Department of Mathematics https://umoar.mu.edu.mm/handle/123456789/11 2019-10-14T11:25:10Z Numerical Stability of the Escalator Boxcar Train under reducing System of Ordinary Differential Equations https://umoar.mu.edu.mm/handle/123456789/319 Numerical Stability of the Escalator Boxcar Train under reducing System of Ordinary Differential Equations Tin Nwe Aye; Carlsson, Linus The Escalator Boxcar Train (EBT) is one of the most popular numerical methods used to study the dynamics of physiologically structured population models. The original EBT-model accumulates an increasing system of ODEs to solve for each time step. In this project, we propose a merging procedure to overcome computational disadvantageous of the EBT method, the merging is done as an automatic feature. In particular we apply the model including merging to a colony of Daphnia Pulex. 2017-01-01T00:00:00Z Propagation Property for Nonlinear Parabolic Equations of p-Laplacian-Type1 https://umoar.mu.edu.mm/handle/123456789/281 Propagation Property for Nonlinear Parabolic Equations of p-Laplacian-Type1 Than Sint Khin; Ning Su We study propagation property for one-dimensional nonlinear diffusion equations with convection-absorption, including the prototype model ∂t(um) − ∂x(|∂xu|p−1∂xu) − μ|∂xu|q−1∂xu + λuk = 0, where m, p, q, k > 0, and n-dimensional simplified variant ∂t(um) − Δp+1u = 0, where Δp+1u = div (|∇u|p−1∇u). Among the conclusions, we make complete classification of the parameters in the first equation to distinguish its propagation property. For the second equation we rigorously prove that perturbation of the nonnegative solutions propagates at finite speed if and only if m < p. 2009-01-01T00:00:00Z Local instability of a rotating flow driven by precession of arbitrary frequency https://umoar.mu.edu.mm/handle/123456789/278 Local instability of a rotating flow driven by precession of arbitrary frequency Me Me Naing; Fukumoto, Yasuhide We revisit the local stability, to three-dimensional disturbances, of rotating flows with circular streamlines, whose rotation axis executes constant precessional motion about an axis perpendicular to itself. In the rotating frame, the basic flow is steady velocity field linear in coordinates in an unbounded domain constructed by Kerswell (1993Geophys. Astrophys. Fluid Dyn.72 107–44), and admits the use of the Wentzel–Kramers–Brillouin (WKB) method. For a small precession frequency, we recover Kerswell’s result. A novel instability is found at a large frequency for which the axial wavenumber executes an oscillation around zero; significant growth of the disturbance amplitude occurs in a very short time interval only around the time when the axial wavenumber vanishes. In the limit of infinite precession frequency, the growth rate exhibits singular behavior with respect to a parameter characterizing the tilting angle of the wave vector. (Some figures in this article are in colour only in the electronic version) 2011-01-01T00:00:00Z Local Instability of an Elliptical Flow Subjected to a Coriolis Force https://umoar.mu.edu.mm/handle/123456789/277 Local Instability of an Elliptical Flow Subjected to a Coriolis Force Me Me Naing; Fukumoto, Yasuhide We make the local stability analysis of a rotating flow with circular or elliptically strained streamlines, whose rotation axis executes constant precessional motion about an axis perpendicular to itself, based on the WKB method. In the frame rotating with the precessional angular velocity, the basic flow is a steady velocity field linear in coordinates in an unbounded domain. For the case of slow precession, without strain, the growth rate takes the same value as that of Kerswell (1993) though the basic flow is different. We find that, in the absence of strain, the growth rate approaches the angular velocity of the basic flow as the precessional angular velocity is increased. The cooperative action of the weak Coriolis force and the elliptical straining field is investigated both numerically and analytically. An analysis of using the Mathieu method reveals that the elliptical instability is weakened by the precession, while the precessional instability is either enhanced or weakened depending on the orientation of the strain. 2009-01-01T00:00:00Z