Semi-empirical Formula Research Articles

New Approach to Calculate Nuclear Binding Energies of Nickel Isotopes 57-78Ni28 by Using Shell Model

Depending on the basic assumptions of the Shell Model and by using suitable potentials, we found a new formula to calculate nuclear binding energies of nickel isotopes 57-78Ni28. This formula is related only to the mass number of these isotopes and the number of valence nucleons outside the closed core 56Ni28. When calculating the standard deviation of the experimental data from the theory, we found that our value is better than the value calculated by the Semi-Empirical Mass Formula. It is also better than those calculated by the Integrated Model and calculated by the Modified Integrated Model. This indicates that our inferred formula is better than the most important formulas, which were previously used to calculate the nuclear binding energies for our studied nuclei.

Revision of the semi-empirical mass formula coefficients by using the ame2020 database

This work aims to revise the coefficients of the Bethe-Weizsäcker’s Semi-empirical mass formula by using the latest version release of the Atomic Mass Evaluation Database (AME2020). The updated values of five energy term coefficients are determined based on the binding energy of a total of 2548 nuclei from AME2020 database. Least-squares fitting is used to obtain a new set of mass formula coefficients. The results obtained are in good agreement with the experimental AME2020 data in a wide range of the nuclei binding energy. The relative error, with respect to the experimental data does not exceed 1%, which is less than the oscillations obtained in the other works using earlier database version AME2016 due to the more accurate measurements and the larger data sample. The semi-empirical mass formula provides a good approximation of the atomic masses and thereby, with the refined coefficient values given here, other effects in the nuclear fission engineering can be calculated with higher accuracy.

Modeling in Nuclear Physics of Visual Approach to the Semi-empirical Mass Formula SEMF

An empirical framework that accurately describes radioactive binding energies is the Somewhat Empirical Mass Equation (SEMF). They showcase many implementations and uses of the idea that rely on graphics and printed objects. A key new addition is a contrast with real experiments, as well as a visualization of the energy environment as supplied by the SEMF. The shortcomings of the empirical theory are shown by our visualization of this differential energy scenery, which also highlights the significance of what is known as magic numbers—an explanation provided by the outermost approach, which was developed much more recently than the water drop theory. This provides a great chance to talk about the advantages and limitations of simulations everywhere within the framework of science teaching.

Skyrmion crystals stabilized by ω-mesons

We investigate the ground state crystalline structure of nuclear matter in the ω-meson variant of the Skyrme model. After minimizing energy with respect to variations of both the Skyrme field and the period lattice, we find four distinct periodic solutions which are similar to those found in the standard Skyrme model. We use these crystals to calculate coefficients in the Bethe-Weizsäcker semi-empirical mass formula and the compression modulus of infinite nuclear matter, and find a significant improvement as compared with other variants of the Skyrme model.

Lap-slip model of rebar-to-concrete in RC/ECC/UHPC based on GA-BP neural network

Rebar lap splicing is a widely used method of reinforcement connection in precast concrete structures, and the lap-slip model serves as an important prerequisite for conducting detailed mechanical calculations of reinforced concrete lap splice members. Most traditional bond-slip mechanical models are semi-empirical and semi-theoretical formulas derived from experimental data; they do not consider the effect of reinforcement lap spacing, which prevents them from accurately reflecting the force transfer characteristics of lap reinforcement in concrete. In this paper, a Back Propagation (BP) neural network based on a Genetic Algorithm (GA) is used to establish a lap-slip model of reinforced concrete considering rebar spacing, which improves on the current bond-slip mechanical model. Several sets of rebar lap tests based on RC/ECC/UHPC were designed, and full-sample parameter sensitivity analyses were carried out using the lap length, the thickness of the concrete cover, the rebar spacing and the stirrup ratio as test parameters. The results showed that rebar lap spacing was an important influencing factor in the proposed lap-slip model, with a sensitivity coefficient reaching 0.471. The lap-slip model, based on the GA-BP neural network, was developed and compared with existing models; the predictive ability of the model was verified by the ten-fold crossover method. The generalizability of the GA-BP model was verified by randomly selecting non-training test data as well as lap test data of rebar in different types of concrete. The results indicated that the model exhibits high predictive and generalization abilities, with most correlation coefficients exceeding 0.95. The proposed model was compared with a mechanical model established using the traditional fitting formula method, and the results showed that the prediction accuracy of the lap-slip model established based on the GA-BP neural network is slightly lower than that of the mechanical model obtained using the fitting formula method, but it still offers high prediction accuracy, and the prediction results are more objective and realistic, which is of guiding significance for practical applications and related research.

