Search Results (623)

We describe some properties of the hyperbolically symmetric black hole (hereafter referred to as the $HSBH$) proposed a few years ago. We start by explaining the main motivation behind such an idea, and we determine the main differences between this scenario and the classical black hole (hereafter referred to as the $CBH$) scenario. Particularly important are the facts that, in the $HSBH$ scenario, (i) test particles in the region inside the horizon experience a repulsive force that prevents them from reaching the center, (ii) test particles may cross the horizon outward only along the symmetry axis, and (iii) the spacetime within the horizon is static but not spherically symmetric. Next, we examine the differences between the two models of black holes in light of the Landauer principle and the Hawking results on the eventual evaporation of the black hole and the paradox resulting thereof. Finally, we explore what observational signature could be invoked to confirm or dismiss the model. Full article

Vanillin photoinduced deprotonation was evaluated and analyzed. Vibronic states and transitions were computationally investigated. Optimizations and vertical electron transitions in the gas phase and with the continuum solvation model were computed using the time-dependent density functional theory. Static absorption and emission (photostatic optical) spectra were statistically averaged over the excited instantaneous molecular conformers fluctuating on quantum–classical molecular dynamic trajectories. Photostatic optical spectra were generated using the hybrid quantum–classical molecular dynamics for explicit solvent models. Conical intersection searching and nonadiabatic molecular dynamics simulations defined potential energy surface propagations, intersections, dissipations, and dissociations. The procedure included mixed-reference spin–flip excitations for both procedures and trajectory surface hopping for photodynamics. Insignificant structural deformations vs. hydroxyl bond cleavage followed by deprotonation were demonstrated starting from different initial structural conditions, which included optimized, transition state, and several other important fluctuating configurations in various environments. Vanillin electronic structure changes were illustrated and analyzed at the key points on conical intersection and nonadiabatic molecular dynamics trajectories by investigating molecular orbital symmetry and electron density difference. The hydroxyl group decomposed on transition to a σ-molecular orbital localized on the elongated O–H bond. Full article

In this work, the symmetries of a H₂⁺ molecule confined within potential energy wells of various shapes are highlighted. This system has been long regarded as a model for small molecules trapped in crystalline cavities and molecular cages; in this context, the role of symmetry assumes significant importance. Symmetries are determined by the well shape, molecular position, and orientation. They allow the classification of H₂⁺ states, the identification of fixed nodal surfaces for the identification of excited states in Monte Carlo simulations, and the estimation of potential energy surfaces. Full article

Using the Dixmier angle between two closed subspaces of a complex Hilbert space $\mathcal{H}$, we establish the necessary and sufficient conditions for the operator norm of the sum of two orthogonal projections, $P_{{\mathcal{W}}_1}$ and $P_{{\mathcal{W}}_2}$, onto closed subspaces ${\mathcal{W}}_1$ and ${\mathcal{W}}_2$, to attain its maximum, namely $\parallel P_{{\mathcal{W}}_1}+P_{{\mathcal{W}}_2}\parallel =2.$ These conditions are expressed in terms of the geometric relationship and symmetry between the ranges of the projections. We apply these results to orthogonal projections associated with a closed-range operator via its Moore–Penrose inverse. Additionally, for any bounded operator T with closed range in $\mathcal{H}$, we derive sufficient conditions ensuring $\parallel T{T}^{†}+T^{†}T\parallel =2,$ where $T^{†}$ denotes the Moore–Penrose inverse of T. This work highlights how symmetry between operator ranges and their algebraic structure governs norm extremality and extends a recent finite-dimensional result to the general Hilbert space setting. Full article

Air stability caused by the H₂O/CO₂ reaction at the layered oxide NaTMO₂ surface is one of the main obstacles to commercializing sodium-ion batteries (SIBS). The H₂O and CO₂ adsorption properties on the (100) surface of sodium layered transition metal oxide NaTMO₂ (TM = Co, Ni, Mo, Nd) are calculated using the DFT method to study the surface air stability. This study showed that the material bulk phase (symmetry), surface site, element type, and surface termination are all (though not the only) important factors that affect the adsorption strength. Contrary to previous studies, the P phase is not always more air-stable than the O phase; our calculations showed that the NaNiO₂ O phase is more stable than the P phase. The calculated band center and occupation showed a direct relationship with the adsorption energy. The Na site adsorption for CO₂ and H₂O showed the same V-shape trend. However, the TM adsorption for CO₂ and H₂O showed a different trend. With an increased t₂g band center, CO₂ adsorption strength increases. There is no clear trend for H₂O adsorption. Our calculations showed that the electronic structure of the surface atomic of adsorption site plays a decisive role in CO₂ and H₂O adsorption strength. This study demonstrated an effective method for obtaining a stability parameter regarding the electronic structure, which can be used to screen the air-stable layered oxide sodium cathode in the future. Full article

