21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

Past Seminars: Recent development in Mathematical material sciences

COE Mathematics Center for Advanced Study, Special Seminar Series
"Communication between Material Science and Mathematical Science"
The 8th seminar:
Date and Time: 10 March 2005, 15:00-16:30
Place: Conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Ryo Akiyama (Kyushu University)
Title: Entropically Driven Attractive Forces and Crowding Problems in Living Cells
Entropy is usually explained as a measure of the lack of "order" in a system. Howeverwe sometimes meet difficulties if the measure's definition is obscure. For example, the potential of mean force between larger spheres in a binary hard-sphere mixture system has attractive part which is driven by the entropy. Some "ordered" structures are formed by the attractive forces, namely by the maximum entropy principle.
The idea of entropically driven attractive forces gives us various interesting subject in biochemistry. Crowding problem in living cells is a good example. The cytoplasm of the living cell contains a variety of crowding agents (biopolymers) and aqueous electrolyte. The typical volume fraction of crowding agents is 20% or more. Minton et al. have pointed out the importance of the attractive force on some biochemical subjects. The cohesion of proteins in the cells, for example. In those treatments the solvent is a structureless inert background although the total number of small solvent molecules is much larger than that of crowding agents.
We examine the solvent effects on the potentials of mean force between macromolecules using the integral equation theory of liquid (the OZ-HNC theory). The results are qualitatively different from those of conventional treatments. We will talk about those results and a new picture of the entropically driven attractive force in this seminar. The crowding problem in the cohesion of proteins, the protein fording and so on will be discussed.
The 7th seminar:
Date and Time: 4 March 2005, 16:45-17:45
Place: Lecture Hall, conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Alexander Mikhailov (Berlin)
All stainless steels can undergo localized pitting corrosion, which rapidly leads to their failure. The corrosion sets on suddenly, as the salt concentration, temperature or electric potential are changed only slightly. It is preceeded by the appearance of metastable pits: tiny corrosion seeds with the size of a few micrometers which remain active for about a second and then undergo passivation. Although pitting corrosion is of high practical importance (for example, a third of all chemical plants failures are attributed to it), the mechanisms of its onset remained unclear. Our theory [1] explains the sudden corrosion onset as a cooperative critical phenomenon involving autocatalytic reproduction cascades of metastable pits and diffusion-induced spreading of fronts, similar to spreading of an infectious disease. In our laboratories, first real-time microscopic in situ visualizations of corrosion onset were performed [1] . These experiments, using specially designed contrast-enhanced optical microscopy and ellipsometry for surface imaging (EMSI), have confirmed theoretical predictions. Understanding corrosion mechanisms opens new perspectives for its control and prevention.
[1] C. Punckt et al., Sudden onset of pitting corrosion on stainless steel as a critical phenomenon, Science 305, 1133 (2004)

Note: Before this seminar, Workshop "Mathematical Aspects of Material Sciences" will be held.
The 6th seminar:
Date and Time: 20 January 2005, 13:30-15:00
Place: Conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Kazushige Kawabata (Hokkaido University)
Title: Hierarchical Dynamics of Single Cells
Cell migration is widely common in biological phenomena at tissue level. This plays a central role in healing of wounded tissue and self-organizing of the early embryo. Many researchers have studied intensively molecular processes on mechanisms of the cell migration. However, the cell migration is considered one of difficult phenomena to explain at molecular level, because it results from cooperative interactions among numerous proteins. On the other hand, biological systems have hierarchy inherently in their functions. The macroscopic and cooperative phenomena of a system are considered to originate in properties of its constitutive elements. In order to clarify a cooperative mechanism for cell migration, we focus on mechanical properties of a single cell, which consist of cytoskeleton networks, focal adhesion and intracellular contraction. In this meeting, we present our following recent results.
  1. 1) Mechanical-Scanning Probe Microscopy measurements for local stiffness of a single living cell
  2. 2) Drastic changes in the local stiffness of the cell, corresponding to its movement
  3. 3) Stabilization of the stiffness when a cell is deformed externally using deformable elastic sheets.
  4. 4) Collective motion of a large number of cells on a soft collagen gel surface.
  1. T. Mizutani, H. Haga, and K. Kawabata, Cell Motil. Cytoskeleton (2004) 59.242-248(2004).
  2. M. Nagayama, H. Haga, M. Takahashi, T. Saitoh, and K. Kawabata, Exp. Cell Res. 300 (2004) 396-405.
  3. H. Haga, C. Irahara, R. Kobayashi, T. Nakagaki and K. Kawabata, Biophysical J. (2005) in press
The 5th seminar:
Date and Time: 14 January 2005, 15:00-16:30
Place: Conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Hiizu Nakanishi (Kyushu University)
Title: Modeling of Sweeping Dynamics and Interface Instability
It is fascinating to see that beautiful patterns are formed simply by drying the mixture of powder and water between two glass plates; during the drying process, powder is swept away by the surface of the water to form a labyrinthian pattern. In order to understand this phenomenon, we have constructed three types of models, which show an instability of growing inteface.
The 4th seminar:
Date and Time: 7 January 2005, 13:30-15:00
Place: room 309, Department of Mathematics Bldg #8, Hokkaido University
Speaker: Tomoki Minoguchi (University of Tokyo)
Title: Interesting properties of point vortices in superfluid helium film
It is know that liquid helium does not freeze down to zero Kelvin under ordinary pressure. Instead, the liquid undergoes somewhat strange liquid (helium II) at low temperature, named superfluid. Superfluid actually has strange characters such as zero viscosity and divergingly large heat conductivity. In particular, vorticity or circulation is quantized: vortices, which are frequently excited thermally, should has discrete vorticity.

