Mathematical Sciences based on Modeling, Analysis and Simulation Seminar

(MAS Seminar)

- Meiji institute for Advanced Study of Mathematical Science (MIMS)

（Organizers: M. Mimura, D. Ueyama, Y. Wakano, K. Ikeda and S. Kinoshita） - MAS seminar is partly supported by, the Meiji University Global COE program “Formation and Development of Mathematical Sciences Based on Modeling and Analysis”

Access to IKUTA Campus:

- http://www.meiji.ac.jp/koho/campus_guide/ikuta/access.html (アクセス・地図)

- http://gcoe.mims.meiji.ac.jp/eng/access/index.html (in English)

Date: Jan. 17, 2013, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus, Build 2 Annex A, Room A207

Mohcine Chraibi

(Julich Supercomputing Centre, Research Centre Julich, Germany)

Pedestrian Dynamics: Experiments, Measurements and ModelingAbstract:

Pedestrian dynamics can be defined as the study of properties and characteristics emerging from the collective motion of pedestrians. In everyday life a pedestrian moves in space freely without any restrictions from his environment. However, up the time where a pedestrian enters a building or an area where in the same time other pedestrians reside, this “freedom” of movement becomes manifestly restricted. In such cases security concerns rise and necessitate thoroughly understanding of the dynamics. In the past several aspects of pedestrian dynamics were investigated e.g., analysis of design issues of facilities in urban areas, evacuation planning, computer animation and computer vision [1]. Independently of the investigated issue the central concern is how accurate and realistic the modeling of pedestrian dynamics is.

The first part of the presentation gives a brief overview of different experiments performed under laboratory conditions and measurement methods providing results on an individual scale.

In the second part the goodness of force-based models of pedestrian dynamics is discussed. Having the quantitative validation of mathematical models in focus principle questions will be addressed throughout the presentation: Is it manageable to describe pedestrian dynamics solely with the equations of motion derived from the Newtonian dynamics? Another important issue is the geometrical representation of modeled pedestrians. Does the geometrical shape of a two dimensional projection of the human body matter when modeling pedestrian movement? If yes which form is most suitable? This point is investigated in the third part while introducing the Generalized Centrifugal Force Model (GCFM) [2]. Moreover, we highlight a frequently underestimated aspect in force-based modeling which is to what extent the steering of pedestrians influences their dynamics? Finally, validation and verification of the GCFM is demonstrated by means of several simulations in different geometrical scenarios.

- Andreas Schadschneider and Armin Seyfried. Modeling pedestrian dynamics - from experiment to theory and back. In Traffic and Granular Flow ’09, 2009.
- Mohcine Chraibi, Armin Seyfried, and Andreas Schadschneider. The generalized centrifugal force model for pedestrian dynamics. Phys. Rev. E, 82:046111, 2010.

Date: Oct. 4, 2012, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A206

Tai-Chia Lin (National Taiwan University)

A new model of ion channels: PNP-steric equationsAbstract:

A class of approximate Lennard-Jones (LJ) potentials with a small parameter is found whose Fourier transforms have a simple asymptotic behavior as the parameter goes to zero. When the LJ potential is replaced by the approximate LJ potential, the total energy functional becomes simple and exactly the same as replacing the LJ potential by a delta function. Such a simple energy functional can be used to derive the Poisson-Nernst-Planck equations with steric effects, called PNP-steric equations being a new mathematical model for the LJ interaction in ionic solutions. Stability and instability conditions for the 1D PNP-delta equations with the Dirichlet boundary conditions for one anionic and cationic species are expressed by the valences, diffusion constants, ionic diameters and coupling constants.This is the first step to study the dynamics of solutions of the PNP-steric equations.

Date: Jul. 26, 2012, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A401

Li-Chang Hung (Meiji University)

Traveling Wave Solutions of Competitive Lotka-Volterra Systems :

Constructing Solutions for a System of PDEs from Solutions for a Single PDEAbstract:

In theoretical ecology, a frequently-used model to describe thecompetition among n distinct species is the competitive Lotka-Volterrasystem of n species with diffusion. From the viewpoint of ecology,determining which species will survive in a competitive system is offundamental importance. In order to study this problem, we can usetraveling wave solutions. In this talk, we investigate the existenceof traveling wave solutions for Lotka-Volterra systems of n competingspecies. For the case n=2, we show that new exact traveling wavesolutions exist by introducing appropriate ansätzes. In addition, someopen problems and conjectures related to the 2-species case arepresented. The case n=3 is more complicated and contains rich andinteresting phenomenon to be explored. Motivated by the results ofexact solutions for n=2, exact traveling wave solutions of the 3species case are found. Based on these exact solutions, AUTO is usedto obtain the global branch of non-trivial traveling wave solutions when some parameter is varied. Semi-exact traveling wave solutions are also found for the case n=3. In particular, it is notable that many elementary but tedious computations when finding exact solutions are done by Mathematica.

Date: Jul. 19, 2012, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Shunji Satoh (The University of Electro-Communications)

Engineering and scientific approaches on vision science to develop novel algorithm and to solve paradox between physiology and perception.Abstract:

You may have an ultimate, effective, but mysterious system for information processing on image analysis; it's your vision system. The system enables character/face recognition, motion analysis, color processing and so on. Moreover, its ability surpasses existing image processing algorithm implemented in robots or OpenCV for example. If we understand our vision system theoretically, we will have a novel and effective algorithm or corresponding programming codes. However, our vision system is not perfect as known as visual illusion. For two image patches moving with equal speed but with different contrast, lower speed is perceived for the patch with lower contrast [Thompson, 1982]. Physical defects also exist in our eyes; both retinas have blind spots in which no photoreceptor exists. If we did not have filling-in algorithm to recover the lacking image, we would see big holes in front of you. From engineering viewpoints, this is just a topic on “digital image inpainting” which restores damaged films automatically [Bertalmio et al., 2000]. In this seminar, I will present a way for unifying knowledge obtained from interdisciplinary research on vision by taking up my researches: (2) Filling-in process at the blind spots. (1) A MT model resolves a paradox between physiology and psychology.

Date: Jun. 21, 2012, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Yoshihiro Yamazaki (Waseda University)

Collective behavior of bistable units with global and asymmetric local interactions

Spatio-temporal patterns on peeled adhesive tapes Stocastic CA model Nullcline of the bistable units affected by noiseAbstract:

Recently we have extracted the following dynamical system from the experiment of peeling an adhesive tape[1].

(1) The system consists of bistable units affected by noise.

(2) Between the units, there exist global and asymmetric local interactions. Based on the above properties for the system, we have constructed the dynamical model [2] and the stocastic cell automaton model[3]. These models have the following characteristic properties.

(a) Noise-induced bistability (from the dynamical model): The existence of the noise alters the stability of the system from monostable to bistable.

(b) Spatio-temporal intermittency (from the stocastic cell automaton model): The statistical and fractal properties, such as the existence of percolation threshold and power-law behaviors,

are confirmed and consistent with the real experiments of peeling adhesive tape.[1] Y. Yamazaki and A. Toda: Physica D 214 (2006) 120-131

[2] Y. Yamazaki: Prog. Theor. Phys. 125 (2011) 641-652.

