Tangential Pressure Research Articles

Modeling and analyzing stability of hybrid stars within [formula omitted] gravity

This study uses the Krori–Barua type metric to represent hybrid stars within the f(Q) theory of gravity. We postulate that the hybrid star also contains strange quark matter in addition to regular baryonic matter. To investigate the physical viability of the hybrid star model, we present the graphical behavior of the energy density, radial pressure, and tangential pressure, equation of state parameters, anisotropy, and stability analysis, respectively, by choosing the compact star EXO 1785-248 with a mass of 1.3−0.2+0.2M⊙ and radius 8.849−0.4+0.4 km with five different values of the coupling constants as a=2, a=4, a=6, a=8, and a=10. The maximum allowed masses and corresponding radii have been calculated using the M−R curve for three different coupling parameter ’a’ values which match the observational data of three distinct compact stars, namely LMC X-4, SMC X-1, and 4U 1538-52. So, the f(Q) theory of gravity can provide results that are plausible for describing the macroscopical characteristics of hybrid star candidates.

Parametric design of curved hydrocyclone using data points and its separation enhancement mechanism

Based on parametric design of curves using data points, two novel hydrocyclones were designed: Spline-Curved-Cone hydrocyclone (H2) and Expassoc-Curved-Cone hydrocyclone (H3). These designs are improvements on the traditional biconical hydrocyclone (H1). Numerical simulations and experimental validation by PIV measurement were used to investigate the effects of cone section profiles on the flow characteristics and separation efficiency. The results showed both H2 and H3 achieved higher separation efficiency than H1. Specifically, the highest efficiency of H3 increased by 24.71%, and that of H2 increased by 16.22% compared with H1. It was also found the curved design of cone section profile directly affects the tangential velocity distribution and pressure distribution of the flow field inside hydrocyclones. H3 exhibited better flow field stability and highest separation efficiency due to its optimized cone section space and flow structure. This study provides scientific basis and data support for the optimization and industrial application of the cylinder-on-cone hydrocyclones.

Analytical model of friction at low shear rates for soft materials in 3D printing.

The biological properties of silicone elastomers such as polydimethylsiloxane (PDMS) have widespread use in biomedicine for soft tissue implants, contact lenses, soft robots, and many other small medical devices, due to its exceptional biocompatibility. Additive manufacturing of soft materials still has significant challenges even with major advancements that have occurred in development of these technologies for customized medical devices and tissue engineering. The aim of this study was to develop a mathematical model of tangential stress in relation to shear stress, shear rate, 3D printing pressure and velocity, for non-Newtonian gels and fluids that are used as materials for 3D printing. This study used FENE (finitely extensible nonlinear elastic model) model, for non-Newtonian gels and fluids to define the dependences between tangential stress, velocity, and pressure, considering viscosity, shear stress and shear rates as governing factors in soft materials friction and adhesion. Experimental samples were fabricated as showcases, by SLA and FDM 3D printing technologies: elastic polymer samples with properties resembling elastic properties of PDMS and thermoplastic polyurethane (TPU) samples. Experimental 3D printing parameters were used in the developed analytical solution to analyse the relationships between governing influential factors (tangential stress, printing pressure, printing speed, shear rate and friction coefficient). Maple software was used for numerical modelling. Analytical model applied on a printed elastic polymer, at low shear rates, exhibited numerical values of tangential stress of 0.208-0.216 N m - 2 at printing velocities of 0.9 to 1.2 mm s - 1, while the coefficient of friction was as low as 0.09-0.16. These values were in accordance with experimental data in literature. Printing pressure did not significantly influence tangential stress, whereas it was slightly influenced by shear rate changes. Friction coefficient linearly increased with tangential stress. Simple analytical model of friction for elastic polymer in SLA 3D printing showed good correspondence with experimental literature data for low shear rates, thus indicating possibility to use it for prediction of printing parameters towards desired dimensional accuracy of printed objects. Further development of this analytical model should enable other shear rate regimes, as well as additional soft materials and printing parameters.

