Parameters Of Equation Research Articles

Vapor Pressure and Evaporation Studies of Saline Solutions on Natural and Synthetic Fabrics for Industrial Water Treatment.

In the present paper, we have conducted a comprehensive analysis of vapor pressures of both saturated and unsaturated solutions, alongside a study of evaporation using synthetic and natural fabrics for industrial applications in brackish water treatment under zero liquid discharge (ZLD) philosophy. By determining the vapor pressures of saturated solutions, we obtained results consistent with those of other researchers, extending the range of tested temperatures from 1 to 50 °C and successfully fitting the parameters of an Antoine-type equation. Similarly, positive results were achieved for unsaturated solutions, where various parameters of different equations accounting for the salt concentration were estimated, simplifying the fitting procedure. Natural evaporation tests from water surfaces using saturated solutions revealed that salts with higher associated vapor pressures exhibit higher evaporation rates. On the other hand, hydrated salts retain water in their structure and are significantly affected by ambient humidity. Evaporation studies on natural and synthetic fabrics with saturated NaCl and CuSO4·5H2O solutions showed distinct behaviors. NaCl increased both the evaporation rate and salt deposition with each cycle. In contrast, CuSO4·5H2O reduced the absorption capacity by blocking the fabric's structure, decreasing the evaporation efficiency over successive cycles.

Cyclohexane dehydrogenation: Critical evaluation of parameter estimation procedures for kinetic modeling

In the present paper a comparison between different parameter estimation procedures commonly used for the kinetic modeling of chemical reaction is performed, based on experimental measurements of the cyclohexane dehydrogenation to benzene. The obtained results show that, when the Arrhenius equation parameters are estimated from estimates of the rate constant taken at different temperatures, larger parameter uncertainties and correlations are obtained, particularly when the variances of the experimental measurements are not considered during the estimation process. It is also observed that an apparent kinetic compensation effect occurs when the experimental data are separated according to the inlet partial pressure and catalyst mass in the reactor, mainly due to the existing and unavoidable experimental uncertainties and parameter correlations. Additionally, it is shown that larger uncertainties and correlations are obtained when the parameter estimates are computed through the differential method, which can also lead to poorer model predictions of the experimental data. Finally, it is shown that the simultaneous one-step estimation of all model parameters through the integral method and considering the available experimental uncertainties can provide the most accurate parameter estimates, making use of mathematical expressions that describe how variances of the experimental measurements depend on the experimental conditions.

A Simple Equation of State Parameter and its Complex Consequences in Cosmology

A Simple Equation of State Parameter and its Complex Consequences in Cosmology

Exponential quintessence: curved, steep and stringy?

We explore the possibility that our universe’s current accelerated expansion is explained by a quintessence model with an exponential scalar potential, V = V0e−λ ϕ, keeping an eye towards λ ≥ 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{2} $$\\end{document} and an open universe, favorable to a string theory realisation and with no cosmological horizon. We work out the full cosmology of the model, including matter, radiation, and optionally negative spatial curvature, for all λ > 0, performing an extensive analysis of the dynamical system and its phase space. The minimal physical requirements of a past epoch of radiation domination and an accelerated expansion today lead to an upper bound λ ≲ 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{3} $$\\end{document}, which is driven slightly up in the presence of observationally allowed spatial curvature. Cosmological solutions start universally in a kination epoch, go through radiation and matter dominated phases and enter an epoch of acceleration, which is only transient for λ > 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{2} $$\\end{document}. Field distances traversed between BBN and today are sub-Planckian. We discuss possible string theory origins and phenomenological challenges, such as time variation of fundamental constants. We provide theoretical predictions for the model parameters to be fitted to data, most notably the varying dark energy equation of state parameter, in light of recent results from DES-Y5 and DESI.

