponents of the bubble displacement with respect to $\gamma _{{w}}$ .

Asymptotically consistent analytical solutions for the non-Newtonian Sakiadis boundary layer

The Sakiadis boundary layer induced by a moving wall in a semi-infinite fluid domain is a fundamental laminar flow field relevant to high speed coating processes. This work provides an analytical solution to the boundary-layer problem for Ostwald–de Waele power law fluids via a power series expansion and extends the approach taken for Newtonian fluids [Naghshineh et al. “On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs,” IMA J. of Appl. Math. 88, 43 (2023)] in which variable substitutions (which naturally determine the gauge function in the power series) are chosen to be consistent with the large distance behavior away from the wall. Contrary to prior literature, the asymptotic behavior dictates that a solution only exists in the range of power law exponents, α, lying in the range of 0.5<α≤1. An analytical solution is obtained in the range of approximately 0.74≤α<1, using a convergent power series with an asymptotically motivated gauge function. For power laws corresponding to 0.5<α<0.74, the gauge function becomes ill-defined over the full domain, and an approximate analytical solution is obtained using the method of asymptotic approximants [Barlow et al. “On the summation of divergent, truncated, and underspecified power series via asymptotic approximants,” Q. J. Mech. Appl. Math. 70, 21–48 (2017)]. The approximant requires knowledge of two physical constants, which we compute a priori using a numerical shooting method on a finite domain. The utility of the power series solution is that it can be solved on the entire semi-infinite domain and—in contrast to a numerical solution—does not require a finite domain length approximation and subsequent domain length refinement.

Impacts of low-order aberrations on capacity of orbital-angular-momentum quantum states

We use Hypergeometric Gaussian-II (HyGG-II) modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme. The capacity of HyGG-II modes can be higher than that of Laguerre–Gaussian modes via modulating the hollowness parameter. The influences of low-order turbulence aberrations including tilt, defocus, astigmatism, and coma on the capacity are also explored. Generally, tilt aberration dominates among all low-order aberrations and defocus and astigmatism aberrations are always negligible. By contrast, the effect of coma aberration can be enhanced to be non-negligible when the turbulence strength or the channel zenith angle is enhanced. We also show that only the total and tilt aberrations are sensitive to the non-Kolmogorov power-law exponent. Our results may contribute to the quantum optical communication as well as aberration compensation in turbulent channels utilizing the novel family of vortex beams.

An analysis of the turbulence in the central region of the Orion Nebula (M42) – II. Homogeneity and power-spectrum analyses

ABSTRACT In this second paper, we continue our analysis of the turbulence in the Huygens region of the Orion Nebula (M42). We calculate the associated transverse structure functions up to eighth order and find that the higher-order transverse structure functions are almost proportional to the second-order transverse structure function. We find that, after proper normalization, the higher-order transverse structure functions only differ by very small deviations from the second-order transverse structure function in a subinterval of the inertial range. We demonstrate that this implies that the turbulence in the Huygens region is quasi-log–homogeneous or, to a better degree of approximation, binomially weighted log–homogeneous in the statistical sense. This implies that there is some type of invariant statistical structure in the velocity field of the Huygens region. We also obtain and analyse the power spectrum of the turbulent field. We find that it displays a large tail that follows, very approximately, two power laws: one of the form E(k) ∝ k−2.7 for the initial side of the tail, and one of the form E(k) ∝ k−1 for the end of the tail. We find that the power law with exponent β ∼ −2.7 corresponds to spatial scales of 0.0301–0.6450 pc. We find that the exponent of the first power law β ∼ −2.7 is related to the exponent α2 of the second-order structure function in the inertial range. We interpret the second power law with exponent β ∼ −1 as an indicator of viscous-dissipative processes occurring at scales of δr = 1–5 pixels, which correspond to spatial scales of 0.00043–0.00215 pc.

Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core

PurposeThe purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.Design/methodology/approachThe FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.FindingsA series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.Originality/valueThis paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

Nonlinear vibration characteristic of FGM sandwich cylindrical panel with auxetic core subjected to the temperature gradient

This study deal with the nonlinear vibration of sandwich panel, composed of functionally graded material (FGM) skins and double U auxetic core subjected to heat conduction. The nonlinear equations are obtained by applying Hamilton’s principles in framework higher order shear deformation theory (HSDT) and von Karman’s nonlinear theory. Linear and nonlinear equations of motion are solved by applying the differential quadrature method (DQM) and homotopy perturbation technique, respectively. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of auxetic core, power-law exponent, different boundary conditions, and temperature gradient on the nonlinear frequencies of sandwich panel are studied. Finally, the important findings of this research indicate that the ratio of core thickness, inclined angle, and thickness to inclined length have significant effects on nonlinear frequency response. Based on the results of this article designers can development of different parts of aircraft.

General attached eddies: Scaling laws and cascade self-similarity

We generalize Townsend's classical attached-eddy hypothesis (AEH) to eddies with arbitrary fractal dimension. New scaling laws for the Reynolds stress components are obtained. Preliminary evidence from high-resolution simulations of adverse-pressure-gradient turbulent boundary layers and wing boundary layers are provided. Furthermore, we investigate the cascade self-similarity of general attached eddies, and obtain relationships between the power-law exponents of the probability density, population density, area coverage, volume fraction, and fractal dimension of general attached eddies, leading to insights into the connection between turbulent coherent structures and statistics.

A multifractal model of asset (in)variances

This study extends Mandelbrot’s (2008) multifractal model of asset returns to model realized variances across different time frequencies. In a comparative manner, various degrees of time deformations are explored for implementation of the multiplicative cascade. In doing so, this study focuses on two effects: discontinuity measured by the specific power-law exponent and dependency measured by the Hurst exponent. This study shows that the benchmark model, for which Mandelbrot’s (2008) “cartoon” is the foundation, has some remarkable properties as it is capable of explaining the realized variances for the GBP/USD exchange rate and Bitcoin. Notably, the realized variances for crude oil and the S&P 500 require a more extreme time deformation. The invariance hypothesis is confirmed for all realized variances because the power-law exponents for weekly and monthly data coincide with predictions of the multifractal model. Overall, the novel results derived from the proposed multifractal models suggest that some realized variances of otherwise unrelated asset markets are driven by the same underlying “driving force”—a common multifractal cascade.

Can Self-Similarity Processes Be Reflected by the Power-Law Dependencies?

This work was greatly influenced by the opinions of one of the authors (JS), who demonstrated in a recent book that it is important to distinguish between “fractal models” and “fractal” (power-law) behaviors. According to the self-similarity principle (SSP), the authors of this study completely distinguish between independent “fractal” (power-law) behavior and the “fractal models”, which result from the solution of equations incorporating non-integer differentiation/integration operators. It is feasible to demonstrate how many random curves resemble one another and how they can be predicted by functions with real and complex-conjugated power-law exponents. Bellman’s inequality can be used to demonstrate that the generalized geometric mean, not the arithmetic mean, which is typically recognized as the fundamental criterion in the signal processing field, corresponds to the global fitting minimum. To highlight the efficiency of the proposed algorithms, they are applied to two sets of data: one without a clearly expressed power-law behavior, the other containing clear power-law dependence.