[3] Y. Yamazaki, K. Yamamoto, D. Kadono, and A. Toda: J. Phys. Soc. Jpn. 81 (2012) 043002 (3 pages)

Date: Jun. 14, 2012, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hiroshi Ito (Kyushu University)

Reconstitution and control of circadian clock in a test tube

Abstract:

Circadian rhythms are periodical phenomena with a 24 hours period in living things. What is the central oscillator bringing us the rhythm? This tough issue has been tackled for several decades. My collaborator and I recently shed light on this issue by reconstituting a circadian clock in a test tube. Molecular biologists focused on the circadian rhythms of cyanobacteria fifteen yeas ago. They identified the three clock-related genes kaiA, kaiB, kaiC. When each gene is disrupted by means of molecular biological techniques, the cellular rhythms are abolished. A genetic network including the three genes had been thought to be the central oscillator of cyanobacterial circadian rhythm (Ishiura et al. Scinece 1998). However, we reconstituted circadian rhythms of KaiC phosphorylation by mixing the three proteins, KaiA, KaiB and KaiC with ATP in a test tube. The self-sustained oscillation suggests physiological circadian rhythms are consisted of biochemical oscillation without gene regulatory network (Nakajima et al. Science 2005).

In this seminar I will focus on the several findings after succeeding in the reconstitution. Cellular circadian rhythms in any organisms can be synchronized by environmental light or temperature cycles. I found temperature cycles could successfully entrain the reconstituted oscillator but light cycles failed (Yoshida et al. PNAS 2009). Also, the biochemical oscillator can synchronize among samples with different phases by mixing them (Ito et al. Nat Struct Mol Biol 2007). Cellular circadian rhythm is nullified by chilling it and the reconstituted biochemical rhythms also can not be observed at low temperature. I detected the type of bifurcation for the transition of rhythmicity. I will address the biological meaning of the bifurcation.

Date: Mar. 22, 2012, 16:30〜18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Masahiro Takinoue (Tokyo Institute of Technology)

Challenges to the construction of artificial cell models as micrometer-scaled nonequilibrium dynamic systemsAbstract:

Understanding the essence of life systems is one of the most important issues in science. Although our understanding of the molecular basis of life systems has dramatically increased, the whole picture of life systems as autonomous integrated molecular systems has not been revealed yet. Recently, artificial cell systems as simplified models of natural living cells have been proposed. The artificial cell systems have helped us to characterize life systems as autonomous integrated molecular systems [1]. However, most of proposed artificial cell systems have limitations caused by the difficulty in controlling nonequilibrium conditions in cell-sized systems. It is required to develop experimental methods to control nonequilibrium conditions in cell-sized systems by realizing sustained matter and energy flows into/out of cell-sized systems. In this presentation, we introduce some challenges to the construction of artificial cell models as micrometer-scaled nonequilibrium dynamic systems: (i) a novel method for artificial cell study based on picoliter-sized (cell-sized) water-in-oil (W/O) microdroplets, named Cell-sized continuous-flow stirred-tank reactor ("Cell-sized CSTR"), which realizes nonequilibrium chemically open systems for artificial cell models [2]; (ii) aspontaneous limit cycle rotary motion of micrometer-sized objects in a stationary electric field [3]; (iii) autonomous DNA/RNA molecular computing systems [4]. We believe that these challenges will promote the construction of nonequilibrium artificial cells in future.[1] (review) M. Takinoue et al., Anal. Bioanal. Chem. 400, 1705-1716 (2011).

[2] M. Takinoue et al., Small 6, 2374-2377 (2010).

[3] M. Takinoue et al., Appl. Phys. Lett. 96, 104105 (2010).

[4] M. Takinoue et al., Phys. Rev. E 78, 041921 (2008).

Date: Feb. 16. 2012 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Campus map in Japanese in English

Makoto Iima (Hiroshima University)

Dynamics and Pattern formation in Binary Fluid Convection.Abstract:

We study thermal convection of a binary fluid mixture (binary fluid convection). Unlike ordinary Rayleigh-Benard convection, binary fluid convection shows a rich variety of patterns including spatially-localized pattern in which a small number of convection cells exist in conductive state. Solutions for steady localized convection cells with different number of cells can coexist in a parameter region, and the bifurcation branch shows a snake structure. Solutions for traveling localized convection cells show a different bifurcation structure. These solutions are shown useful for understanding dynamics of the pattern formation dynamics. This work is a collaboration with Dr. Takeshi Watanabe (Hiroshima University) and Prof. Yasumasa Nishiura (Tohoku University).

Date: Jan. 27. 2012 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A306

Campus map in Japanese in English

Deok-Soo Kim (Hanyang University, Korea)

Biogeometry based on the Voronoi diagram and the Beta-complex.Abstract:

The Voronoi/Delaunay structures are everywhere in nature and are useful for understanding the spatial structure of a point set. Being powerful computational tools, their generalization has been made in various directions. One of the generalizations, the Voronoi diagram of spherical balls nicely defines the proximity among the balls. Like its counterpart of the ordinary Voronoi diagram of points or the power diagram, the dual structure can be more convenient in both representing and traversing the topology structure of the Voronoi diagram. This talk will introduce the concept of "biogeometry" using the Voronoi diagram of balls and its dual structure, the quasi-triangulation, particularly in the three-dimensional space. Based on the quasi-triangulation, we define a new geometric structure called the beta-complex which concisely yet efficiently represents the proximity among all spherical balls within the boundary of the input ball set, where its boundary is appropriately defined. It turns out that the beta-complex can be used to efficiently solve many geometry and topology problems for the ball set. Among many potential application areas, the structural molecular biology is the utmost application area because the beta-complex immediately and efficiently solves many geometry problems related to important structural molecular biology problems. Application examples include the computation of the molecular surface, the extraction of pockets on the boundary of molecule, the computation of areas of various types of surfaces defined on a molecule, the computation of various kinds of volumes defined on a molecule, the docking simulation, etc. We will also demonstrate our molecular modeling and analysis software, BetaMol, which is entirely based on the unified, single representation of the quasi-triangulation and the beta-complex.

Date: Dec. 8. 2011 15:30-16:50

Location: Meiji Univ. Ikuta Campus Main Building, Room 0301.

Campus map in Japanese in English

Shuji Ishihara (The University of Tokyo)

Mechanical control of hexagonal cell packing in Drosophila wing.Abstract:

How do mechanical forces control a series of deformations during morphogenesis? Recent studies have revealed that the biased activity and/or localization of force-generating molecules within a cell coordinates the geometrical changes of cells. On the other hand, it remains unclear how the mechanical interaction among cells and the resulting stress field of a tissue are organized to control cellular pattern formation. One of the difficulties comes from the lack of proper experimental methods to directly measure and quantify the forces in the cell population inside the animal body. By adopting Bayesian scheme, we developed a theoretical framework to estimate the pressure of individual cells and the tension of each cell adhesion surface. Responses to laser cutting and myosin distribution agreed with the estimated tensions. Using our method, we studied mechanical basis of hexagonal packing, the increase of hexagonal cells in the Drosophila wing during the pupal stage. Our quantification of developmental changes of the stress distribution within a tissue and of corresponding rearrangements of cells provides a new physical mechanism for cell packing: biased external forces acting on the tissue provide the directional information for local orientation of hexagonal cells which underlies the global hexagonalization. Our force estimation method will become a powerful tool in analyzing how information for orchestrating cellular behaviors during morphogenesis is encoded in distributions of forces within a tissue.