Semi-empirical cross-section formulas for electron-impact ionization and rate coefficient calculations

We propose a semi-empirical formula for the cross section of ionization by electron impact. The formula involves adjustable parameters which are determined by comparison with measured or numerically calculated cross sections. In the latter case, the ions are perturbed by their environment which is a high-density plasma. As a consequence, the cross section is significantly modified. We investigate Be-like carbon, nitrogen and oxygen as well as aluminum ions. We also show that the formula is well-suited for interpolation and extrapolation. Knowing the cross section, we calculate the rate coefficient within the Boltzmann and Fermi–Dirac statistics. In the first case, the rate can be calculated analytically. In the second one, it can be expressed in terms of special functions, but the numerical evaluation is more convenient while providing accurate results. Our results are compared to experiment and to other calculations.

Experimental study on the flow electrification of liquid nitrogen in turbulent flow

Flow electrification occurs in all fluid flow scenarios involving solid–liquid interfaces. Due to electrostatic safety considerations, extensive research, both experimental and theoretical, has been conducted in the petroleum transportation field. However, research on flow electrification related to cryogenic fluids is relatively scarce, with even fewer experimental studies conducted. With the increasing use of cryogenic fluids such as liquid hydrogen and liquefied natural gas in aerospace and energy fields, there is an urgent need to expand the experimental database on cryogenic fluid flow electrification. In this context, a study focusing on cryogenic flow electrification using liquid nitrogen (LN2) as the working fluid was initiated, accompanied by the establishment of a flow electrification experimental platform capable of capturing ultra-low electrical signals at cryogenic conditions. Three measurement methods were designed and implemented, including charge, potential, and current measurements. By comparing their performance, the streaming charge method was identified as the optimal choice due to the stability and linearity of the raw signal. Subsequently, extensive testing was conducted to analyze the effects of various parameters, including flow velocity, pipe diameter, pipe material, and pipe roughness, on flow electrification intensity. The conclusions drawn include: within the experimental measurement range, the current induced by flow turbulence is on the order of 10−12 A for LN2. Moreover, increasing pipe diameter and roughness exacerbate the charge transported. Among the four materials tested, PTFE exhibits the highest intensity of flow electrification, followed by aluminum and stainless steel, with copper showing the weakest effect. Finally, based on the experimental data obtained, a modified semi-empirical correlation formula for the streaming current was proposed, which can reflect the specific effects of flow velocity, pipe diameter, material, and pipe roughness. Our measurement research has significant implications for the study of flow electrification in LN2 and its applications in aerospace and energy security fields.

Evaluating the influence of unpaired nucleon on alpha clusterization in heavy Nuclei with N at 126

The determination of preformation factor was successively done for 343 nuclei: 212Po, 105 even-even, 85 odd-even, 78 even-odd and 75 odd-odd nuclei using the representation of clusterization states (RCS) and cluster-formation model (CFM) (Saleh Ahmed, 2017). As CFM well described the alpha clustering of the ground states of the nuclei, it was considered as bases of describing the effect of the last unpaired nucleon. The typical nucleus 212Po and the nuclei 213Po, 213At and 214At, or Po isoalpha group, which have the same alpha cluster were chosen to evaluate the hindrance of alpha clustering by their last unpaired nucleons. The hindrance was expressed in an initiated factor, named “alpha clustering hindrance factor”. The results agreed with others that have preformation factor using different methods and used to reproduce more accurate alpha decay half lives using Viola-Seaborg semiempirical formula for odd-even Po isotopes The alpha-formation hindrance factor showed an interesting behaviour that plays an important role in the provision of more information about the nuclear structure.