Modeling Compact Object Mergers GW190814 and GW200210 and Other Self-bound Compact Stars with Dark Matter Induced by Gravitational Decoupling and Its Significance to the Mass Gap

We present a rigorous study of compact objects within f(Q) gravity where electrical fields and dark matter are studied and provide novel mass–radius relations with models falling in the mass gap of the events GW190814 and GW200210. After formulating the basic equations and finding their relevant solutions, we impose the boundary conditions on the system under treatment. The decoupled solution for the strange stellar model with the dark matter density profile is obtained. The distribution patterns of the effective energy density and the radial as well as the tangential pressure and anisotropy in the system are intensively examined. The stability properties of the stellar configuration and the influence of dark matter are studied. The recent observations of supermassive compact star candidates such as PSR J1614–2230 and PSR J0952–0607 with observed masses greater than or equal to 2 M ⊙ have been employed in our study. Interestingly, the present study predicts the constraints on mass–radius measurements of the observed stars satisfying the equation of state based on the MIT bag model and employing the condition of mimicking, i.e., ρ θ = χ1ρPI in f(Q) gravity. Our graphical results exhibit that for a particular M–R curve with fixed values of the parameters, neutron stars having mass less than M max exist with larger radii within the context of the f(Q) formalism.

Interacting quark star with pressure anisotropy and recent astrophysical observations

This paper investigates the internal structure and equation of state (EoS) of quark stars (QS) with pressure anisotropy, incorporating recent astrophysical observations. Utilizing perturbative QCD corrections and color superconductivity, the EoS is expressed as a dimensionless function dependent on a single parameter, providing a comprehensive exploration of strong interaction effects. By rescaling the EoS and introducing dimensionless variables, the study encompasses scenarios ranging from noninteracting quark matter to extreme stiffness characterized by a parameter, λ̄. Anisotropic QS configurations are constructed using a spherically symmetric metric, with locally anisotropic matter described by a generalized EoS for tangential pressure. The Tolman–Oppenheimer–Volkoff equations governing star structure are presented in dimensionless form, and numerical solutions explore the parameter space defined by effective bag constants and λ̄. Mass–radius relations and the compactness of anisotropic QSs are analyzed under various model parameter variations, considering constraints from pulsar masses and gravitational wave phenomena. The study highlights the influence of pressure anisotropy on the maximum mass of QSs and discusses the impact of model parameters on internal properties. Additionally, the paper considers static stability, adiabatic index, and sound velocity profiles, providing a comprehensive understanding of QS behavior. Overall, this investigation contributes valuable insights into the properties of QSs and their compatibility with observational constraints, offering a detailed exploration of their EoS and internal structure.

Hydrodynamic characteristics analysis of series hydraulic cyclone separators for pond aquaculture wastewater purification

This study introduces a series of hydraulic cyclone separators designed to efficiently remove sediments and other high-density particulate matter from pond aquaculture wastewater. A three-dimensional two-phase model of these hydraulic cyclone separators was developed using the discrete phase model (DPM) and Reynolds stress turbulence model (RSM) based on numerical simulation theory. The computational fluid dynamics (CFD) method was validated by comparing it with experimental data, and an analysis of the hydrodynamic characteristics of the hydraulic cyclone separators was conducted. Furthermore, the relationships between structural parameters and separation efficiency were examined using Pearson's correlation coefficient. The findings reveal that the length of the first-stage cyclone column significantly influences the tangential velocity distribution within the second-stage cyclone, while the length of the second-stage cyclone column predominantly affects the pressure distribution of the first-stage cyclone. Increasing the column length enhances the overall particulate separation efficiency of the system. Moreover, adjustments in the split ratio of the first-stage cyclone have a notable impact on the tangential velocity and pressure distribution within the second-stage cyclone. Increasing the split ratio proves beneficial in improving the separation efficiency of particulate matter. This study provides valuable insights into the design and optimization of hydraulic cyclone separators, offering a dependable computational model for predicting and understanding their flow behavior and separation performance effectively.

