Exponential Law Research Articles

REDUCTION OF AIR DUST OF THE WORK ZONE AT WOODWORKING ENTERPRISES

The assessment of air dust at the workplaces of the woodworking enterprise was carried out. It was found that the dust in the workplace exceeds the established standard MPC for wood dust by an average of 1.3…2.5 times. The most unfavorable working conditions are observed at the workplaces of grinding and belt machine operators, where the dust concentration reaches 5.7 MPC. The processes of spreading and settling of dust in production facilities have been studied. It is established that regardless of the wood species, the change in the dust content of the working area and the density of dust in the production premises at different distances from the sources of dust removal is subject to the exponential law. Experimental dependences characterizing these changes are obtained. Existing aspiration systems were examined. The discrepancy between the volumes of air removed from the equipment and the design value has been established, which leads to the removal of dust into the air of the work area and causes increased dust in the workplace. Examination of aspiration systems showed that the reason for their unstable operation is the presence of dust deposits on the inner surfaces of horizontal air ducts.

Quantum dots as a probe of fundamental physics: deviation from exponential decay law

We explore a possibility of measuring deviation from the exponential decay law in pure quantum systems. The power law behavior at late times of decay time profile is predicted in quantum mechanics, and has been experimentally attempted to detect, but with failures except a claim in an open system. It is found that electron tunneling from resonance state confined in man-made atoms, quantum dots, has a good chance of detecting the deviation and testing theoretical predictions. How initial unstable state is prepared influences greatly the time profile of decay law, and this can be used to set the onset time of the power law at earlier times. Comparison with similar process of nuclear alpha decay to discover the deviation is discussed, to explain why there exists a difficulty in this case.

Cooccurrence of pH-sensitive shifting blue and immobile green triple surface-state fluorescence in ultrasmall super body-centered cubic carbon quantum dots

Carbon quantum dots are widely used in various fields owing to excellent optical properties and outstanding biocompatibility. We synthesize rare super body-centered cubic (C8) structured carbon quantum dots by using cheap source materials and simple preparation method. They exhibit one shifting blue emission band and two close immobile green bands. They have large Stokes shifts ranging from 0.68 to 1.01 eV and large quantum yields as high as 60%. The three types of emissions are competitive and their intensities vary sensitively and differently with pH. Moreover, their emission intensity versus excitation power curves follow with k values significantly smaller than unity. The blue emission follows the stretched exponential decay law with an intermediate lifetime of ∼3.9 ns and a lifetime-dispersion factor of ∼0.85 whereas the two green emissions exhibit faster and slower decays with respective lifetimes of around 2.0 and 13.0 ns. The results reveal that the blue emission originates from an ensemble of emission sites exhibiting quantum confinement-like effect and two green emissions stem from pH-sensitive surface functional groups-associated fluorophores.

Hydrogeological characterization of heterogeneous volcanic aquifers in the Canary Islands using recession analysis of deep water gallery discharge

Aquifers constitute the main freshwater supply of oceanic islands. Maintaining groundwater quantity and quality is of critical concern as demographic and climatic changes place additional pressures on already fragile water resources systems. Islands with heterogeneous volcanic aquifers pose additional difficulties in assessing their water resources. This work proposes an approach for improving the hydrogeological characterization of heterogeneous volcanic aquifer systems by making use of recession coefficients from deep water gallery discharge. To demonstrate the usefulness of this approach, hydrographs and recession curves from groundwater discharge of 30 water galleries on La Palma (Canary Islands) were evaluated. This analysis allowed us to obtain the main hydrogeological parameters of a volcanic aquifer system, in terms of hydraulic diffusivity. A Maillet-Boussinesq model with an exponential decay law was adopted, according to field observations of drainage discharge. The alpha coefficients of recession values ranged between 10−3 and 4·10−4 day−1 and showed significant spatial correlation with insular geology. Additionally, hydraulic diffusivity values of island hydrogeological domains were obtained from recession coefficients using the Rorabaugh-Singh method. Weighted storage coefficients for volcanic materials were in the range of 3% to 7%, with an average transmissivity in the range of 15 to 150 m2·day−1. The methodology proposed has demonstrated its usefulness in coping with local uncertainty in hydraulic characterization of insular aquifers associated with volcanic heterogeneity. This is an improvement compared to standard pumping tests, thus providing hydraulic parameters prior to numerical analysis for water management planning.