Tetracycline degradation by dual-frequency ultrasound combined with peroxymonosulfate

Tetracycline has received a great deal of interest for the harmful effects of substance abuse on ecosystems and humanity. The effects of different processes on the degradation of tetracycline were compared, with dual-frequency ultrasound (DFUS) in combination with peroxymonosulfate (PMS) being the most effective for the tetracycline degradation. Free radical scavenging experiments showed that O2∙-,SO4∙- and •OH were the main reactive radicals in the degradation of tetracycline. According to the major intermediates of tetracycline degradation identified, three possible degradation pathways were proposed, which are of significance for translational studies of tetracycline degradation. Notably, these intermediates were found to be significantly less toxicity. The number of active bubbles in the degradation vessel was calculated using a semi-empirical formula, and a higher value of 1.44 × 108 L-1s−1 of bubbles was obtained when using dual-frequency ultrasound at 20 kHz (210 W/L) and 80 kHz (85.4 W/L). Therefore, compared to 20 kHz, although the yield of strong oxidizing substances from individual active bubbles decreased slightly, a significant increment of the number of active bubbles still resulted in a higher synergistic effect, and the combination of DFUS and PMS should be effective in promoting the generation of reactive free radicals and mass transfer processes within the degradation vessel, which provides a method for efficient removal of tetracycline from wastewater.

Excess properties and intermolecular interactions of 2-methoxyethanol + ethylenediamine binary system: Density, viscosity, spectral analyses, computational chemistry, and CO2 absorption property

To examine the fundamental physicochemical properties as well as intermolecular interactions for the 2-methoxyethanol (EGME) (1) + ethylenediamine (EDA) (2) binary system, this work systemically measured the density (ρ) and viscosity (η) values of the binary system with various mole ratios at P = 100.5 kPa and T = (298.15–318.15) K with the growth gap of 5 K. The as-measured values of the pure substances were compared with literature data. Multiple semi-empirical formulas were used to fit ρ and η values, and the absolute average deviations (AAD%) were calculated. After that, the excess molar volume (VmE), partial molar volume (V¯), apparent molar volume (Vφ), viscosity deviation (Δη), excess activation of Gibbs free energy (ΔG∗E), and several thermodynamic properties of the binary system were systemically analyzed. According to analysis results, it has been proven that the interaction exists between EGME and EDA molecules. And then, excess properties were fitted to the Redlich-Kister equation using multi-parametric nonlinear regression analyses, and standard deviations (σ) were calculated. In addition, based on various characterization methods including Raman, ultraviolet (UV), and nuclear magnetic resonance hydrogen (1H NMR) spectral analyses and density functional theory (DFT) calculation results, it is demonstrated that there is intermolecular hydrogen bonds in EGME (1) + EDA (2) binary system as the form of –OH⋯NH2–, which was consistent with the existence forms of intermolecular hydrogen bonds in different alcohol-amine systems from references. Finally, CO2 absorption capacity by pure EDA, pure EGME, and the EGME (1) + EDA (2) binary system were severally determined.

Predictions for the Alpha Decay of Z = 127–138 Super Heavy Nuclei Using the CYE Model

In recent years, the synthesis and identification of Superheavy elements have been of a great interest in the area of both experimental and theoretical nuclear physics. Using the CYE model, the alpha decay, cluster decay, and spontaneous fission in the heavy and superheavy nuclei have been studied. In the current work, we will investigate the α decay and obtain cluster decay half lifetimes in the interval Z = 127–138 and the spontaneous fission half lifetimes using the two-sphere approximation and will compare the results with the other theoretical values and the semiempirical formula by Xu et al. We believe that the predicted decay half-lifetimes are valuable for future tests, because they are in a good agreement with other theoretical formalisms.

Tailoring the electrical and magneto-electric transport properties of ZnO films via Ti ion implantation

A significant development toward semiconductor-based electronic devices is based on the electric and magneto-electric control of the transport properties of the charge carriers. This study unprecedentedly investigates the Ti implantation and thereafter the effect of structural defects on the electrical and magneto-electric transport properties of Ti-implanted RF-sputtered ZnO thin films. Theoretical stopping and range of ions in matter simulations along with the experimental structural and elemental studies reveal that Ti ion implantation generates a significant amount of oxygen vacancy (VO) defects apart from Ti-related impurities in post-implantation annealed films. The film implanted with 8 × 1015 ions/cm2 (TZO815) exhibits the lowest resistivity (4.68 × 10−3 Ω cm) and the highest carrier concentration (6.61 × 1020 cm−3) values. Resistivity measurements over a temperature range of 5-300K indicate semiconducting behavior for all the films implanted up to fluences of 5 × 1015 ions/cm2 identified with a grain boundary dominated thermally activated band, nearest neighbor hopping, and Mott and Efros–Shklovskii (ES) variable range hopping conduction mechanisms at various temperature intervals. Notably, the gradual decrease in both Mott and ES hopping ranges following Ti implantation indicates the formation of more localized states. Interestingly, the TZO815 film exhibits metal-semiconductor transition around 220 K, suggesting the formation of a degenerate band within the ZnO conduction band upon Ti implantation. Remarkably, the magnetoresistance results align with a semiempirical formula proposed by Khosla and Fischer, indicating that a negative magneto resistance in the TZO thin films is attributed to the spin-dependent scattering of conduction electrons by the localized magnetic moments induced mainly by the implantation induced VO defects.

