Semi-empirical Formula Research Articles

Predictions of Peak Discharge of Dam Failures Based on the Combined GA and BP Neural Networks

In this paper, the Artificial Neural Network (ANN) was utilized to predict the peak discharge of dam failures, which was based on the combined Genetic Algorithm (GA) and Back Propagation (BP) neural network. The dataset comprises 40 samples from self-conducted experiments and available literature. To compare the efficiency of the suggested approach, three evaluation metrics, including the coefficient of determination (R2), the root mean square error (RMSE) and the mean absolute error (MAE), were analyzed for both the BP neural network and the GA-BP neural network. The findings suggest that (1) The prediction accuracy of the GA-BP was better than that of the BP; and (2) Compared to BP, GA-BP demonstrated a 9.07% average improvement in R2, a 57.36% average reduction in MAE, and a 57.53% average reduction in RMSE. In addition, the results of GA-BP and semi-empirical formulas were compared and the effect of three parameters on the peak discharge was analyzed. The results showed that the GA-BP model could effectively predict the peak discharge of dam failures.

Prediction of binding energy using machine learning approach

The liquid drop model is an empirical hypothesis established on the idea that nuclei can be thought of as incompressible liquid droplets. The AME2020 dataset was used in this work to determine binding energy using a semi-empirical mass formula and compare it with binding energies predicted by a machine learning algorithm. Random forest regressor, MLPRegressor, and XGBoost models were employed. In terms of accuracy, root mean square error, and mean absolute error, machine learning models performed better than the semi-empirical mass formula. Compared to RFR, XGBoost, and SEMF, MLPRegressor performed better in predicting binding energies for lighter nuclei. Using estimated binding energies, nuclear masses were computed, and it was shown that all three models adequately predicted nuclear masses with minimal error. This finding highlights how machine learning can be applied to nuclear physics to predict various nuclei’s properties.

Superheavy magic nuclei: Ground-state properties, bubble structure and α-decay chains

A systematic investigation of superheavy nuclei in the isotopic chains of proton numbers Z=106, 114, 120, and 126 together with isotonic chains of neutron numbers N=162, 172, and 184 is presented in the theoretical framework of relativistic mean-field density functionals based on density-dependent meson-nucleon couplings. Ground-state properties, including binding energy, shape, deformation, density profile, and radius, are estimated to provide compelling evidence of magicity in these even-even nuclei, aligning with the concept of the ‘island of stability.’ The analysis reveals central depletion in the charge density, indicating a bubble-like structure, primarily attributed to the substantial repulsive Coulomb field and the influence of higher l-states. A thorough examination of potential decay modes, employing various semi-empirical formulas, is presented. The probable α-decay chains are evaluated, demonstrating excellent agreement with available experimental data.

Mean Excitation Energies of all ionization stages of all atoms with [formula omitted]

The presented work provides values of Mean Excitation Energy (MEE) for all atoms and their ions with atomic numbers 1≤Z≤86. To fill in the gaps in the available data, we propose an approximate atomic model for ions of high-Z elements, that uses a semi-empirical formula based on the Local Plasma Approximation (LPA). Despite the fact that the LPA, in its original form, poorly predicts MEE for high ionization states, a relatively simple modification utilizing a fit function can amend this shortcoming. We assess the importance of relativistic effects for the MEE for highly ionized atoms and compare the proposed formula to other approximations available for high-Z elements. We estimate the uncertainty of the presented data to be less than 40% in absolute value for the worst cases and less than 20% for most ions. This corresponds to an uncertainty of the order of few percent for the logarithm of MEE, which is the value of interest in the case of Bethe’s theory of stopping power.

Economic Justification of Design Features for a Universal Dry Cargo Vessel

The economic efficiency of ships is an important indicator of transport vessels, and estimating the economic efficiency of ships is an important task in making investment decisions during the early stages of shipbuilding. This article, based on semi-theoretical and semi-empirical formula methods using the prototype ship of the RST12C project as a basis, estimates and analyzes the main economic indicators of mixed-navigation oil/chemical tankers according to different cargo capacities and speed combinations, for reference by relevant departments.

