International Journal of Mathematics and Physics

Influence of additive white noise forcing on solutions of mixed NLS equations

2024-05-15T07:31:27+00:00

In this paper, the influence of an additive white noise forcing term on the numerical solution for a class of deterministic nonlinear one-dimensional Schrödinger equations with mixed concave convex was studied, sub-super nonlinearities, that is, the stationary states and the blowing-up solutions. Such a perturbation occurs when the size of the noise, described by the real-value parameter is positive. The size of the noise is controlled by the parameter We also proved that as approaches zero, the solution of the perturbed problem converges to the unique trajectory of the deterministic equation, which is the solitary wave. The stochastic model appears to be more realistic, and one can observe, for small values of , a similar evolution phenomena about the solution as that given by the deterministic case. However, an explosion of the solution and a blow-up phenomena can be noted as becomes bigger.

Keywords: Nonlinear Schrödinger equation, Mixed nonlinearity, Blow-up phenomena, Finite difference scheme, White noise, Solvability.

Soft intersection almost subsemigroups of semigroups

2024-02-21T10:12:12+00:00

Semigroups are the building blocks of algebra as they have application in automata, coding theory, formal languages, and theoretical computer science. They are also used in the solutions of graph theory and optimization theory. For the advanced study of algebraic structures and their applications, ideals are essential. The generalization of ideals in algebraic structures is necessary for further research on algebraic structures. The main purpose of this paper is to present the notion of soft intersection almost subsemigroup of a semigroup, which is a generalization of soft intersection subsemigroup and investigate its basic properties in detail. In this context, we also obtain many striking relationships between almost subsemigroups and soft intersection almost subsemigroups concerning minimality, primeness, semiprimeness and strongly primeness.

Keywords: semigroups, soft intersection, algebraic structures, almost subsemigroup of a semigroup, graph theory, optimization theory, minimality, simplicity, semi-simplicity and strong simplicity.

Mass diffusion of MHD flow over an unsteady stretched surface with moving free stream

2024-04-10T10:10:06+00:00

An exploration is carried out to examine mass diffusion of unsteady ‘boundary layer’ (bl) motion of viscous liquid passed a stretched leaky piece with variable mass flux. For several engineering applications, moving free stream is considered here. This makes this research unique. The leading ‘partial differential equations’ (PDEs) accompanied by the ‘boundary conditions’ are converted to ‘ordinary differential equations’ (ODEs) with the help of ‘similarity transformations’ and ‘numerical solutions’ are attained by MATLAB software. The effect of pertinent ‘parameters’ on fluid ‘flow, concentration, skin friction coefficient’ and wall concentration are discussed ‘graphically’ and numerically. When suction/blowing parameter increases from -0.2 to 0.2, skin friction coefficient decreases 18.235%. Fluid concentration reduces with growing values of velocity ratio parameter for all cases considered. Compared to the case for static free stream, fluid velocity is higher when the free stream moves. Also higher concentration is noted in presence of moving free stream. The presence of moving free stream causes to diminish the effect of suction/blowing on flow and concentration fields. The increasing strength of suction causes to decrease the fluid velocity more significantly than that for blowing.

Keywords: Unsteady stretching sheet, MHD, Mass diffusion, Variable free stream, Variable mass flux.

Ether as an electro-gravimagnetic field, its density and properties

2024-05-14T05:35:53+00:00

Based on biquaternion wave (biwave) equations, a biquaternionic model of the ether is developed - an electro-gravimagnetic field, the state of which is described by the biquaternion of the strength of EGM field. Its complex scalar part determines the density of the ether, and the complex vector part characterizes the strength of the electric and gravimagnetic fields. The biquaternion gradient of the ether biquaternion determines the biquaternion of EGM charge-current, which contains in the scalar part the electric charge and gravitational mass, and the vector part is formed by electric and gravimagnetic currents. Special cases of these biwave equations are the biquaternionic representation of the Maxwell and Dirac equations. Representations of biquaternion of photons and elementary atoms are obtained as partial stationary solutions of biwave equations with a fixed oscillation frequency. The presence of a gravitational component of the EGM field of the photon is shown, which explains the light pressure. Using the biquaternion model of the atom, a periodic system of atoms is constructed based on the structure of a simple musical scale.
A field analogue of Newton's second law is presented as a biquaternion generalization of the Dirac system of equations. It describes the transformation of the EGM charge-current biquaternion under the influence of an external EGM field. It contains, in addition to all known physical forces, a number of new forces that are proposed for discussion and experimental verification.
The biquaternion representation of Newton's third law of action and reaction in the scalar part is a well-known analogue of Betti's law on the power of forces acting on EGM charges and currents.

