Date
Speaker:
Yumiko IMAI, Project Leader, Ph.D.
Regulation for Intractable Infectious Diseases
Center for Vaccine & Adjuvant Research
National Institutes of Biomedical Innovation, Health and Nutrition (NIBIOHN)
Date
Speaker:
Prof. Hitoshi Okamura
Department of System Biology, Graduate School of Pharmaceutical Sciences
Kyoto University
Date
TQM unit is pleased to invite you to the seminar!
Date
★DISTINGUISHED LECTURE
Professor Yoshikazu Giga, The University of Tokyo
Title: On a singular limit of a single-well Modica-Mortola functional and its applications
Abstract:
It is important to describe the motion of phase boundaries by macroscopic energy in the process of phase transitions. Typical energy describing the phenomena is the van der Waals energy, which is also called a Modica-Mortola functional with a double-well potential or the Allen-Cahn functional. It turns out that it is also important to consider the Modica-Mortola functional with a single-well potential since it is often used in various settings including the Kobayashi-Warren-Carter energy, which is popular in materials science. It is very fundamental to understand the singular limit of such a type of energies as the thickness parameter of a diffuse interface tends to zero. In the case of double-well potentials, such a problem is well-studied and it is formulated, for example, as the Gamma limit under
convergence.
However, if one considers the Modica-Mortola functional, it turns out that
convergence is too rough even in the one-dimensional problem.
We characterize the Gamma limit of a single-well Modica-Mortola functional under the topology which is finer than
topology. In a one-dimensional case, we take the graph convergence. In higher-dimensional cases, it is more involved. As an application, we give an explicit representation of a singular limit of the Kobayashi-Warren-Carter energy. Since the higher-dimensional cases can be reduced to the one-dimensional case by a slicing argument, studying the one-dimensional case is very fundamental. A key idea to study the one-dimensional case is to introduce “an unfolding of a function” by changing an independent variable by the arc-length parameter of its graph. This is based on a joint work with Jun Okamoto (The University of Tokyo), Masaaki Uesaka (The University of Tokyo, Arithmer Inc.), and Koya Sakakibara (Okayama University of Science, RIKEN).
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Date
Our speaker will be Michelle Maiese on Mindshaping, Racist Habits, and White Ignorance. We will be meeting on Monday, November 8, 2021 at 9:30 am, Japan time (GMT +9).
Date
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer – Dr. J. Eli Bourassa and Dr. Ilan Tzitrin, Xanadu
Date
CFF unit is pleased to invite you to the seminar.
Date
Dr. Po Lam Yung, Australian National University
Title: Sobolev norms revisited
Abstract:
In this talk, we will describe some new ways of characterising Sobolev norms, using sizes of superlevel sets of suitable difference quotients. They provide remedy in certain cases where some critical Gagliardo-Nirenberg interpolation inequalities fail, and lead us to investigate real interpolations of certain fractional Besov spaces. Some connections will be drawn to earlier work by Bourgain, Brezis and Mironescu. Joint work with Haim Brezis, Jean Van Schaftingen, Qingsong Gu, Andreas Seeger and Brian Street.
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Date
Language: English