50‐1: Invited Paper: Flexible Imager with Organic Photodetector for Sensing Applications

We developed a flexible imager comprising low‐temperature polycrystalline silicon thin‐film transistors and organic photodiodes. The developed flexible imager has high‐resolution and high‐speed readout characteristics. Owing to these characteristics, pulse wave signals can be measured, and the images of fingerprints and veins can be obtained. Furthermore, we developed three‐axis tactile pressure sensors by integrating flexible optical components. The sensors can detect both normal and tangential pressures.

Spherically symmetric anisotropic charged neutron stars in f(Q, T) gravity

In this work, we have investigated a new solution for charged anisotropic compact stellar system in the framework of an extended theory of symmetric teleparallel gravity known as f(Q, T) gravity with the non-metricity term Q and the trace T for energy–momentum tensor. We have constructed a complete set of the gravitational field equations for a non-linear function f(Q,T)=αQ+β(1+Q2)+λT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q,T)=\\alpha Q + \\beta (1+Q^{2}) + \\lambda T$$\\end{document} with α,β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha , \\beta $$\\end{document} and λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} are dimensionless constant parameters in case of static spherically symmetric space-time. To evaluate the expression of relevant unknown constants interior space-time has been matched with exterior Reissner–Nordstro¨\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ddot{\ extrm{o}}$$\\end{document}m metric. We have performed a graphical discussion in detail to test the behavior of physical parameters in the interior region of a stellar system like energy density, radial and tangential pressure, anisotropies of matter portion, electric field intensity etc. Also, to check the physical validity of our solutions, we have performed various tests viz., energy conditions, stability, mass–radius relation, surface redshift etc. The hydrostatic equilibrium position of our stellar system has been analysed through the TOV equation. Finally, we have determined that our stellar structure solutions satisfy all required physical conditions for viability and acceptability in the context of some pulsar like neutron stars. So our model can be used to characterise the neutron stars in f(Q, T) modified gravity.

Surface tension of aqueous electrolyte solutions. A thermomechanical approach.

We determine the surface tension of aqueous electrolyte solutions in contact with non-polar dielectric media using a thermomechanical approach, which involves deriving the stress tensor from the thermodynamic potential of an inhomogeneous fluid. To obtain the surface tension, we calculate both the normal and tangential pressures using the components of the stress tensor, recently derived by us [Y. A. Budkov and P. E. Brandyshev, J. Chem. Phys. 159, 174103 (2023)] within the framework of Wang's variational field theory. Using this approach, we derive an analytical expression for the surface tension in the linear approximation. At low ionic concentrations, this expression represents the classical Onsager-Samaras limiting law. By utilizing only one fitting parameter, which is related to the affinity of anions to the dielectric boundary, we successfully approximated experimental data on the surface tension of several aqueous electrolyte solutions. This approximation applies to both the solution-air and solution-dodecane interfaces, covering a wide range of electrolyte concentrations.

A comparative study of wormhole geometries under two different modified gravity formalism

In the current article, we discuss the wormhole geometries in two different gravity theories, namely 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}$$\ exttt{F}(\ exttt{Q, T})$$\\end{document} gravity and F(R,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{F}(\ exttt{R, T})$$\\end{document} gravity. In these theories, Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{Q}$$\\end{document} is called a non-metricity scalar, R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{R}$$\\end{document} stands for the Ricci scalar, and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{T}$$\\end{document} denotes the trace of the energy–momentum tensor (EMT). The main goal of this study is to comprehensively compare the properties of wormhole solutions within these two modified gravity frameworks by taking a particular shape function. The conducted analysis shows that the energy density is consistently positive for wormhole models in both gravity theories, while the radial pressure is positive for 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}$$\ exttt{F}(\ exttt{Q, T})$$\\end{document} gravity and negative in F(R,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{F}(\ exttt{R, T})$$\\end{document} gravity. Furthermore, the tangential pressure shows reverse behavior in comparison to the radial pressure. By using the Tolman-Oppenheimer-Volkov (TOV) equation, the equilibrium aspect is also described, which indicates that hydrostatic force dominates anisotropic force in the case 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}$$\ exttt{F}(\ exttt{Q, T})$$\\end{document} gravity theory, while the reverse situation occurs in F(R,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{F}(\ exttt{R, T})$$\\end{document} gravity, i.e., anisotropic force dominates hydrostatic force. Moreover, using the concept of the exoticity parameter, we observed the presence of exotic matter at or near the throat in the case 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}$$\ exttt{F}(\ exttt{Q, T})$$\\end{document} gravity while matter distribution is exotic near the throat but normal matter far from the throat in F(R,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ exttt{F}(\ exttt{R, T})$$\\end{document} gravity case. In conclusion, precise wormhole models can be created with a potential NEC and DEC violation at the throat of both wormholes while having a positive energy density, i.e., ρ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho >0$$\\end{document}.

