Volume 80, Issue 4

The concept of the oxidation state of an atom in a chemical compound is formulated in terms of the quantum theory of many-electron systems and illustrated by calculations of oxidation numbers of calcium(I, II), phosphorus(0–V), sulfur(0–VI), fluorine(–I), oxygen(–II), and krypton(0) in CaCB 11 H 6 Cl 6 , CaCB 11 H 12 , CaC 5 H 5 , C a ( C 5 H 5 ) 2 $\mathrm{C}\mathrm{a}{\left({\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{5}}\right)}_{\mathrm{2}}$ , Ca@C 60 , P@C 60 , PF, PF 3 , PF 5 , POF 3 , P 4 O 6 , P 4 O 10 , SO, OSSO, SO 2 , SF 2 , SF 4 , SF 6 , SOF 4 , SO 2 F 2 , S 3 O 9 , and Kr@C 60 molecules. In [ P O 4 ] 3 − @ a q u a ${\left[\mathrm{P}{\mathrm{O}}_{\mathrm{4}}\right]}^{\mathrm{3}-}\mathrm{@}aqua$ , [ P 3 O 9 ] 3 − @ a q u a ${\left[{\mathrm{P}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{9}}\right]}^{\mathrm{3}-}\mathrm{@}aqua$ , [ P F 6 ] − @ a q u a ${\left[\mathrm{P}{\mathrm{F}}_{\mathrm{6}}\right]}^{-}\mathrm{@}aqua$ , [ S O 3 ] 2 − @ a q u a ${\left[\mathrm{S}{\mathrm{O}}_{\mathrm{3}}\right]}^{\mathrm{2}-}\mathrm{@}aqua$ , and [ S O 4 ] 2 − @ a q u a ${\left[\mathrm{S}{\mathrm{O}}_{\mathrm{4}}\right]}^{\mathrm{2}-}\mathrm{@}aqua$ ions, high oxidation states of phosphorus(V) and sulfur(IV, VI) are realized.

In this study, we conduct a comprehensive investigation of the novel characteristics of the (2 + 1)-dimensional stochastic Hirota–Maccari System (SHMS), which is a prominent mathematical model with significant applications in the field of nonlinear science and applied mathematics. Specifically, SHMS plays a critical role in the study of soliton dynamics, nonlinear wave propagation, and stochastic effects in complex physical systems such as fluid dynamics, optics, and plasma physics. In order to account for the abrupt and significant fluctuation, the aforementioned system is investigated using a Wiener process with multiplicative noise in the Itô sense. The considered equation is studied by the new extended direct algebraic method (NEDAM) and the modified Sardar sub-equation (MSSE) method. By solving this equation, we systematically derived the novel soliton solutions in the form of dark, dark-bright, bright-dark, singular, periodic, exponential, and rational forms. Additionally, we also categorize and analyze the W -shape, M -shape, bell shape, exponential, and hyperbolic soliton wave solutions, which are not documented by researchers. The bifurcation, chaos and sensitivity analysis has been depicted which represent the applicability of the system in different dynamics. These findings greatly advance our knowledge of nonlinear wave events in higher-dimensional stochastic systems both theoretically and in terms of possible applications. These findings are poised to open new avenues for future research into the applicability of stochastic nonlinear models in various scientific and industrial domains.

In a series of our papers ( e . g ., A.L. Kholmetskii, et al. Ann. Phys . 392 , 49 (2018)) we proposed to redefine the momentum operator for an electrically charged quantum particle in an electromagnetic (EM) field through the sum of its mechanical momentum ( P M ) and the interactional electromagnetic momentum ( P EM ), instead of the standard definition of this operator, associated with the canonical momentum of the particle. In the present contribution, we represent our three-step way to the new momentum operator and focus on one of its principal implications, named the “generalized Heisenberg uncertainty relation”, where, in comparison to its standard form, the mechanical momentum of a charged particle P M is replaced by the sum of P M and P EM . We then apply the generalized uncertainty relation to the analysis of the Fermi motion of quarks in the proton and neutron and show that a quark with a unique charge ( i.e ., the d -antiquark in the proton and the u -antiquark in the neutron) should have a more narrow momentum distribution compared to the wider momentum distribution of the remaining quarks (the two u -quarks in the proton and the two d -quarks in the neutron) in their Fermi motion. The agreement of these results with the available experimental data does not touch the validity of the results of calculation of quantum chromodynamics (QCD) regarding the description of the proton and neutron, but rather enriches their physical interpretation.

