Browsing by Author "Mathematical Sciences, School of Science"

Now showing 1 - 10 of 231
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    3D simulation of a viscous flow past a compliant model of arteriovenous-graft annastomosis
    (Elsevier, 2019-03) Bai, Zengding; Zhu, Luoding; Mathematical Sciences, School of Science
    Hemodialysis is a common treatment for end-stage renal-disease patients to manage their renal failure while awaiting kidney transplant. Arteriovenous graft (AVG) is a major vascular access for hemodialysis but often fails due to the thrombosis near the vein-graft anastomosis. Almost all of the existing computational studies involving AVG assume that the vein and graft are rigid. As a first step to include vein/graft flexibility, we consider an ideal vein-AVG anastomosis model and apply the lattice Boltzmann-immersed boundary (LB-IB) framework for fluid-structure-interaction. The framework is extended to the case of non-uniform Lagrangian mesh for complex structure. After verification and validation of the numerical method and its implementation, many simulations are performed to simulate a viscous incompressible flow past the anastomosis model under pulsatile flow condition using various levels of vein elasticity. Our simulation results indicate that vein compliance may lessen flow disturbance and a more compliant vein experiences less wall shear stress (WSS).
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    A Candy Lover Learns to Optimize
    (University of Regina, 2023-03) Do, Anh Phuong; Rashid, Mamunur; Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    A container has two types of candies: Type A and Type B. Concerned about her child's well-being, a wise mom pronounces, “Each day, you can choose two candies from the container random. If they are of different types, you can eat them both. If they are of the same type, eat only one and return the other to the container.” We analyze the expected number of days needed to eat all candies in the container and the proportion of days the child eats two candies. Several other variations are either worked out or left for readers to solve.
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    A conclusive theorem on Finsler metrics of sectional flag curvature
    (arXiv, 2018-12-22) Huang, Libing; Shen, Zhongmin; Mathematical Sciences, School of Science
    If the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.
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    A Literature Review of Similarities Between and Among Patients With Autism Spectrum Disorder and Epilepsy
    (Springer Nature, 2023-01-18) Assuah, Freda B.; Emanuel, Bryce; Lacasse, Brianna M.; Beggs, John; Lou, Jennie; Motta, Francis C.; Nemzer, Louis R.; Worth, Robert; Cravens, Gary D.; Mathematical Sciences, School of Science
    Autism spectrum disorder (ASD) has been shown to be associated with various other conditions, and most commonly, ASD has been demonstrated to be linked to epilepsy. ASD and epilepsy have been observed to exhibit high rates of comorbidity, even when compared to the co-occurrence of other disorders with similar pathologies. At present, nearly one-half of the individuals diagnosed with ASD also have been diagnosed with comorbid epilepsy. Research suggests that both conditions likely share similarities in their underlying disease pathophysiology, possibly associated with disturbances in the central nervous system (CNS), and may be linked to an imbalance between excitation and inhibition in the brain. Meanwhile, it remains unclear whether one condition is the consequence of the other, as the pathologies of both disorders are commonly linked to many different underlying signal transduction mechanisms. In this review, we aim to investigate the co-occurrence of ASD and epilepsy, with the intent of gaining insights into the similarities in pathophysiology that both conditions present with. Elucidating the underlying disease pathophysiology as a result of both disorders could lead to a better understanding of the underlying mechanism of disease activity that drives co-occurrence, as well as provide insight into the underlying mechanisms of each condition individually.
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    A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers
    (MDPI, 2022-03-08) Andalib, Vahid; Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    Assuming exponential lifetime and repair time distributions, we study the limiting availability 𝐴∞ as well as the per unit time-limiting profit 𝜔 of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either by an in-house repairer within an exponential patience time T or by an external expert who works faster but charges more. When there are two repair facilities, we allow the regular repairer to begin repair or to continue repair beyond T if the expert is busy. Two models arise accordingly as the expert repairs one or all failed units during each visit. We show that (1) adding a second spare to a one-unit system already backed by a spare raises 𝐴∞ as well as 𝜔; (2) thereafter, adding a second repair facility improves both criteria further. Finally, we determine whether the expert must repair one or all failed units to maximize these criteria and fulfill the maintenance management objectives better than previously studied models.