Physical properties and maximum allowable mass-radius relation of complexity-free compact stellar objects within modified gravity formalism* *The authors MKJ and SKM acknowledge that this work is carried out under TRC Project (BFP/RGP/CBS/22/014). This study is also supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2024/R/1445). The authors are thankful to the Deanship of Graduate Studies and Scientific

This paper investigates the physical properties and predicted radii of compact stars generated by the Tolman-IV complexity-free model within the background of modified gravity theory, particularly the -gravity theory, under complexity formalism for a spherically symmetric spacetime proposed by L. Herrera [Phys Rev D 97: 044010, 2018]. By solving the resulting set of differential equations, we obtain the explicit forms of the energy-momentum (EM) tensor components, including the density, radial pressure, and tangential pressure. The influence of the parameter χ on various physical properties of the star is thoroughly investigated. The model undergoes a series of rigorous tests to determine its physical relevance. The findings indicate that the model exhibits regularity, stability, and a surface with vanishing pressure. The boundary of this surface is determined by carefully selecting the parameter space. The complexity method employed in gravity offers an interesting approach for developing astrophysical models that are consistent with observable events as demonstrated by recent experiments. In this regard, we use observational data from the GW190814 event, detected by the LIGO and Virgo observatories, to investigate the validity of the Tolman-IV model in gravity. The analysis includes comparing the model's predictions with the observed characteristics of the compact object involved in the merger. In addition, data from two-millisecond pulsars, PSR J1614-2230 and PSR J0952-0607, are incorporated to further constrain the theoretical theories. However, we present a diagram depicting the relationship between the total mass and radius of the compact object candidates for different values of χ.

Realistic compact objects in the f(R, T) gravity in the background of polytropic and barotropic gas models

The f(R, T) gravity in the background of the polytropic and barotropic fluid has been investigated in this work. We have selected the TOV equation to determine the internal spacetime of a spherically symmetric galactic object. With the use of the Einstein equation, we have selected KB-spacetime to calculate the mass, compactness, and surface redshift of a spherically symmetric body. Explicit conditions for model parameters have been constructed for the boundary conditions of the interior and exterior spacetime, and the Schwarzschild solution has been employed in the modified f(R, T) gravity theory to evaluate different matching criteria. An increasing pattern in compactness with respect to the different radii is evident in the graphical representation of the compactness evolution for each of the individual star models. After selecting a non-vacuum field equation for higher order curvature, we reformulated f(R, T) for R and T. As a result, the tangential pressure, radial pressure, and matter density have all been calculated. According to the study, as the radius goes to infinity, the tangential and radial pressures display asymptotic flatness and converge to zero. Polytropic and barotropic gas EoS have been adopted since the star model confronts the presence of an isotropic fluid backdrop. It has been noted that in a polytropic background, density and pressure increase with distance from the star’s core, but in a barotropic background, the pressure exhibits an ascending pattern as a function of radius.

