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Abstract Hybrid oils ensure multifaceted technological (self‐lubricating and favorable fatty acid properties), and sustainable (environmental, economic, and societal) benefits towards biodiesel conversions. The hybrid oils (Hydnocarpus wightiana oil and waste cooking oils [40:60 v/v]) were synthesized to methyl ester with alkaline catalyst sodium hydroxide through the base‐transesterification process. The resulting hybrid oil methyl ester (HOME) is 96.68%. The crude oil (CO) and its HOME underwent characterization using gas chromatography–mass spectrometry, Fourier transform infrared spectroscopy, and hydrogen‐1 nuclear magnetic resonance spectroscopy. The physicochemical properties of crude oils and hybrid biodiesel were analyzed and compared to pure diesel. Different blends of biodiesel–diesel, including binary (20% HOME + 80% diesel [D]), ternary (60% D + 20% HOME + 20% heptanol [H]), and quaternary (20% HOME + 20% H + 10% CO + 50% D) blends, were tested in a single‐cylinder compression ignition (CI) engine under various load conditions to assess their performance, emissions, and combustion properties. Experimental findings indicate that the addition of heptanol to diesel or hybrid biodiesel (ternary blend) enhances brake thermal efficiency, reduces brake‐specific fuel consumption, and leads to longer ignition delays, resulting in higher internal combustion pressure and thermal energy release rates compared to the quaternary blend. Additionally, compared to pure diesel, the ternary blend exhibits decreased emissions of carbon monoxide (CO) and hydrocarbon (HC), with a slight increase in nitrous oxide (NOx) and carbon dioxide (CO2). Notably, the ternary blend emerges as a distinct alternative biodiesel blend suitable for direct use in CI engines without requiring any engine modifications.

Abstract In this work, we study metric-Palatini gravity extended by the antisymmetric part of the affine curvature. This gravity theory leads to general relativity plus a geometric Proca field. Using our previous construction of its static spherically-symmetric AdS solution (Eur Phys J. C 83(4):318, 2023), we perform a detailed analysis in this work using the observational quasiperiodic oscillations (QPOs) data. To this end, we use the latest data from stellar-mass black hole GRO J1655-40, intermediate-mass black hole in M82-X1, and the super-massive black hole in SgA* (our Milky Way) and perform a Monte-Carlo-Markov-Chain (MCMC) analysis to determine or bound the model parameters. Our results shed light on the allowed ranges of the Proca mass and other parameters. The results imply that our solutions can cover all three astrophysical black holes. Our analysis can also be extended to more general metric-affine gravity theories.

This paper addresses the need for innovative optimization solutions in automotive manufacturing. Through advanced algorithms, we review existing methods and introduce novel ap- proaches tailored to this sector. Our literature review identifies gaps and limitations in current methodologies. We define a specific optimization problem within automotive manufacturing, emphasizing its unique challenges. Our key contributions include: (a) Exploring hybrid optimization algorithms, combining genetic algorithms with simulated annealing for a 15% improvement in convergence speed, (b) Integrating machine learning techniques, resulting in a 20% reduction in optimization error compared to static settings, (c) Incorporating multiobjective optimization, achieving a 25% improvement in simultaneous cost and efficiency optimization, and (d) Proposing dynamic optimization algorithms, reducing decision-making latency by 30% during rapid environmental changes. Case studies demonstrate practical ap- plication, with quantitative results highlighting the superiority of our approaches over traditional methods. Additionally, the data analysis was conducted using Python, contributing to the robustness and accuracy of our findings.

Abstract In the present work we study the geodesic motion and accretion process of a test particle near an Anti-de Sitter (ADS) BH surrounded by a dark fluid with a Chaplygin-like equation. Within the defined paradigm, we investigate on the equatorial plane and examine circular geodesics along with their features related to stabilities, radiation energy flux, oscillations and orbits. The general form of the fluid accretion onto the AdS BH through dynamical analysis and mass expansion also has discussed in a depth. Additionally, a few more interesting topics, e.g. the effective potential, angular momentum, specific energy, radiation energy and epicyclic frequencies have also been examined thoroughly. All the attributes are physically acceptable within the observational signatures and ranges.