Effects of interface diffusion and shock strength on shock-accelerated SF6 cylinder

The effects of interface diffusion and incident shock strength on the evolution of a shock-accelerated SF6 cylinder are numerically instigated. These two effects are manifested by measuring two essential issues that determine the material mixing of a shock–cylinder interaction (SCI), namely, the variations of the cylinder area and the material line length. Three interface types (with one sharp interface and two diffuse interfaces) and five incident shock strengths (Mach number ranges from 1.21 to 2.00) are examined. The numerical results provided in the present study show that both these effects play important roles in deforming the SF6 cylinders and the corresponding cylinder area and material line stretching. The cylinder area variation histories of the present results prove that the one-dimensional theoretical prediction of Giordano and Burtschell [“Richtmyer–Meshkov instability induced by shock–bubble interaction: Numerical and analytical studies with experimental validation,” Phys. Fluids 18, 036102 (2006)] applies not only to those sharp interface cylinders but also to these diffuse interface cylinders. The material line stretching histories prove that the exponential law of Yang et al. [“Applications of shock-induced mixing to supersonic combustion,” AIAA J. 31, 854 (1993)] applies well for diffuse interfaces but not for sharp interfaces. It is found that the exponential growth of the material line for the diffuse cylinders is dominated by the mass transport, and that the secondary instabilities only play their role in the primary vortex region. Finally, a predictive law of the development of material line length on the basis of circulation prediction theory is built. It is interesting that the use of the original circulation prediction model can be extended in such a way.

Вероятностная оценка эффективности функционирования социальных систем в условиях негативных факторов

An approach to the quantitative assessment of the open social system efficiency of a non-technical nature is con-sidered. The task is formulated from the standpoint of assessing complex indicators that take into consideration the conditions of external influences on an open non-technical system. Formalizing the formulated problem is carried out within the framework of the reliability theory methods. A two-parameter generalized analytical expression is obtained for calculating a probabilistic assessment of the open system efficiency, taking into consideration the nature of destructive impacts. An approach to calculating the probability of failure-free operation of such systems is substantiated, considering the frequency of failures caused by negative consequences from destructive impacts. The results of analytical modelling are presented in assessing the probabilistic indicators of open non-technical systems, in which the degradation of ongoing processes can be described on the basis of an exponential law. The processes of a non-technical nature corresponding to the specified distribution are given, which include the aging of information, the level of residual knowledge, the number of divorces by the number of years lived, motivational stability, etc., characteristic of such areas as pedagogy and psychology. The author considers an example of applying a reasonable approach in relation to the “burnout syndrome” based on analysing control points and time intervals, which allows predicting the future state of the diagnosed person according to the current assessments. Conclusions are made and directions for further research are determined.

Propagation of shock wave in a non-ideal dusty gas in rotating medium using Lie group theoretic method: Isothermal flow

This paper concerns with the similarity solutions using Lie group theoretic method for one-dimensional unsteady isothermal flow behind the shock wave in the mixture of non-ideal gas and small solid particles in rotating medium. Group theoretic technique brings the different possible cases of potential solutions with the power law, particular case of power law and exponential law shock paths with the different choices of constants present in the generators of the Lie group of transformations. Similarity solutions for non-ideal dusty gas (a mixture of non-ideal gas and small solid dust particles) exist if the density of the ambient medium is constant. Solutions are obtained for both exponential law and power law shock paths. The effects of the variation of the physical parameters on the flow variables distribution behind the shock wave front, and on the shock are discussed. The shock strength increases with an increase in the ratio of the specific heat of the solid particles to the specific heat of the gas at constant volume [Formula: see text], the initial azimuthal velocity variation index [Formula: see text], and the ratio of the density of solid particles to the initial density of the gas [Formula: see text]. The shock wave decays with an increase in the value of gas non-idealness parameter [Formula: see text].