Keywords: biquaternion wave, electro-gravimagnetic field, Betti's law, complex vector, bigradients.

A new transform for solving linear second-orders ODE with variable coefficients

2024-05-15T05:30:51+00:00

In this paper, we present a novel symmetry-enhanced transform
to evaluate Gaussian integrals commonly used in mathematical and
physical domains, particularly in quantum field theory. Additionally,
we utilize this original transformation methodology to solve a wide
range of second-order linear ordinary differential equations (ODEs)
that have variable coefficients, which is a common occurrence in physics.
Notable examples encompass Weber, Euler-Cauchy, and Bessel equa-
tions, highlighting the broad applicability of our proposed method.
Diverging from established transforms like the widely used Laplace
transform, our innovative approach introduces a symmetrical model,
offering a distinct and founding perspective to the field.

Keywords: New integral transform, Gaussian integral, Equation of free oscillations, Weber’s equation, Euler-Cauchy Equation, Bessel’s equation.

Comparing the efficiency of GPU and CPU in gravitational lensing simulation

2024-05-14T09:17:09+00:00

In this study, we investigate the computational advancements in simulating gravitational lensing, particularly focusing on the Schwarzschild black hole model. The traditional approach of back ray tracing, where photons are traced back from the observer to the source, is computationally intensive, especially when aiming to achieve high-resolution images of lensing effects around black holes. By employing a numerical method that integrates the Schwarzschild metric with initial conditions derived from the observer's plane, we map the deflection of light around a black hole to generate simulated images of gravitational lensing.
The core of our study is the comparison between traditional CPU-based computations and GPU-accelerated processes using the Numba library. Our findings reveal that GPU acceleration, with its parallel processing capabilities, significantly reduces computation time, particularly as the complexity of the simulation increases with larger grid sizes. This computational efficiency is crucial for simulations of gravitational lensing, where the number of independent calculations grows exponentially with the resolution and accuracy of the desired image.
Our research underscores the importance of leveraging GPU technology for astrophysical simulations, offering a substantial improvement in performance over CPU-based methods.

Keywords: Gravitational Lensing, GPU Parallelization, Schwarzschild Black Hole, Ray Tracing Methods, Numba Library.

Radiative characteristics of accretion disks around rotating regular black holes

2024-05-20T12:27:03+00:00

Our research focuses on examining the characteristics of thin accretion disks encircling rotating regular black holes. In this study, we investigate the important features of accretion disks surrounding Bardeen's regular black holes, which play a crucial role in addressing the singularity issue. The horizon configuration of rotating Bardeen black holes is analyzed in details, as well as the innermost stable circular orbits related to this spacetime. The primary goal is to derive quantitively the radiative flux, differential and spectral luminosities of the accretion disk. Within the specified gravitational field, particularly, by taking the parameter r_0*>0 and fixing the j=0.2, our findings show that the corresponding accretion disk’s luminosity exceeds that one predicted by the Kerr metric at identical value of spin parameter ( j=0.2). Making the juxtaposition of Bardeen’s black hole parameter with the spin parameter of the Kerr black hole we reveal that the spacetime corresponding to the non-rotating Bardeen black holes, in some certain cases, can imitate the Kerr spacetime.

Keywords: rotating Bardeen spacetime, angular velocity, angular momentum, energy and radiative flux.

Determination of variation of compositions of (1-х)ZnO-0.25Al2O3-0.25WO3-хBi2O3 glass-like ceramics on protective characteristics in gamma radiation shielding

2024-05-28T08:32:30+00:00

The work is devoted to the study of the effect of variation of the ratio of oxides in the composition of (1-х)ZnO-0.25Al₂O₃-0.25WO₃-хBi₂O₃ glass-like ceramics on shielding characteristics when employed as materials to mitigate the adverse effects of gamma radiation with different energy. The primary incentive behind these investigations is to discover novel protective shielding materials that lack lead or its oxide forms yet possess high shielding efficiency. Additionally, the aim is to identify the most promising compositions for potential practical applications in shielding. During the studies of shielding characteristics, it was observed that partial replacement of zinc oxide with bismuth oxide leads to a pronounced increase in shielding for low-energy gamma rays, for which, according to the data obtained, an increase in the concentration of bismuth oxide leads to an increase in the linear and mass coefficient by more than 0.8 – 1.2 times. An analysis of the influence of variations in the ratio of zinc and bismuth oxides in the composition of glass-like ceramics on the shielding characteristics revealed that the replacement of zinc oxide with bismuth oxide, leading to an elevation in density of the order of 10 – 15 %, leads to a steep rise in the shielding efficiency for low-energy gamma rays (more than 120 %), and to a 15 – 17 % growth in shielding efficiency in the case of gamma-quanta shielding for which the main interaction mechanisms are the Compton effect and the formation of electron-positron pairs.