FLRW cosmology in metric-affine F(R,Q) gravity* *Supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (AP14870191)

We investigated some Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models in the context of metric-affine gravity, as proposed in [arXiv: 1205.5266v6]. Here, R and Q are the curvature and nonmetricity scalars using non-special connections, respectively. We obtained the modified field equations using a flat FLRW metric. We then found a connection between the Hubble constant , density parameter , and other model parameters in two different situations involving scalars u and w. Next, we used new observational datasets, such as the cosmic chronometer (CC) Hubble and Pantheon SNe Ia datasets, to determine the optimal model parameter values through a Markov chain Monte Carlo (MCMC) analysis. Using these best-fit values of the model parameters, we discussed the results and behavior of the derived models. Further, we discussed the Akaike information criterion (AIC) and Bayesian information criterion (BIC) for the derived models in the context of the Lambda cold dark matter (ΛCDM). We found that the geometrical sector dark equation of state parameter behaves just like a dark energy candidate. We also found that both models are transit phase models. Model-I approaches the ΛCDM model in the late-time universe, whereas Model-II approaches quintessence scenarios.

Innovative design and construction of a closure joint for inland-river immersed tunnels via dry-land construction methods: A case study of the Yuliangzhou tunnel in China

Closure joints constructed to fill the spaces between immersed tunnel elements or between the tunnel elements and adjacent cut-and-cover tunnels are crucial for the longitudinal stability of immersed tunnels and affect the overall cost and duration of tunnel construction. To avoid the obstruction of navigation and reduce the difficulty of constructing closure joints, dry-land construction methods have been widely applied to construct closure joints for inland-river immersed tunnels, in particular using procedures involving axial dry docks. However, the traditional dry-land construction method has many inherent drawbacks. For example, the construction of underwater large-scale reinforced concrete antiretreat structures involves many underwater works, complicated construction processes, long operation time spans and high costs. Based on the Yuliangzhou immersed tunnel in China, a new dry-land construction method for closure joints of inland-river immersed tunnels based on tunnel–soil interface friction was developed to address the abovementioned problems. Considering the adverse influences of back-silting sediment on tunnel–soil interface friction, large-scale laboratory and onsite shear tests were carried out to derive the interface friction coefficients between the tunnel element base slabs and prelaid pebble foundation beds. A composite concrete steel sandwich (CCSS) water-retaining system was designed and assembled to separate the water in the dry dock from the river course. A simplified analysis method based on numerical simulations for the determination of the equivalent horizontal thrust P applied to element ES caused by the dewatering of the axial dry dock was proposed. Based on horizontal antisliding stability analyses of the tunnel elements during the axial dry dock dewatering stage, equations for the key design parameters of the new dry-land construction method were established. Through examination of the static equilibrium of the tunnel elements in the tunnel longitudinal direction, temporary longitudinal displacement constraint (LDC) structures at the immersion joints were designed. Furthermore, the following key construction techniques for the new dry-land construction method were systematically designed: installation of a CCSS water-retaining system at the entrance of the axial dry dock, water sealing at contact gaps, installation of finish-rolled screw-thread (FRST) steel bars as the LDC structures at the immersion joints, and construction of rigid connections between tunnel element ES and the cut-and-cover tunnel. Finally, onsite observation of the deformation states of Gina gaskets and monitoring of the tensile forces of FRST steel bars at the immersion joints verified the successful implementation of the new dry-land construction method, supporting the use of these techniques in closure joint design and construction for inland-river immersed tunnels.

Comprehensive study of bouncing cosmological models in f(Q, T) theory

The main objective of this article is to investigate the viability of bouncing cosmological scenarios using different forms of scale factors with perfect matter configuration in the framework of extended symmetric teleparallel theory. This modified proposal is defined by the function f(Q, T), where Q characterizes non-metricity and T denotes the trace of energy-momentum tensor. We investigate the modified field equations of this theory using different parametric values of the Hubble parameter and non-metricity to derive viable solutions. These solutions are relevant in various cosmological bounce models such as symmetric-bounce, super-bounce, oscillatory-bounce, matter-bounce and exponential-bounce models. Furthermore, we examine the behavior of energy density and pressure to analyze the characteristics of dark energy. A comprehensive analysis is also conducted to explore the behavior of the equation of state parameter and deceleration parameter to examine the evolutionary eras of the cosmos. Our findings show that the f(Q, T) gravity describes the cosmic expansion in the vicinity of the bouncing point during the early and late times of cosmic evolution.

