Open Access
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Dr. Nirelle V. Aumont, Dr. Kaien R. Luskami, Dr. Lioren J. Kevrand (Author) 1
Pages: 50-56 || Published: 2024-12-27
From the flow of galaxies to the waves in our oceans, much of the physical world is governed by a class of equations known as hyperbolic conservation laws. Simulating these laws on computers is a monumental task, especially because they often produce sharp, sudden changes like shockwaves. For decades, scientists have hand-crafted complex nume... More >
Open Access
Articles
Dr. Lenric A. Voswain, Dr. Tharuni M. Kavelin, Dr. Jorvan E. Milbrant (Author) 1
Pages: 1-8 || Published: 2024-12-01
This article explores the fascinating world of non-local operators and the challenges they pose when confined to domains with boundaries. We focus on a class of operators that, while powerful, lack the convenient symmetries of well-studied examples like the fractional Laplacian. These operators often fail to meet the stringent "transmission c... More >
Open Access
Articles
Dr. Keeran V. Alnore, Dr. Mihita R. Solven (Author) 1
Pages: 57-62 || Published: 2024-12-30
When materials break, the process is incredibly complex. To predict and analyze these failures, engineers and scientists use computational tools called Cohesive Zone Models (CZMs)1. These models fall into two main camps: potential-based models, which use a single energy function to describe the fracture process, and non-potential-based models... More >
Open Access
Articles
Dr. Rinel M. Ostavar, Dr. Velina T. Crovan, Dr. Jashwin E. Maltren (Author) 1
Pages: 9-19 || Published: 2024-12-07
The coupled interplay of mechanical, thermal, and magnetic fields presents a significant area of scientific inquiry, driven by its extensive applications in diverse fields such as geophysics, structural engineering, and aeronautics. This investigation introduces a novel and generalized thermoelastic model to elucidate the magneto-thermo-mecha... More >
Open Access
Articles
Dr. Elian M. Vortenz (Author) 1
Pages: 20-25 || Published: 2024-12-15
The numerical simulation of incompressible fluid dynamics, governed by the Navier-Stokes equations (NSEs), presents persistent challenges related to computational efficiency and numerical stability, especially for higher-order accurate methods. This paper introduces and analyzes a new class of fully decoupled, higher-order consistent splittin... More >
Open Access
Articles
Dr. Sorin D. Veltrax, Dr. Nireen A. Makov, Dr. Kaito L. Fenjara, Dr. Elmera T. Qasrin (Author) 1
Pages: 26-33 || Published: 2024-12-22
This study investigates a nonlinear viscoelastic wave equation subject to acoustic boundary conditions and a nonlinear distributed delay feedback acting on the boundary. The analysis of the asymptotic behavior of such systems is of paramount importance for both theoretical advancements in the field of partial differential equations and for pr... More >
Open Access
Articles
Dr. Jalen T. Rovimar (Author) 1
Pages: 34-49 || Published: 2024-12-24
This paper introduces a novel extremum seeking (ES) scheme specifically designed for identifying the first derivative of an unknown nonlinear map, particularly in systems subject to constant transmission delays. Traditional approaches often rely on predictor-based methods to compensate for delays, which can introduce significant complexity. I... More >
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