Best-Corrected Visual Acuity Quantitative Prediction for Cataract Patients: AI-Assisted Clinical Diagnostics Facilitation via the Inverse Problem Algorithm

Objective: This study provided a quantitative prediction of best-corrected visual acuity (BCVA) for cataract patients using the inverse problem algorithm (IPA) technique earlier proposed by the authors. Methods: To this end, seven risk factors (age, BMI, MAP, IOP, HbA1c, LDL-C, and gender) were linked by a semi-empirical formula by normalizing each factor into a dimensionless range of −1.0 to +1.0. The adopted inverse problem algorithm (IPA) technique was run via a self-developed program in STATISTICA 7.0, featuring a 29-term nonlinear equation considering seven risk factors, cross-interaction between various pairs of factors, and one constant term [7 + (7 × 6)/2 + 1 = 29]. The IPA neglected quadratic, triple, or quadruple factors′ cross-interactions. This study used a dataset of 632 cataract patients to attain a reliable BCVA prediction with a variance of 0.929. A verification dataset of 160 patients with similar symptoms was used to verify this approach′s feasibility, reaching a good correlation with R2 = 0.909. Results: The verification group′s derived average AT (agreement) (9.12 ± 27.00%) indicated a slight deviation between the theoretical prediction and practical BCVA. The significant factors were age, body mass index (BMI), and intraocular pressure (IOP), whereas mean arterial pressure (MAP), hemoglobin A1c (HbA1c), low-density-lipoprotein cholesterol (LDL-C), and gender insignificantly contributed to BCVA. Conclusions: The proposed approach is instrumental in AI-assisted clinical diagnosis, yielding robust BCVA predictions for individual cataract patients based on their biological indices before the ophthalmological examination procedure.

Experimental and kinetics of the oxidation of ammonium sulfite by hydrogen peroxide in ammonia flue gas desulfurization

ABSTRACT The oxidation of ammonium sulfite obtained from ammonia-based flue gas desulfurization by hydrogen peroxide in aqueous solutions was studied using a stirred reactor. An experimental study of the kinetic parameters of the oxidation process was investigated in the pH of 4.2–5.2 at 25–50°C. r = k 3 H + HS O 3 − H 2 O 2 is valid at sulfite concentrations of 10−4 mol/L for the pH range 4.2–5.2. At 298K and pH of 5.0, third-order rate constant k 3 was found to be (6.9 ± 0.21)×107 (mol/L)−2s−1. When the concentration of sulfite is 0.01 mol/L, the reaction first-order with respect to sulfite and hydrogen peroxide, and the second-order reaction rate constant at pH of 4.2–5.4 is lg k 2 = − 1.0135 pH + 7.4862 . Activation energy of E a = 32.26 kJ/moL. Kinetic data were compared with previous studies. A semi-empirical formula can express the effect of ionic strength on k 3. The kinetic data of ammonium sulfite oxidation with hydrogen peroxide have potential applications in the wet ammonia desulfurization process.

Regression prediction of critical exhaust volumetric flow rate in tunnel fire with two-point extraction ventilation based on neural network method

