Current Issue : January-March Volume : 2025 Issue Number : 1 Articles : 5 Articles
In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential- sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixthorder hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments....
Metamaterials have emerged as a focal point in contemporary science and technology due to their ability to drive significant innovations. These engineered materials are specifically designed to couple the phenomena of different physical natures, thereby influencing processes through mechanical or thermal effects. While much of the recent research has concentrated on frequency conversion into electromagnetic waves, the field of acoustic frequency conversion still faces considerable technical challenges. To overcome these hurdles, researchers are developing metamaterials with customized acoustic properties. A key equation for modeling nonlinear acoustic wave phenomena is the dissipative Westervelt equation. This study investigates analytical solutions using ansatzbased methods combined with Lie symmetries. The approach presented here provides a versatile framework that is applicable to a wide range of fields in metamaterial design....
This study examines the effects of heat, mass, and boundary layer assumptions- based nanoparticle characteristics on the hybrid effects of using MHD in conjunction with mixed convective flow through a sloped vertical pore plate in the existence of medium of porous. Physical characteristics such as thermodiffusion, injection-suction, and viscous dissipation are taken into consideration, in addition to an equally distributed magnetic force utilized as well in the completely opposite path of the flow. By means of several non-dimensional transformations, the momentum, energy, concentration, and nanoparticle volume fraction equations under investigation are converted in terms of nonlinear boundary layer equations and computationally resolved by utilizing the sixth-order Runge-Kutta strategy in combination together with the iteration of Nachtsheim-Swigert shooting procedure. By contrasting the findings produced for a few particular examples with those found in the published literature, the correctness of the numerical result is verified, and a rather good agreement is found. Utilizing various ranges of pertinent factors, computing findings are determined not only regarding velocity, temperature, and concentration as well as nanoparticle fraction of volume but also concerning with local skin-friction coefficient, local Nusselt and general Sherwood numbers associated with nanoparticle Sherwood number. The findings of the study demonstrate that increasing the fluid suction parameter decreases the velocity and temperature of the flow field in conjunction with concentration and has a variable impact on the nanoparticle fraction of volume, despite an increasing behavior in the local skin friction coefficient and local Nusselt as well as general Sherwood numbers and an increasing behavior in the local nanoparticle Sherwood number. Furthermore, enhancing a Schmidt number leads to a reduction in the local nanoparticle Sherwood number and a rise in the nanoparticle proportion of volume. Along with concentration, it also reduces temperature and velocity. However, it also raises the local Sherwood and Nusselt numbers and reduces the local skin friction coefficient....
This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector field ζ dual to dψ does not change its causal character, then P is homothetic, or ζ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field....
Cornachia’s algorithm can be adapted to the case of the equation x2 + dy2 = n and even to the case of ax2 + bxy + cy2 = n . For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2 + y2 = n ). Starting from a quadratic form with two variables f (x, y) = ax2 + bxy + cy2 and n an integer. We have shown that a primitive positive solution (u,v) of the equation f (x, y) = n is admissible if it is obtained in the following way: we take α modulo n such that f (α ,1) ≡ 0mod n , u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn D ) (possibly α itself) and the equation f (x, y) = n . has an integer solution u in y . At the end of our work, it also appears that the Cornacchia algorithm is good for the form n = ax2 + bxy + cy2 if all the primitive positive integer solutions of the equation f (x, y) = n are admissible, i.e. computable by the algorithmic process....
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