-
Research Article
Semi-analytical Solution of One-dimension Advection Diffusion Equation Coupled with Linear Partial Differential Equation with Constant Coefficient
Mohammad Jawad Qasimi*
,
Norma Alias
Issue:
Volume 14, Issue 2, April 2026
Pages:
39-45
Received:
27 January 2026
Accepted:
9 February 2026
Published:
5 March 2026
Abstract: This paper presents a semi-analytical solution for one-dimensional advection-diffusion equation coupled with a linear partial differential equation with constant coefficients. The mathematical model describes a grain-fumigant-air system during fumigation processes, where fumigant gas transports through a storage silo. The coupled system considers both diffusion and advection mechanisms with constant velocity and diffusivity parameters. The solution methodology employs the Laplace transformation technique to convert the partial differential equations into ordinary differential equations in the Laplace domain. The Stehfest numerical algorithm is subsequently applied to invert the Laplace transforms and obtain the time-domain solution. Numerical computations are performed using MATLAB software to simulate the fumigant concentration distributions. Graphical results illustrate the fumigant gas concentration in air versus vertical height within the silo for different time intervals. Additional plots demonstrate the fumigant concentration absorbed by grain particles over time. The analysis examines effects of varying initial gas concentration and flow velocity on the transport process. Results indicate that higher initial concentrations and increased velocities accelerate the fumigation process, requiring less time to fill the silo completely. The proposed solution provides a mathematical framework for optimizing fumigation parameters in agricultural storage applications.
Abstract: This paper presents a semi-analytical solution for one-dimensional advection-diffusion equation coupled with a linear partial differential equation with constant coefficients. The mathematical model describes a grain-fumigant-air system during fumigation processes, where fumigant gas transports through a storage silo. The coupled system considers b...
Show More
-
Research Article
Finite Subgroup Automorphism of Infinite Group and Its Application to Symmetric Cryptography
Issue:
Volume 14, Issue 2, April 2026
Pages:
46-52
Received:
16 February 2026
Accepted:
2 March 2026
Published:
16 March 2026
DOI:
10.11648/j.ajam.20261402.12
Downloads:
Views:
Abstract: The study of automorphisms of algebraic structures plays a central role in understanding their internal symmetries and structural behavior. This work investigates the automorphism structure induced by finite subgroups within infinite groups, with particular emphasis on how these automorphisms can be characterized, classified, and effectively utilized. The focus is on the interaction between a finite subgroup and the ambient infinite group, analyzing how subgroup-preserving automorphisms extend to global automorphisms and how constraints imposed by finiteness influence the overall automorphism group. Special attention is given to classes of infinite groups such as abelian, conjugacies, and certain residually finite groups where finite subgroup automorphisms exhibit rich and tractable behavior. Building on this theoretical framework, this work explores applications to symmetric cryptography, where algebraic symmetry and complexity are essential for secure cryptographic design. Finite subgroup automorphisms are shown to provide a promising foundation for constructing cryptographic primitives, including key generation mechanisms, conjugacy-based encryption schemes, and secure mixing transformations. The inherent difficulty of reversing automorphism actions in large infinite groups, combined with the controlled structure of finite subgroups, offers a balance between computational efficiency and cryptographic strength. In overall, this work bridges abstract group theory and practical cryptographic applications, demonstrating that finite subgroup automorphisms of infinite groups constitute a viable and mathematically robust framework for advancing symmetric cryptographic systems.
Abstract: The study of automorphisms of algebraic structures plays a central role in understanding their internal symmetries and structural behavior. This work investigates the automorphism structure induced by finite subgroups within infinite groups, with particular emphasis on how these automorphisms can be characterized, classified, and effectively utiliz...