Dependence of Tunneling Mechanism on Two-Dimensional Material Parameters: A High-Throughput Study

A band-to-band tunneling FET (TFET) with an atomical two-dimensional (2D) channel is a potential candidate for the next-generation electronic device in view of its steep subthreshold swing and low power consumption. However, how to establish a precise physical model between the band property of 2D channel materials and the device performance of 2D TFETs is the key to accelerate their practical applications. Herein, through high-throughput first-principles calculations, we study the tunneling transport properties of 44 representative 2D materials with four kinds of crystal system. Particularly, we propose a well-defined and striking exponential scaling law $(\mathrm{SS}=A{\mathrm{e}}^{B{m}_{r}}+C)$ between the subthreshold swings (SSs) and reduced effective masses $({m}_{r})$ of 10-nm TFETs. According to the exponential model, 2D orthorhombic and trigonal crystal TFETs with the steep SS hold the reduced effective masses of more than 0.1 and $0.2\phantom{\rule{0.25em}{0ex}}{m}_{0}$, which could inhibit tunneling leakage current. These insights provide guidance for material screening in the construction of post-Moore 2D low-power transistors.

Design of Robust Integral Terminal Sliding Mode Controllers with Exponential Reaching Laws for Solar PV and BESS-Based DC Microgrids with Uncertainties

In this paper, an integral terminal sliding mode controller (ITSMC) based on a modified exponential reaching law (MERL) is developed for providing large-signal DC-bus voltage stability while smoothing power flow in DC microgrids (DCMGs). It is worth mentioning that this control approach is not employed in DCMG applications yet to adjust the DC-bus voltage while preserving power balance. The proposed DCMG is made up of a solar photovoltaic (PV) unit, a battery energy storage system (BESS), and DC loads. A DC-DC boost converter (DDBC) and a bidirectional DC-DC converter (BDDC) are employed to connect the solar PV and BESS, respectively, with the DC-bus, which not only controls the output power of these units but also regulates the DC-bus voltage. First, a detailed dynamical model including external disturbances is developed for each component, i.e., the solar PV and BESS. Then, the proposed control approach is employed on these units to get their corresponding control signals. Afterward, the overall stability of each unit is ensured using the Lyapunov stability theory. Moreover, to ensure the robustness of the proposed controller, external disturbances are also bounded based on the value of user-defined constants. Finally, simulation results are used to evaluate the effectiveness of the proposed control approach in a variety of operational scenarios. Additionally, simulation results of the proposed control strategy are compared to those of existing controllers to demonstrate its superiority.

Phase-Dynamic Analysis of the Food Fermentation Process

There is a lactic acid formation followed by milk casein coagulation in the fermented dairy products obtained by fermentation. A man observes the metabolic activity of microorganisms during fermentation. Decomposition and synthesis reactions accompany the vital activity process of microorganisms leading to significant changes in the culture medium. It gives the products produced the specified rheological, organoleptic and required functional properties. The priority direction of the dairy production evolvement is the development of products with regulated technological processes. The article considers the phase-dynamic acid accumulation process possibility in dairy products, namely, by the example of yogurt with fat mass fraction of 2.5% during the fermentation period. The researchers modeled changes regression dependences in the rate and acceleration of the acid accumulation process during fermentation using the MathCAD computer mathematical system. A man specified the acid accumulation phases in the studied object by experimental and analytical studies: the active phase – in the first 6 hours of fermentation; the passive phase – from 6 to 10 hours. The acidity growth rate is proportional to the number of lactic acid bacteria. Initially, the increase in acidity occurred according to the exponential law; then, the increase began to slow down as the nutrient content (lactose) decreased and the concentration of microbial waste products increased; and assumed the maximum value eventually. The phase-dynamic portrait of acid accumulation in fermented milk products enables to quantify the separate influence of the microorganism reproduction and its inactivation effects on the acidity growth process.