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    Ability and Diversity of Skills
    (AMS, 2023) Geller, William; Misiurewicz, Michał; Mathematical Sciences, School of Science
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    Accessibility of the Boundary of the Thurston Set
    (Taylor & Francis, 2023) Silvestri, Stefano; Pérez, Rodrigo A.; Mathematical Sciences, School of Science
    Consider two objects associated to the Iterated Function System (IFS) {1+𝜆⁢𝑧,−1+𝜆⁢𝑧}: the locus ℳ of parameters 𝜆∈𝔻∖{0} for which the corresponding attractor is connected; and the locus ℳ0 of parameters for which the related attractor contains 0. The set ℳ can also be characterized as the locus of parameters for which the attractor of the IFS {1+𝜆⁢𝑧,𝜆⁢𝑧,−1+𝜆⁢𝑧} contains 𝜆−1. Exploiting the asymptotic similarity of ℳ and ℳ0 with the respective associated attractors, we give sufficient conditions on 𝜆∈∂ℳ or ∂ℳ0 to guarantee it is path accessible from the complement 𝔻∖ℳ.
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    An asymptotic expansion for the expected number of real zeros of Kac-Geronimus polynomials
    (Rocky Mountain Mathematics Consortium, 2021) Aljubran, Hanan; Yattselev, Maxim L.; Mathematical Sciences, School of Science
    Let {φi(z;α)}i=0∞, corresponding to α∈(−1,1), be orthonormal Geronimus polynomials. We study asymptotic behavior of the expected number of real zeros, say 𝔼n(α), of random polynomials Pn(z):= ∑i=0nηiφi(z;α), where η0,…,ηn are i.i.d. standard Gaussian random variables. When α=0, φi(z;0)=zi and Pn(z) are called Kac polynomials. In this case it was shown by Wilkins that 𝔼n(0) admits an asymptotic expansion of the form 𝔼n(0)∼2πlog(n+1)+ ∑p=0∞Ap(n+1)−p (Kac himself obtained the leading term of this expansion). In this work we obtain a similar expansion of 𝔼(α) for α≠0. As it turns out, the leading term of the asymptotics in this case is (1∕π)log(n+1).
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    Arithmetic properties of 3-cycles of quadratic maps over Q
    (Elsevier, 2022-11) Morton, Patrick; Raianu, Serban; Mathematical Sciences, School of Science
    It is shown that c = -29/16 is the unique rational number of smallest denominator, and the unique rational number of smallest numerator, for which the map fc(x) = x2 + c has a rational periodic point of period 3. Several arithmetic conditions on the set of all such rational numbers c and the rational orbits of fc(x) are proved. A graph on the numerators of the rational 3-periodic points of maps fc is considered which reflects connections between solutions of norm equations from the cubic field of discriminant -23.
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    Assessing the hemodynamic contribution of capillaries, arterioles, and collateral arteries to vascular adaptations in arterial insufficiency
    (Wiley, 2019) Arciero, Julia; Lembcke, Lauren; Franko, Elizabeth; Unthank, Joseph; Mathematical Sciences, School of Science
    Objective There is currently a lack of clarity regarding which vascular segments contribute most significantly to flow compensation following a major arterial occlusion. This study uses hemodynamic principles and computational modeling to demonstrate the relative contributions of capillaries, arterioles, and collateral arteries at rest or exercise following an abrupt, total, and sustained femoral arterial occlusion. Methods The vascular network of the simulated rat hindlimb is based on robust measurements of blood flow and pressure in healthy rats from exercise and training studies. The sensitivity of calf blood flow to acute or chronic vascular adaptations in distinct vessel segments is assessed. Results The model demonstrates that decreasing the distal microcirculation resistance has almost no effect on flow compensation, while decreasing collateral arterial resistance is necessary to restore resting calf flow following occlusion. Full restoration of non‐occluded flow is predicted under resting conditions given all chronic adaptations, but only 75% of non‐occluded flow is restored under exercise conditions. Conclusion This computational method establishes the hemodynamic significance of acute and chronic adaptations in the microvasculature and collateral arteries under rest and exercise conditions. Regardless of the metabolic level being simulated, this study consistently shows the dominating significance of collateral vessels following an occlusion.