Comparison of Several Methods for Analysis Slope Length Index Factor at A Watershed Scale

Slope length and steepness factor index (LS) is one of the parameters for the Universal Soil Loss Equation (USLE) to estimate soil erosion. Currently, several methods for LS analysis, i.e. Wischmeier-Smith, Moore-Nieber, and Desmet – Govers. This study aims to compare the Wischmeier-Smith method, Moore–Nieber method, and Desmet–Govers method to analyze LS in the watershed in Manokwari – West Papua. This research consists of 4 main stages, i.e. data inventory, watershed boundary delineation, LS analysis, and LS comparison. The research showed that the Wischmeier-Smith method gave a higher LS value than the Moore – Nieber method and the Desmet – Govers method. Meanwhile, the Desmet – Gover method gives a lower average LS value than the Wischmeier-Smith method and the Moore – Nieber method. Based on the T-test, the LS produced by the Wischmeier-Smith, Moore-Nieber, and Desmet–Govers methods has significant differences in analyzing LS in the watershed in Manokwari – West Papua. Keywords: Desmet – Govers, Moore – Nieber, Universal Soil Loss Equation, Watershed, Wischmeier-Smith

Forward osmosis for concentrating lithium-enriched brine: From membrane performance to system design

Using concentrated salt-lake brine as the draw solution (DS), forward osmosis (FO) has been proposed as the low carbon footprint concentration technology for extracting water from lithium-enriched brine. From membrane modules to a process, there exist tremendous risks when considering total cost in time and investment for a trial. To address this issue, a bridge between the FO membrane/ module characteristics and a FO system design is highly desirable. This study for the first time developed a system design model using hollow fiber (HF) FO membrane modules for FO concentration of lithium-enriched brine. The concentration polarization along the module, the membrane structural parameters (S), crossflow velocity, and DS concentration were the main factors considered in the model. The effect of all factors on module water flux and total membrane area was systematically investigated for a typical industrial output of 10 k ton of Li2CO3. A master curve of the water flux verse feed concentration for the tailor-made HF modules was utilized as the basis. On a module scale, the structural parameter S is of first importance and indicates requirement of FO membranes with low S. The crossflow velocity has relatively small impact to the membrane area, but not negligible. On a system scale, the empirical equation of the structural parameters and crossflow velocity on the theoretical minimum system membrane area was summarized. The results show that increasing the stages can reduce the number of modules and required DS flow. Increasing DS dilution rate in system design efficiently utilizes the osmotic pressure of DS. The present model serves as a practical solution for process optimization and FO membrane selection. The methodology is valuable for other FO applications using HF FO membranes.

A four core fiber temperature and strain dual parameter sensor based on T-shaped taper

A four core fiber temperature and strain dual parameter sensor based on T-shaped taper is proposed and prepared. The sensor is composed of single-mode fiber (SMF), multi-mode fiber (MMF), and four core fiber (FCF). Among them, MMF plays a role in beam expansion, and FCF is tapered and fused with SMF to form a T-shaped taper structure, thereby preparing a sensor based on Mach Zehnder interference principle. When the external environmental temperature and strain change, due to thermal effect and elastic optical effect, the refractive index of the FCF cladding and fiber core changes differently, resulting in shift in the interference spectrum. Based on the temperature and strain sensitivity at different interference valleys, the temperature and strain dual parameter matrix equation of the sensor can be obtained. The experimental results indicate that when the temperature rises within the range of 30 ℃ to 90 ℃, the sensor spectrum shows a red shift phenomenon, and the maximum temperature sensitivity can reach 55 pm/ ℃. When the strain increases within the range of 0 με∼ 2000 με, the transmission spectrum of the sensor exhibits a blue shift phenomenon, and the maximum strain sensitivity can reach −2.6 pm/ με. Finally, based on the experimental results, the matrix equation for dual parameter sensing can be obtained. This sensor is easy to manufacture and has high sensitivity. It can measure sensing parameters normally in micro magnetic and micro electric field environments.

