Browsing by Author "Hsia, Chun-Hsiung"

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On mathematical analysis of synchronization to bidirectionally coupled Kuramoto oscillators
(2020-12-01)
Chen, Shih-Hsin
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Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
This article is concerned about the synchronization problem of the bidirectionally coupled Kuramoto model. In this model, each oscillator only interacts with the oscillators with adjacent labeling numbers. Namely, the oscillator theta(i) only interacts with theta(i+1) and theta(i-1). In real applications, this is a typical setting of concatenation connection. We first prove the global convergence of frequency synchronization for the identical oscillators. Also, we present two results of phase synchronization for the identical case in relatively wide initial configuration regimes. In the case that the coupling strength is sufficiently large (equivalent to the difference of the natural frequencies is sufficiently small), we show that for non-identical oscillators within a suitable initial configuration regime, the bidirectionally coupled Kuramoto model achieves a frequency synchronization. The supportive numerical simulations are presented as well. (C) 2020 Elsevier Ltd. All rights reserved.
On the Asymptotic Stability Analysis and the Existence of Time-Periodic Solutions of the Primitive Equations
(2013)
Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
In this article, we prove an asymptotic stability criterion for the solutions of primitive equations defined on a three-dimensional finite cylindrical domain with time-dependent forcing terms. Under a suitable smallness assumption on the nontrivial forcing terms, we obtain the existence of the time periodic solution for the primitive equations. Moreover, this time-periodic solution is asymptotically stable in L-2 sense.
On the long-time stability of a temporal discretization scheme for the three dimensional viscous primitive equations
(2018-05-01)
Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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應用數學系
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Department of Applied Mathematics
In this article, a semi-discretized Euler scheme to solve the three dimensional viscous primitive equations is studied. Based on suitable assumptions on the initial data and forcing terms, the long-time stability of the proposed scheme is proven by showing that the norm (in space variables) of the solutions is bounded at each time step when the time step satisfies certain smallness condition.
On time periodic solutions, asymptotic stability and bifurcations of Navier-Stokes equations
(2017-02)
Hsia, Chun-Hsiung
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Jung, Chang-Yeol
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Thien Binh Nguyen
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Shiue, Ming-Cheng
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應用數學系
In this article, we investigate the time periodic solutions for two-dimensional Navier-Stokes equations with nontrivial time periodic force terms. Under the time periodic assumption of the force term, the existence of time periodic solutions for two-dimensional Navier-Stokes equations has received extensive attention from many authors. With the smallness assumption of the time periodic force, we show that there exists only one time periodic solution and this time periodic solution is globally asymptotically stable in the sense. Without smallness assumption of the force term, there is no stability analysis theory addressed. It is expected that when the amplitude of the force term is increasing, the time periodic solution is no longer asymptotically stable. In the last part of the article, we use numerical experiments to study the bifurcation of the time periodic solutions when the amplitude of the force is increasing. Extrapolating to the heating of the earth by the sun, the bifurcation diagram hints that when the earth receives a relatively small amount of solar energy regularly, the time periodic fluid patterns are asymptotically stable; while/when the earth receives too much solar energy even though in a time periodic way, the time periodic pattern of the fluid motions will lose its stability.
Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability
(2015-09-02)
Hsia, Chun-Hsiung
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Shiue, Ming-Cheng
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數學建模與科學計算所(含中心)
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Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
This article is devoted to the study of the asymptotic stability of the three-dimensional viscous primitive equations for large-scale moist atmosphere in the pressure coordinate system. An asymptotic stability criterion for the solutions of such model with time-dependent forcing terms is obtained. In particular, under the assumptions that the associated forces are both time-periodic and small (in a suitable sense), we obtain the existence of the time-periodic solution for the primitive equations of large-scale moist atmosphere. Moreover, this time-periodic solution is asymptotically stable in L-2 sense.