In this current investigation, the experimental performance of a solar still basin was significantly enhanced by incorporating snail shell biomaterials. The outcomes of the snail shell-augmented solar still basin (SSSS) are compared with those of a conventional solar still (CSS). The utilization of snail shells proved to facilitate the reduction of saline water and enhance its temperature, thereby improving the productivity of the SSSS. Cumulatively, the SSSS productivity was improved by 4.3% over CSS. Furthermore, the SSSS outperformed in energy and exergy efficiency of CSS by 4.5 and 3.5%, respectively. Economically, the cost per liter of distillate (CPL) for the CSS was 3.4% higher than SSSS. Moreover, the SSSS showed a shorter estimated payback period (PBP) of 141 days which was 6 days less than CSS. Considering the environmental impact, the observed CO2 emissions from the SSSS were approximately 14.6% higher than CSS over its 10-year lifespan. Notably, the SSSS exhibited a substantial increase in the estimated carbon credit earned (CCE) compared to the CSS. Ultimately, the research underscores the efficacy of incorporating snail shells into solar still basins as a commendable approach to organic waste management, offering economic benefits without compromising environmental considerations. HIGHLIGHTS The snail shell biomaterial is used in solar still for clean water production.; The hourly productivity of SSSS is enhanced by 6.8% than CSS.; The energy efficiency of SSSS and CSS is about 24.1% and 23%, respectively.; The pay back period of SSSS is 141 days, whereas it is 147 days for CSS.;

Abstract We investigate the strong gravitational lensing phenomena caused by a black hole with a dark matter halo in the presence of cloud string and quintessence. This study examines strong gravitational lensing with two significant dark matter models: the universal rotation curve model and the cold dark matter model. To do this, we first numerically estimate the strong lensing coefficients and strong deflection angles for both the universal rotation curve and cold dark matter models. It is observed that the deflection angle, denoted as $$\alpha _D$$ α D , increases with the parameter $$\alpha $$ α while holding the value of $$2M \gamma $$ 2 M γ constant. Additionally, it increases with the parameter $$2M \gamma $$ 2 M γ while keeping the value of $$\alpha $$ α constant. The strong deflection angle $$\alpha _D$$ α D , for the black hole with a dark matter halo, with parameters $$\alpha $$ α and $$2\,M \gamma $$ 2 M γ , greatly enhances the gravitational bending effect and surpasses the corresponding case of the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$ A = B = 0 = α = 2 M γ ). Furthermore, we investigate the astrophysical consequences through strong gravitational lensing observations, using examples of two supermassive black holes, namely $$M87^{*}$$ M 87 ∗ and $$Sgr A^{*}$$ S g r A ∗ , located at the center of nearby galaxies. It is observed that black holes with dark matter halos in the presence of cloud string and quintessence can be quantitatively distinguished and characterized from the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$ A = B = 0 = α = 2 M γ ). The findings in our analysis suggest that observational tests for black holes influenced by dark matter halos, cloud string and quintessence are indeed feasible and viable.

The focus of this paper is to examine the properties of thermodynamics and weak gravitational lensing about the geometry of black holes within the context of a non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter. We examine the geometric mass and thermal temperature in this context to discuss the stability of the black hole solution. We examine the phase transition and stability while calculating the specific heat. We also research the black hole's energy emission process. We deduce that our researched black hole solution is thermally stable based on its thermodynamic features. Furthermore, we analyze uniform and non-uniform plasma by calculating the deflection angle, and we examine gravitational lensing in the weak plasma field. It is observed that in uniform plasma, the deflection angle is larger than in non-uniform plasma. We also looked at the image magnification caused by source brightness and found that the source image is enlarged more in uniform plasma than in non-uniform plasma.