Date: Nov. 2. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A306

Naoki Masuda (The University of Tokyo)

Predictability of conversation partners.Abstract:

Recent developments in sensing technologies have enabled us to examine the nature of human social behavior in greater detail. By applying an information-theoretic method, we examine the predictability in conversation events. The predictability in the sequence of one's conversation partners is defined as the degree to which one's next conversation partner can be predicted given the current partner. We quantify this predictability by using the mutual information. We examine the predictability of conversation events for each individual using the longitudinal data of face-to-face interactions collected from two company offices in Japan. Each subject wears a name tag equipped with an infrared sensor node, and conversation events are marked when signals are exchanged between sensor nodes in close proximity. We find that the conversation events are predictable to a certain extent. Much of the predictability is explained by longtailed distributions of interevent intervals. However, a predictability also exists in the data, apart from the contribution of their long-tailed nature. In addition, we show that an individual's predictability is correlated with the position of the individual in the static social network derived from the data. This work has been done in collaboration with Taro Takaguchi (Univ. Tokyo), Mitsuhiro Nakamura (Univ. Tokyo), Nobuo Sato (Hitachi), and Kazuo Yano (Hitachi).

Date: Oct. 27. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A305

Terumasa Tokunaga (Meiji Univ.)

Detection of the substorm precursor from ground-magnetometer data.Abstract:

Auroral substorm is one of the energy release process of solar wind stored Earth’s magnetosphere. It has been reported that huge auroral substorm sometimes cause a massive power outrage. It is not peculiar to auroral substorm but all geophysical phenomena that occur suddenly could be threats for human activity. Hence, it is important to detect precursory events in terms of the imminent prediction. In the field of Solar- Terrestrial Physics, it is widely recognized that the occurrence of auroral substorm could be detectable as an increase in the northward component of the Earth’s magnetic filed observed at mid and low latitudes. However, since their initial movement is quite gradual, it is difficult to detect them. Recently, Tokunaga et al. (2010) introduced the Change-Point detection method, called Singular Spectrum Transformation (SST), to detect the precursor of auroral substorms from ground-magnetometer data. SST is a powerful method to detect gradual, minute signals from real world time series data. In this seminar, firstly, I define the problem setting of real world precursory detections and consider its difficulties. Second, the basic concept of SST is introduced. Third, we apply SST to geomagnetic time series data.

Date: Sep. 28. 2011 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A306

Chandrajit Bajaj (University of Texas, USA)

A-periodic Tilings and Icosahedral Viral Capsid Protein AssembliesAbstract:

We shall briefly review the theory of 3D quasi-crystals, 6D icosahedral Bravais lattices, and their projections that yields aperiodic (Penrose) tilings . We shall show how this theory allows one to characterize the global and local symmetric icosahedral packings of proteins, that define the architecture of viral capsid shells. These capsid shells house the nucleic acids genome of parasitic viruses that are causative of many human, animal and plant diseases.

Date: Jul. 12. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A306

Akiko Kaminaga (Kagoshima Univ.)

Microemulsions as reaction-diffusion medium - Diverse reaction-diffusion patterns in the BZ-AOT system

Abstract:

The First example of Turing patterns in chemical system was observed in the chlorite-iodide-malonic acid (CIMA) reaction in gel, which should reduce effective diffusivity of activator. To change the diffusivity of chemical species, water-in-oil microemulsions consist of oil, surfactant and water can also serve as reaction-diffusion media for pattern formation. Property of microemulsions can easily modified by changing the composition of microemulsions. In the case of BZ-AOT system, microemulsion in which Belousov-Zhabotinsky (BZ) reaction mixture was dispersed in alkane with the aid of anionic surfactant, aerosol OT (AOT), inhibitor can diffuse faster via the oil phase. Variety of patterns, some of those never observed in homogeneous aqueous system, has been found in this system.

Date: Jul. 7. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Takao K. Suzuki (National Institute of Agrobiological Sciences)

Morphological design and evolutionary emergence of leafy moth/butterfly wing patternsAbstract:

Camouflage is a fascinated defensive Strategy of organisms, typically resemblance to natural objects, such as leaves and leichen. Despite much progress in our understanding of coloration of camouflage, however, the pattern itself has been little investigated. Here, we conducted quantitative analysis and historical tracing to elucidate functional integration and Evolutionary emergence of leafy moth-wing pattern. In this seminar, I will introduce morphological aspects of camouflage patterns and their possible evolutionary scenario, and also briefly review various way of pigmental pattern formation of organisms, including spot patterns in fly and turing patterns in fish.

Date: Jun. 23. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Akiko Nakamasu (Meiji Univ.)

From Pigment Pattern to Morphogenesis – The Turing Pattern in Developmental Biology

(a), Series of laser ablation to measure the relationship between the pigment cells (b), Phenotipic plasticity in the leaf morphology of Neobeckia aquaticaAbstract:

In 1952, Alan Turing put forward the idea of a reaction-diffusion system that explained the autonomous formation of patterns in regions where none had pre-existed. Such patterns could provide the positional information that is thought to be used in various developmental processes. But it had long been difficult to prove whether the patterns were actually dependent on a reaction-diffusion system. With this background, I had participated in experiments using the skin pigment pattern on fish (specifically, the model organism zebrafish) which is a living example of a pattern formation system. In this seminar, I will show that the interactions among zebrafish pigment cells include short range activation and long range inhibition which satisfy the conditions necessary to form a Turing pattern. Then, I will talk about the potential for using the reaction-diffusion model to explain plant leaf morphogenesis.

Date: Jun. 9. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Ryoko Okajima (Meiji Univ.)

The Cause of Phenotypic Discontinuity: Shell Shapes of Terrestrial GastropodsAbstract:

The phenotypic distribution is often discontinuous and dispersed. As an example of such a distribution, we studied the shell shapes of terrestrial gastropods, which exhibit a bimodal distribution. In this presentation, I would like to talk about our simple model to test the hypothesis that the bimodal distribution relates to the shell balance on different substrates. Additionally, the study of geometric constraint on shell shapes is discussed.

Date: May 26. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hirofumi Niiya (Hiroshima Univ.)

A theoretical study of morphodynamicsof dunes using dune skeleton modelAbstract:

Sand dunes, which are the largest granular objects on the Earth, form several distinct patterns. These patterns are determined by two dominant factors; the steadiness of wind direction and the amount of available sand constructs dunes. For example, unidirectional wind generates barchans or transverse dunes. The former, crescent-shaped dunes, are formed in dune fields with small amount of available sand, whereas the latter extending perpendicular to the wind direction, are formed in dune fields with the larger amount of available sand than the barchan-rich field. In recent years, rescaled water tank experiments have successfully been conducted to form distinct dune shapes under control. Computer models also reproduced various shapes of dune formation process. However, the theoretical methodology explaining the basic mechanism for the complex morphodynamicsof dunes beyond the mere numerical reproduction of their formation process is yet to be developed.