Wave-gravity-induced sediment transport on steep shoreface

ABSTRACT This research is dedicated to examining downslope sediment transport on steep shorefaces. We present a model that incorporates nonlinear surface wave profiles, sediment movement thresholds, and slope effects, utilizing a set of semi-empirical formulas. The model quantitatively assesses the disparity between wave-augmented upslope transport and gravity-augmented downslope transport, and computes sediment transport rates using a single calibration coefficient. Validation of the model is carried out in the Fuji coast of Japan, where offshore wave conditions and seabed topography with a uniform grain size distribution serve as inputs. The computational outcomes reveal that sediment transport primarily occurs under high wave conditions, and downslope transport dominates on steep slopes. The calibration coefficient is determined through a comparison with observed data, demonstrating a strong agreement in the average annual sediment loss in the target area. Moreover, the model offers insights into the possible mechanism behind the existence of a transition area between the upper and lower shoreface, marked by an abrupt change in seabed slope.

Systematics of fusion of light nuclei

We have constructed the empirical formula for fusion barrier height (VB), fusion barrier position (RB), and inverted parabola (ħω) of light nuclei with atomic number in the range 2≤ZC≤10. This formula is obtained by studying the fusion barrier characteristics of 333 projectile target combinations. The values produced by the present formula are also compared with experiments. The present semi-empirical formula produces fusion barrier characteristics of light nuclei with the simple inputs of mass number (A) and atomic number (Z) of projectile targets. This semi-empirical formula can be utilized to calculate and interpret fusion barrier characteristics in light nuclear systems.

Расчет времени охлаждения надземного водовода с теплоизоляцией в условиях отрицательных температур

Objective: transport infrastructure facilities include a variety of water supply systems. In the event of an emergency, after stopping the movement of water in the pipeline, it is cooled first, and then there is a risk of freezing and destruction of water pipelines. This work is devoted to the calculation of the cooling time of water in the above-ground water conduit with thermal insulation from the specified temperature value in the initial state to the freezing temperature. Methods: when building a mathematical model of the water cooling process, an approach is used based on averaging the equations of hydrodynamics by the volume of water in the pipeline and averaging the equations of thermal conductivity in the wall of the pipeline and in the layer of the heat insulator by the polar angle. To obtain a quasi-stationary form of equations, a comparative analysis of the rates of thermal processes in different layers of the water conduit is used. Results: a new mathematical model for cooling the water pipeline is formulated — a model of average temperatures. The applicability of the quasi-stationary form of the equations of the model is justified and its analytical solution is found. Explicit formulas are obtained for cooling time of water conduit as a function of its parameters. Cooling time was calculated in a wide range of parameters. The results of model calculations are compared with calculations according to traditional semi-empirical formulas. Practical importance: the formulas obtained in the work can be used to estimate the cooling time of water in an above-ground water pipeline with heat insulation to the freezing temperature in the case when the ambient temperature drops to negative values.

A combined computational/experimental study of anode-concerned voltage drop in aqueous primary Mg-air batteries

The voltage drop appearing at Mg anode-electrolyte interface is a critical issue for the battery power and energy density of aqueous primary Mg-air batteries. The respective voltage loss is typically assigned to the deposits layer forming on the anode surface during discharge. In this work, we experimentally and computationally investigate the critical factors affecting the voltage drop at Mg anode towards a deeper understanding of the contribution of deposit and its growth. A two-dimensional (2D) mathematical model is proposed to compute the voltage drop of Mg-0.15Ca wt.% alloy (Mg-0.15Ca) by means of a semi-empirical formulas and experiments-based modification model, considering the effect of discharge current density, the negative difference effect (NDE) and surface deposits layer itself. This model is utilized to simulate the discharge potential of the anode at predefined experimental current densities. The computed voltage drop (half-cell voltage) is in good agreement with the experimental value. The applicability of the mathematical model is successfully validated on the second material (namely high-purity Mg).

