Power Exponential Function Research Articles

Mechanical properties and constitutive model of deep marble under alternating creep-fatigue action

Given the time dependence and susceptibility to disturbance of deep rocks, this paper analyzes mechanical properties, acoustic emission (AE) signals, and pore radius distribution characteristics of deep marble under alternating creep-fatigue (ACF) action at different confining pressures by experiment and theoretical analysis. The results show that: (1) the alternation of creep and fatigue accelerates the rock damage, and the number of alternations increases with the increasing confining pressure. (2) Strain increments exhibit a pattern of first decreasing and then increasing, and they undergo a transformation from “V”-type to “U”-type with the increase of confining pressure. (3) The AE ringing count is mainly generated in the fatigue segment. The radius of large pores inside the rock is constrained by the confining pressure. (4) The ACF constitutive model is established, where model parameters show a nonlinear decreasing trend of the power exponential function with the strain increment.

The sliding mode controller with composite reaching law for upper limb rehabilitation robot

Purpose Assisted training using upper limb rehabilitation robots is beneficial for flaccid paralysis patients in recovering their functional abilities. In the assisted training mode, the patient’s motor ability is limited by factors such as limb muscle tension, and it is prone for the rehabilitation robot to deviate from the prescribed training trajectory. A sliding mode control method based on a fixed time observer is proposed to address the problem of delayed trajectory tracking response of upper limb rehabilitation robots caused by external disturbances such as patient limbs. Design/methodology/approach First, aiming at the problem of estimating and compensating for external disturbances in the upper limb rehabilitation robot system, a fixed time observer was designed based on the robot’s dynamic model. Second, the composite sliding mode reaching law combining the smooth function and the power-exponential function is proposed to shorten the convergence time of system states in the startup phase, thereby reducing chattering in the control process and realizing the real-time tracking of the training trajectory by the control system. Findings The proposed method provides a solution for the trajectory tracking speed of upper limb rehabilitation robot controllers. In the circular trajectory tracking control, compared to the sliding-mode control method combined with the variable-exponential composite reaching law based on the fixed-time observer, the method in this paper reduces the time for the system state to reach the sliding surface by 0.89 s and improves the response speed by 0.66%. Originality/value The composite sliding mode approach law based on smooth function and power exponent function can reduce the time it takes for the system state to reach and remain on the sliding surface and improve the trajectory tracking speed of upper limb rehabilitation robots. This controller improves the accuracy of trajectory control and ensures the robustness of auxiliary rehabilitation training.

Single-molecule tracking technology based on symmetric power exponential phases.

We present a design approach for a symmetric power exponential phase, resulting in a phase-modulated point-spread function with two symmetrical mainlobes that can be steered toward the optical axis opposite the x axis. This design offers nanoscale 3D localization capabilities suitable for 3D single-molecule tracking and localization imaging. The axial probing depth of this symmetric power exponential point-spread function can be adjusted as needed by manipulating specific parameters. Optimization of the symmetric power exponential phase involves truncation filtering to reduce sidelobes and the utilization of a phase inversion-based optimization algorithm to enhance transfer function efficiency and localization precision. A successful multi-molecule 3D tracking experiment was conducted at a 10 µm axial depth using a numerical aperture of 1.4 to validate the efficacy of the proposed design methodology.

Static in-situ curing characteristics of CFRP based on near infrared laser

Study on static in-situ curing characteristics of CFRP based on near infrared laserThe quick curing method of carbon fibre reinforced plastics (CFRP) is one of the hotspots in current research. A static in-situ curing method for CFRP prepreg based on near-infrared laser was put forward in this study. The in-situ curing structural characteristics and the mechanism of CFRP were investigated through real-time surface temperature measurement, COMSOL temperature field simulation, 3D measurement of curing morphology and resin curing degree test. The thermal conductivity of the CFRP along the fiber direction is considerably higher than that along the perpendicular fiber direction. As a result, the temperature profile in the plane takes on an elliptical shape. During the transfer, the temperature field gradually decreases, resulting in an ellipsoidal 3D high-temperature distribution. The different shrinkage phenomena in the different curing regions between the layers lead to an irregular ellipsoidal solidification morphology of the unidirectional CFRP. The temperature in the center of the heat affected zone increases as a power exponential function with time. The area and depth of the heat-affected zone increases with the laser power, and the curing area is positively correlated with the degree of curing. As a result, curing temperature governing equations based on laser power and layer thickness have been proposed, while relationship equations based on laser power, curing depth and curing morphology have been developed. In addition, prediction equations based on curing morphology have been developed for curing degree, in order to achieve precise curing of CFRP.

Probing the Temperature-Dependent Thermal Conductivity of Violet Phosphorus via Optothermal Raman Spectroscopy.