In our presentation, in order to theoretically analyze the basic mechanism hidden in formation and migration process of dune, we propose a Dune skeleton model that consists of coupled ordinary differential equations each of which represents the dynamics of two-dimensional cross sections (hereafter, 2D-CSs). Present model shows that; I) Three typical shapes of dunes; straight transverse dune, wavy transverse dune, and barchan, are reproduced depending on the amount of available sand and wind strength. Also, the increase in the amount of available sand and inter 2D-CSs flow enhances the stability of the shape of transverse dune, whereas the decrease in the amount of available sand and the increase in intra 2D-CS flow destabilizes its shape to enforce the deformation to a barchan[1]. II) A linear stability analysis of two 2D-CSs system showed the bifurcation structure of fixed point and identified the stability condition of the straight and wavy transverse dune. These theoretical results qualitatively correspond to the observation and the experimental facts.

Reference

[1] H. Niiya, A. Awazuand H. Nishimori. J. Phys. Soc. Jpn. 79 063002 (2010).

Date: May 12. 2011 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Ryusuke Kon (Meiji Univ.)

Permanence induced by life-cycle resonances:the periodical cicada problemAbstract:

Periodical cicadas (Magicicadaspp.) are insects inhabiting the Eastern United States. They are known for their unusually long life cycle for insects and their prime periodicity of either 13 or 17 years (i.e., their life span is either 13 or 17 years and they emerge periodically from the ground exactly every 13th or 17th year). One of the explanations for the prime periodicity is that the prime periods are selected to prevent cicadas from resonating with hypothetical predators with submultipleperiods. In this talk, we consider this hypothesis by investigating a mathematical model for dynamically interacting periodical predator and prey. This study shows that if the periods of the two periodical species are not coprime, then the predator cannot resist the invasion of the prey since the invasion of the prey is always facilitated by its well-timed cohorts. On the other hand, if the periods are coprime, then the predator can resist the invasion of the prey. It is also shown that if the periods are not coprime, then the life-cycle resonance induces a permanent system, in which no cohorts are missing in both populations. This contrasts with the result that systems consisting of coprimeperiodical species cannot be permanent. These results suggest that prime periodicities are not advantageous even under hypothetical periodic predation pressure.

Date: Feb. 24, 2011, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Shogo Kato (The Institute of Statistical Mathematics)

A Markov process for circular dataAbstract:

We propose a discrete time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered. Finally, an application of the model to wind direction data is provided.

Date: Feb. 10, 2011, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Kensuke Yokoi (Cardiff University, UK)

Numeircal studies of droplet impacting and splashingAbstract:

In this presentation, I would like to talk about 3D numerical simulations of various types of droplet impacting phenomena such as droplet impacting into a thin liquid layer (milk crown?), droplet depositions onto dry surfaces and droplet splashing on dry surfaces.

The numerical framework is based on the CLSVOF method, the CIP-CSL method, VSIAM3 and the CSF model. I will also take about the importance of dynamic contact angle for dr oplet behaviours on dry surfaces.

There are some animation examples on my website:http://www.kensuke.biz/kensuke

Date: Jan. 26, 2011, 17:30-18:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A401

Danielle Hilhorst (CNRS and University Paris-Sud11)

A nonlinear parabolic-hyperbolic PDE model for contact inhibition of cell-growthAbstract:

We consider a parabolic-hyperbolic system of nonlinear partial differential equations which describes a simplified model for contact inhibition of growth of two cell populations. In one spacedimension it is known that global solutions exist and that they satisfy the segregation property which reflectstheinhibition mechanism: if initially the two populations are segregated –in mathematical terms this translates in disjoint spatial supports of their densities -this property remains valid for all later times. The space-time curves which separate the two populations are free boundaries. In this talk,we userecent results on transport equations and Lagrangianflows to obtain similar results in the case of several spatial variables. This is joint work with Michiel Bertsch, Hirofumi Izuhara and Masayasu Mimura.

Date: Jan. 26, 2011, 16:20-17:20

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A401

Sergiy Klymchuk (Auckland University of Technology, New Zealand)

Different Contexts in Teaching Mathematical Modelling and Applications to Engineering Students: Students’ Attitudes and DifficultiesAbstract:

In this talk the results of two studies are discussed. The first study analyses engineering students’ attitudes towards non-traditional for them contexts in teaching/learning of mathematical modelling and applications: environment and business. On the one hand, the contexts are not directly related to engineering. On the other hand, chances are that most of the graduates in engineering will be dealing with the environmental and business issues in one way or another in their future work because nearly every engineering activity has an impact on the environment and leads to commercial implications. The second study investigates engineering students’ difficulties in the formulation step of solving a typical application problem from a calculus course. The research question was to find reasons why most of the students could not use their knowledge to construct a simple function in a familiar context. It was neither lack of mathematics knowledge nor an issue with the context. The students’ difficulties are analysed along with their suggestions on how to improve their skills in solving application problems.

Date: Dec. 20, 2010, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A310

Masashi Aono (RIKEN)

Amoeba-based Neurocomputing: Spatio-Temporal Dynamics for Overall Optimization in Resource Allocation and Decision MakingAbstract:

A single-celled amoeboid organism, the true slime mold Physarum polycephalum, exhibits rich spatiotemporal oscillatory behavior and sophisticated computational capabilities. Our aim is to clarify how the organism achieves the "overall optimization," the maximization of the benefit of the whole body, which cannot always be realized by simply summing selfish behaviors of the organism's components pursuing their partial interests. We created a biocomputer that incorporates the organism as a computing substrate to search for solutions to various optimization problems with the assistance of optical feedback to implement recurrent neural network models. The organism changes its shape by alternately growing and withdrawing its photosensitive branches so that its body area can be maximized and the risk of being illuminated can be minimized. In this way, the organism succeeded in finding the optimal solution to the four-city Traveling Salesman Problem with a high probability. Considering the organism as a network of dynamical systems that compete for constant amounts of intracellular resources, we formulated two mathematical models to extract essential dynamics of the amoeba-based computing. 1) Resource-Competing Oscillator Network (RCON) model is an ordinary differential equation model of a particular kind of coupled oscillators. RCON model reproduces well the organism's experimentally observed behavior, as it generates a number of spatiotemporal oscillation modes and spontaneous switching among the different modes. 2) Tug-Of-War (TOW) model is a star network of discrete-time-state dynamical systems capable of efficient and adaptive decision making in solving the Multi-armed Bandit Problem (MBP), a problem of finding the most rewarding one from a number of probabilistic slot machines. TOW model exhibits better performances compared with well-known algorithms for MBP. In our models the resource conservation law seems to play important roles for the efficient and adaptive computation, as it leads the amoeba-like branches to perform spatiotemporally correlated parallel search.