This study employs diverse machine learning models, including classic artificial neural network (ANN), hybrid ANN models, and the imperialist competitive algorithm and emotional artificial neural network (EANN), to predict crucial parameters such as fresh water production and vapor temperatures. Evaluation metrics reveal the integrated ANN-ICA model outperforms the classic ANN, achieving a remarkable 20% reduction in mean squared error (MSE). The emotional artificial neural network (EANN) demonstrates superior accuracy, attaining an impressive 99% coefficient of determination (R2) in predicting freshwater production and vapor temperatures. The comprehensive comparative analysis extends to environmental assessments, displaying the solar desalination system's compatibility with renewable energy sources. Results highlight the potential for the proposed system to conserve water resources and reduce environmental impact, with a substantial decrease in total dissolved solids (TDS) from over 6,000 ppm to below 50 ppm. The findings underscore the efficacy of machine learning models in optimizing solar-driven desalination systems, providing valuable insights into their capabilities for addressing water scarcity challenges and contributing to the global shift toward sustainable and environmentally friendly water production methods. HIGHLIGHTS The study employs diverse machine learning models to predict crucial parameters such as fresh water production and vapor temperatures.; Machine learning models including classic artificial neural network (ANN), hybrid ANN models, and the imperialist competitive algorithm (ANN-ICA) and emotional artificial neural network (EANN); The EANN model emerges as the most accurate in predicting freshwater production and vapor temperatures.;

This paper investigates the application of three nature-inspired optimisation algorithms – SHO, MFO, and GOA – combined with four machine learning methods – Gaussian Processes, Linear Regression, MLP, and Random Forest – to enhance carbon dioxide emission prediction in the OECD – Asia and Oceania region. The study uses historical carbon dioxide emissions data, socioeconomic indicators such as GDP, population density, energy consumption, and urbanisation rates, and environmental indicators such as temperature, precipitation, and forest cover. Through comprehensive experimentation, the study evaluates the performance of each combination, revealing varying effectiveness levels. The MFO-MLP combination achieved the highest accuracy with R2 values of 0.9996 and 0.9995 and RMSE values of 11.7065 and 12.8890 for the training and testing datasets, respectively. The GOA-MLP configuration achieved R2 values of 0.9994 and 0.99934 and RMSE values of 15.01306 and 14.59333. The SHO-MLP combination, while effective, showed lower performance with R2 values of 0.9915 and 0.9946 and RMSE values of 55.4516 and 41.575. The findings suggest hybrid techniques can significantly enhance prediction accuracy compared to conventional methods. This research provides valuable insights for policymakers and stakeholders, indicating that optimised machine learning models can support more informed and effective environmental policy-making and sustainability efforts in the OECD – Asia and Oceania region. Future research should explore additional optimisation algorithms and ensemble techniques to improve prediction robustness and accuracy. These findings offer a robust tool for policymakers to forecast emissions more accurately, aiding in developing targeted strategies to reduce carbon footprints and achieve climate goals.

We investigate the horizon structure and ergosphere in a charged rotating black hole within 4D Einstein-Gauss-Bonnet gravity, which introduces additional parameters (Q) because of the charge and Gauss-Bonnet parameter (β), besides the mass (M) and rotation parameter (a). Interestingly, for each value of the parameter Q (β), there is a critical GB parameter β=βE (Q=QE) that corresponds to an extremal black hole with degenerate horizons. For ββE (Q>QE), no black hole exists. The extremal value βE (QE) is also affected by the GB parameter α and the ergosphere. We also study the collision of two equal-mass particles near the horizon of this black hole and explicitly show the effect of the parameter β (Q). The innermost stable circular orbits (ISCO) and the effective potential, which governs the motion of particles in spacetime, have been analyzed for different parameter values. The centre-of-mass energy (ECM) depends on the rotation parameter a and the parameters β and Q. We investigate the ECM of two colliding particles near the horizon for both extremal and non-extremal cases. It is shown that in extremal cases, when one of the colliding particles has a critical angular momentum, the ECM can be arbitrarily high, suggesting that the charged rotating in 4D Einstein-Gauss-Bonnet gravity can function as a particle accelerator. Despite the complexity of the BH solution, an exact expression for the thermodynamic quantities of black holes, such as the mass, Hawking temperature, and entropy, is derived in terms of the horizon radius. These quantities show significant deviations from the Kerr solution because of the influence of the Gauss-Bonnet parameter and electric charge.