The temperature-dependent thermal conductivity of violet phosphorus on a perforated SiO2/Si substrate has been investigated via optothermal Raman spectroscopy. The obtained temperature coefficients of the Tg mode and Ptub mode of the violet phosphorus sample are -0.01268 and -0.01789 cm-1 K-1, respectively. On the basis of the temperature coefficients and power coefficients, the thermal conductivity of the violet phosphorus has been calculated to be 44.642 ± 4.995 W/mK at room temperature, which is higher than that of other two-dimensional materials such as black phosphorus and MoS2 due to the effect of boundary scattering and the phonon mean free path. Additionally, the thermal conductivity of violet phosphorus decreases as a power exponential function of the temperature, which is primarily associated with the phonon mean free path and phonon group velocity. This work provides a scientific foundation for thermal management and heat dissipation in designing micro-nano devices with violet phosphorus.

Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization.

By using the power-exponential function method and the extended hyperbolic auxiliary equation method, we present the explicit solutions of the subsidiary elliptic-like equation. With the aid of the subsidiary elliptic-like equation and a simple transformation, we obtain the exact solutions of Hirota equation which include bright solitary wave, dark solitary wave, bell profile solitary wave solutions and Jacobian elliptic function solutions. Some of these solutions are found for the first time, which may be useful for depicting nonlinear physical phenomena. This approach can also be applied to solve the other nonlinear partial differential equations.

Normal Contact Model of Fractal Surfaces Considering Friction and Asperity Interactions

Friction as well as asperity interactions have significant influence on the contact area and force of rough surfaces. In this work, a single-asperity, elastoplastic contact model, considering friction, is established by means of continuum mechanics and power-exponential functions. Then, the deformation of the asperity interactions is modeled by the displacement of the average line for asperity height. Using fractal theory, the actual deformation and contact stiffness of an asperity are derived, which take the friction and asperity interactions into account. Furthermore, the actual contact area and normal stiffness models for fractal surfaces are developed, accounting for friction and asperity interactions. The accuracy of the developed models is confirmed by using published experimental results. The developed models are closer to experimental results than the reported fractal contact models. Finally, the effects of the friction coefficient and surface morphology parameters on contact characteristics are discussed.

Analysis of the Fracture Characteristics and Crack Propagation Mechanism of Fractured Sandstone under Dynamic Loading

In order to study the impact of fracture thickness on the dynamic mechanical properties of rock specimens, impact compression tests on prefabricated sandstone specimens with different fracture thicknesses and intact specimens were carried out by using a split Hopkinson pressure bar (SHPB) test device, and the dynamic mechanical parameters of the fractured sandstone specimens were obtained. The results showed that the dynamic stress–strain curves of the prefabricated fractured sandstone specimens are similar to those of the intact sandstone specimens, which can be divided into three stages: elasticity, plasticity, and failure. With the increase in the thickness of prefabricated cracks, the dynamic compressive strength of the sandstone specimens decreases in a quadratic function, the dynamic strain decreases in a power exponential function, and the dynamic elastic modulus decreases linearly. Attempts were made to quantitatively analyze the crushing degree of sandstone specimens. The average particle size of the crushed specimens was negatively correlated with the thickness of prefabricated cracks, and the fractal dimension was linearly negatively correlated with the dynamic compressive strength. The 1.5–2.5 mm prefabricated fractured sandstone specimens produced airfoil cracks and secondary cracks; the 3–3.5 mm prefabricated fractured specimens produced airfoil cracks, coplanar secondary cracks, and secondary oblique cracks; and the complete specimens were subjected to axial failure to produce axial cracks.

Digital design of a spatial-pow-STDP learning block with high accuracy utilizing pow CORDIC for large-scale image classifier spatiotemporal SNN

The paramount concern of highly accurate energy-efficient computing in machines with significant cognitive capabilities aims to enhance the accuracy and efficiency of bio-inspired Spiking Neural Networks (SNNs). This paper addresses this main objective by introducing a novel spatial power spike-timing-dependent plasticity (Spatial-Pow-STDP) learning rule as a digital block with high accuracy in a bio-inspired SNN model. Motivated by the demand for precise and accelerated computation that reduces high-cost resources in neural network applications, this paper presents a methodology based on COordinate Rotation DIgital Computer (CORDIC) definitions. The proposed designs of CORDIC algorithms for exponential (Exp CORDIC), natural logarithm (Ln CORDIC), and arbitrary power function (Pow CORDIC) are meticulously detailed and evaluated to ensure optimal acceleration and accuracy, which respectively show average errors near 10–9, 10–6, and 10–5 with 4, 4, and 6 iterations. The engineered architectures for the Exp, Ln, and Pow CORDIC implementations are illustrated and assessed, showcasing the efficiency achieved through high frequency, leading to the introduction of a Spatial-Pow-STDP learning block design based on Pow CORDIC that facilitates efficient and accurate hardware computation with 6.93 × 10–3 average error with 9 iterations. The proposed learning mechanism integrates this structure into a large-scale spatiotemporal SNN consisting of three layers with reduced hyper-parameters, enabling unsupervised training in an event-based paradigm using excitatory and inhibitory synapses. As a result, the application of the developed methodology and equations in the computational SNN model for image classification reveals superior accuracy and convergence speed compared to existing spiking networks by achieving up to 97.5%, 97.6%, 93.4%, and 93% accuracy, respectively, when trained on the MNIST, EMNIST digits, EMNIST letters, and CIFAR10 datasets with 6, 2, 2, and 6 training epochs.