Date: Dec. 2, 2010, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hisa-Aki Tanaka (UEC)

Design of optimal entrainment of a weakly forced oscillatorAbstract:

A theory for obtaining waveform for the effective entrainment of a weakly forced oscillator is presented. Phase model analysis is combined with calculus of variation to derive a waveform with which entrainment of an oscillator is achieved with minimum power forcing signal. Optimal waveforms are calculated from the phase response curve and a solution to a balancing condition. The theory is tested in chemical entrainment experiments in which oscillations close to and further away from a Hopf bifurcation exhibited sinusoidal and higher harmonic nontrivial optimal waveforms, respectively.

Date: Nov. 15, 2010, 17:30-18:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A310

Yukie Sano (Nihon Univ.)

Statistics of collective human behaviors observed in blog entriesAbstract:

As a reflection of social human interaction, we focus on statistical properties of the number of Japanese blog entries. From the data that contains more than 1,200 million blog entries, we present the results from two different aspects.

First, we focus on the time series fluctuation of the number of blog entries that contain a target word. In case that we choose a commonly used word as a target, we show that the standard deviation of the time series can be described by its average. Especially for frequently appearing words, we confirm that the standard deviation increases linearly according to its average, following Taylor's power law. Additionally, we also discuss in the case that the sudden increase in the number of a word is strongly depending on external factors such as news.

Secondly, we show the statistical results of individual blogger's behaviors. We found that there are two different types of distributions in posting intervals. Further, Zipf's law on word frequency is confirmed to be universally independent of individual activity types. Finally, we also present a few new issues from our works.

Date: Nov. 15, 2010, 16:20-17:20

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A310

Akinori Awazu (Hiroshima Univ.)

Molecular number smallness induced slow nonstationary fluctuations in catalytic reaction networksAbstract:

Slow fluctuations around equilibrium and self-organized critical behavior under nonequilibrium conditions of catalytic reaction networks induced by smallness in the molecule number were investigated.

Most intra-cellular reactions progress with the aid of catalysts (proteins), and all catalysts have to be synthesized as a result of such catalytic reactions. Thus, studies in catalytic reaction networks have gathered much attention, in order to develop a theory of the origin of life, as well as to unveil universal statistical characteristics in the present cells. Cells generally consist of a large number of chemical specie, and some chemical species play an important role even at extremely low concentrations amounting to only a few molecules per cell. Then, the fluctuation and discreteness in the molecule number are not negligible.

In our presentation, in order to study the general features of the reaction dynamics in living systems, we focus on the following slow nonstationary dynamics of the catalytic reaction networks, which appear when the molecule number is smaller than the characteristic values; I) The slowing down of the relaxation of the fluctuations around equilibrium where the relaxation time is prolonged compared to that of the case of infinite number of molecules [1], and II) self-organized critical behavior induced by the molecule number discreteness under a flow of chemicals [2].

References

[1] A. Awazu and K. Kaneko. Phys. Rev. E 81, 051920, (2010).

[2] A. Awazu and K. Kaneko. Phys. Rev. E 80, 010902(R), (2009).

Date: Oct. 14, 2010, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Kumiko Hayashi (Osaka Univ.)

Fluctuation theorem applied to bio-motorsAbstract:

Fluctuation theorem (FT) is the physical law of entropy productioncaused when an operation is added to a small system, which issensitive to thermal noise. When applied to a macroscopic system, FT is equivalent to the second law of thermodynamics. Since 1993when FT was discovered, it has been studied theoretically andexperimentally for various physical systems. In our study, FT was first applied to bio-motors in order to measuretheir driving forces. For example we applied FT to F1-ATPase, whichis a rotary motor protein, and measured its rotary torque by using FT.Being practically useful for rotary motors when our results werecompared with those obtained in previous studies, FT has begun tobe used for the torque measurements of ofF1 mutants and V1 mutants. Now we try to apply FT to measure driving forces exerted by motorproteins in vivo or in a cell. Concretely we observed mitochondriontransported by motor proteins in the axon of PC12 cells. We wouldlike to discuss whether we can measure the driving force acting on amitochondria. We will show our primitive data related to this issue.Reference:

[1] KumikoHayashi,Hiroshi Ueno, RyotaIino and Hiroyuki Noji,Phys. Rev. Lett.104, 218103 (2010).

Date: Sep. 27, 2010, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hiroya Nakao (Kyoto Univ.)

Turing patterns in network-organized activator-inhibitor systemsAbstract:

Turing instability in activator–inhibitor systems provides a paradigm of non-equilibrium self-organization; it has been extensively investigated for biological and chemical processes. Turing instability should also be possible in networks, and general mathematical methods for its treatment have been formulated previously by Othmer& Scrivenin 1971. However, only examples of regular lattices and small networks were explicitly considered. We study Turing patterns in large random networks with strong degree heterogeneity, using the classical Mimura-Murray model on scale-free networks as an example, which reveal striking differences from the classical behavior. The initial linear instability leads to spontaneous differentiation of the network nodes into activator-rich and activator-poor groups but periodic structures are not formed. The emerging Turing patterns become furthermorestrongly reshaped at the subsequent nonlinear stage. Multiple coexisting stationary states and hysteresis effects are observed. This peculiar behavior can be understood in the framework of a mean-field theory. Our results offer a new perspective on self-organization phenomena in systems organized as complex networks. Potential applications include ecological metapopulations, cellular networks of early biological morphogenesis, etc. If time permits, I would also like to touch on diffusion-induced chaos in coupled limit-cycle oscillators on scale-free networks, which can be understood almost in parallel with the network Turing patterns.[1] H. Nakao& A. S. Mikhailov, Turing patterns in network-organized activator-inhibitor systems. Nature Phys. 6, 544-550 (2010).

[2] H. Nakao& A. S. Mikhailov, Diffusion-induced instability and chaos in random oscillator networks. Phys. Rev. E 79, 036214 (2009).

Date: July 22, 2010, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hai-Yen Siew (Meiji Univ.)

The generalizedt-distribution on the circleAbstract:

An extended version oft-distribution on the unit circle is generated by conditioning a normal mixture distribution, which is broadened to include not only unimodalityand symmetry, but also bimodality and asymmetry, depending on the values of parameters. After reparametrization, the distribution contains four circular distributions as special cases: symmetric Jones-Pewsey, generalized von Mises, generalized cardioidand generalized wrapped Cauchy distributions. As illustrative examples, the proposed model is fitted to the number of occurrences of the thunder in a day and the monthly wind directions of Ryoriin 1995.

Date: July 8, 2010, 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Shin I. Nishimura (Hiroshima Univ.)