Deriving exponential and power law slow crack growth parameters from dynamic fatigue of indented or as-polished window material coupons

Knowledge of slow crack growth rate in a window material is required to determine the design life of a window in which cracks grow under the influence of applied service stress. Parameters that characterize crack growth rate can be measured by dynamic fatigue in which coupons are taken to failure at several constant stress rates. The slower the stress rate, the more time is available for cracks to grow during the strength measurement, and the lower the stress at which the coupon fails. That is, coupons tested at a slower stress rate are weaker than coupons tested at a faster stress rate. The rate of slow crack growth is commonly fit to either a power law or an exponential law. The exponential law provides the more conservative estimate of design life and is prescribed for use by the U.S. National Aeronautics and Space Administration to design windows for manned vehicles. Well-established analytical equations are used to derive the power law crack growth parameters from dynamic fatigue measurements of as-polished (unindented) coupons. There are no exact analytical equations to derive power law parameters from indented coupons or to derive exponential law parameters from unindented or indented coupons. Approximate procedures have been used to derive crack growth parameters when there are no exact equations. We now describe a numerical method that gives the power and exponential laws for both unindented and indented coupons by least-squares fitting of dynamic fatigue measurements. A MATLAB code is provided to carry out the calculations.

Optimal Slip Ratio Tracking Integral Sliding Mode Control for an EMB System Based on Convolutional Neural Network Online Road Surface Identification

As the main branch of the brake-by-wire system, the electro-mechanical brake (EMB) system is the future direction of vehicle brake systems. In order to enhance the vehicle braking effect and improve driver safety, a convolutional neural network (CNN) online road surface identification algorithm and an optimal slip ratio tracking integral sliding mode controller (ISMC) combined EMB braking control strategy is proposed in this paper. Firstly, according to the quarter-vehicle model and Burckhardt tire model, the vehicle braking control theory based on the optimal slip ratio is analyzed. Secondly, using the VGG-16 CNN method, an online road surface identification algorithm is proposed. Through a comparative study under the same dataset conditions, it is verified that the VGG-16 method has a higher identification accuracy rate than the SVM method. In order to further improve the generalization ability of VGG-16 CNN image identification, data enhancement is performed on the road surface image data training set, including image flipping, clipping, and adjusting sensitivity. Then, combined with the EMB system model, an exponential approach law method-based ISMC is designed to achieve the optimal slip ratio tracking control of the vehicle braking process. Finally, MATLAB/Simulink software is used to verify the correctness and effectiveness of the proposed strategy and shows that the strategy of real-time identifying road surface conditions through vision can make the optimal slip ratio of vehicle braking control reasonably adjusted, so as to ensure that the adhesion coefficient of wheel braking always reaches the peak value, and finally achieves the effect of rapid braking.

Study on fracture behaviour of basalt fibre reinforced asphalt concrete with plastic coupled cohesive model and enhanced virtual crack closure technique model

