Exponential Power Research Articles

Theoretical study of kinetic arrest, shear elastic modulus, and yielding in simple biphasic colloidal mixtures.

Based on integrating microscopic statistical mechanical theories for structure and ideal kinetic arrest at the naive mode coupling level, we study dynamic localization, the linear elastic shear modulus, applied stress induced modulus softening, and the absolute yielding of simple biphasic binary mixtures composed of equal diameter hard and attractive spheres. The kinetic arrest map is a rich function of total packing fraction, strength of attraction, and mixture composition. The gel to attractive ideal glass transition, the degree of glass melting re-entrancy, and the crossover boundary separating repulsive glasses from attractive glasses vary with the mixture composition. Exponential and/or apparent (high) power law dependences of the elastic shear modulus on the total packing fraction are predicted with effective exponents or exponential prefactors that are sensitive to mixture composition and location in the kinetic arrest map. An analysis of the effective mean square force on a tagged particle that induces dynamic localization reveals a compensation effect between structural correlations and degree of particle localization, resulting in the emergence of a weaker dependence of the shear modulus on mixture composition at very high attraction strengths. Based on a microrheologically inspired formulation of how external stress weakens particle localization and the shear modulus, we analyze mechanical-induced modulus softening and absolute yielding, defined as a discontinuous solid-to-fluid stress-induced transition that can occur in either one or two steps. Estimates of the corresponding yield strains predict that the binary mixture becomes more brittle with increasing sticky particle composition and/or attraction strength.

Experimental and numerical analysis of the effect of stress change on methane diffusion in coal matrix

ABSTRACT As a clean energy source and disaster gas, coal gas migrates not only under in-situ conditions, but also under stress disturbance due to mining. Although diffusion/desorption is key to gas extraction effects and gas disaster prevention, but the influence study of stress change is insufficient. This study aims to investigate the mechanism of action of stress change to gas diffusion, and a gas transport model considering stress effects is developed. Firstly, the diffusivity of anthracite coal under different stress conditions was measured using an experimental platform of coal-rock diffusivity. When the loaded stress for coal sample reduces 95%, the diffusion coefficient enhances 34%. Subsequently, the determining mechanism and rule of the pore size for gas diffusion in coal matrix were researched theoretically. The results suggest that the relationship between the diffusion flux and the matrix porosity is a power function, with the power exponent between 1 and 1.5, much smaller than the fractures. Experimental and theoretical studies have shown that the methane diffusivity minishes approximately linearly with increased effective stress. Then a methane transport model that involves the impact of stress change is constructed to analyze the effect on gas extraction. Numerical simulations show that the stress relief of a large diameter borehole has a significant effect on the diffusion, generating a larger drop of gas pressure near the borehole compared to the normal borehole. In the presence of regional stress relief, the diffusivity increases due to stress unloading, resulting in larger pressure drop around the borehole and gas drainage amount. The above results provide an important theoretical foundation for calculating gas migration with disturbed stress.

Optimized Design of Scoring Criteria for Large-Scale Innovation Competitions

The reasonable and reliable evaluation score calculation scheme wins the top priority in large-scale innovation-competitions currently. Due to the disparity among individual experts, and the existing standard score calculation model merely based on the experts' own circumstance, it cannot fully reflect the comprehensive level of players, resulting in a certain degree of error in the evaluation results. From the perspective of individual and decision-making of a group, this paper improves existing models and introduces the concept of modified scores. To verify the feasibility of the model, four schemes were designed based on the analysis of data distribution. Consistency and difference factors were applied to compare. Come to a conclusion: scheme adopted the new standard score calculation model ranked the top, indicating that the new calculation model is more reliable. Next, considering that the volatile correction factor affected by data, there is a possibility of some poor actual results with high correction scores. To rectify this case, a power exponent is added to the correction factor and a sign function is adopted to specify the positive or negative of correction scores. To verify the feasibility of the model, four sets of controlled experiments were designed with the introduction of two factors: power exponent and reconsideration bonus, as well as the ranking consistency test based on the condition that the award order of the expert agreement was consistent. In the end, it was found that the scheme that introduced both power exponent and reconsideration bonus points had a sorting consistency rate of 74%, which increased by 30% compared to the original model, indicating the rationality of the modification. The expert evaluation standard score calculation model established in this paper comprehensively considers individual and group decision-making, and provides reasonable correction for the differential scoring between experts. At the same time, this scheme provides a reference basis for further optimizing large-scale innovation competition plans in the future.