A semi-empirical formula of beach slope on flat lower platforms

The beach slope β is a key component characterizing the coastal response to wave forcing. Here we investigate the rapid adaptation of the upper beach slope to a given wave forcing, for the case of a lower flat platform. Such types of morphology are found on coral and rocky reef beaches and low tide terrace environments. The influence of the lower platform on this rapid equilibrium beach state is shown to be significant depending on the breaking wave regime. In particular, the width of the platform and its water level can affect the wave dissipation along the inner surf and thus the wave structure entering the swash. This paper provides a classification of the beach slope equilibrium values as a function of the Dean number on a short time scale (individual wave action), based on both offshore and swash wave conditions. A decreasing trend of the beach slope with increasing offshore Dean number (Ω0) is found for Ω0≲2.7. For Ω0≳2.7 it is observed that the beach slope gradient is strongly controlled by the surf zone dissipation and it becomes necessary to define the swash Dean number (Ωsw) to classify the slope. Finally, a semi-empirical formula for the beach slope evolution in the case of a low tide platform is introduced and tested on two natural low-tide terrace beaches.

Ultimate bearing capacity of geosynthetic reinforced soil abutment centrifuge model tests

Five centrifuge models of geosynthetic reinforced soil (GRS) abutments with segmental block facing were loaded in the acceleration field under plane strain condition. Influencing factors including reinforcement tensile strength, setback and bearing area width were considered and analysed. Results show that the abutment with stronger reinforcement remained stable under the maximum loading capacity. However, abutments with weaker reinforcement showed excessive vertical strain, local deformation or even collapse. The ultimate bearing capacity increased with the lengthening of setback but decreased due to a larger bearing area. The rupture of reinforcements was observed and considered as the cause of the failures. Compared with the measured ultimate bearing capacity, the values calculated by the semi-empirical formula of design guidelines were significantly conservative. The failure surface of failed abutment developed from the rear edge of the bearing area to the middle height of the abutment at an angle of nearly 45° + φ/2. The setback and the bearing area width affected the form and position of the failure surface. The difference between the potential failure surface predicted by available methods and the measured failure surfaces has been discussed, and suggestions for the design and ultimate bearing capacity prediction of GRS abutments with segmental block facing are provided.

Generalized skyrmion crystals with applications to neutron stars

In this article we study properties of isospin asymmetric nuclear matter in the generalized L0246-Skyrme model. This is achieved by canonically quantizing the isospin collective degrees of freedom of the recently found skyrmion multiwall crystal. We obtain, for the first time, an equation of state from the Skyrme model which interpolates between infinite isospin asymmetric nuclear matter and finite isospin symmetric atomic nuclei. This enables us to describe neutron stars with crusts within the Skyrme framework. Furthermore, we observe that the symmetry energy tends to a constant value at zero density, which can be identified with the asymmetry coefficient in the semiempirical mass formula for atomic nuclei. The symmetry energy also reveals a cusp in its structure below the nuclear saturation point n0 at n*∼3n0/4. This cusp density point n* can be interpreted as the nuclear density whereby the infinite crystalline multiwall configuration undergoes a phase transition to a finite isolated multiwall configuration. Both of these observations are observed to be generic features of skyrmion crystals that tend asymptotically to somewhat isolated skyrmion configurations in the zero density limit. We find that the resulting neutron stars from our study agree quite well with recent NICER/LIGO observational data. Published by the American Physical Society 2024

Solar photovoltaic panel soiling accumulation and removal methods: A review

AbstractPhotovoltaic (PV) power generation has become a key area for investment worldwide. Solar PV panels are the core components of PV power generation systems, and the accumulation of soiling on their surfaces has numerous adverse effects on power generation. This paper provides an overview of the soiling accumulation on PV panels and the existing soiling removal methods. Firstly, the sources of soiling particles and the mechanism of soiling fall are analyzed, based on which the accumulation of soiling on the surface of the PV panels is described in detail, and then the effect of the surface soiling on the PV panels is investigated in the order of optics‐thermology‐electrical, with the necessary semiempirical formulas provided to assist in more in‐depth analyses. In addition, the principles, status quo, effects, costs, advantages, and disadvantages of existing soiling removal methods are specifically described, thus providing a reference for the selection of soiling removal methods in different regions. The paper also analyses the soiling accumulation and removal challenges of PV panels in different regions of China. The results of the study are important for the improvement of the effectiveness of soiling removal and the rational optimization of the soiling removal scheme.