Strategies for Chemotaxis of Amoeboid CellsAbstract:

Chemotacticbehaviors in eukaryotic cellsanimalcells are widely known phenomena.Though a straight motion toward the chemical source can be observed in chemotaxis, cells do not necessarily move in a straight way but often move in fluctuated zigzag ways. For understanding such variety of behaviors, we build a simple model for chemotacticeukaryotic cells, which describes changes in cell shape on the two-dimensional plane by considering a cell membrane, actinfilaments embedded in the membrane, and an intracellular control factor. We also introduce three models of environment around cells: (a) simple chemical gradient, in which the chemical guidance (chemotacticsignal) spreads everywhere in a two-dimensional field with a uniform gradient; (b) flipping chemical gradient, with which the uniform gradient is reversed at a moment everywhere in the space; and (c) a maze around a chemical source, in which maze-like walls separate the source and cells to block cell’s locomotion. Some parts in those walls permeate the chemical guidance to confuse cells. The simulated results show that in the case (a) cell’s behavior is most efficient when the cell takes a crescent shape like “keratocyte” and moves in a straight way. In contrast, in cases of (b) and (c) the behavior is efficient when the cell takes a typical amoeboid-like shape and moves in zigzag ways. These results suggest that the fluctuated zigzag locomotion of amoeboid cell has an advantage in some “complex” environment.

Date: Jun. 24, 2010 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hiroki Takada (Fukui Univ.)

Mathematical models in biosignalsAbstract:

The aim of mathematical modeling is to understand the mechanisms that govern the working of complex systems and to detect anomalous signals by using model coefficients or theoretical indices. For instance, detection is effective for diagnosing diseases. Anomalous signals can be generated by the degeneration of the potential function in the dynamical equation systems (DESs) or by fundamental changes in the DESs themselves, for instance, an increase in the degrees of freedom or the addition of stochastic factors. Visible determinism in the latter case would be different from that in the case without random variables. DESs were obtained as mathematical models that regenerated time series data such as those obtained from electrocardiography, electrogastrography, body sway, etc. It is especially well known that the mathematical models of some biosignalscan be developed by using stochastic processes. A correspondence has been obtained between the distributions of time series and temporally averaged potential functionsin stochastic differential equations. By performing time series analysis of the biosignals, the authors have succeeded in identifying the nonlinearity in a potential function that has several minima. Fluctuations could be observed in the neighborhood of the minima. We discuss the metamorphism in the potential function due to the application of a specific artificial load.

Date: Jun. 10, 2010 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hiroshi Kori (OchanomizuUniv.)

Issues on coupled oscillator networks: feedback engineering of synchronization and dependence of temporal precision on network structureAbstract:

In nature, there are many situations in which a population of oscillators forms a collective oscillation. Understanding dynamical properties of oscillator networks is an important issue because oftheir broad applications in disciplines ranging from biology to engineering. In this presentation, I will first review synchronization. In particular, useful mathematical models, called phase models, will be briefly explained. Then, I will talk about a few issues from my recent works.

Date: May. 27. 2010 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Yoshihiko Hasegawa (Tokyo Univ.)

Noise Inhomogeneitywithin Biological ModelingAbstract:

Since many biological mechanisms function under fluctuant environments, their dynamics can be well accounted for by Langevinequations driven by white noise. Although the white noise can reflect the nature of microscopic aspect of fluctuations, it is regular in a mesoscopictime scale and does not capture long-range fluctuations. In this presentation, we show effects of noise inhomogeneityon biological mechanisms. An approximation method considering the inhomogeneityis also presented.

Date: May. 13. 2010 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Kenta Odagiri (OchanomizuUniv.)

Pattern formation in autocatalytic proliferation systemsAbstract:

Autocatalytic process is often associated with pattern formation, ranging from the atomic scale phenomena to the morphology of living bodies.In my talk, I focus on pattern formation and its dynamics in autocatalytic proliferation systems. I will first present the very simple model that represents autocatalytic cell proliferation subject to the distribution of nutrition and natural death of the cells by starvation. I will show what is essential togenerate a branching pattern like actual bacterial colonies in the model, by comparing the cellular automata approach with the reaction-diffusion equation approach. I next present two kinds of three-component autocatalytic proliferation systems. One consists of consumer (X), its inhibitor (I), and nutrition (N), and the other consists of two different consumers (A, B) and N. Focusing on the“competitive” relation in these models, I will show various kinds of pattern formation and its transitionphenomena induced by the change of control parameters of the competition.

Date: Apr. 27. 2010 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Takuya Machida (Meiji Univ.)

The limit theorems for a time-dependent discrete-time quantum walk on the lineAbstract:

The quantum walks describes quantum versions of classical random walks. Relating with computer science, quantum walks are investigated as quantum search algorithms. The quantum search algorithms, e.g. Grover's algorithm, expressed by quantum walks are expected more exponentially faster than their classical counterparts. We study time-dependent discrete-time quantum walks on the one-dimensional lattice. By using the Fourier analysis, we cancompute the limit distribution of a two-period quantum walk defined by two orthogonal matrices or special unitary matrices. For the symmetric case, the distribution is determined by one of two matrices. Moreover, we consider two special cases and present limit theorems. In this case, the probability distribution becomes a one-period (usual) quantum walks.

Date: Apr. 13. 2010 16:30-18:00

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A207

Hirofumi Notsu (Meiji Univ.)

Characteristics finite element schemes for flow problemsAbstract:

In this talk, finite element schemes based on the method of characteristics are considered. It is known that the conventional Galerkinmethod gives oscillating results for high Péclet/Reynolds number problems. To deal with such phenomena, many upwind type schemes have been developed. We focus on schemes based on the method of characteristics in the upwind type ones. The method rests on an approximation of the material derivative along the trajectory of the fluid particle, and is natural from the physical point of view. Moreover, the method has an advantage that the matrix for the system of linear equations is symmetric, which leads to symmetric linear solvers, e.g., CG method, although the convection term usually gives a non-symmetric matrix. We show usefulness of the schemes including ours with numerical examples.

Date: Dec 16. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Kitsunezaki So (Nara Women’s Univ.)

Crack Formation Processes in Drying PasteAbstract:

A wide variety of granular materials consolidate by adding a small amount of water, as well known as clay paste and paint. Cracking induced by drying contraction is a typical solid-like behavior of paste, while water can give rheological and porous properties unlike usual solids to granular material sand affect the cracking processes. We review two types of cracking in a uniform layer of drying paste. One is quasi 2-dimensional cracking of paste shrinking on a fixed or frictional boundary. Although resulting cellular structures, named mud crack patterns, have been studied by using an elastic theory, recent studies reveal that such cracking occurs in an earlystage of a drying process and plasticity is significantly important for both creation and growth of cracks. Another type of cracking can be observed in starch pastes in a late-stage of drying process. Cracks are formed gradually from the drying surface and develop into a 3-dimensional prismatic structure. These cracks grow with a propagating drying front, which can be explained by nonlinear water transportation in a porous material. We report analytical and numerical approaches based on spring-network models for these two types of cracking.

Date: Nov 25. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Tohru Wakasa (Waseda Univ.)

Reaction-diffusion model on tumour growth with contact inhibitionAbstract:

For the last two decades, the mathematical modeling of tumour growth have been investigated by many researchers. In this talk I will introduce a reaction diffusion model describing spatio-temporal dynamics between two populations of normal cells and abnormal cells, which takes account of the effect of contact inhibition. The purpose of this talk is to understand the qualitative behavior of solutions of our model in one dimensional case. In particular, if the initial supports of two population densities are segregated, then there is a segregated solution in some sense. Moreover, it is observed from the numerical simulations that segregated solutions propagate with constant speed like traveling wave. Then, I will discuss the existence, uniqueness and stability of segregated traveling wave solution of our model.

