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The Van der Pol differential equation was constructed for an autonomous regime using link's law. The Van der Pol equation was studied analytically to determine fixed points, stability criteria, existence of limit cycles and solved numerically. The graphs of the equation are drawn for different values of damping coefficient μ., 1 Introduction Balthazar Van der Pol (1899-1959) was a Dutch electrical engineer who initiated experimental dynamics in the laboratory during the 1920's and 1930's. He first introduced his (now famous) [...]

Studies of the effects of SiO2 and CO2 absorption on pristine single walled magnesium oxide nanotube (SWMgONT) were done by means of density functional theory. This research considered SiO2 and CO2 gases as our case study because literature studies revealed that SWMgONT acted against CO and NO gases. Based on the results calculated, it has been found that the band gap of SWMgONT is closed as a result of absorption of either SiO2 or CO2 which transformed it from semiconductor state to conductor state. The general decrease in the HOMO–LUMO energy gap of SWMgONT upon absorption of these gases exposes SWMgONT as a promising candidate for sensor applications. In terms of optical absorption, the calculated optical band gap of 2.5 eV which fell in the range 1.2 eV – 2.8 eV exposed the pristine SWMgONT as better photocatalyst. SWMgONT showed higher absorptions with SiO2 and CO2, higher optical refractions and transmissions were also observed as a results of interactions with these gases. So there are significant differences in the absorption spectra for SWMgONT, SiO2MgONT and CO2@MgONT even thou they have the same geometric configurations. The presence of absorption peaks above 2 eV revealed that SiO2@MgONT and CO2@MgONT are potential candidates for the next generations UV–Vis sustainability science and technology such as LED, TMTs and optical lens applications. [ABSTRACT FROM AUTHOR]

The solution to Einstein's gravitational field equations exterior to time varying distributions of mass within regions of spherical geometry is used to study the behaviour of test particles and photons in the vicinity of the mass distribution. Equations of motion are derived and an expression for deflection of light in this gravitational field is obtained. The expresion obtained differs from that in Schwarzschild's field by a multiplicative time dependent factor. The concept of gravitational lens in this gravitational field is also studied., 1 Introduction In [1], the covariant metric tensor exterior to a homogeneous time varying distribution of mass within regions of spherical geometry is defined as: [g.sub.00] = - [1 + [...]

This paper deals with the problem of steady laminar flow of viscous incompressible fluid between two parallel porous plates with bottom injection and top suction. The flow is driven by a pressure gradient [partial derivative]p/∂x and uniform vertical flow is generated i.e. the vertical velocity is constant everywhere in the field flow i.e. v = [v.sub.w] = constant. Also a solution for the small and large Reynold number is discussed and the graph of velocity profile for flow between parallel plates with the bottom injection and top suction for different values of Reynold numbers is drawn., 1 Introduction The two dimensional steady laminar flow in channels with porous walls has numerous application in field of Science and Engineering through boundary layer control, transpiration cooling and biomedical [...]

Einstein's planetary equation can be solved by the method of successive approximations. This yields two linearly independent solutions. An analytical solution is presented for this equation. This solution produces eight linearly independent mathematical solutions, two of which are given approximately by the well-known method of successive approximations., 1 Introduction Einstein's planetary equation is given [1] by [d.sup.2]u/d[[phi].sup.2] + u -k/[l.sup.2] = 3k/[c.sup.2] [u.sup.2] (1) where [phi] and u are the instantaneous angular and reciprocal radial displacements of [...]

The conditions for the Sun and oblate spheroidal planets in the solar system to reduce to black holes is investigated. The metric tensor exterior to oblate spheroidal masses indicates that for the Sun to reduce to a black hole, its mass must condense by a factor of 2.32250 x [10.sup.5]. Using Schwarzschild's metric, this factor is obtained as 2.3 649 x [10.sup.5]. Similar results are obtained for oblate spheroidal planets in the solar system., 1 Introduction It is well known that whenever an object becomes sufficiently compact, general relativity predicts the formation of a black hole: a region of space from which nothing, not [...]

In this article, the gravitational scalar potential due to an oscillating electric dipole antenna placed in empty space is derived. The gravitational potential obtained propagates as a wave. The gravitational waves have phase velocity equal to the speed of light in vacuum (c) at the equatorial plane of the electric dipole antenna, unlike electromagnetic waves from the dipole antenna that cancel out at the equatorial plane due to charge symmetry., 1 Introduction Gravitational waves were predicted to exist by Albert Einstein in 1916 on the basis of the General Theory of Relativity. They are usually produced in an interaction between [...]

The motion of test and photons in the vicinity of a uniformly charged spherically symmetric mass distribution is studied using a newly developed relativistic dynamical approach. The derived expressions for the mechanical energy and acceleration vector of test particles have correction terms of all orders of [c.sup.-2]. The expression for the gravitational spectral shift also has additional terms which are functions of the electric potential on the sphere., 1 Introduction In a recent article [1], the relativistic dynamical approach to the study of classical mechanics in homogeneous spherical distributions of mass (Schwarzschild's gravitational field) was introduced. Here, the [...]