The process of creating a porous metal-ceramic material based on Ni-Al alloy and gadolinium-doped cerium oxide (CGO) using the thermal explosion method has been investigated. This study aims to analyze the effect of CGO on the thermal explosion parameters and the architecture of the resulting Ni-Al-CGO materials. In this regard, the influence of adding CGO powder to the Ni-Al system on the synthesis process and structure formation during controlled heat loss thermal explosion has been studied. Dependencies of temperature and time characteristics of the thermal explosion on initial parameters have been measured. It has been demonstrated that the concentration of CGO in the initial mixture and heat dissipation from the sample significantly affect the rate of the exothermic reaction. The phase composition of the obtained porous materials, depending on the CGO content and the temperature of subsequent vacuum annealing, was analyzed using X-ray diffraction. The chemical composition and microstructure of the synthesis products were examined through electron microscopy and energy-dispersive X-ray spectroscopy. The possibility of forming metal-ceramic composites with a porosity of 60–65 % for use as supporting substrates for solid oxide fuel cells with a NiO/CGO anode has been shown. An anodic layer of NiO/CGO was applied to a metal-ceramic base of the composition (Ni+25 %Al)+5 %CGO using screen printing, which was then annealed in an air atmosphere at 1300 °C and reduced at 900 °C in a hydrogen atmosphere. The dilatometric method determined that adding 40 wt.% Cr to a mixture of Ni-Al powders reduces the average coefficient of thermal expansion of the new material.

Abstract The current manuscript deals with the tidal force effects, geodesic deviation, and shadow constraints of the Schwarzschild-like black hole theorised in Starobinsky–Bel-Robinson gravity exhibiting M-theory compactification. In the current analysis, we explore the radial and angular tidal force effects on a radially in-falling particle by the central black hole, which is located in this spacetime. We also numerically solve the geodesic deviation equation and study the variation of the geodesic separation vector with the radial coordinate for two nearby geodesics using suitable initial conditions. All the obtained results are tested for Sag A* and M87* by constraining the value of the stringy gravity parameter $$\beta $$ β using the shadow data from the event horizon telescope observations. All the results are compared with Schwarzschild black hole spacetime. In our study, we found that both the radial and angular tidal forces experienced by a particle switch their initial behaviour and turn compressive and stretching, respectively, before reaching the event horizon. The geodesic deviation shows an oscillating trend as well for the chosen initial condition. For the constrained value of $$\beta $$ β , we see that the spacetime geometry generated by Sag A* and M87* is effectively same for both Schwarzschild and Starobinsky–Bel-Robinson black hole. Furthermore, we also calculated the angular diameter of the shadow in Starobinsky–Bel-Robinson black hole and compared with the Schwarzschild black hole. It is observed that the angular diameter of shadow for M87* and Sgr A* in Starobinsky–Bel-Robinson black hole is smaller than the Schwarzschild black hole. The calculated results satisfy the event horizon telescope observational constraints.

Abstract Extended metric-Palatini gravity, quadratic in the antisymmetric part of the affine curvature, is known to lead to the general relativity plus a geometric Proca field. The geometric Proca, equivalent of the non-metricity vector in the torsion-free affine connection, qualifies to be a distinctive signature of the affine curvature. In the present work, we explore how shadow and photon motion near black holes can be used to probe the geometric Proca field. To this end, we derive static spherically symmetric field equations of this Einstein-geometric Proca theory, and show that it admits black hole solutions in asymptotically AdS background. We perform a detailed study of the optical properties and shadow of this black hole and contrast them with the observational data by considering black hole environments with and without plasma. As a useful astrophysical application, we discuss constraints on the Proca field parameters using the observed angular size of the shadow of supermassive black holes M87 $$^*$$ ∗ and Sgr A $$^*$$ ∗ in both vacuum and plasma cases. Overall, we find that the geometric Proca can be probed via the black hole observations.

This paper is devoted to studying thermodynamics and particle acceleration around charged rotating BHs surrounded by perfect fluid dark matter. In the beginning, we discuss BH horizons, ergosphere and inner stable circular orbits in the framework of perfect fluid dark matter. It is observed that perfect fluid dark matter effects Hawking's temperature, Gibbs free energy, and other physical quantities related to thermodynamics. Some different aspects of thermodynamics are discussed within the scope of different values of the involved parameters. Further, we discuss the thermal fluctuations of considered BH solutions, which refer to the random motion of particles around a BH due to temperature fluctuations. Specifically, thermal fluctuations are affecting the entropy and Hawking radiation of a BH, which are crucial for understanding the behavior of physical quantities. It is found that corrected thermodynamical quantities of charged rotating perfect fluid dark matter BHs are smaller than the charged rotating BH without perfect fluid dark matter. We emphasize that the assumptions made in the literature and the thermodynamics of the previous BH solutions are well consistent with our results.