The superfluid transition occurs even when the liquid is atomically thin, and there the quantized vortices ('point' vortices (PV) in this case) play a dramatic role. In this talk,
  1. we will enjoy experimental movie to see what the superfluid actually is,
  2. and for two dimensional (2D) superfluid (the superfluid film adsorbed on a flat surface) we will touch an important theory (the Kosterlitz-Thouless (KT) theory) that how the PV play in the superfluid transition,
  3. and finally, for branched superfluid film, 'branch cut' which nominally exists between PV for the 2D superfluid gets a physically important character. If the film is multiply-branched (such a case as the film adsorbed on porous medium), we will see that the branch cut becomes a unit circulation in a 'string' connecting PV and reduces the KT transition(*).

If time allows, some unusual movies on the crystallization of superfluid under high pressures will be also presented.

(*) Minoguchi and Nagaoka, Prog. Theor. Phys., Vol.80, 397-416, 1988
The 3rd seminar:
Date and Time: 19 November 2004, 15:00-16:30
Place: Conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Miles P. Blencowe (Department of Physics and Astronomy, Dartmouth College, Hanover NH, USA)
Title: Coupled dynamics of Nanoelectromechanical Systems
The emerging field of nanoelectromechanical systems (NEMS) involves the study of very small mechanical resonators that are coupled electrostatically to very small electronic devices. Single electrons flowing randomly through such a device can give significant 'kicks' to the mechanical resonator, interrupting its deterministic motion, while in turn the resonator's motion can affect the electron flow. There has been considerable effort recently to understand this coupled dynamics through the use of various approximate master equations, i.e., coupled PDEs in the oscillator and electronic device coordinates. These equations include both deterministic and random terms. We give some examples of the master equations that have been written down to describe various NEMS, as well as describe the solutions to these equations where known. Open problems to solving some of these equations are also pointed out.
The 2nd seminar:
Date and Time: 5th November 2004, 15:00-16:30
Place: Conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Yoshimi TANAKA (Creative Research Initiative "Sousei", Hokkaido University)
Title: Impacts of non-linear elastic body
Impacts of soft gel balls are investigated. Experiment shows that the deformation time, defined as the period between on-set of the impacts and the maximum deformation, converges on a constant value with increasing the impact velocity. A simple model is developed to explain the behavior.
The 1st seminar:
Date and Time: 22 October 2004, 13:30-15:00
Place: Conference room 2F, Research Institute for Electronic Science (Hokkaido University)
Speaker: Peter Bates (Michigan State University)
Title: Some mathematical models arising in materials science
Starting with a lattice model of a material with long range interaction between lattice sites, a variety of equations are derived for the evolution of the state of the material. The state will be described by an order parameter that might be conserved or not, depending on its physical interpretation. Rigorous results related to the existence and nature of solutions will be presented with some ideas about their proofs given, time permitting.
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Short-term Intensive Seminars
"Application of Computational Homology to Topology"
Date and Time: 21 January, 2005
Place: Lecture Hall, Research Institute for Electronic Science (Hokkaido University)

Speaker: Yasuaki Hiraoka (Osaka University)
Title: An introduction to the computational homology I

Speaker: Yasuaki Hiraoka (Osaka University)
Title: An introduction to the computational homology II
Abstract: TBA

Speaker: Yoshihito Oyama (Hokkaido University)
Title: Installing ChomP and applying to Internet topology
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21st Century COE Program : Mathematics of Nonlinear Structure via Singularity