ABSTRACT In this study, the plastic coupled cohesive model and enhanced virtual crack closure technique (VCCT) are used to investigate the fracture behaviour of the basalt fibre reinforced asphalt concrete (BFRAC). In the plastic coupled cohesive model, the separation and traction response along the cohesive zone advance ahead of a crack tip is governed by an exponential cohesive law. The double-K fracture theory is integrated into the enhanced VCCT model. It is shown that the simulated load-cracking mouth opening displacement (P-CMOD) curves from both the plastic coupled cohesive model and the enhanced VCCT model compares favourably with the measured curves from the single-edge notched beam. The parameters used in the plastic coupled cohesive model cannot directly be obtained from the standard test, and the inverse analysis method is always necessary for identifying the fracture parameters. On the contrary, the fracture parameters in the enhanced VCCT method can be directly calculated from the P-CMOD curves based on the double-K fracture theory and the finite plastic fracture theory (Hutchinson, Rice, Rosengren singular crack tip fields, abbreviated as HRR field). Meanwhile, compared with the plastic coupled cohesive model, the enhanced VCCT model coupled with the Ramberg–Osgood elasto-plastic harden model is promising for investigating the physical mechanism underlying the nonlinear fracture of BFRAC. This paper proposed two concrete and valuable models in the finite element method for simulating the fracture behaviour of the huge structure with asphalt and asphalt concrete.

A Study on Dynamic Behaviour of Thermally Distributed Exponentially Graded Rotor System with Induced Porosities

The present work deals with the dynamic analysis of exponential law-based functionally graded (FG) rotor-bearing systems. The effect of thermal gradation and porosity on dynamic characteristics of FG rotor shafts has been studied first time, using exponential law with a novel two-nodded FG rotor element based on Timoshenko beam theory (TBT). Porous material properties are assorted using exponential law and thermal gradation across the cross section of the FG shaft using exponential temperature distribution (ETD). The effects of temperature and porosity on natural frequencies and whirl frequencies are studied. It has been observed that there is a significant reduction in natural frequencies and whirl frequencies with an increase in volume fraction of porosity and temperature. Attempts have been made to obtain suitable reasons for the behaviours based on the material properties. Furthermore, the steady-state and transient vibration responses have been simulated using the Houbolt time marching technique for the ceramic-based FG rotor shaft system. The result shows the maximum amplitude of the steady-state and transient vibration responses is increased, and the critical speed of the FG rotor system shifts towards the left with the increase in volume fraction of porosity and temperature.

Ligand Modified and Light Switched On/Off Single-Chain Magnets of {Fe 2 Co} Coordination Polymers via Metal-to-Metal Charge Transfer

Ligand Modified and Light Switched On/Off Single-Chain Magnets of {Fe ₂ Co} Coordination Polymers via Metal-to-Metal Charge Transfer

Third-Order Robust Fuzzy Sliding Mode Tracking Control of a Double-Acting Electrohydraulic Actuator

In the industrial sector, an electrohydraulic actuator (EHA) system is a common technology. This system is often used in applications that demand high force, such as the steel, automotive, and aerospace industries. Furthermore, since most mechanical actuators' performance changes with time, it is considerably more difficult to assure its robustness over time. Therefore, this paper proposed a robust fuzzy sliding mode proportional derivative (FSMCPD) controller. The sliding mode controller (SMC) is accomplished by utilizing the exponential law and the Lyapunov theorem to ensure closed loop stability. By replacing the fuzzy logic control (FLC) function over the signum function, the chattering in the SMC controller has been considerably reduced. By using the sum of absolute errors as the objective function, particle swarm optimization (PSO) was used to optimize the controller parameter gain. The experiment results for trajectory tracking and the robustness test were compared with the sliding mode proportional derivative (SMCPD) controller to demonstrate the performance of the FSMCPD controller. According to the findings of the thorough study, the FSMCPD controller outperforms the SMCPD controller in terms of mean square error (MSE) and robustness index (RI). Keywords—tracking control, electrohydraulic actuator (EHA), robust control design, fuzzy sliding mode proportional derivative (FSMCPD), particle swarm optimization (PSO).