Cosmographic analysis of anisotropic Kaniadakis holographic dark energy model

In this paper, we investigate the anisotropic and spatially homogeneous Bianchi type-I universe with Kaniadakis holographic dark energy in Saez–Ballester [Phys. Lett. A 113, 467 (1986)] theory of gravitation. We determine Kaniadakis holographic dark energy model by assuming a correlation between the metric potentials to solve the field equations of the model. This results in a dynamical deceleration parameter which demonstrates an accelerating expansion of the universe. Our model’s equation of state parameter [Formula: see text] close to [Formula: see text] ([Formula: see text] model) at late-times and is in agreement with the most recent observations. Next, we obtained the squared sound speed ([Formula: see text]) and found that it is positive, implying stability against perturbations. The [Formula: see text] plane is constructed to investigate the evolution of the models’ EoS parameter turned out to be in a freezing zone. As should be the case in an expanding universe, the strong energy conditions of the model are violated. Statefinders [Formula: see text], and [Formula: see text] planes were also examined. Our model includes the Chaplygin gas, [Formula: see text] limit, and is inclined towards the steady-state model.

N-level complex helical structure modeling method

This paper primarily explores the modeling method of n-level complex helical structures with coal mining machine cables as the research object. The paper first elaborately introduces the modeling method of n-level helix curves based on parametric equations and coordinate transformations, and compensates for the n-level helix curves with corrected pitch, which can obtain more accurate n-level helix curves and improve the accuracy of n-level helix curves modeling. Subsequently, based on this high-precision n-level helix curves modeling method, the paper elaborates on the method of solving pitch and twisting radius of multi-layer helical structure. Calculation scripts were written based on the above methods, which can be used to batch calculate the twisting radius and pitch of each layer structure in multi-layer structures when satisfying the conditions of in-layer tangency, inter-layer tangency, and extrusion deformation, and retain the actual results through logical judgment. Then, based on the above two methods, the paper developed a modeling method for braided structures based on piecewise functions containing fifth-order polynomials, which can effectively avoid the problem of insufficiently dense arrangement of braided lines and easy interference in traditional methods. Finally, a set of modeling tools was developed using C# and Python in Grasshopper to implement the modeling algorithm. Taking the MCPT-1.9/3.3 3120 + 170 + 4 * 10 coal mining machine cable as an example. The cable was modeled using both the method proposed in this paper and the traditional method. Comparative data shows that the method proposed in this paper can reduce errors by 3.31E6 times in the second-level and above helical structures. In addition this paper compares the standard line length, measured line length, and the line length established by the proposed model, showing that the relative errors are both less than 0.1941%. This paper provides a new, systematic, high-precision, and full-process cable modeling method, in which all parameters except the process parameters are accurately solved by equations. It lays a theoretical foundation for the high-precision simulation and intelligent sensing cables, which is of great significance for improving the safety, stability, and efficient development of the coal mining industry. The research results of the paper can not only be applied to the modeling of coal mining machine cables but also can be extended to the modeling of other complex multi-layer helical structures.

Oscillometry Reference Values for Children and Adolescents

BackgroundOscillometry devices allow quantification of respiratory function at tidal breathing but device-specific reference equations are scarce: the present study aims to create sex-specific oscillometric reference values for children and adolescents using the Resmon PRO FULL device.MethodsHealthy participants (N=981) aged 6 to 17 years of the Austrian LEAD general population cohort were included. Subjects had normal weight (BMI≤99th percentile) and normal lung volumes (total lung capacity (TLC)≥lower limit of normal). Oscillometry data were collected using a single frequency mode of 8 Hz. Sex-specific prediction equations were developed for total (tot), inspiratory (insp) and expiratory (exp) resistance (R) and reactance (X) as well as for the modulus of impedance (Z) value using the LMS (lambda, mu, sigma) method. Height was used as a single covariate.ResultsReference equations for all oscillometry parameters were created for Caucasian children aged 6 to 17 years with a height span from 101 to 183 cm and a lung volume span from 1.7 L to 8.8 L TLC. R and Z values progressively decrease and X values increase with increasing height. Oscillometry parametersversuslung volume curves differ from thoseversusheight curves. Stratified for lung size, no sex differences are found for oscillometry parameters.ConclusionOur study provides reference values for oscillometry parameters in children and adolescents using strictly defined criteria for weight and lung volumes. No sex related differences in oscillometry parameters corrected for height or lung size are found.

