物理与天体物理最新文献

Lagrangian multiform theory is a variational framework for integrable systems. In this article, we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a finite-dimensional integrable hierarchy on an equal footing. This formulation allows a streamlined one-step derivation of both the multi-time Euler–Lagrange equations and the closure relation (encoding integrability). We argue that any Lagrangian one-form for a finite-dimensional system can be recast in our new framework. This framework easily extends to non-commuting flows, and we show that the equations characterising (infinitesimal) Hamiltonian Lie group actions are variational in character. We reinterpret these equations as a system of compatible non-autonomous Hamiltonian equations.

This review provides a comprehensive overview of Myrzakulov gravity, emphasizing key developments and significant results that have shaped the theory’s current understanding. The paper explores the foundational principles of this modified gravity framework, delving into the intricate structure of field equations, the incorporation of non-metricity, and the role of torsion in determining gravitational interactions. The theory’s implications extend beyond traditional gravitational physics, offering new perspectives on cosmology, astrophysical phenomena, and the behavior of matter and energy in the presence of strong gravitational fields. A particular focus is placed on the formulation of field equations within Myrzakulov gravity and their relation to standard Einstein-Hilbert theory, highlighting how the introduction of additional geometric terms and scalar fields influences the dynamics of the universe. The role of non-metricity is examined in detail, revealing how it modifies the geodesic motion and curvature of spacetime, leading to distinct observable effects compared to General Relativity. We discuss the incorporation of the modified Einstein-Hilbert action, which allows for the accommodation of dark energy and dark matter in the context of cosmological expansion and structure formation. Additionally, the paper surveys the applications of Myrzakulov gravity to a variety of astrophysical scenarios, such as black holes, gravitational waves, and the cosmic acceleration observed in the late universe. These applications illustrate the potential of the theory to offer alternative explanations for phenomena typically attributed to dark matter and dark energy. The review also highlights important constraints derived from observational data, including cosmological measurements and tests of gravitational wave propagation, that help refine the model’s predictions and determine its compatibility with the current understanding of the universe. With a selective focus on the most impactful outcomes and experimental validations, this review aims to provide a concise yet thorough examination of Myrzakulov gravity, addressing both its theoretical underpinnings and observational constraints. By presenting the theory in the broader context of modified gravity approaches, we explore its potential to reshape fundamental physics and offer novel insights into the mysteries of the cosmos.

A facile strategy was used for the synthesis of chromium oxide nanoparticles using leaf extract of Tinospora cordifolia via sol–gel auto combustion method and its photocatalytic performance was observed. The green synthesized Cr₂O₃ nanoparticles were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), EDAX, UV–Vis spectroscopy, transmission electron microscopy (TEM), selected area electron diffraction (SAED), and photoluminescence (PL). XRD pattern confirmed the purity of Cr₂O₃ nanoparticles. The SEM images showed porosity of Cr₂O₃ NPs. The band gap, as determined using UV–visible spectra, was measured to be 3.41 eV. TEM images revealed the crystalline shape and size of the nanoparticles. The PL spectra showed the emission peak at around 465 nm. In this study, inter-molecular interactions were examined using Hirshfeld surface analysis. The green synthesized Cr₂O₃ nanoparticles exhibit photodegradation efficiency up to 89.74% against malachite green dye after 25 min of UV irradiation. This investigation assessed the antimicrobial properties of Cr₂O₃ nanoparticles synthesized via a green route using Tinospora cordifolia leaf extract. The results revealed significant antibacterial activity against a panel of microorganisms, including Gram-positive Staphylococcus sp., Bacillus sp., and Gram-negative bacteria (Klebsiella sp., E. coli), as well as potent antifungal activity against Aspergillus niger. Further, the interaction of Cr₂O₃ with key protein targets, FtsZ and DHFR, was evaluated using Autodock Vina. The molecular docking results indicated a strong binding affinity of Cr₂O₃ to the active sites of both FtsZ and DHFR proteins, with a docking score of − 2.66 and − 2.84, respectively.

When (gamma =frac{3}{2}), we construct some analytical solutions to the compressible Euler-Korteweg equations, where (gamma ) is the adiabatic exponent. For the one-dimensional case, we provide a self-similar analytical solution for the vacuum free boundary problem on a finite interval, the vacuum free boundary problem on a half line and the Cauchy problem, respectively. From the constructed solutions, we find that the free boundary for the vacuum free boundary problem on a finite interval expands out linearly in time, this is same to the case when the capillarity force is absent. But for the vacuum free boundary problem on a half line and the Cauchy problem, we find that the capillarity effect plays a crucial role in preventing the smooth solutions from blowing up. We also extend these results to the N-dimensional radially symmetric case and the three-dimensional cylindrically symmetric case, respectively.