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.

Neuroadaptive Performance Guaranteed Control for Multiagent Systems With Power Integrators and Unknown Measurement Sensitivity.

This article investigates the adaptive performance guaranteed tracking control problem for multiagent systems (MASs) with power integrators and measurement sensitivity. Different from the structural characteristics of existing results, the dynamic of each agent is a power exponential function. A method called adding a power integrator technique is introduced to guarantee that the consensus is achieved of the MASs with power integrators. Different from existing prescribed performance tracking control results for MASs, a new performance guaranteed control approach is proposed in this article, which can guarantee that the relative position error between neighboring agents can converge into the prescribed boundary within preassigned finite time. By utilizing the Nussbaum gain technique and neural networks, a novel control scheme is proposed to solve the unknown measurement sensitivity on the sensor, which successfully relaxes the restrictive condition that the unknown measurement sensitivity must be within a specific range. Based on the Lyapunov functional method, it is proven that the relative position error between neighboring agents can converge into the prescribed boundary within preassigned finite time. Finally, a simulation example is proposed to verify the availability of the control strategy.

Dynamic splitting response and mechanical effect of joint angle in sandstone containing various weak-filling joints

Weak-filling joints substantially degrade the integrity and load-bearing capacity of rock masses, thus increasing the complexity and unpredictability of their mechanical response behavior. One of the main mechanical properties of jointed rocks is their splitting performance, which heavily influences their failure mode. To study the effects of joint angles on splitting mechanical properties, we conducted dynamic splitting tests on sandstone samples with seven different inclination angles of weak-filling joints. These tests were conducted using the Brazilian disc method and a modified split Hopkinson bar apparatus. The splitting mechanical response, energy rate characteristics, joint angle damage factors, failure modes, micromorphology characteristics, and the mechanical effects of joint angles were systematically analyzed. The findings suggested that varying joint angles led to different initial damage levels in the rock mass, which can be described by a power exponential function. The observed relationship between peak load and joint angle was corroborated by integrating a damage parameter into the theoretical derivation of the mechanical effect of the joint angle. Weak-filling joints reduced the brittle failure characteristics and peak loads of the samples but enhanced their ability to deform. Furthermore, the energy reflection rate exhibited an inverse relationship with the joint angle, which is contrary to the trends observed in energy transmission and absorption rates. Additionally, both macroscopic and microscopic morphology analyses confirmed that the joint angle primarily determined the fracture trajectory of the samples, causing a gradual shift in the failure modes of jointed samples from shear to tensile failure.

Asymmetric gradient penalty based on power exponential function for imbalanced data classification

Model bias is a tricky problem in imbalanced data classification. An asymmetric gradient penalty method is proposed based on the power exponential function to alleviate this. The methodology integrates a power exponential function as a moderator into the cross-entropy loss of the negative samples, driving the model to focus on hesitant samples while ignoring easy and singular samples. The rationality of the algorithm is explored from the gradient point of view, and it is demonstrated that the approach improves focal loss and asymmetric focal loss. Then, the imbalanced data classification experiments were deployed on MNIST, CIFAR10, CIFAR100, and Caltech101, respectively. For binary classification, datasets with several imbalance ratios constituted by varying the sample size of the majority class and minority class are included in the experiments. In the multi-category classification experiments, we discuss imbalanced datasets with only a single majority category and those with several majority categories and examine step-imbalance datasets and linear-imbalance datasets. The results reveal that the proposed method exhibits competitiveness on various imbalanced datasets and better robustness on high imbalance ratio datasets. Finally, the approach is deployed on the pulsar candidate dataset HTRU, and the state-of-the-art results are yielded. Our code is available at https://github.com/gzmtzly/GPPE.