Stability of a realistic astrophysical pulsar and its mass–radius relation in higher-order curvature gravity

The objective of this research is to explore compact celestial objects while considering the framework of an extended gravitational theory known as R+f(G) gravity. The notations R and G denote the Ricci scalar and the Gauss–Bonnet invariant, respectively. Radio pulsars, which are neutron stars with masses greater than 1.8 times that of the Sun (M⊙), provide exceptional opportunities for delving into fundamental physics in extraordinary environments unparalleled in the observable universe and surpassing the capabilities of experiments conducted on Earth. Through the utilization of both the linear and quadratic expressions of the function f(G)=α1G2, where α1 (with dimensional units of [length6]) are incorporated, we have achieved an accurate analytical solution for anisotropic perfect-fluid spheres in a state of hydrostatic equilibrium. By integrating the dimensional parameters α1 and the compactness factor, defined as C=2GMRc2, we showcase our capacity to encompass and depict all physical characteristics within the stellar structure. We illustrate that the model is capable of producing a stable arrangement for the pulsar PSR J0740+6620, encompassing its geometric and physical properties. We illustrate that by utilizing the quadratic form of G in the R+f(G) framework, the Krori-Barua ansatz establishes semi-analytical relationships between radial pressure (pr), tangential pressure (pt), and density (ρ). Remarkably, in the context of the positive/negative α1 quadratic R+f(G) gravity framework, the maximum compactness is inherently restricted to values fail below the Buchdahl limit when the surface density exceeds 4×1014 g/cm3. This differs from General Relativity (GR) in which the compactness is unlikely to approach the black hole limit. The model predicts a core density that is multiple times greater than the saturation nuclear density, represented as ρnuc=4×1014 g/cm3, and a surface density ρs that surpasses the nuclear saturation density. We offer the mass–radius diagram associated with the boundary density we have determined, and this diagram has been shown to be consistent with other observational discoveries.

Modelling Einstein cluster using Einasto profile

We demonstrate a general relativistic approach to model dark matter halos using the Einstein cluster, with the matter stress-energy generated by collisionless particles moving on circular geodesics in all possible angular directions and orbital radii. Such matter, as is known, allows an anisotropic pressure profile with non-zero tangential but zero radial pressure. We use the Einasto density profile for the Einstein cluster. Analytical studies on its properties (metric functions) and stability issues are investigated. Further, to establish this model (with the Einasto profile) as one for a dark matter halo,we use the SPARC galactic rotation curve data and estimate the best-fit values for the model parameters. General relativistic features (beyond the Keplerian velocities) such as the tangential pressure profile, are quantitatively explored. Thus, Einstein clusters with the Einasto profile, which tally well with observations, may be considered as a viable model for dark matter halos.

Harmonic expansion and nonsmooth dynamics in a circular contact region with combined slip-spin motion

We analyse a rigid body in planar motion while touching a rough plane at a finite-sized, circular contact area. Assuming Coulomb friction between the tangential and normal pressure distributions, the resultant forces and torques can be expressed formally with a nonsmooth dependence on the kinematic variables. In the literature, the exact form of the tangential forces is available for special pressure distributions expressed by transcendent functions; recently, an approximate linear model was introduced. Now, we present a nonlinear extension of the approximation, which can be used effectively to characterise slipping-sticking transitions between the bodies.

Modified Gravity Model fQ,T and Wormhole Solution

We investigate wormhole solutions using the modified gravity model fQ,T with viscosity and aim to find a solution for the existence of wormholes mathematically without violating the energy conditions. We show that there is no need to define a wormhole from exotic matter and analyze the equations with numerical analysis to establish weak energy conditions. In the numerical analysis, we found that the appropriate values of the parameters can maintain the weak energy conditions without the need for exotic matter. Adjusting the parameters of the model can increase or decrease the rate of positive energy density or radial and tangential pressures. According to the numerical analysis conducted in this paper, the weak energy conditions are established in the whole space if α<0 and 12.56<β<25.12 or α>0 and β>25.12. The analysis also showed that the supporting matter of the wormhole is near normal matter, indicating that the generalized fQ,T model with viscosity has an acceptable parameter space to describe a wormhole without the need for exotic matter.

