Department of Mathematicshttps://umoar.mu.edu.mm/handle/123456789/112019-05-09T16:48:24Z2019-05-09T16:48:24ZNumerical Stability of the Escalator Boxcar Train under reducing System of Ordinary Differential EquationsTin Nwe AyeCarlsson, Linushttps://umoar.mu.edu.mm/handle/123456789/3192019-03-14T04:00:17Z2017-01-01T00:00:00ZNumerical 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.
2017-01-01T00:00:00ZPropagation Property for Nonlinear Parabolic Equations of p-Laplacian-Type1Than Sint KhinNing Suhttps://umoar.mu.edu.mm/handle/123456789/2812018-11-18T15:05:25Z2009-01-01T00:00:00ZPropagation 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.
2009-01-01T00:00:00ZLocal instability of a rotating flow driven by precession of arbitrary frequencyMe Me NaingFukumoto, Yasuhidehttps://umoar.mu.edu.mm/handle/123456789/2782018-03-22T13:00:04Z2011-01-01T00:00:00ZLocal 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)
2011-01-01T00:00:00ZLocal Instability of an Elliptical Flow Subjected to a Coriolis ForceMe Me NaingFukumoto, Yasuhidehttps://umoar.mu.edu.mm/handle/123456789/2772018-11-18T15:04:30Z2009-01-01T00:00:00ZLocal 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