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...
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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
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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...
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