Study of exponential wormhole metric in f(R) gravity

In this work, we have studied ‘the exponential form’ of space-time metric in some of the viable f(R) gravity models, viz. exponential gravity model, Starobinsky gravity model, Tsujikawa model, and Gogoi-Goswami f(R) gravity model. Here, we have calculated the parameters including energy density, tangential pressure, and radial pressure for these corresponding models of f(R) gravity. Subsequently, we have investigated the energy conditions, viz. null energy condition (NEC), weak energy condition (WEC), strong energy condition (SEC), and dominant energy condition (DEC) for the considered models. We have also explained the suitable stability conditions for these models through related plots. We observed that the exponential wormhole metric obeys all the necessary energy conditions in f(R) gravity without violating any flare-out or stability conditions. Out of four considered viable f(R) gravity models, the exponential, the Tsujikawa, and the Gogoi-Goswami f(R) gravity models are found to be more suitable for the exponential wormhole to exist, although all these models have some constraints on the ranges of the parameters used.

Orbit design and attitude control of diffractive sail and validation with solar polar mission

Liquid crystal diffractive sails can generate controllable tangential radiation pressures, which have advantages in the Solar Polar Imager mission (SPI). This paper proposes a composite diffractive sail design consisting of an ideal passive diffraction grating sail and liquid crystal polarization gratings (LCPGs). The main diffractive grating sail generates thrust for orbital transfer with a sun-facing attitude. An optimal 3.8-year transfer trajectory is obtained by an improved direct method. Small-area LCPGs distributed around the edge are used for three-axis attitude control. The LCPGs can continuously modulate the force and torque by controlling the applied voltage based on the electro-optical characteristic of liquid crystal materials. A control strategy, including an adaptive attitude-tracking PD controller and a control allocation method, is designed to track the attitude profile generated by the transfer trajectory. Finally, the attitude-orbit coupling dynamics are used to simulate the whole process, and the results show that orbital insertion errors are minor.

Vorticity dynamics at partial-slip boundaries

In this paper we discuss the dynamics of vorticity at partial-slip boundaries. We consider the total vector circulation, which includes both the total vorticity of the fluid and the slip velocity at the boundary (the interface vortex sheet). The generation of vector circulation is an inviscid process, which does not depend on either viscosity or the slip length at the boundary. Vector circulation is generated by the inviscid relative acceleration between the fluid and the solid, due to either tangential pressure gradients or tangential acceleration of the partial-slip wall. While the slip length does not affect the creation of vector circulation, it governs how vector circulation is distributed between the total vorticity of the fluid and the interface vortex sheet. Specifically, the partial-slip boundary condition prescribes the ratio between boundary vorticity and the strength of the interface vortex sheet, and the viscous boundary flux transfers vector circulation between the interface vortex sheet and the fluid interior to maintain this condition. The interaction between a vortex ring and a partial-slip wall is examined to highlight various aspects of this formulation. For the head-on collision, the quantity of vector circulation diffused into the fluid as secondary vorticity increases as the slip length is decreased, resulting in a stronger secondary vortex and increased rebound of the vortex ring. For the oblique interaction, the extent to which the vortex ring connects to the boundary increases as the slip length is increased.

Enhanced transfer performance of sun-facing diffractive sails in solar polar imager missions

A diffractive sail represents an advancement in solar sailing technology, capable of generating tangential radiation pressure force when oriented towards the sun. This unique property allows for varied radiation pressure distributions, making it a potential candidate for complex space missions. This paper delves into the transfer performance of the sun-facing diffractive solar sail in a solar polar imager mission.We establish both the radiation pressure force model and the time-optimal control problem specific to the sun-facing diffractive solar sail in interplanetary transfers. Applying an indirect method and a combined approach of parameter optimization with the direct method, we explore how different diffractive angles and acceleration capacities affect transfer times. This research offers insights to the design and fabrication of thin novel optical metamaterial films that efficiently diffract light at appropriate angles for potential solar sails in the solar polar imager mission. Compared with reflective sails, the diffractive sail demonstrates remarkable transfer efficiency and simplicity in attitude control, making it a more suitable choice in the solar polar imager mission.