A novel Seasonal Fractional Incomplete Gamma Grey Bernoulli Model and its application in forecasting hydroelectric generation

With the arrival of the first truly global energy crisis, how to precisely forecast the hydroelectric generation becomes a hot spot for allowing governments to obtain more valuable information. A novel forecasting model, Seasonal Fractional Incomplete Gamma Nonlinear Grey Bernoulli Model (SFIGNGBM(1, 1)), is proposed in this paper to precisely forecast the hydroelectric generation in some countries. First, the seasonal raw data are classified into four seasonal groups based on their significant seasonal fluctuations. Second, a novel SFIGNGBM(1, 1) model is established by combining the Bernoulli equation, the fractional-order accumulation operator, and the incomplete gamma function to further optimize partial parameters in the forecasting model and improve the forecasting performance. Third, the Whale Optimized Algorithm (WOA) is employed to optimize the Bernoulli power exponent η, the fractional order parameter r, and the incomplete coefficient h for minimizing the MAPE values and enhancing the fitting precision. Finally, our results present that our proposed model outperforms a set of baseline forecasting models with the smallest three error measure values in all fitting results, and its MAPE values converge before 10 iterations. This indicates that our proposed model has a favorable forecasting performance with fast-convergence for hydroelectric generation in the elected countries.

Tenets and Methods of Fractal Analysis (1/f Noise).

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?

Multiple Parameters Determination Method of Hardening Soil Model Based on Particle Swarm Optimization

The utilization of numerical analytic techniques has become essential in evaluating the environmental consequences of excavation in foundation pits. The careful selection of suitable soil constitutive models has significant importance in this regard. The Hardening Soil (HS) model has become widely utilized in the numerical analysis of foundation pits among the several models considered. The essence of a constitutive model is in the identification and determination of its calculation parameters. The stress–strain curve is derived by conducting triaxial testing, utilizing the inherent properties of the particle swarm optimization (PSO) technique. The objective function entails quantifying the disparity between stress–strain curves obtained from various parameters and experimental curves while iteratively searching for five crucial parameters of soil‐hardening models: effective internal friction angle φ, effective cohesion, failure ratio Rf, stiffness level‐dependent power exponent, and standard triaxial‐drained test secant stiffness . The objective of this research is to create a computational software utilizing the Python programming language to execute PSO with the purpose of determining sets of five fundamental soil constitutive parameters. This research employs optimized parameters acquired from PSO to construct a numerical model for foundation pits and performs numerical computations. Accurate findings may be reached by comparing the measured deformation in the numerical simulation with that seen in actual foundation pits. The results demonstrate a high degree of consistency between the experimental curves and the five parameter combinations obtained through the PSO algorithm, with an error rate not exceeding 8.2%. Moreover, the optimized curves exhibit closer alignment with theoretical expectations. The settlement values calculated using a numerical model based on optimized parameters show only a 6.12% deviation from actual measurements while closely following the trend of the observed curve. This outcome has the potential to greatly alleviate the burden of conducting indoor tests and holds considerable practical value in engineering applications. The observable optimization impact of PSO also serves as evidence of its viability in improving soil constitutive parameters, providing new perspectives and sources of information for future progress in this domain.

Evaluation of Acupuncture Efficacy in Modulating Brain Activity with Periodic-aperiodic EEG Measurements.

Acupuncture is an important therapeutic method of traditional Chinese medicine and can effectively modulate brain disorders. The therapeutic efficacy of acupuncture is hard to evaluate due to lacking of effective measurements of brain activity. In this work, we design an EEG-based monitoring system to evaluate therapeutic effect of acupuncture on human brain by extracting periodic-aperiodic features. Power spectral density is estimated to compute the adjusted power of periodic oscillatory rhythm in EEG under acupuncture stimulation. It is exhibited that the brain activity in alpha band (8-12 Hz) is significantly enhanced during acupuncture, especially in parietal and occipital lobe regions. To probe the modulatory effect of acupuncture on aperiodic brain activity, we calculate the aperiodic exponent based on the parameterization of EEG power spectra. The aperiodic exponent decreases along with acupuncture process, which is more significant in central and frontal lobe regions. Furthermore, sensitivity of different brain regions to acupuncture is assessed by the integration of adjusted power and aperiodic exponent. Experimental results demonstrate the effectiveness of proposed periodic-aperiodic measurements of EEG signals, by which different effects of four acupuncture manipulations are precisely evaluated and a knowledge graph is established. The monitoring system provides a new perspective to quantitatively evaluate acupuncture effect on human brain and improve its therapeutic efficacy in clinical applications for neural disorders.