Abstract We investigate the null geodesics and the shadow cast by the Kerr–Newman–Kiselev–Letelier (KNKL) black hole for the equation of state parameter $$\omega _q=-2/3$$ ω q = - 2 / 3 and for different values of the spacetime parameters, including the quintessence parameter $$\gamma $$ γ , the cloud of string (CS) parameter b, the spin parameter a and the charge Q of the black hole. We notice that for the increasing values of the parameters $$\gamma $$ γ and b the size of the shadow of the KNKL black hole increases and consequently the strength of the gravitational field of the black hole increases. On the other hand with increase in the charge Q of the black hole the size of the shadow of the black hole decreases. Further with the increase in the values of the spin parameter a of the KNKL black hole, we see that the distortion of the shadow of the black hole becomes more prominent. Moreover we use the data released by the Event Horizon Telescope (EHT) collaboration, to restrict the parameters b and $$\gamma $$ γ for the KNKL black hole, using the shadow cast by the KNKL black hole. To this end, we also explore the relation between the typical shadow radius and the equatorial and polar quasinormal mods (QNMs) for the KNKL black hole and extend this correspondence to non-asymptotically flat spacetimes. We also study the emission energy rate from the KNKL black hole for the various spacetime parameters, and observe that it increases for the increasing values of both the parameters $$\gamma $$ γ and b for fixed charge-to-mass and spin-to-mass ratios of the KNKL black hole. Finally, we investigate the effects of plasma on the photon motion, size and shape of the shadow cast by the KNKL black hole. While keeping the spacetime parameters fixed, we notice that with increase in the strength of the plasma medium the size of the shadow of the KNKL black hole decreases and therefore the intensity of the gravitational field of the KNKL black hole decreases in the presence of plasma.

Abstract The detailed study of horizon structure and the shadow cast by a Kerr-like black hole (BH) is performed. The trajectory of light rays forming the shadow of BH is found using the solutions of geodesic equation for the motion and effective potential of a photon around Kerr-like BH for different values of deviation parameter l in Kerr-like spcetime metric. It is observed that with an increase in the parameter l the size of the shadow of the BH is decreased. Additional, we have consider effect of plasma on BH shadow and the plasma influence on the shadow of Kerr-like BH, the size of observable radius of BH shadow and oblateness are explored with more details.

Abstract In this paper, we have studied the particle dynamics, gravitational lensing and energy processes around the black hole (BH) in Kalb–Ramond (KR) gravity. The motion of particles is considered with parameters in KR BH and investigated for massive and massless particles. From this work, we have got the horizon structure, photon orbit of photon and ISCO (inner stable circular orbit) of a mass particle with parameters in KR gravity. The effective potential is also studied for the massless and mass particles. Additionally, we tested energy extracted from BH using the BSW (Banados–Silk–West) method and derived the expression of center mass-energy in KR gravity. The impact of the model parameters $$\gamma $$ γ and $$\lambda $$ λ is checked to study the size of the BH shadow in the KR gravity. Gravitational weak lensing has been explored using the general method and the derived deflection angle of light rays around the BH for the plasma of various concentration distributions. The magnification of brightness is obtained using the angle of deflection of the light rays.

Abstract We investigate the thermodynamic properties and Joule–Thomson expansion for conical or BTZ-like black holes. To analyze the thermal stability, we discuss the temperature and thermal stability relative to the horizon radius for different values of model parameters $$\beta _0$$ β 0 and $$\alpha _2$$ α 2 . Moreover, we analyze thermodynamical geometries like Ruppeiner, Weinhold and Hendi Panahiyah Eslam Momennia formulation and calculate respective scalar curvatures for BTZ-like black holes. Interestingly, the black holes have no singularity in some cases, i.e., completely regular. We obtain the inversion temperatures and inversion curves and investigate the similarities and differences between van der Waals and charged fluids. To discuss this expansion, we use a BTZ-like black hole. Further, we establish the position of the inversion point versus different values of mass $$\mu $$ μ , and the parameters $$\beta _0$$ β 0 and $$\alpha _2$$ α 2 for such a BTZ-like black hole. The Joule–Thomson coefficient $$\mu $$ μ at this point disappears. A crucial trait upon which we relied to inspect the sign of quantity $$\mu $$ μ to get the cooling-heating areas. We also investigate the energy emission depending upon the frequency $$\omega $$ ω .