Graphitic Carbon Nitride (g-C 3 N 4) photocatalyst is considered a prime material for environmental remediation and solar energy conversion application. It drew attention in the field of artificial photosynthesis, i.e. solar fuel (hydrogen) generation via photocatalytic water splitting due to its high chemical and thermal stability, appealing optical properties, low cost, suitable band structure, non-toxicity, easy synthesis, and/or visible light band gap (∼2.7 eV) Herein, this review focuses on the recent advances on g-C 3 N 4 -based materials for efficient solar fuel (Hydrogen) generation via photocatalytic water-splitting, especially synthesis approach, morphological strategies (0D, 1D, 2D, and 3D, g-C 3 N 4)), modification of g-C 3 N 4 including doping strategies and heterostructure formation. Different challenges associated with g-C 3 N 4 , hindering its overall performance are also identified. Also, the recent advancement of g-C 3 N 4 -based materials towards solar fuel (hydrogen) generation application is reviewed. The preparation approach for g-C 3 N 4 , photocatalytic reaction and structural and electronic modification are reviewed. Importantly, the solar H 2 production improvements achieved in the study of the g-C 3 N 4 material as the main photocatalyst have been exclusively reviewed and discussed. Based on the findings in this review, Ti 3 C 2 /N,S-TiO 2 /g-C 3 N 4 is the compound with highest hydrogen production rate of 49506 μmol h−1 g−1, using thermal annealing and ultrasonic assisted impregnation method with H 2 O as the only sacrificial agent. Thus, this review would likely motivate researchers to broaden the applications for g-C 3 N 4 -based materials in solar fuel (hydrogen) generation. • Synthesis approach of g- C 3 N 4 -based material was reviewed and discussed. • Modification strategies of g-C 3 N 4 were discussed in details. • Challenges associated with g-C 3 N 4 , hindering its overall performance are also identified. • The recent advances of g-C 3 N 4 towards hydrogen generation application was reviewed. [ABSTRACT FROM AUTHOR]

As a semiconductor material, graphitic carbon nitrate (g-C 3 N 4) has gained a remarkable interest and attracted the attention of many scholars in environmental photocatalysis, due to its outstanding properties such as: low toxicity, easy synthesis, good thermal and electronic properties, suitable energy band gap (∼2.7 eV), and/or visible light absorption. However, despite all these unique properties there are still some drawbacks that affect its photocatalytic performance for H 2 generation via photocatalytic water-splitting such as; massive charge carriers' recombination, low surface area and low visible light absorption. A lot of attempts and/or efforts has been made to address these drawbacks for better performance of g–C 3 N 4 –based material. However, despite all these attempts, there is still little review papers that discuss more on the recent synthesis method and strategies to enhance the performance of g–C 3 N 4 –based photocatalyst. Herein, this review focused on recent development and future prospect to enhance the photocatalytic H 2 performance of g–C 3 N 4 –based photocatalyst for photocatalytic water splitting. The study also goes further to discuss more on the structure and properties of g-C 3 N 4 , important of H 2 as a fuel, photocatalysis, water splitting (H 2 and O 2 evaluation reaction), recent synthesis methods, forming heterojunctions, loading sacrificial reagent, and elemental doping, as well as photocatalytic performance of H 2 generation of g–C 3 N 4 –based materials. This review has explored the necessary roadmap of achieving higher H 2 generation rate using g–C 3 N 4 –based photocatalysts. [Display omitted] • Structure and properties of g-C 3 N 4 for photocatalytic H 2 generation were discussed. • Recent synthesis approaches of g-C 3 N 4 and the most appropriate method of preparation was discussed. • Hydrogen production using g-C 3 N 4 as main photocatalyst and that of g-C 3 N 4 -based materials were also reviewed. • Modification strategies to improved hydrogen production using g-C 3 N 4 photocatalyst were discussed. [ABSTRACT FROM AUTHOR]

This study investigated the photocatalytic properties of MoS 2 -doped boron nitride nanotubes (BNNTs) for overall water splitting using popular density functional theory (DFT). Calculations of the structural, mechanical, electronic, and optical properties of the investigated systems were performed using both the generalized gradient approximation and the GW quasi-particle correction methods. In our calculations, it was observed that only (10, 10) and (12, 12) single-walled BNNTs (SWBNNTs) turned out to be stable toward MoS 2 doping. Electronic property calculations revealed metallic behavior of (10, 10)-MoS 2 -doped SWBNNTs, while the band gap of (12, 12) SWBNNT was narrowed to 2.5 eV after MoS 2 doping, which is within the obtained band gaps for other photocatalysts. Hence, MoS 2 influences the conduction band of pure BNNT and improves its photocatalytic properties. The water-splitting photocatalytic behavior is found in (12, 12) MoS 2 -doped SWBNNT, which showed higher water oxidation (OH - /O 2 ) and reduction (H + /H 2 ) potentials. In addition, optical spectral calculations showed that MoS 2 -doped SWBNNT had an optical absorption edge of 2.6 eV and a higher absorption in the visible region. All of the studied properties confirmed MoS 2 -doped SWBNNT as a better candidate for next-generation photocatalysts for hydrogen evolution through the overall water-splitting process., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)