Residual stress plays a crucial role in determining the structural reliability and mechanical performance of nano-multilayers. In the present study, nano-multilayers composed of ZrO_xN_y and V₂O₃ were deposited via magnetron sputtering, with the N:Ar flow ratio systematically varied during the process. Through the precise control of the deposition conditions, the compressive residual stress within the films was effectively reduced to approximately 0 GPa, thereby improving their mechanical robustness. It was observed that the optimization of the stress distribution was strongly influenced by the structural symmetry of the multilayer configuration. This symmetrical design not only mitigated stress accumulation but also ensured uniform mechanical response throughout the multilayer structure. The results from nanoindentation testing revealed a steady hardness value near 10.6 GPa. Furthermore, the maximum H³/E² and H/E ratios recorded were 0.054 GPa and 0.073, respectively, suggesting enhanced resistance to both plastic deformation and cracking. Full article

In this paper, a novel type of polarization-insensitive terahertz metal metasurface with cross-shaped holes is presented, which is designed based on the theory of bound states in continuous media. The fundamental unit of the metasurface comprises a metal tungsten sheet with a cross-shaped hole structure. A thorough analysis of the optical properties and the quasi-BIC response is conducted using the finite element method. Utilizing the symmetry-breaking theory, the symmetry of the metal metasurface is broken, allowing the excitation of double quasi-BIC resonance modes with a high quality factor and high sensitivity to be achieved. Analysis of the multipole power distribution diagram and the spatial distribution of the electric field at the two quasi-BIC resonances verifies that the two quasi-BIC resonances of the metasurface are excited by electric dipoles and electric quadrupoles, respectively. Further simulation analysis demonstrates that the refractive index sensitivities of the two quasi-BIC modes of the metasurface reach $404.5 \mathrm{G}\mathrm{H}\mathrm{z}/\mathrm{R}\mathrm{I}\mathrm{U}$ and $578.6 \mathrm{G}\mathrm{H}\mathrm{z}/\mathrm{R}\mathrm{I}\mathrm{U}$, respectively. Finally, the functional material PHMB is introduced into the metasurface to achieve highly sensitive sensing and detection of CO₂ gas concentrations. The proposed metallic metasurface structure exhibits significant advantages, including high sensitivity, ease of preparation, and a high Q-value, which renders it highly promising for a broad range of applications in the domains of terahertz biosensing and highly sensitive gas sensing. Full article

Medium- and large-scale heat sinks are critical for thermal load management in high-performance systems. However, their high heat flux densities and limited space complicate cooling, leading to risks of overheating, performance degradation, or failure. This study employs the Cascaded Lattice Boltzmann Method (CLBM) to enhance their thermal performance. This numerical approach is known for being stable, accurate when dealing with complex boundaries, and efficient when computing in parallel. The numerical code was validated against a benchmark configuration and an experimental setup to ensure its reliability and accuracy. While previous studies have explored mixed convection in cavities or heat sinks, few have addressed configurations involving side air injection and boundary conditions periodicity in the transition-to-turbulent regime. This gap limits the understanding of realistic cooling strategies for compact systems. Focusing on mixed convection in the transition-to-turbulent regime, where buoyancy and forced convection interact, the study investigates the impact of Rayleigh number values ($5\times {10}^7$ to $5\times {10}^8$) and Reynolds number values (${10}^3$ to $3\times {10}^3$) on heat transfer. Simulations were conducted in a rectangular cavity with periodic boundary conditions on the vertical walls. Two heat sources are located on the bottom wall ($T_h$ = 50 °C). Two openings, one on each side of the two hot sources, force a jet of fresh air in from below. An opening at the level of the cavity ceiling’s axis of symmetry evacuates the hot air. Mixed convection drives the flow, exhibiting complex multicellular structures influenced by the control parameters. Calculating the average Nusselt number (Nu) across the surfaces of the heat sink reveals significant dependencies on the Reynolds number. The proposed correlation between Nu and Re, developed specifically for this configuration, fills the current gap and provides valuable insights for optimizing heat transfer efficiency in engineering applications. Full article