In the present paper, we investigate the thermodynamics of a new perturbed black hole solution in symmetric teleparallel gravity. Our main focus is on the solution for a nonlinear model like Q+αQ2. We study new features of null geodesics and quasi-normal modes that occur for the current perturbed black hole solution. We inspect the critical behavior of thermal fluctuation and phase transitions in the background of a considered black hole solution and get the Davies points. To complete this study, we also explore the interesting aspects of the emission energy and quantum fluctuations. We highlight that our results are in good agreement with the thermodynamics of the previous black hole solutions and assumptions presented in the literature.

A Correction to this paper has been published: 10.1140/epjc/s10052-020-8346-3

The effect of spacetime curvature on optical properties may provide an opportunity to suggest new tests for gravity theories. In this paper, we investigated gravitational weak lensing around a Bardeen black hole with the string clouds parameter. First, we examined the horizon structure in the presence of string clouds around the gravitational compact object defined by Bardeen spacetime. The effect of gravitational weak lensing in a plasma medium is also discussed. According to the findings, the influence of the string cloud parameter on the circular orbits of a light ray around the black hole is greater than that in the Schwarzschild case, while the influence of the charge is reversed. The deflection angle of light rays in weak lensing is also used to study how much the image is magnified.

Abstract This paper is devoted to study weak gravitational lensing properties around black hole surrounded plasma medium in modified gravity (MOG). We have investigated the effects of the MOG-parametr and plasma medium on the deflection angle and total magnification of the images. we have presented the comparisons of the effects of the uniform plasma, singular isothermal sphere and non-singular isothermal sphere. We have also shown that the uniform plasma effects significantly stronger than the other models of plasma medium.Through the studies of the total magnifications of images of a remote source we have shown that the effects of the MOG parameter and plasma medium are similar and the increase of the MOG parameter and plasma frequency cause to increase the total magnification. Moreover, we have explored and analyzed how the MOG effects can reflect the plasma medium providing the same values of the total magnification of images.

Abstract We have studied the null geodesics in the background of the Kerr–Newman black hole veiled by a plasma medium using the Hamilton–Jacobi method. The influence of black hole’s charge and plasma parameters on the effective potential and the generic photon orbits has been investigated. Furthermore, our discussion embodies the effects of black hole’s charge, plasma and the inclination angle on the shadow cast by the gravity with and without the spin parameter. We examined the energy released from the black hole as a result of the thermal radiations, which exclusively depends on the size of the shadow. The angle of deflection of the massless particles is also explored considering a weak-field approximation. We present our results in juxtaposition to the analogous black holes in General Relativity, particularly the Schwarzschild and Kerr black hole.

Here we study particle motion in the specific Lorentzian wormhole spacetime characterized, in addition to the total mass M, with the dimensionless parameter λ. In particular we calculate the radius of the innermost stable circular orbit (ISCO) for test particles and the photonsphere for massless particles. We show that the effect of the dimensionless wormhole parameter decreases the ISCO radius and the radius of the photon orbit. Then, we study plasma effects on gravitational weak lensing in wormhole spacetime and obtain the deflection angle of the light. We show that the effect of λ decreases the deflection angle. We study the effects of uniform and non-uniform plasma on the light deflection angle separately, and show that the uniform plasma causes the deflection angle to be smaller in contrast to the non-uniform plasma.

We consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with Ωr^, Ωφ^, and Ωω^ in a particular region of parameter space around black string spacetime geometry. We study the effect of a compact extra spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur in the allowed region when particles move along the black string. We find that the presence of the compact extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits. Interestingly we also find that isofrequency pairing of geodesic orbits in the region of parameter space cannot be realized beyond the critical value Jcr≈0.096 of the conserved quantity of the motion arising from the compact extra spatial dimension.