Extended power hazard rate distribution and its application

A new model four-parameter model called the odd generalized exponential power hazard rate (OGE-PHR) distribution has been introduced. Some statistical properties for OGE-PHR are obtained. The moments, quantile, mode, reliability, and order statistics are discussed. Estimation of parameters, maximum likelihood technique is employed. Two real data sets are discussed with applications.

Modified Exponential Power distribution with properties and applications

We have developed the Modified Exponential power distribution, a new and adaptable probability distribution, in this work. An additional shape parameter is added to the exponential power distribution to create this distribution. Numerous statistical properties of suggested model are derived and analyzed. Cramer-Von-Mises (CVME), maximum likelihood (MLE), and least-squares (LSE) are used to estimate the model's parameters. P-P and Q-Q charts are used to assess the validity of the model. Several information criteria are applied in model comparisons, including the Bayesian Information Criterion (BIC), the Hannan-Quinn Information Criterion (HQIC), the Corrected Akaike Information Criterion (CAIC), and the Akaike Information Criterion (AIC). These criteria help determine the best model by balancing goodness-of-fit with model complexity. Test statistics, together with their corresponding p-values, are also utilized to evaluate the recommended model's goodness of fit. These tests consist of the Kolmogorov-Smirnov (KS), Cramer-Von Mises (CVM), and Anderson-Darling (An) tests. R programming is used for the dataset analysis and visualization.

Modelling biochar long-term carbon storage in soil with harmonized analysis of decomposition data

The climate change mitigation benefits of biochar systems arise largely from carbon storage in biochar. However, while biochar is increasingly recognized as a carbon dioxide removal technology, there are on-going scientific discussions on how to estimate the persistence of biochar carbon when biochar is used in soils. Estimates vary from decades to millennia, building on different modelling approaches and evidence. Here, we revisited the persistence estimates derived from extrapolation of biochar incubation experiments, with the aims of making incubation data available, modelling choices transparent, and results reproducible. An extensive dataset of biochar incubations, including 129 biochar decomposition time series, was compiled and is made available alongside code for its analysis. Biochar persistence correlations were sensitive to data selection procedures and to the curve fitting modelling step, while soil temperature adjustments methods had less impact. Biochar H/C ratio remained the main predictor of biochar persistence, in line with previous research, regardless of the extrapolation assumptions (multi-pool exponential functions or power function) used in curve fitting. The relation between H/C and percentage of biochar carbon remaining after 100 years (BC100) was better explained by a power model than a linear model, with R2 values between 0.5 and 0.9. Using multi-pool exponential functions, estimated BC100 varied between 90 % and 60 % for H/C from 0 to 0.7. However, using power functions, BC100 was constrained between 90 % and 80 % for the same H/C range. Additional information about the biochar, the pyrolysis conditions or the environmental incubation conditions did not significantly increase explained variance. Notably, the dataset lacks observations at H/C ratios below 0.2, of biochar made from manure and biosolids, biochar from processes other than slow pyrolysis, field studies, and incubation temperatures below 10 °C, which should guide future experimental work. The detailed analysis performed in this study does not cast doubts on the longevity of biochar carbon storage; rather, it confirms previous knowledge by critically examining the modelling, elucidating the assumptions and limitations, and making the analysis fully reproducible. There is a need for further interdisciplinary work on integration of various theories and approaches to biochar persistence, ultimately leading to the formulation of policy-relevant conclusions.

Logarithmic singularity subtraction for matrix‐friendly layered medium Green's functions

AbstractA subtraction procedure is proposed to evaluate the logarithmic singularity for matrix‐friendly layered medium Green's functions. In this subtraction procedure, an integral of the Bessel function combined with the exponential function and power function, where the sum of the power of and the order of the Bessel function is −1, is designed to fit the oscillation of the tail integral. After subtracting the designed integral, the integrand of the remainder decreases rapidly. Accordingly, the remainder can be calculated without finding any surface poles or steepest descent path, while the subtracted part can be calculated analytically. Several numerical examples are provided to reveal the feasibility and the accuracy of the proposed method.