In this study, a Genetic Algorithm-Backpropagation Neural Network (GA-BPNN) model was developed to predict critical exhaust volumetric flow rate in tunnel fires with two-point extraction ventilation system. Seven influencing factors served as inputs for the model, while the critical exhaust volumetric flow rate was the output. Experimental data from two reduced-scale tunnels were utilized to both train and validate the GA-BPNN model. The results demonstrate a satisfactory prediction performance, with key metrics such as Mean Absolute Percentage Error (MAPE), Relation Coefficient (R2), and Root Mean Square Error (RMSE) achieving values of 0.0384, 0.9989, and 3.5258, respectively. Importantly, the model maintains a maximum Absolute Percentage Error (APE) below 10 %. In contrast, the traditional BPNN model exhibited an APE of approximately 18.9 %. Moreover, the predictive results of the GA-BPNN model were compared with those of a previously semi-empirical formula. It was observed that the semi-empirical predictions exhibited APE exceeding 20 % for certain data points. This further underscores the superiority of the GA-BPNN model in predicting critical exhaust volumetric flow rates in tunnel fires with two-point ventilation system. These findings affirm the feasibility and effectiveness of GA-BPNN regression model as a reliable method for predicting critical exhaust volumetric flow rates under multiple factors.

Experimental and calculated electronic stopping force determination of 24Cr, 28Ni and 22Ti ions crossing PVC and Mylar foils in the ion energy domain of LSS theory

Energy loss measurements for heavy ions (28Ni,24Cr and 22Ti) crossing thin polymeric foil such as PVC and Mylar in the energy range 0.1–0.3 MeV/n have been carried out utilizing the 6MV Tandem accelerator facility at iThemba-labs in Johannesburg (South Africa). These measurements deduced experimental stopping force data have been compared with those calculated using Lindhard, Scharff and Schiott formulation (LSS) and SRIM-2013 predictions. A large significant deviation has been observed between experimental values and those calculated by LSS formula. Based on physical postulate, we have developed a reasonably simple semi-empirical formula that takes in to account a mean residual projectile charge Z1¯ and suitable ξe factor which depend on Z1 and Z2. This new modified LSS formula has been tested and the calculated stopping force values generated by this formula are in close agreement with the measured ones.

Ionic current blockade in a nanopore due to an ellipsoidal particle.

Nanopores in solid-state membranes have been used to detect, identify, filter, and characterize nanoparticles and biological molecules. In this work, we simulate an ionic flow through a nanopore while an ellipsoidal nanoparticle translocates through a pore. We numerically solve the Poisson-Nernst-Planck equations to obtain the ionic current values for different aspect ratios, sizes, and orientations of a translocating particle. By extending the existing theoretical model for the ionic current in the nanopore to the particles of ellipsoidal shape, we propose semiempirical fitting formulas which describe our computed data within 5% accuracy. We also demonstrate how the derived formulas can be used to identify the dimensions of nanoparticles from the available experimental data which may have useful applications in bionanotechnology.

Performance degradation evaluation of square steel tubes with local penetration damage

Steel tubular structures are susceptible to welding defects, cracking defects and environmental corrosion, which can negatively affect the stability and reliability of structure. This study tested the axial compression performance of twenty-six square steel tubular stubs with localized penetration damage simulated by artificial notch, considering the influence of notch length, orientation, and position. The test results showed that the failure mode of the specimens was dominated by the local buckling along the direction of the notch axis. The failure mode of the specimen with vertical notch showed notch opening, while those with horizontal notch showed notch closing, resulting in the secondary peak value in the load-displacement curve. The existence of local penetration damage reduced the ultimate strength and ductility of the tubular stubs. Compared to the ultimate strength of the specimens with middle notch, those with corner notch were weakened more, up to 27 %. Furthermore, the effects of notch dimension, position, orientation, and tube wall thickness on the axial bearing capacity of square steel tubular stubs are discussed by using a validated finite element model. Owing to the analysis, the ultimate strength of the stubs is reduced by increasing notch length, width and depth, whereas the reduction effect tends to be weakened as the notch orientation angle increases. The notch located in the corner is the most unfavorable for the axial compression performance of the square steel tubular stubs. A semi-empirical formula for evaluating the ultimate strength of square steel tubular stubs with local penetration damage is proposed by introducing the strength reduction factor. An artificial neural network-based ultimate strength prediction model is developed that can consider the effects of wide-range parameters, achieving high accuracy.

