Abstract We overview the second solution of the Dirac equation for hydrogen atoms that became legitimate with the allowance for the actual charge density distribution inside the protons. It led to the possible existence of hydrogen atoms having only the S-states and therefore not interacting with the electromagnetic radiation – remaining dark . The actual existence of such Second Flavor of Hydrogen Atoms (SFHA) is evidenced by three different types of atomic experiments. In addition to their application for explaining the atomic experiments, they were the basis for resolving the long-standing puzzle of the neutron lifetime. Also, the SFHA was the basis for explaining the baffling astrophysical observation of the anomalous absorption in the 21 cm line from the early Universe, what made the SFHA the leading candidate for baryonic dark matter. Further, by comparing astrophysical observations with atomic experiments, it was demonstrated that the SFHA constitutes the majority of baryonic dark matter. Lastly, it was shown that neutron stars slowly but continuously generate new baryonic dark matter in the form of the SFHA and that there is astrophysical evidence of this process.

Abstract A lattice gas model with short-range interactions is considered in this paper. Through Monte Carlo simulations, it was found that the system shows glassy relaxation behaviors. Moreover, an exotic hexagonal tiling order emerges at low temperatures. Similar real-space configurations have been observed in an alloy before. The novel order also brings about novel percolations. The order and the percolations have profound effects on the dynamics of the system and are responsible for the dynamic heterogeneity.

Abstract This work examines the Casson nanofluid flow on a varying porous bi-directional stretchable sheet that has not yet conducted with effects of inclined magnetic field by incorporating Levenberg-Marquardt back propagation (LMBP) through ANN approach. The effect of temperature and space dependent heat sources have incorporated in energy equations along with thermal radiations effects. The flow system is affected by magnetic field in inclined direction. The diffusions of mass and heat has controlled through the use of thermophoresis and Brownian motion effects. In this examination the boundary value solver (bvp4c) serves as the data source for artificial neural networks (ANNs) known as Levenberg-Marquardt back-propagation (LMBP). As outcomes of this study, it has established that both primary and secondary velocities are retarded with growth in magnetic factor, variable porous factor and concentration of nanoparticles. Thermal profiles have amplified with escalation in radiation factor, thermal dependent heat source factor, nanoparticles concentration, thermal Biot number and thermal relaxation time factor. Concentration distribution amplified with progression in thermophoresis factor and concentration Biot number while deteriorated with surge in Schmidt number and mass relaxation time factor. For all the eight cases the gradient values are associated at 3.6671 × 10 −6 , 8.88 × 10 −6 , 8.32 × 10 −6 , 7.5442 × 10 −7 , 2.38 × 10 −8 , 8.34 × 10 −7 , 8.70 × 10 −7 and 8.35 × 10 −7 with corresponding epochs 790, 712, 692, 864, 1,000, 1,000, 864 and 712. The outcomes of this study can be applied in various engineering and industrial processes where heat and mass transfer play a critical role, such as cooling of electronic devices, polymer processing, thermal management in energy systems, and biomedical engineering involving nanofluids.

Abstract In this mini-review, we summarize one of the most widely used methodologies for obtaining exact wave solutions of nonlinear partial differential equations (NLPDEs), with a particular focus on traveling-wave solutions, which are of significant interest in physical systems. We then survey some fractional extensions of this approach, illustrating how the same methodology has been adapted to derive exact wave solutions within the framework of fractional NLPDEs.

Abstract The study of nonlinear partial differential equations through analytical methods is arguably the most important and fascinating to grasp various complex physical and engineering phenomena. The positive Gardner–Kadomtsev–Petviashvili equation, which combines the dimensions effects of the KP equation with the dispersion properties of the Gardner equation, is investigated in this study. Non-linear wave systems, fluid dynamics, plasma physics, and wave interactions are all explained by this equation. A Hamiltonian formulation is presented, followed by chaos analysis, which visualizes fractal structures and reveals underlying deterministic patterns in seemingly random systems. A new extended algebraic method is introduced to solve the positive–Gardner-KP equation, yielding rational, exponential, and trigonometric solutions. The graphical propagation of soliton solutions is examined, illustrating their behavior under various parametric conditions. The results highlight the efficiency of the proposed method in understanding the dynamics of shallow water waves, particularly in the absence of surface tension and viscosity, with implications for atmospheric and oceanic wave phenomena.

Abstract In a recent paper (Open Physics 2021;19:679–682), Khalil Salim Al-Ghafri investigated the soliton structures of the integrable Kundu–Mukherjee–Naskar (KMN) equation in optical fiber communication. Some exact solutions such as the W-shaped soliton solution, the bright soliton solutions (type-I and type-II) and dark soliton solution are derived using the ansatz approach. In this erratum article, we show that all these four solutions presented in Open Physics 2021;19:679–682 do not satisfy the original KMN equation; hence they are not the exact solutions of the integrable KMN equation.