Physically adjusted ground motion prediction equations for induced seismicity at Preston New Road, UK

Predicting ground motions due to induced seismicity is a challenging task owing to the scarcity of data and heterogeneity of the uppermost crust. Dealing with this requires a thorough understanding of the underlying physics and consideration of inter-site variability. The most common ground motion model used in practice is the parametric ground motion prediction equation (GMPE), of which hundreds exist in the literature. However, relatively few are developed with a focus on induced seismicity. Developing GMPEs that are specific to an appropriate magnitude-distance range (R<30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R < 30$$\\end{document} km; 2≤M≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \\le M \\le 6$$\\end{document}) is important for induced seismicity applications. This paper proposes a framework for the development of physically-based GMPEs to provide more accurate and reliable estimates of the potential induced-seismicity ground motion hazard, allowing for better risk assessment and management strategies. To demonstrate this approach, a new set of GMPEs for the 2018-2019 induced seismicity sequence at the Preston New Road (PNR) shale gas site near Blackpool, United Kingdom, is presented. The physically-based GMPE was developed based on a pseudo-finite-fault stochastic ground motion simulation, calibrated with parameters derived from the spectral analysis of weak-motion records from induced seismic events. An optimization-based calibration technique using the area metric (AM) was subsequently performed to calibrate optimal parameters for simulating ground motion at the PNR site. Finally, using a suite of forward simulations for events with 1≤M≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\le M \\le 6$$\\end{document} recorded at distances up to 30 km, combined with empirical data, a location-specific GMPE was derived through adjustment of an existing model.

Study on energy-saving techniques of the lithium-ion batteries cooling system using a backup battery

The power battery in an electric vehicle is an essential part, and the damage to the battery will have a substantial impact on its thermal characteristics. In order to improve the reliability of the air-cooled lithium-ion battery packs in the high temperature environments, this paper offers a more useful and general optimization strategy for the design of the thermal management system for the batteries which have a damaged battery. To ensure the optimal heat dissipation and prolong the battery string operation, the damaged batteries should be swapped out with the backup batteries. The relationship between the target and the design variables which was established using the quadratic polynomial response function is examined. The experimental cases are selected using the optimal Latin hypercube design approach. After optimizing through the multi-island genetic approach, the error between the simulation results and the prediction results is only 0.06 %. The maximum temperature and the maximum temperature difference of the ideal structure are reduced by 4.58 % and 28.05 %, respectively. Then, the backup battery is selected as the sole battery that has the highest temperature of the ideal structure, and each broken battery is replaced by the backup battery when the damaged position is determined. Finally, a parametric equation connecting the temperature and the flow rate is created, and the inlet flow rate is tuned to match the optimal heat dissipation state of the battery pack. The results of the battery thermal management system having a damaged battery in various situations have an important significance for adjusting the operating conditions of the cooling system for the batteries.

Stability analysis of charged neutron stars and Darmois junction conditions

This research article examines the impact of f(Q,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {Q}},{\\mathcal {T}})$$\\end{document} theory on the geometry of charged neutron stars filled with anisotropic matter configuration. Here, Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {Q}}$$\\end{document} represents non-metricity and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {T}}$$\\end{document} denotes the trace of energy-momentum tensor. We use a particular functional form of this modified theory to reduce the system’s complexity and derive explicit relations of the energy density and pressure components. Further, we consider viable non-singular solutions to analyze the internal structure of the charged neutron stars. The unspecified parameters in the metric coefficients are evaluated through Darmois junction conditions, which ensures consistency between interior and exterior solutions of the stellar objects. These parameters are then used to explore different physical characteristics such as the behavior of energy density, pressure components, anisotropy, energy bounds, equation of state parameter, compactness and redshift function in the interior of charged neutron stars. The stability and equilibrium states of the charged stellar objects are discussed using the Tolman–Oppenheimer–Volkoff equation and the speed of sound, respectively. Our results suggest that the charged neutron stars are viable and stable in the presence of dark source terms.

