Kyushu University Academic Staff Educational and Research Activities Database
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Murakawa Hideki Last modified date:2018.06.13

Academic Degree
Field of Specialization
Applied Mathematics, Numerical Analysis
Outline Activities
I am interested in various phenomena and problems in nature and sciences. I have been studying, for exaple, ice-water phasetransision, groundwater flow, competition and coorperation between animal species, cell culture, precipitation and dissolution reactions in chemistry etc. The aim of my research is to analyze model equations for such phenomena from both the mathematical and numerical points of view. Recently, I have constructed and analyzed highly accurate numerical methods for the above problems and versatile, easy to implement and stable numerical methods for general problems.
Research Interests
  • Applied Mathematics, Numerical Analysis
    keyword : Nonlinear diffusion problem, Reaction-diffusion system, Free boundary problem, Cell adhesion, Mathematical model
Academic Activities
1. H. Murakawa, An efficient linear scheme to approximate nonlinear diffusion problems, Jpn. J. Ind. Appl. Math., 35, 1, 71-101, 2018.03.
2. E. Mainini, H. Murakawa, P. Piovano and U. Stefanelli, Carbon-nanotube geometries as optimal configurations, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 15, 4, 1448-1471, 2017.10.
3. M. Iida, H. Monobe, H. Murakawa and H. Ninomiya, Immovable, moving and vanishing interfaces in fast reaction limit, J. Differential Equations, 263, 5, 2715-2735, 2017.09.
4. H. Murakawa, A linear finite volume method for nonlinear cross-diffusion systems, Numer. Math., 136, 1, 1-26, 2017.05.
5. E. Mainini, H. Murakawa, P. Piovano and U. Stefanelli, Carbon-nanotube geometries: analytical and numerical results, Discrete Contin. Dyn. Syst. S, 10, 141-160, 2017.02.
6. Y. Matsunaga, M. Noda, H. Murakawa, K. Hayashi, A. Nagasaka, S. Inoue, T. Miyata, T. Miura, K. Kubo and K. Nakajima, Reelin transiently promotes N-cadherin-dependent neuronal adhesion during mouse cortical development, Proc. Natl. Acad. Sci. USA, 114, 8, 2048-2053, 2017.02, Reelin is an essential glycoprotein for the establishment of the
highly organized six-layered structure of neurons of the mammalian
neocortex. Although the role of Reelin in the control of
neuronal migration has been extensively studied at the molecular
level, the mechanisms underlying Reelin-dependent neuronal layer
organization are not yet fully understood. In this study, we directly
showed that Reelin promotes adhesion among dissociated neocortical
neurons in culture. The Reelin-mediated neuronal aggregation
occurs in an N-cadherin–dependent manner, both in vivo and
in vitro. Unexpectedly, however, in a rotation culture of dissociated
neocortical cells that gradually reaggregated over time, we found
that it was the neural progenitor cells [radial glial cells (RGCs)],
rather than the neurons, that tended to form clusters in the presence
of Reelin. Mathematical modeling suggested that this clustering
of RGCs could be recapitulated if the Reelin-dependent
promotion of neuronal adhesion were to occur only transiently.
Thus, we directly measured the adhesive force between neurons
and N-cadherin by atomic force microscopy, and found
that Reelin indeed enhanced the adhesiveness of neurons to
N-cadherin; this enhanced adhesiveness began to be observed
at 30 min after Reelin stimulation, but declined by 3 h. These
results suggest that Reelin transiently (and not persistently)
promotes N-cadherin–mediated neuronal aggregation. When
N-cadherin and stabilized β-catenin were overexpressed in the
migrating neurons, the transfected neurons were abnormally
distributed in the superficial region of the neocortex, suggesting
that appropriate regulation of N-cadherin–mediated adhesion is important
for correct positioning of the neurons during neocortical
7. H. Murakawa and H. Togashi, Continuous models for cell-cell adhesion, J. Theor. Biol., 2015.06, Cell adhesionisthebindingofacelltoanothercellortoanextracellularmatrixcomponent.Thisprocess
is essentialinorganformationduringembryonicdevelopmentandinmaintainingmulticellular
structure. Armstrongetal.(2006)[J.Theor.Biol.243,pp.98–113]proposedanonlocaladvection–
diffusion systemasapossiblecontinuousmathematicalmodelforcell–cell adhesion.Althoughthe
certain situations.Weidentifytheproblemsandchangeunderlyingideaofcellmovementfrom “cells
moverandomly” to “cells movefromhightolowpressureregions”. Thenweprovideamodified
continuous modelforcell–cell adhesion.Numericalexperimentsillustratethatthemodified modelis
able toreplicatenotonlySteinberg'scellsortingexperimentsbutalsosomephenomenawhichcannot
be capturedatallbyArmstrong–Painter–Sherratt model..
8. D. Hilhorst and H. Murakawa, Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium, Networks and Heterogeneous Media, 2014.12.
9. H. Murakawa, Error estimates for discrete-time approximations of nonlinear cross-diffusion systems, SIAM J. Numer. Anal., 2014.04.
10. H. Murakawa, A relation between cross-diffusion and reaction-diffusion, Discrete Contin. Dyn. Syst. S, 5, 147-158, 2012.02.
11. H. Murakawa, A linear scheme to approximate nonlinear cross-diffusionsystems, Math. Mod. Numer. Anal., 45, 1141-1161, 2011.11.
12. H. Murakawa and H. Ninomiya, Fast reaction limit of a three-componentreaction-diffusion system, J. Math. Anal. Appl., 379, 150-170, 2011.07.
13. A. Ducrot, F. Le Foll, P. Magal, H. Murakawa, J. Pasquier and G. Webb, An in vitro cell population dynamics model incorporating cellsize, quiescence, and contact inhibition, Math. Models Methods Appl. Sci., 21, 871-892, 2011.04.
14. R. Eymard, D. Hilhorst, H. Murakawa and M. Olech, Numerical approximation of a reaction-diffusion system with fast reversible reaction, Chinese Annals of Mathematics B, 31, 631-654, 2010.09.
Membership in Academic Society
  • The Japan Society for Industrial and Applied Mathematics
  • Japanese society of developmental biologists