The thermal convection of compressible, partially ionized plasma has been investigated using nonlinear and linear analyses across three boundary configurations. Nonlinear analysis was carried out via the energy method, while linear analysis was assessed using the normal mode method. For free-free boundaries, exact solutions were obtained, whereas, for rigid-rigid and rigid-free boundaries, the higher-order Galerkin-weighted residual method was employed for numerical results. The critical Rayleigh numbers for both analyses coincide, indicating global stability and confirming the absence of subcritical regions. The impact of collisional frequency on energy decay was quantified, revealing a significant effect on the decay rate, although it does not affect the Rayleigh number. The principle of exchange of stabilities was confirmed in the linear analysis. Compressibility delays the onset of convection. The critical Rayleigh numbers were computed as 986.267, 2,561.64, and 1,650.97 for the free–free, rigid–rigid, and rigid–free cases, respectively, demonstrating that plasma confined between rigid–rigid surfaces exhibits the highest thermal stability.

This study investigates a bifunctional cloak composed of concentric metamaterials arranged in 4N thin layers, where N denotes the number of periodic layer pairs within the structure. The structure includes an inner circular domain, an outer domain, and alternating sequences of 2N layers between them. We explore two models: one using isotropic materials and another one using anisotropic materials. The anisotropic model demonstrates superior cloaking performance for both electrical and thermal fields. Analytical solutions based on the Effective Medium Theory and boundary-value problems reveal the structure’s response under quasi-static conditions. Numerical simulations using COMSOL validate these findings, highlighting the cloak’s and concentration’s ability to manipulate external thermal and electric fields efficiently.

Two-dimensional transition metal dichalcogenides (TMDCs) stand as pivotal materials with extraordinary physical and chemical properties, showcasing immense potential across various fields including sensors, catalysts, medicine, energy storage, and conversion. Among these, molybdenum disulfide (MoS 2 ), a prominent TMDCs member, has captured considerable attention due to its graphene-like layered structure, small band gap (∼1.8 eV), and superior theoretical capacity relative to graphene. This review paper has meticulously presented an analysis of MoS 2 structural properties encompassing various phases 2H (hexagonal), 1T (trigonal), and 3R (rhombohedral) alongside their respective lattice constants. Additionally, diverse synthesis approach like hydrothermal, sol–gel, and solvothermal methods have been discussed. The primary emphasis of this review has been MoS 2 applications in energy storage, specifically its role in lithium-ion batteries and supercapacitors. This review underscores the significant impact of MoS 2 in advancing energy-related technologies and hints at its potential in catalysts and sensors for medical and energy conversion applications.

The exploration of high-performance coatings is specifically necessary for enhancing the mechanical, thermal, and corrosion-resistant characteristics of structural steels in response to the demand for cutting-edge materials in engineering applications. The current study addresses an existing void in the development of durable coatings that gain benefits from the distinctive characteristics of CoCrFeNiCu high entropy alloys (HEA) for stainless steel substrates, with a particular emphasis on SS 304. The primary objective was to examine the microstructural, mechanical, and corrosion behaviors of SS 304 that had been coated with CoCrFeNiCu HEA employing a microwave cladding process. HEA particles were prepared through mechanical milling, and a controlled cladding process was conducted under an inert environment. A variety of meticulous investigations, including Scanning Electron Microscopy (SEM), X-ray Diffraction (XRD), and wear rate measurements, have been performed to thoroughly assess crucial parameters, including surface hardness, resistance to corrosion, and wear behavior. This study explores the influence of a CoCrFeNiCu high entropy alloy (HEA) coating (20 % each component) on SS-304 steel. Utilizing microwave cladding, the coating demonstrated a substantial impact on wetting behavior, interfacial microstructure, hardness, and corrosion resistance. Surface hardness was substantially enhanced by the cladding process, resulting in a 54.76 % rise from 210 HV to 325 HV. This enhancement substantially raised the mechanical strength of the steel. Under 120 h of corrosion testing in 3.5 wt.% NaCl, a minimal weight loss of 0.342 mg was observed, suggesting that the material exhibited substantial corrosion resistance. In addition, the material’s capacity to resist abrasive forces has been demonstrated by the relatively minimal wear rate of 0.0012 mm 3 /m that was noticed throughout wear resistance experiments. Effective interfacial adhesion, bonding strength, and uniform distribution were observed by the coating, which resulted in enhanced mechanical characteristics and durability in harsh circumstances. Wetting characteristics indicated enhanced hydrophobicity/hydrophilicity compared to the uncoated surface. SEM images displayed a well-adhered, homogeneous interfacial region, signifying a robust metallurgical bond. The cladding surface exhibited a uniform distribution of CoCrFeNiCu HEA particles. Notably, the steel’s surface hardness increased by approximately 54.76 % postdeposition. These findings underscore the potential of CoCrFeNiCu HEA coatings in advancing steel surface properties for improved performance and durability. The potential of CoCrFeNiCu HEA coatings to enhance the performance and longevity of SS 304 steel in chemical, marine environments, etc., applications that necessitate superior resistance to wear, protection against corrosion, and structural or mechanical integrity is underscored by these findings.