Enhancing neural network classification using fractional-order activation functions

In this paper, a series of novel activation functions is presented, which is derived using the improved Riemann–Liouville conformable fractional derivative (RLCFD). This study investigates the use of fractional activation functions in Multilayer Perceptron (MLP) models and their impact on the performance of classification tasks, verified using the IRIS, MNIST and FMNIST datasets. Fractional activation functions introduce a non-integer power exponent, allowing for improved capturing of complex patterns and representations. The experiment compares MLP models employing fractional activation functions, such as fractional sigmoid, hyperbolic tangent and rectified linear units, against traditional models using standard activation functions, their improved versions and existing fractional functions. The numerical studies have confirmed the theoretical observations mentioned in the paper. The findings highlight the potential usage of new functions as a valuable tool in deep learning in classification. The study suggests incorporating fractional activation functions in MLP architectures can lead to superior accuracy and robustness.

Propagation Properties of Generalized Schell-Model Pulse Sources in Dispersive Media

A model of a generalized pulse source, whose complex degree of temporal coherence is described by a function of the nth power difference of two instants, was constructed. As examples, we consider the generalized Gaussian and multi-Gaussian Schell-model pulse sources and study their propagation in dispersive media. It is indicated that such pulse beams present unique self-focusing, off-axis self-shifting and asymmetric self-splitting characteristics by adjusting the power exponent and phase parameters. Further, we explicitly discuss how the coherence time, summation factor as well as the dispersive coefficient significantly affect the self-focusing and self-shifting behaviors of the pulse beam. The results will benefit some applications involving pulse shaping, optical trapping and remote sensing.

Constitutive Behavior of Olivine Gouge Across the Brittle‐Ductile Transition

AbstractThe bottom of the lithosphere is characterized by a thermally controlled transition from brittle to ductile deformation. While the mechanical behavior of rocks firmly within the brittle and ductile regimes is relatively well understood, how the transition operates remains elusive. Here, we study the mechanical properties of pure olivine gouge from 100 to 500°C under 100 MPa pore‐fluid pressure in a triaxial deformation apparatus as a proxy for the mechanical properties of the upper mantle across the brittle‐ductile transition. We describe the mechanical data with a rate‐, state‐, and temperature‐dependent constitutive law with multiple thermally activated deformation mechanisms. The stress power exponents decrease from 70 ± 10 in the brittle regime to 17 ± 3 and 4 ± 2 in the semi‐brittle and ductile regimes, respectively. The mechanical model consistently explains the mechanical behavior of olivine gouge across the brittle‐ductile transition, capturing the gradual evolution from cataclasis to crystal plasticity.

Thermal Blooming Effect of Power-Exponent-Phase Vortex Beams Propagating through the Atmosphere

The thermal blooming effect of power-exponent-phase vortex (PEPV) beam propagating in the atmosphere is investigated by employing the multiple phase screen method. The influences of propagation distance, topological charge, power exponent, wind speed, and absorption coefficient on thermal blooming effect are analyzed in detail. The results show that (1) the thermal blooming effect exhibits a significant perturbation on the intensity and phase distribution of PEPV beams, with its influence becoming more pronounced as the propagation distance increases; (2) when the power exponent is fixed at 4, comparing the thermal blooming effect of PEPV beams with different topological charges indicates that a PEPV beam with topological charges of 3 is the most sensitive to thermal blooming; (3) when the topological charge is fixed at 3, the thermal blooming effect decreases with the increase in power exponent; and (4) an increase in wind speed or a decrease in absorption coefficient can reduce the thermal blooming effect. The research results obtained in this article have guiding significance for the application of research into high-energy PEPV beams in the atmosphere.

Experimental and numerical study on the Izbash equation coefficients in rough single fractures

The Izbash equation has been widely used in the subsurface applications. However, the Izbash equation is still empirical, and its coefficients (scaling factor λ and power exponent M) have not been systematically characterized and quantified. In this study, laboratory experiments and numerical simulations of fluid flow across a wide range of hydraulic gradients (J = 0–4) in horizontal rough fractures were conducted to comprehensively characterize and quantify the influence of fracture geometric attributes and fluid inertial effects on λ and M. The results showed that λ increased with fracture relative roughness (RSD). The fluid inertial effect (quantified by the non-Darcy effect factor E and Re) had a two-stage influence on λ. When the fluid flow was laminar, λ increased with E. However, when the fluid flow regime starts to transition from laminar flow to turbulent flow, λ decreased with increasing E. M is positively correlated with RSD and the fluid inertia effect E. We found that the transition of flow regime from laminar to turbulent flow depended on whether the recirculation zones are fully developed. The fully developed recirculation zones determine the distortions of the velocity field and flow field, which induced the turbulent flow. The quantitative models of λ and M were obtained based on numerical simulations, which quantified the coupling influence of the fracture geometric property and fluid inertial effect. The validity of quantitative models was verified by laboratory experiments. Our work provided a new understanding of the Izbash coefficients and laid a foundation for theoretical background exploration of the Izbash equation.