A new fractal pore-throat chain model for non-Darcy flow through porous media

Non-Darcy flow through porous media is of great significance in hydraulics, oil and gas engineering, biomedical science, chemical and civil engineering etc. However, it is difficult to fully grasp the nature of fluid flow through porous media from macroscopic scale alone. Based on the statistically fractal scaling laws of pore structures, a new fractal pore-throat chain model (FPTCM) for non-Darcy flow through the isotropic porous media is developed. The analytical expressions for the Darcy and non-Darcy permeability as well as non-Darcy coefficient are derived accordingly. In order to explore the local flow field of high-speed non-Darcy flow through porous media, the finite element method is also carried out on an equivalent pore-throat unit. The predicted permeability by FPTCM shows better agreement with present numerical results and available experimental data, compared with commonly used semi-empirical formulas including Kozeny-Carman and Ergun equations. It has been found that both Darcy and non-Darcy permeability as well as non-Darcy coefficient strongly relate to the pore structures of porous media. The non-Darcy permeability is positively correlated to porosity, pore fractal dimension and Darcy permeability, while it is negatively related to tortuosity fractal dimension and pore size range. The non-Darcy coefficient shows opposite correlation with these parameters. The present work can provide theoretical basis for oil and gas development, nuclear waste treatment, carbon dioxide geological sequestration etc.

Improved semi-empirical formula for cluster radioactivity half-lives

An improved semi-empirical formula for cluster radioactivity half-lives is proposed by incorporating the influences of reduced mass, the blocking effect of unpaired nucleons and mass asymmetry on the basis of the original Tavares formula [Eur. Phys. J. A 49 (2013) 6]. Using this improved semi-empirical formula, the calculated results of the cluster radioactivity half-lives for the daughter nuclei around [Formula: see text]Pb or its neighbors can reproduce the experimental data well with a corresponding root-mean-square deviation [Formula: see text]= 0.570, which proves the feasibility of this formula to calculate cluster radioactivity half-lives in trans-lead nuclei. The accuracy of the improved semi-empirical formula is improved by approximately 37% compared to its predecessor whose the root-mean-square deviation is 0.902. Meanwhile, the influence of deformation effect for cluster radioactivity is also briefly discussed. In addition, we extend this improved semi-empirical formula to predict the half-lives of 51 possible cluster radioactive candidates whose cluster radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, some empirical and/or semi-empirical formulae are also used.

Effect of physicochemical properties on critical sinking and attachment of respirable coal mine dust impacting on a water surface

Respirable coal mine dust (RCMD) inhalation is identified as the main cause of the resurgence of coal worker’s pneumoconiosis (CWP) since the mid-1990s. At present, the predominant dust control technology is the water spray system. However, in practice, the capture efficiency of RCMD by this technology is relatively low. To understand the capturing mechanism and develop improvement strategies, this research is focused on the surface chemistry study of RCMD and its impact on a water surface using a dynamic model. Proximate analysis, chemical, and mineral composition of a run-of-mine (ROM) coal sample from Appalachian region were analyzed using a proximate analyzer, Inductively Coupled Plasma Mass Spectrometry (ICP-MS), and X-ray Diffraction (XRD), respectively. Contact angles were measured by capillary rise test using the Washburn equation. Based on the dynamic model, the effects of particle size, density, contact angle, and surface tension on the critical sinking were investigated. It was pointed out in this work that reducing surface tension, in turn, decreases contact angle, which has been neglected in the literature. Regime maps for different minerals were created and showed that organic matter has the highest critical velocity due to its low density and high contact angle. Reducing water surface tension to the critical solid surface tension of coal around 30 mN/m could maximize the attachment efficiency. Scaling laws, constructed by force balance, led to the criteria of critical sinking: Ucr∼61-cosθ2D+1γlvρlR, i.e., Wecr∼121-cosθ2D+1. A semi-empirical formula for critical velocity was obtained by fitting the simulation data, Ucr=1.0961-cosθ2D+1γlvρlR. Attachment efficiency was defined and formulated as Pa=U02Ucr2=We0Wecr, establishing relationships between attachment efficiency and the physicochemical properties of RCMD and water droplets.