Date: Nov 18. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Nobuhiko J. Suematsu (Hiroshima Univ.)

Localized Bioconvection of Euglena Caused by Phototaxis in the Lateral DirectionAbstract:

A group of micro-organisms often generates a macroscopic ordered pattern such as a bacteria colony and bioconvection. The bioconvection is one of fluidic patterns caused by an upward swimming of the micro-organisms. The oriented swimming is induced in response to an external stimulus or force field, e.g., a gradient in oxygen concentration, light illumination, and gravity. We focused on a swimming micro-organism exhibiting phototaxis, Euglena. In contrast to a general bioconvection appearing all over a chamber, Euglena formed a bioconvection in a part of a chamber. In this seminar, we would like to introduce to the characteristic behavior of bioconvection of Euglena, and discuss the mechanism of the pattern formation based on both experimental results and numerical calculation.

Date: Nov 11. 2009 16:30-17:30

Vladimir Chalupecky (Kyushu Univ.)

Phase-field models of liquid-phase epitaxyAbstract:

Liquid phase epitaxy is an epitaxial technique for producing thin semiconductor films from liquid supersaturated solutions. In my talk, I will present some mathematical models and their numerical solution that describe the film growth process in the phase-field framework. First, the physical process of crystal growth by liquid phase epitaxy is presented together with various growth morphologies. Single spiral growth is modelled by a phase-field formulation of the Burton-Cabrera- Frank model. Then, we consider a two-scale model that couples the diffusion-convection transport of concentration of atoms in a three-dimensional volume above the epitaxial surface and the microscopic spiral growth at the crystal surface. This model is obtained via a homogenization procedure from the microscopic model. The numerical scheme is based on finite-difference discretization on rectangular cell-centered and stagerred grids. The two-scale nature of the model allows us to use a coarse grid in the three-dimensional volume and a fine grid on the two-dimensional epitaxial surface, thus making the algorithm more efficient. Finally, we also present results of some numerical experiments.

Date: Nov 4. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Takashi Nakazawa (Okayama Univ.)

Numerical and mathematical analyses of water-circulator-induced flow in pondsAbstract:

Pollution and muddiness of natural and artificial reservoirs that are used to supply water irrigation have become important problems in recent years. A rotating propeller operating at low speed set on a lake surface is proposed because it is expected that the device can induce vertical circulating flow by the centrifugal force. Although various experiments have shown clearly that the water quality in a lake is improved by operation of such equipment, the flow mechanism is not fully understood. This study is in- tended to characterize vertical circulating flow resulting from the propeller’s action. To survey such a fluid motion numerically and mathematically in simple systems, the flow induced by the top boundary condition which forces a horizontal rotating flow is investigated here. Simulations of flows created by the top boundary condition are carried out to obtain steady-state solutions with various Reynolds numbers and to obtain a transition diagram.

Date: Oct 14. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Kazumichi Ohtsuka

(Univ. of Tokyo, Research Center for Advanced Science and Technology)

New type of evaluation method for level of service criterion using financial theoryAbstract:

The new type index on the level of service (LOS) criterion is proposed. To identify values of the LOS, we apply the net present value (NPV) method to congestion dynamics formulated by the Logistic equation. We have succeeded in measuring values of infrastructures on the basis of personal available space discounted by waiting time periods. It allows us to rate infrastructures quantitatively including passenger satisfaction. We also compare the theory with the LOS values from raw data observed at immigration counters in an airport. The results statistically reflect intertemporal satisfaction factors that the conventional LOS criterion does not take into consideration.

Date: Oct 7. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Hirofumi Izuhara (Meiji Univ.)

Pattern formation in smoldering combustion under micro-gravityAbstract:

It is observed from experiments that the behavior of smoldering combustion under microgravity is completely different from that on the earth. When a piece of paper is burnt in a micro-gravitational environment, interesting ash patterns are observed on the paper. In order to understand how these observed patterns form a model was proposed which has been studied both analytically and numerically. In this talk we will focus on some numerical results, in particular threat from rekindling. As all of the paper is not completely burnt, combustion is sustained by rekindling. We numerically suggest that rekindler occurs from the mathematical model.

Date: Jul 29. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Daichi Yanagisawa (Univ. of Tokyo, Research Fellow of JSPS, DC1)

Research for Evacuation and Pedestrian Queueing SystemsAbstract:

In my talk, I briefly summarize microscopic models for pedestrian dynamics and introduce my two research topics.We have obtained the mathematical formulation for the pedestrian flow, which includes the effect of conflicts and turning. It enables us to verify the specific phenomena for an evacuation theoretically. In the congested evacuation situation, the pedestrian flow decreases when all pedestrians try to evacuate faster and increases when we put an obstacle in front of the exit. When there are plural service windows, the queueing theory indicates that a fork-type queueing system (M/M/s), which collects people into a single queue, is more efficient than a parallel-type queueing system(M/M/ 1×s), i.e., queues for each service windows. However, in our new walking-distance introduced queueing theory, we find that the parallel-type queueing system is more efficient when sufficiently many people are waiting in the queues.

Date: Jul 22. 2009 16:30-17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Shiro Horiuchi (Meiji Univ.)

A hidden edge effect on animal group size and density: an agent-based model revealedAbstract:

Apart from the foraging conditions and predation pressure, which are often studied concerning the ecological edge effects, we aimed to clarify the boundary nature of edges, from which animals cannot move any farther. By simulating animal groups interacting with one another, we made an agent-based model in a computational space. Assuming no predation pressure, we changed only the resource conditions in contrast between the habitat (comprising ‘interiors’ and ‘edges’) and its ‘exteriors’. The obtained results were robust---only when the resources are sufficiently richer in the habitat than in the exteriors, the group density and size tend to be greater in the interiors than in the edges (i.e. boundaries between the interiors and exteriors); otherwise and more often the group density and size tend to be greater in the edges, or differ little. These were discussed with reference to relevant studies of primates in particular as exemplary group-living animals. We also show that expelling monkeys from edges to interiors---or from farmlands to mountains---work effectively only where the density of monkeys is low, such as Tohoku or Hokuriku areas in Japan Island.

Date: Jul 15. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Yuki Taniguchi (Meiji Univ.)

The stability of a flow on a rotating polar capAbstract:

An analytic solution of two-dimensional, steady, linear, viscous flow on a rotating spherical cap is obtained. We calculate a nonlinear solution to the linear solution and observe the stability from the time development of the minute perturbation around the nonlinear flow. As an inflow increases, the nonlinear solution whose configuration differs from that of the linear solution is obtained. The inflow is increases more, the nonlinear solution is unstable by Hopf bifurcation. The position of the occurrence of the instability is first the outlet and second the inlet on the boundary of the spherical cap.