A Data-Driven Modeling Method for Stochastic Nonlinear Degradation Process With Application to RUL Estimation

This article proposes a novel modeling method for the stochastic nonlinear degradation process by using the relevance vector machine (RVM), which can describe the nonlinearity of degradation process more flexibly and accurately. Compared with the existing methods, where degradation processes are modeled as the Wiener process with a nonlinear drift function formulized as the power law or exponential law, this kind of modeling method can characterize degradation processes with more nonlinear behavior. Instead of modeling the drift coefficient of the Wiener process directly, the weighted combination of basis functions is utilized to express the increment of the Wiener process and the parameters are calculated by a sparse Bayesian learning algorithm. Based on the proposed model, a numerical approximation formula for the probability density function (PDF) of the remaining useful life (RUL) is derived. Finally, comparison studies, including a numerical simulation and a practical case, are provided to demonstrate the effectiveness and the accuracy of the proposed methods for RUL estimation.

Exponential Continuous Non-Parametric Neural Identifier With Predefined Convergence Velocity

This paper addresses the design of an exponential function-based learning law for artificial neural networks (ANNs) with continuous dynamics. The ANN structure is used to obtain a non-parametric model of systems with uncertainties, which are described by a set of nonlinear ordinary differential equations. Two novel adaptive algorithms with predefined exponential convergence rate adjust the weights of the ANN. The first algorithm includes an adaptive gain depending on the identification error which accelerated the convergence of the weights and promotes a faster convergence between the states of the uncertain system and the trajectories of the neural identifier. The second approach uses a time-dependent sigmoidal gain that forces the convergence of the identification error to an invariant set characterized by an ellipsoid. The generalized volume of this ellipsoid depends on the upper bounds of uncertainties, perturbations and modeling errors. The application of the invariant ellipsoid method yields to obtain an algorithm to reduce the volume of the convergence region for the identification error. Both adaptive algorithms are derived from the application of a non-standard exponential dependent function and an associated controlled Lyapunov function. Numerical examples demonstrate the improvements enforced by the algorithms introduced in this study by comparing the convergence settings concerning classical schemes with non-exponential continuous learning methods. The proposed identifiers overcome the results of the classical identifier achieving a faster convergence to an invariant set of smaller dimensions.

A computer simulation of population reproduction rate on the basis of their mathematical models

The article deals with the adoption of computer modeling as one of the leading areas of introduction of modern information technology in the modernization of content, forms and methods of teaching. In order to implement interdisciplinary integrated learning, the possibilities of interdisciplinary integration of learning content have been identified, the practice of using software environments in the process of modeling biological problems based on mathematical models has been analyzed, the possibilities of implementing algorithms of mathematical models in computer modeling have been investigated. A set of research tasks in biology as a basis for the implementation of interdisciplinary integration: nature - mathematics -computer science has been introduced into the educational process. The mathematical models of Verhulst, Arim, Leslie and the exponential law of direct proportional dependence or proportional rate of reproduction depending on the number of individuals of a population were used to design computer models of reproduction of ecological processes. They were implemented using the computer mathematics system MathCad and using programming environments Python, C#, C++. The expediency of the proposed method of interdisciplinary integration of learning content has been justified through a developmental and productive integrated approach, the use of certain collective forms of activity, the practical orientation of professional training disciplines to form algorithmic competence of students as a basis for professional competence in computer modeling of mathematical models of biological processes.

Multichannel decay law

It is well known, both theoretically and experimentally, that the survival probability for an unstable quantum state, formed at t=0, is not a simple exponential function, even if the latter is a good approximation for intermediate times. Typically, unstable quantum states/particles can decay in more than a single decay channel. In this work, the general expression for the probability that an unstable state decays into a certain i-th channel between the initial time t=0 and an arbitrary t>0 is provided, both for nonrelativistic quantum states and for relativistic particles. These partial decay probabilities are also not exponential and their ratio turns out to be not a simple constant, as it would be in the exponential limit. Quite remarkably, these deviations may last relatively long, thus making them potentially interesting in applications. Thus, multichannel decays represent a promising and yet unexplored framework to search for deviations from the exponential decay law in quantum mechanical systems, such as quantum tunneling, and in the context of particle decays.