Calibrating the WSA Model in EUHFORIA Based on Parker Solar Probe Observations

We employ Parker Solar Probe (PSP) observations during the latest solar minimum period (years 2018–2021) to calibrate the version of the Wang–Sheeley–Arge (WSA) coronal model used in the European Heliospheric Forecasting Information Asset (EUHFORIA). WSA provides a set of boundary conditions at 0.1 au necessary to initiate the heliospheric part of EUHFORIA, namely, the domain extending beyond the solar Alfvénic point. To calibrate WSA, we observationally constrain four constants in the WSA semiempirical formula based on PSP observations. We show how the updated (after the calibration) WSA boundary conditions at 0.1 au are compared to PSP observations at similar distances, and we further propagate these conditions in the heliosphere according to EUHFORIA’s magnetohydrodynamic (MHD) approach. We assess the predictions at Earth based on the dynamic time-warping technique. Our findings suggest that, for the period of interest, the WSA configurations that resembled optimally the PSP observations close to the Sun were different from the ones needed to provide better predictions at Earth. One reason for this discrepancy can be attributed to the scarcity of fast solar wind velocities recorded by PSP. The calibration of the model was performed based on unexpectedly slow velocities that did not allow us to achieve generally and globally improved solar wind predictions compared to older studies. Other reasons can be attributed to missing physical processes from the heliospheric part of EUHFORIA but also the fact that the currently employed WSA relationship, as coupled to the heliospheric MHD domain, may need a global reformulation beyond that of just updating the four constant factors that were taken into account in this study.

Theoretical predictions of nuclear binding energy for the observed nuclei: the influence of coefficients and terms in a semi-empirical mass formula

The aim of this study is to calculate the nuclear binding energy for the 2457 nuclei which experimentally observed, as tabulated in the atomic mass evaluation AME2020, by using the semi-empirical mass formula based on the renowned liquid drop model (LDM). The Bethe-Weizsäcker (BW) mass formula-four terms (BWMF-4T) is extended to incorporate an additional six terms, resulting in a formula of ten terms. Our findings demonstrate commendable accuracy and reliability, as substantiated by the acceptable level of uncertainty observed when compared them to experimental data and existing models. The influence of coefficients and terms in the semi-empirical mass formula has been determined. All possible combinations of the terms are fitted in turn to the measured nuclear masses, and the outcomes are analyzed in order to reveal correlations and mutual influences between the various terms in all observed mass regions of the periodic table. The fitted surface energy and symmetry coefficients in the semi-empirical mass formula-ten terms (SEMF-10T) are remaining 26.4 and 33.3 MeV respectively. In contrast, coefficients fitted in the classic BW formula with and without one or two additional terms are around 17 and 23 MeV, respectively. The interplay between different terms in this mass formula is found to be significant and interesting.

Development of a Meshless Kernel-Based Scheme for Particle-Field Brownian Dynamics Simulations.

We develop a meshless discretization scheme for particle-field Brownian dynamics simulations. The density is assigned on the particle level using a weighting kernel with finite support. The system's free energy density is derived from an equation of state (EoS) and includes a square gradient term. The numerical stability of the scheme is evaluated in terms of reproducing the thermodynamics (equilibrium density and compressibility) and dynamics (diffusion coefficient) of homogeneous samples. Using a reduced description to simplify our analysis, we find that numerical stability depends strictly on reduced reference compressibility, kernel range, time step in relation to the friction factor, and reduced external pressure, the latter being relevant under isobaric conditions. Appropriate parametrization yields precise thermodynamics, further improved through a simple renormalization protocol. The dynamics can be restored exactly through a trivial manipulation of the time step and friction coefficient. A semiempirical formula for the upper bound on the time step is derived, which takes into account variations in compressibility, friction factor, and kernel range. We test the scheme on realistic mesoscopic models of fluids, involving both simple (Helfand) and more sophisticated (Sanchez-Lacombe) equations of state.

