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學術專區

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研討會
活動開始時間2017-11-30 14:20:00
活動結束時間2017-12-01 10:10:00
活動名稱Workshop on Dynamical Systems and Applied Mathematics(11/30~12/1)
主講者Takashi Teramoto (Asahikawa Medical University, Japan)
Petrus van Heijster (Queensland University of Technology, Australia)
Yasumasa Nishiura (Tohoku University, Japan)
活動地點綜合三館4F Lecture Room B
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參考連結 
備註Workshop on Dynamical Systems and Applied Mathematics
Date: 2017.11.30 – 2017.12.1

1.
Date: November 30 (Thu.), 2017
Time: 14:20
Speaker: Takashi Teramoto (Asahikawa Medical University, Japan)
Title: Localized solutions in reaction-diffusion systems on curved surface
Venue: Lecture Room B, 4F, General Building III

Abstract
We consider the motion of spot solutions on two-dimensional curved surface. In the framework of weak interaction theory by Ei, the dynamics of spot position is governed by ordinary differential equations (ODEs). The spot motion is determined by the curvature of surface. In this talk, I will start to talk about the results of numerical simulations of localized spot solutions in reaction-diffusion systems and
their dynamics in heterogeneous media. The key of our analysis is that the curved surface can be regarded as a spatial heterogeneity in two dimension. This is a joint with S.-I. Ei and A. Sekisaka.
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2.
Date: November 30 (Thu.), 2017
Time: 16:30
Speaker: Petrus van Heijster (Queensland University of Technology, Australia)
Title: The stability of travelling wave solutions in a Keller–Segel model with logarithmic chemosensitivity
Venue: Lecture Room B, 4F, General Building III

Abstract
In this talk, I will discuss some recent results we obtained regarding the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function. Upon linearising around the travelling wave solutions, we locate the essential, absolute, and point spectrum of the associated linear operators. We find that all travelling wave solutions have parts of the essential spectrum in
the right half plane in the standard unweighted Banach space. However, we show that there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus
be weighted into the open left half plane. In addition, we determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. Most notably, we observe that this crossing always
occurs off of the real axis. To complete the story, we (numerically) locate the point spectrum of the travelling wave solutions. This is joint work with P.N. Davis and R. Marangell.
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3.
Date: December 1 (Fri.), 2017
Time: 10:10
Speaker: Yasumasa Nishiura (Tohoku University, Japan)
Title: Interplay between Internal and External Interactions for Morphological Transitions arising in Block Copolymer Nanoparticles
Venue: Lecture Room B, 4F, General Building III

Abstract:
Annealing of copolymers has become a tool of great importance to reconfigure nanoparticles. Herein, we present experimental results of annealing copolymer nanoparticles and a theoretical model to describe the morphological transformation from lamellae to onion. A good correspondence
between experimental findings and predictions of the model is observed. The model based on finding the steepest direction of decent of an appropriate free energy leads to a set of Cahn-Hilliard equations that correctly describes the dynamical transformation from lamellae particles to
onion and reverse onion-like particles, regardless of the nature of the annealing process. This universality makes possible to describe a variety of experimental conditions involving nanoparticles underlying a heating process. A notable advantage of the proposed approach is that it makes
possible to selectively control the interaction between the confined copolymer and the surrounding media. This feature endows the model with great versatility to reproduce several combined effects of surfactants in diverse conditions, including cases with reverse affinities for the copolymer segments. A phase diagram to describe a variety of morphologies is presented. We employ relations between the temperature-dependent Flory-Huggins parameter and the width of the interfaces to account for changes in temperature due to the heating process. Simulation results correctly show how the transformation evolves as the temperature increases.
This increment in temperature corresponds to progressively smaller values of the interfacial width. We anticipate that the proposed approach will facilitate the design and a more precise control of experiments involving various kinds of annealing processes. This is a joint work with E. Avalos, T. Teramoto, H. Komiyama, and H. Yabu.
最後更新日期2017-11-24 16:24:22
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