Wave-particle duality in dissipative systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654018
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tohoku University
• Principal Investigator: NISHIURA Yasumasa 東北大学, 原子分子材料科学高等研究機構, 教授 (00131277)
• Co-Investigator(Kenkyū-buntansha): TERAMOTO Takashi 旭川医科大学, 医学部, 准教授 (40382543) ; OBUSE Kiori 東北大学, 原子分子材料科学高等研究機構, 助教 (90633967)
• Research Collaborator: GAO Zhijun 東北大学, 大学院理学研究科数学専攻
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 自己組織化 / トンネル現象 / 反応拡散系 / 流体 / 応用数学

Outline of Final Research Achievements

Dynamics of traveling pulses and spots with oscillatory tails were investigated, especially focusing on the properties of wave-particle duality. This duality reflects on the two aspects of the localized traveling waves: one is the particle-like behavior coming from spatial localization and the other is the wave dynamics from the oscillatory tails. Oscillation of the tail part makes the interaction with other objects much more complicated than the monotone tail case. In fact, it is confirmed numerically that the traveling spots display an interference pattern when they go through the heterogeneity of slit type. A finite dimensional ODE system was also derived near a drift bifurcation point and existence and stability of critical points are rigorously shown for the 1D heterogeneous problem.

Free Research Field

応用数学