Modernizing and mechanizing agriculture are vital to increasing productivity and meeting the growing global food demand. Timely harvesting decisions, traditionally based on farmers’ experience, are crucial for crop management. This study introduces the Brinjal Harvesting Decision System (BHDS), an automated, real-time framework designed to optimize harvesting decisions using a portable, low-power edge computing device. Unlike conventional object detection models, which require substantial pre-training and curated datasets, the BHDS integrates automated data acquisition and dynamic image quality assessment, enabling effective operation with minimal data input. Tested on diverse farm layouts, the BHDS achieved 95.53% accuracy in data collection and captured quality images within an average of 3 s, reducing both time and energy for dataset creation. The brinjal detection algorithm employs pixel-based methods, including background elimination, K-means clustering, and symmetry testing for precise identification. Implemented on a portable edge device and tested in actual farmland, the system demonstrated 79% segmentation accuracy, 87.48% detection precision, and an F1-score of 87.53%, with an average detection time of 3.5 s. The prediction algorithm identifies ready-to-harvest brinjals with 89.80% accuracy in just 0.029 s. Moreover, the system’s low energy consumption, operating for over 7 h on a 10,000 mAh power bank, demonstrates its practicality for agricultural edge applications. The BHDS provides an efficient, cost-effective solution for automating harvesting decisions, minimizing manual data processing, reducing computational overhead, and maintaining high precision and operational efficiency. Full article

Let X be a compact Riemann surface of genus $g\ge 2$, G be a complex semisimple Lie group, and ${\mathcal{M}}_G\left(X\right)$ be the moduli space of stable principal G-bundles. This paper studies the fixed point set of involutions on ${\mathcal{M}}_G\left(X\right)$ induced by an anti-holomorphic involution $\tau$ on X and a Cartan involution $\theta$ of G, producing an involution $\sigma ={\theta }_{\ast }\circ {\tau }_{\ast }$. These fixed points are shown to correspond to stable $G_{\mathbb{R}}$-bundles over the real curve $(X_{\tau },\tau )$, where $G_{\mathbb{R}}$ is the real form associated with $\theta$. The fixed point set ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ consists of exactly $2^r$ connected components, each a smooth complex manifold of dimension ${\displaystyle \frac{(g-1)\dim G}{2}}$, where r is the rank of the fundamental group of the compact form of G. A cohomological obstruction in $H^2(X_{\tau },{\pi }_1\left(G_{\mathbb{R}}\right))$ characterizes which bundles are fixed. A key result establishes a derived equivalence between coherent sheaves on ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ and on the fixed point set of the dual involution on the moduli space of $G^{\vee }$-local systems, where $G^{\vee }$ denotes the Langlands dual of G. This provides an extension of the Geometric Langlands Correspondence to settings with involutions. An application to the Chern–Simons theory on real curves interprets ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ as a $(B,B,B)$-brane, mirror to an $(A,A,A)$-brane in the Hitchin system, revealing new links between real structures, quantization, and mirror symmetry. Full article

This study introduces a novel fractional-order derivative, termed the Mittag-Leffler–Caputo–Fabrizio (MLCF) fractional derivative, which is characterized by a singular kernel. Symmetry plays a key role in the structure and behavior of fractional operators, and our formulation reflects this by incorporating symmetric properties of the Mittag-Leffler function and its integral representation. To numerically approximate the MLCF derivative, we apply a two-point finite forward difference scheme to estimate the first-order derivative of the function $u(\lambda )$ within the integral component of the definition. This leads to the construction of a new numerical differentiation scheme. Our analysis demonstrates that the proposed approximation exhibits first-order convergence, with absolute errors decreasing as the time step size h diminishes. These errors are quantified by comparing our numerical results with exact analytical solutions, reinforcing the accuracy of the method. Full article

This study investigates the connection between coherent structures in the flow around a vehicle and the aerodynamic forces acting on its body. Dynamic Mode Decomposition (DMD) was applied to analyze the flow field of a squareback Ahmed body at $R{e}_H=7.7\times {10}^5$. DMD enabled the identification of coherent structures in the near and far wake by isolating their individual oscillation frequencies and spatial energy distributions. These structures were classified into three regimes based on their underlying mechanisms: symmetry breaking, bubble pumping, and large-scale vortex shedding in range of $St\le 0.2$. The energy contributions of these flow regimes were quantified across different regions of the flow field and compared to the aerodynamic forces on the body. Additionally, the linear correlation between pressure and velocity components was examined using Pearson correlation coefficients of DMD spectral amplitudes. The locations of maximum and minimum correlation values, as well as their relationship to energy contributions, were identified and analyzed in detail. Full article