Show More
-
Research Article
Existence of Law Density of a Pair (d-dimensional Diffusion X, First Component Running Maximum M) with Coefficients Depending on (X, M), d > 1
Balauze Téo*,
Pontier Monique
Issue:
Volume 14, Issue 2, April 2026
Pages:
53-65
Received:
2 February 2026
Accepted:
24 February 2026
Published:
18 March 2026
DOI:
10.11648/j.ajam.20261402.13
Downloads:
Views:
Abstract: The purpose of this paper is to consider a stochastic differential equation guiding X a continuous d-dimensional diffusion process, the coefficients of which depending on the pair (X, M) , where M is the running supremum of the first component X1. As an application of our work, we could think of a firm the activity of which is characterized by a set of processes (X1,···, Xd). But one of them, for instance X1, could be linked to an alarm. Such a (d + 1)- dimensional process (X, M) could present a crucial interest in this case where M could be an alarm. Indeed, the possibility of an alarm at time t namely the event {∃s ≤ t : X1s > u} is identical to the event {Mt> u} > when the specific (and dangerous) threshold u is exceeded. This means that the law of M is closely linked to the law of the hitting time when X1 reaches such a dangerous level u. Here is proved that, for all positive real number t; the law of the (d+1)-dimensional random vector (Xt, Mt) admits a density with respect to the Lebesgue measure. The solution of such a stochastic differential equation is built using a recursion method. The existence of the density of the law of (X, M) is based on Malliavin calculus. This density is solution of a partial differential equation in a weak sense. Moreover, such a recursive construction will allow to build simulated solutions. So finally such a tool could allow us to build an alarm system to detect the hitting time when the alarm could occur.
Abstract: The purpose of this paper is to consider a stochastic differential equation guiding X a continuous d-dimensional diffusion process, the coefficients of which depending on the pair (X, M) , where M is the running supremum of the first component X1. As an application of our work, we could think of a firm the activity of which is characterized by a se...
Show More
-
Research Article
Unsteady Magnetohydrodynamic Flow of a Nonlinear
Third-grade Fluid with Variable Viscosity and Radiative Heat Transfer
Chukuwuemeka Paul Amadi,
Iyowuna Winston Gobo*
Issue:
Volume 14, Issue 2, April 2026
Pages:
66-73
Received:
25 February 2026
Accepted:
6 March 2026
Published:
19 March 2026
DOI:
10.11648/j.ajam.20261402.14
Downloads:
Views:
Abstract: This study investigates the unsteady Magnetohydrodynamic (MHD) flow and heat transfer characteristics of a nonlinear third-grade non-Newtonian fluid with temperature-dependent viscosity and nonlinear thermal radiation, which are commonly encountered in advanced engineering systems such as polymer processing, metallurgical operations, liquid-metal cooling technologies, and energy conversion devices. Owing to its viscoelastic nature, which deviates from classical Newtonian assumptions, the fluid behavior is described by coupled nonlinear momentum and energy equations incorporating magnetic field effects, viscous dissipation, nonlinear shear contributions, variable thermal conductivity, and wall suction. The governing equations are non-dimensionalised to identify the key controlling physical parameters and solved numerically using an explicit finite difference scheme, enabling a detailed parametric analysis of the effects of magnetic strength, nonlinear material parameters, radiation intensity, and viscosity variation on velocity and temperature distributions within the boundary layer. The results indicate that increasing magnetic field strength suppresses fluid motion through Lorentz force effects, thereby thinning the momentum boundary layer and providing an effective mechanism for electromagnetic flow control. Additionally, nonlinear rheological parameters significantly alter momentum transport, while radiative heat transfer and viscous dissipation elevate the thermal energy within the fluid, and variations in thermal conductivity strongly influence heat diffusion and temperature gradients. These findings offer valuable design insights for enhancing flow regulation and thermal performance in industrial systems involving electrically conducting non-Newtonian fluids operating under magnetic fields and high-temperature conditions.
Abstract: This study investigates the unsteady Magnetohydrodynamic (MHD) flow and heat transfer characteristics of a nonlinear third-grade non-Newtonian fluid with temperature-dependent viscosity and nonlinear thermal radiation, which are commonly encountered in advanced engineering systems such as polymer processing, metallurgical operations, liquid-metal c...
Show More