A physics-informed neural network approach for predicting fatigue life of SLM 316L stainless steel based on defect features

Defects in additively manufactured materials severely limit the performance of parts in practical applications, often exposing them to the risk of fatigue failure. In order to improve the reliability and performance of additively manufactured parts, it becomes crucial to accurately predict the fatigue life of the material. Although traditional semi-empirical formulas can assess the effect of defects on the fatigue performance of parts, they still lack detailed research and consideration of defect morphology features. Therefore, this study proposes a method based on Physics-Informed Neural Networks (PINN). This method improves the predictive capability of the model and enhances its interpretability by extracting the sensitive features of critical defects and embedding known physical knowledge or fracture mechanics methods as loss functions into the training process of the neural network. Additionally, the method effectively captures the complex relationship between defect features and fatigue life, providing a deeper understanding of the model prediction results. The results show that the PINN model considering feature-related knowledge has higher prediction accuracy and reliability, and all predicted fatigue life are narrowed within 2-factor bands, enabling more accurate prediction of fatigue life for SLM 316L stainless steel under different processing conditions.

РАЗРАБОТКА ФИЗИКО-МАТЕМАТИЧЕСКОЙ МОДЕЛИ РАЗРУШЕНИЯ ПЛОТИН СМЕШАННОГО ТИПА

When the body of dams of various types is destroyed, the problems of interaction of water flows with soil from local materials and with the concrete base of the dam, as well as the development of filtration processes in the body of the dam, become relevant. This model allows us to describe both the mechanism of failure of mixed-type dams and the erosion of soil in the coastal zone, for example, formed as a result of a breakthrough wave, which leads to catastrophic consequences. To obtain practical results, there is a need to simplify the processes being studied. The main problem in problems of soil erosion by turbulent water flow is an adequate description of sediment transport. Typically, for these purposes, semi-empirical formulas are used, obtained for various conditions (extremely rarely specified) and giving very different results. In this work, to describe the processes of soil erosion, the theory of the bottom layer is used, which makes it possible to derive a formula for sediment consumption theoretically. The proposed model combines approaches developed in well-known models of continuum theory and hydraulics.

A Review of the Hydrodynamic Damping Characteristics of Blade-like Structures: Focus on the Quantitative Identification Methods and Key Influencing Parameters

Abstractcean energy has progressively gained considerable interest due to its sufficient potential to meet the world’s energy demand, and the blade is the core component in electricity generation from the ocean current. However, the widened hydraulic excitation frequency may satisfy the blade resonance due to the time variation in the velocity and angle of attack of the ocean current, even resulting in blade fatigue and destructively interfering with grid stability. A key parameter that determines the resonance amplitude of the blade is the hydrodynamic damping ratio (HDR). However, HDR is difficult to obtain due to the complex fluid–structure interaction (FSI). Therefore, a literature review was conducted on the hydrodynamic damping characteristics of blade-like structures. The experimental and simulation methods used to identify and obtain the HDR quantitatively were described, placing emphasis on the experimental processes and simulation setups. Moreover, the accuracy and efficiency of different simulation methods were compared, and the modal work approach was recommended. The effects of key typical parameters, including flow velocity, angle of attack, gap, rotational speed, and cavitation, on the HDR were then summarized, and the suggestions on operating conditions were presented from the perspective of increasing the HDR. Subsequently, considering multiple flow parameters, several theoretical derivations and semi-empirical prediction formulas for HDR were introduced, and the accuracy and application were discussed. Based on the shortcomings of the existing research, the direction of future research was finally determined. The current work offers a clear understanding of the HDR of blade-like structures, which could improve the evaluation accuracy of flow-induced vibration in the design stage.