Adequacy of the Gravity Model of Railway Passenger Flows

The most accurate modelling of spatial distribution of passenger flows is a prerequisite for successful planning of development of the transport system. It is the basis for calculation of a predictive trip matrix. An approach based on the gravity model is among main modelling methods.The work investigates the issue of the adequacy of the gravity model with a double constraint and an exponential-power function of gravitation. It is this specification of the model and its particular cases with exponential and power functions of gravitation that are most often used to estimate spatial distribution of passenger flows both in theoretical and applied research.Calibration and validation of the specified model is shown on the observed (actual) matrix of railway passenger origin­destination matrix. It was built with the help of the data of Express [railway ticketing] ADB ACS: the number of tickets sold for long-distance trains for all the pairs of directly linked stations.Since calibration of the gravity model can be carried out by different methods (depending on how the model incorporates stochasticity, which is responsible for differences between the modelled and observed data), after a detailed analysis of the most common methods for calibrating the gravity model, the approach was chosen based on the maximum likelihood estimation. The work also analyses the gravity model validation tools used to estimate the proximity between the observed and modelled trip matrices.Comparison of the modelled and observed trip matrices resulted in the conclusion that the gravity model under consideration predicts several aggregate indicators with a high degree of accuracy: total passenger turnover, average travel distance, and travel distance distribution. At the same time, it is shown that the error in the forecast of passenger flow for most individual origin-destination trips is quite large. This circumstance significantly reduces the possibility of practical application of the gravity model or the analysis and modelling of passenger flows in long-distance railway passenger traffic.

Complex climate networks of nonlinearly correlated time series

A climate anomaly is defined as the difference between a climate variable and a baseline, which is often the climate normal. In climate change studies, climate anomalies are more important than the average climate. Positive and negative extremes of climate anomalies are equally important, because they represent quite opposite climate events. Therefore, extreme event based synchronization is a proper choice for measuring the similarity of event-like series. However, the traditional event synchronization method cannot incorporate positive and negative extremes simultaneously. In this study, a newly proposed event synchronization (ES) measure is adopted as similarity measure of climate anomaly time series, where both positive and negative extremes are identified as extreme events. Then, global complex climate networks based on this similarity measure of surface air temperature (SAT) anomaly time series have been constructed and analyzed. Exponential function and power function have been fitted to the empirical degree distribution of positive and negative climate networks, respectively. The prominent atmospheric teleconnection pattern (North Atlantic Oscillation, NAO) as well as the remote impacts of ENSO have been correctively detected by the global climate networks. The advantages of ES-based complex networks have also bee discussed. This study provides an illustrative example of constructing complex climate network model for nonlinearly correlated climate time series with both positive and negative extremes.

Electrical properties and thermally induced aging processes in eco-friendly Cu0.1Ni0.1Co1.6Mn1.2O4 and Cu0.1Ni0.8Co0.2Mn1.9O4-based thick-film structures for multisensor systems

The electrical properties and kinetic dependences of thermally induced drift of electrical resistance in eco-friendly single- and multilayer temperature-sensitive thick-film structures based on Cu0.1Ni0.1Co1.6Mn1.2O4 (with p+-type electrical conductivity) and Cu0.1Ni0.8Co0.2Mn1.9O4 (with p-type of electrical conductivity) ceramics for multisensor nanosystems. It has been established that in the p- and p+-type thick films the processes of burning out the residues of the organic bond between grain spinels and simultaneous penetration of metallic silver into the space are activated. Such processes are described by a compressed exponential-power relaxation function. Thick-film p+-p structures are characterized by own aging processes, which manifest themselves in an increase in electrical resistance. Kinetics of their thermally-induced aging is adequately described by an extended exponential-power function.

Dynamic Event-Triggered Adaptive Tracking Control for Multiagent Systems with Power Exponential Function Using Fuzzy Disturbance Observer

Dynamic Event-Triggered Adaptive Tracking Control for Multiagent Systems with Power Exponential Function Using Fuzzy Disturbance Observer

Multivariate exponential power Lévy processes and random fields

Two multivariate exponential power Lévy processes are introduced in this paper via compound Poisson representations, which are so termed because their characteristic exponents are the linear combination of certain positive or negative power functions. They can be represented as the time changed multivariate Brownian motions using the time changes that are two exponential power subordinators, respectively. Two multivariate exponential power random fields are also proposed as elliptically contoured random fields, whose finite-dimensional characteristic functions are made up of the exponential power functions and enjoy the infinitely divisible property.

Simplified optimised prescribed performance control for high-order multiagent systems with privacy preservation

This paper studies the consensus tracking problem based on optimised backstepping technique for multiagent systems with power exponential functions and the privacy protection. Under the optimised backstepping technique, the controllers with power functions are designed by utilising the reinforcement learning strategy. Moreover, the synchronisation error converges to a predetermined region within a user-defined settling time by utilising a speed function. To ensure the safety of communication, the privacy protection is applied to multiagent systems, which effectively prevent information exposure. Based on Lyapunov stability theory, the tracking errors of the system with power exponential functions converge to a predetermined region, and a simulation example proves the feasibility of the proposed strategy.