Browsing by Author "Sakai, Kaoru"

Now showing 1 - 4 of 4
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    Derivations and Spectral Triples on Quantum Domains I: Quantum Disk
    (2017) Klimek, Slawomir; McBride, Matt; Rathnayake, Sumedha; Sakai, Kaoru; Wang, Honglin; Mathematical Sciences, School of Science
    We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.
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    A note on spectral properties of the p-adic tree
    (AIP, 2016) Klimek, Slawomir; Rathnayake, Sumedha; Sakai, Kaoru; Department of Mathematical Sciences, School of Science
    We study the spectrum of the operator D∗D, where the operator D, introduced in Klimek et al. [e-print arXiv:1403.7263v2], is a forward derivative on the p-adic tree, a weighted rooted tree associated to ℤp via Michon’s correspondence. We show that the spectrum is closely related to the roots of a certain q − hypergeometric function and discuss the analytic continuation of the zeta function associated with D∗D.
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    Simulation of blood flow past distal arteriovenous-graft anastomosis with intimal hyperplasia
    (AIP, 2021-05) Zhu, Luoding (祝罗丁 ); Sakai, Kaoru; Mathematical Sciences, School of Science
    Late-stage kidney disease patients have to rely on hemodialysis for the maintenance of their regular lives. Arteriovenous graft (AVG) is one of the commonly used devices for dialysis. However, this artificially created shunt may get clotted and eventually causes the dialysis to fail. The culprit behind the AVG clotting and failure is the intimal hyperplasia (IH), the gradual thickening of vein-wall in the vicinity of the blood vessel-graft conjunctions. The mechanism of IH is not well understood despite extensive studies. In this work, we investigate the effects of the IH development, including its location and severity on the flow and force fields in the distal AVG anastomosis using computational fluid dynamics. The stenosis due to IH is modeled in the shape of a Gaussian function with two free parameters. The blood is modeled as a viscous incompressible fluid, and the blood flow (pulsatile) is governed by the Navier–Stokes equations which are numerically solved by the lattice Boltzmann model (D3Q19). The fluid-structure interaction is modeled by the immersed boundary framework. Our computational results show that the IH severity has the most significant influences on the wall shear stress, wall-normal stress, and the axial oscillating index. The stenosis location and flow pulsatility do not have pronounced effects on flow and force fields. Our results indicate that the IH progression tends to exacerbate the disease and accelerate the closure of the vein lumen, and hence the dialysis failure.
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    A Value Region Problem for Continued Fractions and Discrete Dirac Equations
    (Project Euclid, 2020-06) Klimek, Slawomir; Mcbride, Matt; Rathnayake, Sumedha; Sakai, Kaoru; Mathematical Sciences, School of Science
    Motivated by applications in noncommutative geometry we prove several value range estimates for even convergents and tails, and odd reverse sequences of Stieltjes type continued fractions with bounded ratio of consecutive elements, and show how those estimates control growth of solutions of a system of discrete Dirac equations.