Keywords: shielding materials, ionizing radiation, glass-like ceramics, absorption efficiency, oxide materials, gamma radiation.

Obtaining hydrophobic coatings from AR+HMDSO using radiofrequency discharge at atmospheric pressure

2024-05-30T12:08:03+00:00

Hydrophobic coatings have attracted much attention due to their wide applications in various industries including electronics, textiles, and automotive. This study deals with the process of creating nanoscale coatings on a substrate achieved by plasma polymerization using plasma flow (jet) using radiofrequency discharge together with the precursor c6h18osi2 and the carrier gas Ar. In this work, we investigate the production of hydrophobic coatings using radiofrequency (RF) discharge at atmospheric pressure using a mixture of argon (Ar) and hexamethyldisiloxane (HMDSO). RF discharge is a versatile and efficient method of plasma generation that allows the deposition of thin films with defined properties. Here we investigate the influence of process parameters such as gas flow rate, discharge power, and substrate temperature on the morphology, chemistry, and hydrophobicity of the deposited coatings. The formation of these coatings was carefully studied under atmospheric pressure conditions, varying the number of cycles of experiments while maintaining optimal plasma parameters. The properties and elemental composition of the coatings were thoroughly studied using scanning electron microscopy (SEM) and energy dispersion spectroscopy (EDS). In addition, the obtained coatings were found to possess hydrophobic properties. The hydrophobicity of these coatings was evaluated by measuring the contact angle with a goniometer with respect to cycles of experiments and long-term durability. This study contributes to a better understanding of the synthesis, structure, and hydrophobic characteristics of nanoscale coatings, opening promising perspectives for various applications. The results show that the hydrophobicity of the coatings can be optimized by tuning the process parameters, resulting in coatings with water contact angles greater than 160 degrees. Additionally, the durability and stability of the hydrophobic coatings are evaluated under different environmental conditions, allowing an assessment of their potential for practical applications.

Keywords: plasma polymerization, atmospheric pressure, superhydrophobic coatings.

On Zagreb Connection Indices of γ Graphyne and its Zigzag Nanoribbon

2024-02-10T12:01:55+00:00

Chemical graph theory is a branch of Mathematical Chemistry that deals with chemical/molecular graphs to predict molecules’ reactivity, stability, and topology through topological indices. γ graphyne is a carbon allotrope, a crystal lattice composed of one acetylene bond connecting two aromatic rings. Since there is no evidence of any economical method for its synthesis to date to study the physicochemical properties, reactivity, and stability, the in-silico methods can be of great help. In this paper, we have considered Zagreb connection indices, which haven’t been explored in a wide range despite their correlation with the physicochemical properties being better than classical Zagreb Indices. Here, Zagreb connection indices of γ graphyne have been calculated using the edge partition technique and their trend in characteristics has been plotted.

Keywords: Chemical graph theory, γ graphyne, Zagreb connection indices.

Vanadium oxides impact on the ZNO-SB2O3-B2O3 glasses dielectric and A.C. conduction mechanisms

2024-03-20T08:38:33+00:00

In the current study, we have looked into the glasses dielectric characteristics as a follow-up to our prior work on the influence of vanadium ions in spectral properties of ZnO-Sb₂O₃-B₂O₃ glasses. B₂O₃ glasses have garnered interest as dielectric materials in addition to their uses as optical functional materials. Glasses of ZnO-Sb₂O₃-B₂O₃ that ranged in V₂O₅ concentration (from 0 to 1.0 mol %) were created using the standard melt and quench procedure. It has been investigated how the samples dielectric constant (ε), dielectric loss (tan δ), and ac conductivity (σ_ac) change with temperature at various frequencies between 10² Hz and 10⁶ Hz. The results were examined in relation to the number of oxidation states of the vanadium ions.

Keywords: Borate glasses, Dielectric constant, ac conductivity, vanadium ions.