This work investigated the optical characteristics of BaWO₄ nanoparticles that were produced through direct mechanochemical synthesis at varying speeds and times. This research expands upon our previous study. We demonstrated that the mechanochemical activation of the precursor of BaCO₃ and WO₃, at elevated milling speeds (850 rpm), facilitates the formation of tetragonal BaWO₄ in a reduced reaction time. The final products were characterized by scanning electron microscopy (SEM), as well as Raman, infrared (IR), UV-Vis diffuse reflectance, and photoluminescence spectroscopies. The crystallite sizes and particles shapes were determined by X-ray diffraction and SEM analysis. Round particles with a size below 50 nm formed under different milling conditions. The Raman spectra of the synthesized samples confirmed the presence of a scheelite-type structure with the typical six distinct vibrational peaks. The symmetry of the structural WO₄ groups was determined by IR spectroscopy. The absorption spectra of both samples exhibited intensive peaks at 210 nm, and the calculated optical band gaps of BaWO₄ were 5.10 eV (3 h/500 rpm) and 5.24 eV (1 h/850 rpm). A strong (400 nm) and weak (465 nm) emission were observed for the BaWO₄ that was obtained at a higher milling speed, while wider emission at 410 nm was visible for the BaWO₄ that was prepared at a lower milling speed. The CIE coordinates of the mechanochemically synthesized BaWO₄ were located within the blue area, exhibiting various positions. Full article

In the present work, we describe the use of the potentially tridentate ligand pyridine-2-amidoxime (NH₂paoH) in Fe-Co chemistry. The 1:1:3 Fe^III(NO₃)₃·9H₂O/Co^II(ClO₄)₂·6H₂O/NH₂paoH reaction mixture in MeOH gave complex [Co^III₂Fe^III(NH₂pao)₆](ClO₄)₂(NO₃) (1) in ca. 55% yield, the cobalt(II) being oxidized to cobalt(III) under the aerobic conditions. The same complex was isolated using cobalt(II) and iron(II) sources, the oxidation now taking place at both metal sites. The structure of 1 contains two structurally similar, crystallographically independent cations [Co^III₂Fe^III(NH₂pao)₆]³⁺ which are strictly linear by symmetry. The central high-spin Fe^III ion is connected to each of the terminal low-spin Co^III ions through the oximato groups of three 2.1110 (Harris notation) NH₂pao⁻ ligands, in such a way that the six O atoms are bonded to the octahedral Fe^III center ({Fe^IIIO₆} coordination sphere). Each terminal octahedral Co^III ions is bonded to six N atoms (three oximato, three 2-pyridyl) from three NH₂pao⁻ groups ({Co^IIIN₆} coordination sphere). The IR and Raman spectra of the complex are discussed in terms of the coordination mode of the organic ligand, and the non-coordinating nature of the inorganic ClO₄⁻ and NO₃⁻ counterions. The UV/VIS spectrum of the complex in EtOH shows the two spin-allowed d-d transitions of the low-spin 3d⁶ cobalt(III) and a charge-transfer NH₂pao⁻ → Fe^III band. The δ and ΔΕ_Q ⁵⁷Fe-Mössbauer parameter of 1 at 80 K show the presence of an isolated high-spin Fe^III center. Variable-temperature (1.8 K–300 K) and variable-field (0–7 T) magnetic studies confirm the isolated character of Fe^III. A critical discussion of the importance of NH₂paoH and its anionic forms (NH₂pao⁻, NHpao²⁻) in homo- and heterometallic chemistry is also attempted. Full article

Electrical transport in 2D materials exhibits unique behaviors due to reduced dimensionality, broken symmetries, and quantum confinement. It serves as both a sensitive probe for the emergence of coherent electronic phases and a tool to actively manipulate many-body correlated states. Exploring their interplay and interdependence is crucial but remains underexplored. This review integratively cross-examines the atomic and electronic structures and transport properties of van der Waals-layered crystals ZrTe₃, 2H-TaS₂, and Cr₂Si₂Te₆, providing a comprehensive understanding and uncovering new discoveries and insights. A common observation from these crystals is that modifying the atomic and electronic interface structures of 2D van der Waals interfaces using heteroatoms significantly influences the emergence and stability of coherent phases, as well as phase-sensitive transport responses. In ZrTe₃, substitution and intercalation with Se, Hf, Cu, or Ni at the 2D vdW interface alter phonon–electron coupling, valence states, and the quasi-1D interface Fermi band, affecting the onset of CDW and SC, manifested as resistance upturns and zero-resistance states. We conclude here that these phenomena originate from dopant-induced variations in the lattice spacing of the quasi-1D Te chains of the 2D vdW interface, and propose an unconventional superconducting mechanism driven by valence fluctuations at the van Hove singularity, arising from quasi-1D lattice vibrations. Short-range in-plane electronic heterostructures at the vdW interface of Cr₂Si₂Te₆ result in a narrowed band gap. The sharp increase in in-plane resistance is found to be linked to the emergence and development of out-of-plane ferromagnetism. The insertion of 2D magnetic layers such as Mn, Fe, and Co into the vdW gap of 2H-TaS₂ induces anisotropic magnetism and associated transport responses to magnetic transitions. Overall, 2D vdW interface modification offers control over collective electronic behavior, transport properties, and their interplays, advancing fundamental science and nanoelectronic devices. Full article