Date: Jul 1. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Shin-ichiro Shima (JAMSTEC)

Micro-Macro Interlocked Simulation of Clouds and PrecipitationAbstract:

Although clouds play a crucial role in atmospheric phenomena, the numerical modeling of clouds remains some what primitive. We have proposed a novel, particle based, probabilistic approach for the simulation of cloud microphysics, which is named the Super-Droplet Method (SDM). This method enables accurate simulation of cloud microphysics with less demanding cost in computation. The outline of SDM and our future prospects will be presented. Especially, the possibility to apply Micro-Macro Interlocked simulation framework to the SDM will be discussed.

~~Date: Jun 24. 2009 16:30~17:30~~

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Hirofumi Izuhara (Meiji Univ.)

Traveling wave solutions to a model of some smoldering combustionAbstract:

It is observed from experiments that the behavior of smoldering combustion under microgravity is completely different from that on the earth. When a piece of paper is burnt in a micro-gravitational environment, interesting ash patterns are observed on the paper. In order to understand how these observed patterns form a model was proposed which has been studied both analytically and numerically. In this talk we will focus on some numerical results, in particular the existence of traveling waves. While these traveling waves are relatively simple solutions, they appear to be fundamental to understanding how the ash patterns develop.

Date: Jun 17. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Thomas Ronald Mollee (Meiji Univ.)

Pattern formation in chemotactic E. coli coloniesAbstract:

Colonies of E. coli cells form stable two-dimensional spot patterns of surprising regularity when grown on semi-solid agar consisting of a mixture of succinate and amino-acids. The spots, which are dense aggregates of cells, form in the wake of an expanding ring of cells called a swarm ring. Central to this pattern formation process is chemotaxis, the motion of bacteria up gradients of a chemoattractant, which in this case the cells excrete themselves. I will discuss a model of E. coli pattern formation that treats separately the roles played by amino acids and succinate in order to produce the spot patterns and account for the observed migration of the swarm ring.

Date: May 27. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Takeshi Ohtsuka (Meiji Univ.)

Interface evolution by unbalanced tristable Allen-Cahn type equationAbstract:

Allen-Cahn equation, which is a reaction-diffusion equation expressing phase separation and diffusion, is introduced to express the motion of grain boundaries between two stable phase in a crystal. Formal asymptotic analysis shows that internal layer of the solution approximates the interface motion by mean curvature flow, and the difference of strength of stability between two stable phase derives the driving force to the interface motion. In this talk we introduce a tristable type of Allen-Cahn equation, which expresses the situation including three stable phase and two internal layers. We shall give a brief introduction to the study of singular limit of tristable Allen-Cahn type equation, and discuss the dynamics of internal layer when stabilities of three phase are unbalanced.

Date: May 20. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Chiyori Urabe (Meiji Univ.)

Fracture Toughness and Maximum Stress in a Disordered Lattice SystemAbstract:

We will report about fracture in a disordered lattice system. In our system, particles are initially arranged on the triangular lattice and each nearest-neighbor pair is connected with a randomly chosen soft or hard Hookean spring. Every spring has the common threshold of stress at which it is cut. We make an initial crack and expand the system perpendicularly to the crack. We find that the maximum stress in the stress-strain curve is larger than those in the systems with soft or hard springs only (uniform systems). Energy required to advance fracture is also larger in some disordered systems, which indicates that the fracture toughness improves. The increase of the energy is caused by the following two factors. One is that the soft spring is able to hold larger energy than the hard one. The other is that the number of cut springs increases as the fracture surface becomes tortuous in disordered systems.

Date: May 13. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Wataru Nakahashi (Meiji Univ.)

Sexual selection by male choice and human evolutionAbstract:

Sexual selection (Darwin, 1871) is as important as natural selection (Darwin, 1859) for sexual species because we must mate with the other sex to produce progeny. Though Darwin (1871) noticed sexual selection by male choice in the human, theoretical and empirical research on sexual selection has mainly addressed decorative male traits and female preferences for such traits. However, not only in the human but also in many other species, there is increasing evidence of male mate choice for female traits. Why do such male mating preferences evolve and how do they affect the evolution of female traits? In this talk, I will explain quantitative genetic models of sexual selection by male choice to answer these questions and discuss how sexual selection by male choice has affected human evolution.

Date: April 22. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Shu-ichi Kinoshita (Meiji Univ.)

Fitness landscapes and the gene regulatory dynamics in complex networksAbstract:

I would like to report two issues: (1) How does the gene network structure influence the fitness landscape in an evolutionary process; (2) How does it influence the dynamics in the gene regulatory network. Long time ago, S. A. Kauffman introduced the so-called "NK-model" that reproduces an evolutionary process of a random network, and he studied fitness landscape under the process, on the one hand. On the other hand, he introduced and studies the famous "Random Boolean network model (RBN)” that describes temporal development of state dynamics of a random network. Both models have been successful to elucidate many important aspects of the random network dynamics. However, recent developments of gene network study have shown that the gene-gene interaction in living cells is not homogeneous like random network but heterogeneous such as scale-free network. Therefore, we need some generalizations of the NK-model and the RBN .So, we have generalized the NK model and the RBN to incorporate the various network structures into the models. Using this generalization, I will discuss the above issues.

Date: April 15. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Akiyasu Tomoeda (Meiji. Univ. and Tokyo Univ.)

Jamming Formation in Trafﬁc Flow

~ Microscopic and Macroscopic Approach ~Abstract:

Various kinds of jamming phenomena are observed in our daily life. In particular, the dynamics of traffic jam have attracted the interest of researchers in many fields, in terms of a non-equilibrium and dynamical system due to collective motion of interacting particles. In contrast to the continuous (macroscopic) model in the previous talk, our stochastic cellular automaton model (microscopic approach) applicable to buses, trains and other dynamics in conveyance system will be explained in this talk.

Date: April 8. 2009 16:30~17:30

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A205

Akiyasu Tomoeda (Meiji. Univ. and Tokyo Univ.)

Jamming Formation in Trafﬁc Flow

~ Microscopic and Macroscopic Approach ~Abstract:

Various kinds of jamming phenomena are observed in our daily life. In particular, the dynamics of trafic jam has attracted the interest of researchers in many fields, in terms of a non-equilibrium and dynamical system due to collective motion of interacting particles. In this study, we have investigated the jamming formation in two new models : one describes the dynamics of one-dimensional trafic flow on a motorway as a compressible fluid model, so-called "macroscopic" approach, and the other describes the dynamics of public conveyance system as a stochastic cellular automaton model, so-called "microscopic" approach. We have shown the unifid results that jamming formation is caused by amplifying the small perturbation in both two different approaches. This fact indicates that common structure marvelously underlies the mathematical models for trafic flow.

Date: March 17. 2009 13:30~16:15

Program:

Location: Meiji Univ. Ikuta Campus Build 2 Annex A Room A401

13:30 ～ 14:15

Alberto Tesei (Rome 1 Univ., Italy)Phase transitions, entropy and hysteresis

14:30 ～ 15:15

Horst Malchow (Univ. Osnabrueck, Germany)

Diffusive predation and competition patterns in a noisy environment Planar traveling Wave in a combustion model15:30 ～ 16:15

Kota Ikeda (池田 幸太) （Meiji Univ. )

Planar traveling Wave in a combustion model