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Terry E. Moschandreou

Western University

Dr. Terry E. Moschandreou, Ph.D., teaches mathematics at the School of Mathematical and Statistical Sciences, University of Western Ontario, Canada, where he also earned his Ph.D. in Applied Mathematics in 1996. The greater part of his professional life has been spent at the University of Western Ontario and Fanshawe College, Ontario, Canada. Dr. Moschandreou also teaches elementary and high school mathematics and science for the Thames Valley District School Board, Ontario, Canada. For a short period, he worked at the National Technical University of Athens, Greece. Dr. Moschandreou is the author of several research articles on blood flow and oxygen transport in microcirculation, general fluid dynamics, and the theory of differential equations. He has also contributed to the field of finite element modeling of the upper airways in sleep apnea as well as surgical brain deformation modeling. Recently, his research has focused on partial differential equations of multiphase flow and level set methods as used in fluid dynamics. Dr. Moschandreou has also submitted significant findings from 2018 to 2024 toward a proposed solution to the Millennium Prize Problem, specifically addressing the regularity of solutions to the Periodic Navier–Stokes Equations on the 3-Torus.

4books edited

4chapters authored

Latest work with IntechOpen by Terry E. Moschandreou

Bifurcation Theory with Applications is a collection of chapters that describe the theory and application of nonlinear dynamics to a wide variety of problems in physics and engineering. Each chapter is self-contained and includes an introduction, main contributions, and details of up-to-date theoretical, computational, and experimental results. The book examines various practical systems, including models of target detection in cells through the analysis of bio-nanomachine, attractant, and repellent concentrations. It addresses the quasistatic evolution of anelastic structures, explores the generation of triangular patterns through anisotropic diffusion, and discusses the stabilization of time-delay distributed bilinear systems in spatial domains. Topics also include optimal control challenges in bilinear systems with unbounded and bounded control sets, forward bifurcation in hepatitis B virus infection models, and the bifurcation of hematological stem cells with feedback control in a biological context. The book is designed for theorists, applied mathematicians, and engineers across diverse scientific disciplines, serving as a valuable resource for anyone interested in bifurcation theory’s wide-ranging applications.

Bifurcation Theory with Applications

Bifurcation Theory with Applications

Edited by Terry E. Moschandreou

Books edited

Differential Equations

Differential Equations

Edited by Terry E. Moschandreou

Blood Cell

Blood Cell

Edited by Terry E. Moschandreou

Chapters authored

RBC-ATP Theory of Regulation for Tissue Oxygenation-ATP Concentration Model

By Terry E. Moschandreou

Part of the book: Blood Cell

Nonlinear Oxygen Transport with Poiseuille Hemodynamic Flow in a Micro-Channel

By Terry E. Moschandreou and Keith C. Afas

In a recent paper by the authors, a well-known governing nonlinear PDE used to model oxygen transport was formulated in a generalized coordinate system where the Laplacian was expressed in metric tensor form. A reduction of the PDE to a simpler problem, subject to specific integrability conditions, was shown, and in the present work, a novel approximate analytical solution is obtained in terms of the degenerate Weierstrass P function using a compatibility relation through the factorization of the reduced almost linear ode and subject to similar boundary conditions for a microfluidic channel used in recent work by the authors. A specific form of the initial equation which was reduced has been used by Nair and coworkers describing the intraluminal problem of oxygen transport in large capillaries or arterioles and more recent work by the corresponding author describing the release of adenosine triphosphate (ATP) in micro-channels. In the present problem, a channel with a central core, rich in red blood cells, and with a thin plasma region near the boundary wall, free of RBCs is considered.

Part of the book: Nonlinear Systems

Periodic Navier Stokes Equations for a 3D Incompressible Fluid with Liutex Vortex Identification Method

By Terry E. Moschandreou and Keith C. Afas

The Incompressible Navier-Stokes Equations (NSEs) are on the list of Millennium Problems, to prove their existence and uniqueness of solutions. The NSEs can be formulated in a periodic 3D domain, where they are termed the Periodic Navier Stokes (PNS) Equations, and can be treated on a subspace spanning a 3-dimensional torus, or T3. Treating the PNS Equations in T3-space, this article demonstrates that a decaying of turbulence occurs in the 3D case for the z component of velocity when non-smooth initial conditions are considered for x, y components of velocity and that ‘vorticity’ sheets in the small scales of 3D turbulence dominate the flow to the extent that non-smooth temporal solutions exist for the z velocity for smooth initial data for the x, y components of velocity. Unlike the Navier-Stokes equations, which have no anti-symmetric vorticity tensor, there are new governing equations which have vorticity tensor and can be decomposed into a rotational part(Liutex), antisymmetric shear and compression and stretching. It is shown that under these recent findings, that there is a strong correlation between vorticity and vorticies for (PNS).

Part of the book: Vortex Simulation and Identification

Introductory Chapter: Introduction to Tangent Vectors, Flows and Bifurcations

By Terry E. Moschandreou

Part of the book: Bifurcation Theory with Applications

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Karolinska Institute , Sweden

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Tahsin Murad Aktan

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Lisa A Mills