Propagation properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beams in turbulent atmosphere

In this paper, the propagation properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beams (RP-RSPEPVBs) in turbulent atmosphere were investigated. Based on the extended Huygens-Fresnel principle and unified theory of coherence and polarization, the theoretical propagation model was established. Then, the numerical simulations were carried out to reveal the evolution of intensity distribution, spectral degree of coherence (DOC) and spectral degree of polarization (DOP) in turbulent atmosphere. The results showed that although the partially coherent RP-RSPEPVBs diverged during the propagation, the spatial structure remains analogous, and the relatively larger waist widths gain smaller divergence. Moreover, the optical pattern can be evidently modulated by optical parameters, as the number of sidelobes can be changed with topological charge l, and the continuity of the light spot as well as the rotating speed around the optical axis can be influenced by power exponent n. Besides, the spectral DOC and DOP would decrease with larger propagation distance and refractive-index structure constant, but decrease less with a shorter coherence width. This work may be helpful in fields such as remote sensing and optical communication.

Adaptive Event-Triggered Neural Network Fast Finite-Time Control for Uncertain Robotic Systems

A fast convergence adaptive neural network event-triggered control strategy is proposed for the trajectory tracking issue of uncertain robotic systems with output constraints. To cope with the constraints on the system output in the actual industrial field while reducing the burden on communication resources, an adaptive event-triggered mechanism is designed by using logarithm-type barrier Lyapunov functions and an event-triggered mechanism. Meanwhile, the combination of neural networks and fast finite-time stability theory can not only approximate the unknown nonlinear function of the system, but also construct the control law and adaptive law with a fractional exponential power to accelerate the system’s convergence speed. Furthermore, the tracking errors converge quickly to a bounded and adjustable compact set in finite time. Finally, the effectiveness of the strategy is verified by simulation examples.

Catalytic oxidation of carbon monoxide over copper oxide with interfering gases involved for industrial buildings: An experimental and theoretical study

With the intention of thoroughly eliminating carbon monoxide (CO) from indoor environment, it is one of the most promising methods of converting it into carbon dioxide (CO2) via catalytic oxidation processes. Therefore, in this study, catalytic oxidation mechanisms of CO over copper oxide (CuO) with interfering gases involved are investigated via theoretical calculations and experimental verification, which mainly include basic catalytic oxidation processes over CuO, effects of different interfering gases and analyses of thermodynamic features. According to results, catalytic oxidation of CO over CuO can be performed in three different routes and rate-determining transition-state (TS) energy barriers vary a lot from route to route at high temperature owing to different thermal stability. In the meantime, SO2, H2O and NO are theoretically proved to affect catalytic oxidation of CO via competitive adsorption, high oxidizability and hydrogen bonds, which are accompanied with different sensitivities to changes of temperature or temperature power exponents. In experiments, it is found that impurity of lattice planes and small specific surface areas in CuO are key to restricting catalytic oxidation performances. What is more, some extra chemical reactions in experiments (e.g. SO2 + O2 + CuO → CuSO4, NO + O2 + CO → CO2 + NO) caused by interfering gases colossally affect catalytic oxidation performances of CuO. The whole study provides crucial information for indoor air purification in industrial buildings by using cheap adsorbents/catalysts.

Analysis of the principle and state-of-art applications for quantum neural network

The Neural Network is a well-known computational model that widely applied in machine learning (ML) inspired by human brains, which can perform the ML tasks including classification and feature extraction. Contemporarily it has been succeeded in all areas functioning as a powerful tool. Quantum computing is an emerging field based on quantum computers, which is a different calculation logic in the context of quantum dynamic theory providing an exponential computation power edge over traditional computers. Quantum Neural Network (QNN) is an intersection of the two areas, leveraging the advantage of quantum computing in the neural network, providing a strikingly powerful algorithm with promising potential. On this basis, this paper will demonstrate the state-of-art of QNN, which briefly explains the basic principle of QNN and an introduction of several typical QNN models. In addition, the current defects and drawbacks will also be discussed simultaneously. Overall, these results serve as a preliminary introduction to the topic, which shed light on guiding further exploration of quantum computing algorithms.