Numerical Simulation Study of Cavity Formation in Soil under Blast Load

The main applications of civil explosives in soils are soil compaction, mass excavation, and in situ pile creation. The suitability of explosives for each of these applications strongly depends upon the explosive properties and the soil properties. For those reasons, a reliable estimation or process simulation regarding cost efficiency and explosive work ability in the soil with known soil parameters is relevant. This paper presents a numerical simulation study of different types of soil (different amounts of gravel, sand, silt, and clay) under a blast load modeled using Ansys 2020 R1 Autodyn 2D hydrocode, with different types of explosives. The calculated results from the Ansys 2020 R1 Autodyn 2D and the experimental results obtained from the in situ cavity formation caused by blasting are presented. The Jones–Wilkins–Lee (JWL) equation of state parameters was calculated using EXPLO5 V7.01.01 supported by experimental data, while the soil and explosive properties were measured in laboratory and in situ.

Criterion for unhomogeneous yielding of porous materials

A criterion is developed for the unhomogeneous yielding of materials containing arbitrarily oriented ellipsoidal voids. The criterion is built upon classical estimates for pure pressure and pure shear. A data-driven approach is then followed to incorporate the effects of void shape and orientation. A large number of micromechanical unit cell results are used to calibrate the yield criterion. A key feature of the criterion is that it predicts a significant reduction of the effective shear yield strength due to mere void inclination, with the reduction increasing with the void dimension perpendicular to the shear. The coupling between tension and shear deformation results in an apparent rotation of the yield surface, which provides a sound micromechanical basis for predicting void closure in shear among other new features. Once supplemented with evolution equations of relevant internal parameters, the resulting constitutive formulation will enable ductile failure simulations heretofore impossible to carry out on a sound physical basis for general loading conditions.

Charged gravastar model in Rastall theory of gravity

Gravastars are considered as exotic compact objects, may be found at the end of gravitational collapse of massive stars, to resolve the complexities of black holes. In this paper, we analyse the role of charge on the possible formation of an isotropic spherically symmetric gravastar configuration in the framework of Rastall gravity. Gravastar contains three distinct layers viz. (i) Interior region characterised by the equation of state, p=−ρ, which defines the repulsive outward pressure in the radial direction at all points on the thin shell, (ii) Thin shell contains an ultra-relativistic stiff fluid, which is denoted by the equation of state p=ρ following Zel'dovich's criteria for a cold baryonic universe, and can withstand the repulsive pressure exerted by the interior region, and (iii) Exterior region which is the vacuum space-time represented by the Reissner-Nordström solution. Following above specifications, we construct and analyse charged gravastar model in the framework of Rastall gravity, which represents several salient features. The basic physical attributes, viz. proper length, energy, entropy and equation of state parameter of the shell are investigated. In this model, it is interesting to note that for a large radius of the hypersurface (R), the equation of state parameter of the thin shell corresponds to a dark energy equation of state with W(R)→−1. However, for small value of R, W(R)→0, defines dust shell. The stability of the model is ensured through the study of gravitational surface redshift and maximisation of shell entropy within the framework of Rastall theory of gravity.

Design and study of the shape parameters for the electrode plates of the electron gun in the four-dimensional transmission electron microscope.

The accelerating electrode of a four-dimensional transmission electron microscope electron gun is modeled. The general expression of the electric-field distribution is derived for any point on the axis in a cylindrical coordinate system, and equations for the shape parameters of the electrode plate are obtained. The accuracy of the field expression is determined for different electrode plate parameters, and the shape parameters of the electron gun electrode are further investigated. This work can provide a theoretical basis for the initial design of a transmission electron microscope electron gun and the retrofit design of a four-dimensional electron gun.