Abstract This study examines a new method for comprehending diffusion and electrical conductivity tensors in the F-region of ionospheric plasma at low latitudes. The research formulates equations for the real diffusion coefficients by combining electrical conductivity and diffusion processes into a single analytical equation. The coefficients of diffusion and electrical conductivity possess both real and imaginary components as a result of the Earth’s real magnetic field configuration. At low latitudes, the constituents of the diffusion tensor display elevated values at night compared to those during the daytime. It has been observed that magnetic diffusion coefficient ratios are minimum in conditions such as equinox days and periods of increased solar activity. This illustrates the impact of solar activity on fluctuations in electron density and ionospheric conductivity. This research examines the equator and demonstrates variability with respect to latitude and temporal factors. The results highlight the influence of the equatorial anomaly on ionospheric diffusion, specifically on the transport of ionized particles caused by the E × B drift, which results in areas of fluctuating electron density. The ultimate goal of this work is to provide numerical evaluations that address a gap in ionospheric transport processes research by integrating diffusion and conductivity into a functional correlation, thus establishing a foundation for future studies.

Abstract This study presents the successful synthesis of an innovative nanospherical As( iii ) oxoiodide/iodide-intercalated poly( N -methylpyrrole) composite (As( iii )OI/I-PNMP NS composite), which serves as an n-type active layer in a high-performance photodetector. The composite is coated onto a polypyrrole (PPy) base, creating a novel As( iii )OI/I-PNMP/PPy heterojunction device that efficiently senses photons. Structural analysis of the synthesized composite shows uniformly distributed spherical nanoparticles, averaging around 100 nm in diameter, on a rough, highly textured surface that improves light–matter interaction. It exhibits a promising crystallite size of 21 nm and an optimal bandgap of 2.35 eV, facilitating effective absorption across a broad spectral range. The optoelectronic performance of the photodetector was systematically tested under varying illumination conditions, employing photons from both UV and visible (Vis) regions. During illumination, the photoresponse was analyzed using current density measurements ( J ph ), highlighting the composite’s essential role in charge carrier generation and transport. The device’s photoresponsivity ( R ) was notably improved, achieving values between 0.23 and 0.28 mA/W, reflecting the material’s high sensitivity to incoming light. Furthermore, the detectivity ( D ), an important performance metric for photodetectors, was calculated to be between 0.52 × 10 8 and 0.63 × 10 8 Jones, indicating excellent proficiency in detecting low-intensity optical signals. In summary, incorporating As( iii )OI with I-doped PNMP into a PPy-based structure signifies a promising strategy for developing broadband, high-efficiency photodetectors, with significant potential for future use in optoelectronic sensing and imaging technologies.

Abstract The gauge invariance is an important phenomenon widely occurring in various matters with many-body interactions. The gauge theories are very important for understanding the evolution of fundamental physical processes in particle physics, high-energy physics, and condensed matter physics. In this work, the origin of nonlocal effects is inspected, and the contributions of nontrivial topological structures to physical properties are investigated in detail for both the three-dimensional (3D) Ising model and the 3D Z 2 lattice gauge model. Then, the exact solution for the 3D Z 2 lattice gauge theory is derived by the duality between the two models. The partition function, the spontaneous magnetization, the true range of correlation, and the critical point are rigorously derived for the 3D Z 2 lattice gauge theory. The critical exponents of the 3D Z 2 lattice gauge theory are in the same universality class as the 3D Ising model, which are α = 0, β = 3/8, γ = 5/4, δ = 13/3, η = 1/8, and ν = 2/3. Several fundamental issues, such as dimensionality, duality, symmetry, manifold and degenerate states, are investigated for these many-body interacting spin systems. The connections with superfluid, superconductors, particle physics, etc. are evaluated. Furthermore, physical significances and mathematical aspects of the 3D Z 2 lattice gauge theory are discussed with respect to topology, geometry, and algebra. The present results for the 3D Z 2 lattice gauge theory are helpful for figuring out the basic features of 3D lattice gauge theories with other symmetries, such as U(1), SU(2), and SU(3). This work shines a light on the interdisciplinarity between many-body interacting systems, algebra, topology, and geometry.

Abstract Carbon nanotubes (CNTs), formed by rolling graphene sheets into cylindrical shapes, are widely used in the development of next-generation lithium-ion batteries due to their outstanding thermal conductivity and large surface area, which enhance electrode performance, enable faster charging, and improve energy capacity. Inspired by such a fascinating application of CNTs, the present investigation examines the flow behavior of an aqueous-based nanofluid containing multi-walled carbon nanotubes (MWCNTs), utilizing the well-established Yamada–Ota thermal conductivity model to assess the influence of nanoparticle radius and length. The proposed flow model novelty lies in incorporating Marangoni convection and temperature-dependent thermophysical properties. The governing partial differential equations are transformed into ordinary differential equations through appropriate similarity transformations. Numerical solutions are obtained using the boundary value problem solver bvp4c, with results illustrated through graphs and tables. The findings indicate that thermal conductivity reaches its peak at specific nanoparticle length L = 25 × 10 − 6 L=25\times {10}^{-6} and radius values R = 150 × 10 − 9 R=150\times {10}^{-9} . Optimizing the length-to-radius ratio of MWCNTs in nanofluids can greatly improve thermal conductivity in high-performance electronic cooling systems as extended nanotube lengths enhance heat transfer, while increased radii tend to reduce it. Additionally, Marangoni convection leads to a reduction in temperature distribution while enhancing the heat transfer rate. An increase in the variable temperature parameter results in a corresponding rise in the temperature profile. Validation of the proposed model is also included in this study.