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Natsuhiko Yoshinaga

Mathematical Science Group, WPI Advanced Institute for Materials Research (WPI-AIMR),
Tohoku University Katahira 2-1-1, Aoba-Ku,
Sendai 9808577, Japan
Room No. 115, WPI-AIMR ANNEX building

Tel: +81-(0)22-237-8017
Fax: +81-(0)22-217- 6335

E-mail address:
Web page:


AIST-TohokuU Mathematics for Advanced Materials-OIL (MathAM-OIL)
Katahira 2-1-1, Aoba-Ku Sendai, 980-8577 JAPAN
Tel: +81-(0)22-237-8195
Web page:

Research Interests

      My research area is the theoretical modelling of soft condensed materials. Soft materials contain various length and time scales correlating in a complicated manner. The importance of this field is that such systems are closely related to biological phenomena, which give us unlimited imagination and intuition. In addition, they are found in most of industrial products sustaining our comfortable lives. We are working on the modelling of soft materials, particularly focusing on nonequilibrium systems. This is called active soft materials. Our studies are close collaboration with experimental groups. Recently, we combine the theoretical modelling of soft materials and machine learning techniques. We apply our theoretical methods not only to soft materials, but also to the broad class of materials science.

Machine Learning for Soft Materials      Can we find a governing equation of soft materials? In forward problems, we use the knowledge of past studies, and try to find the best equation to understand mechanism of experimental results. A good model not only can explain natural phenomena well, but also give a universal interpretation and a good prediction. Significant effort has been made to find the good equation. Thanks to the recent development of machine learning techniques, it is becoming feasible to find a governing equation of soft materials in a systematical way. Still, soft materials are complex and have large degrees of freedom. Naiive machine laerning techniques do not work. We are developing the novel techniques to find the governing equations for soft materials.

My recent talk is here.
- Newton Institute seminar
New statistical physics in living matter: non equilibrium states under adaptive control

Quasicrystals in Soft Materials       Quasicrystals have rotational order, but do not have translational order. Many quasicrystals have been found in metallic alloys, but recently they are also found in soft materials, such as block copolymers, sufactantsm and colloids. We are developing a simple model to reproduce various quasicrystals in two and three dimensions (right figures).

Inverse structural design of colloidal particle assemblies       Quasicrystals have rotational order, but do not have translational order. Many quasicrystals have been found in metallic alloys, but recently they are also found in soft materials, such as block copolymers, sufactantsm and colloids. We are developing a simple model to reproduce various quasicrystals in two and three dimensions.

Application to other materials       Our theoretical approaches are not limited to soft materials, but may be applied to other materials. The phase-field crystal model may be applied to kinetics of dislocations and disclinatinos in crystalline materials. We are also working on spin waves, which can be described by nonlinear partial differential equations.


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Active Soft Materials Self-propelled particles and drops
      Biological systems consume energy and exhibit their functions. Among the variety of phenomena, we are particularly interested in cell motility. Interestingly, cells can move without any external force. This is achieved by active force (stress) generation using energy of ATP. The goal of this study is to understand the mechanism of self-propulsion. As a first step, we are now investigating model chemical systems in which particles and drops move spontaneously.

      Thermophoresis is a phenomenon of directional motion under temperature gradient. This is similar to electrophoresis under an electric field and osmophoresis (difussiophoresis) under a concentration gradient. It was found back in 1856, though the mechanism, particularly microscopic and mesoscopic aspects, remains unclear despite of intensive studies. We have developed hydrodynamic equations, and investigated flow induced by temperature gradient. This phenomenon is strongly dependent on surface properties of objects in phoretic motion.

Deformation induced spontaneous motion
      An important observation for motile cells is that they can deform. Recently, it has been suggested that there is strong correlation between deformation and motion. Although cells are very complex, we believe the essence is shared with artificial model systems which are simpler and exhibit spontaneous motion and deformation. With the aid of hydrodynamics, we are trying to clarify the relation between deformation and motion.

Drift instability of a drop driven by Marangoni flow
     The directional motion of self-propulsion arises either from intrinsic asymmetry of the systems or spontaneous break of rotational symmetry. The latter is related with nonlinear nature of the systems as phase transitions in equilibrium systems. We are now interested in the nonequilibrium phase transition between stationary and moving stales. This has been studied in the field of nonlinear dynamics as drift instability. We have developed hydrodynamics describing this instability for the Marangoni effect.

My recent talk is here.
- Newton Institute (mp4 movie) at the workshop "Dynamics of Suspensions, Gels, Cells and Tissues"
- Newton Institute
seminar (mp4 movie)
- Kavli Institute for Theoretical Physics



Pattern Formation in Biology      
Pattern formation of Min proteins
       Min portens are known to be essential ingredients to determine the cell centre during cell division of E-coli. Nonlinear waves of MinD and MinE occur by their nonlinear interactions. In cells, standings waves, also called pole-to-pole oscillation, are relevant because their node sets the cell centre precisely. Interestingly, artificial systems that have Min proteins together with other ingredients may show waves (see the right figure). The system has surface of a membrane and bulk of cytosol. Min proteins exhbit both chemical reactions and diffusion on the surface and in the bulk. We propose and analyse a model expressed by nonlinear reaction-diffusion equations, and found that the nonlinear waves occur both flat (top figure) and spherical (bottom) geometries. Moreover, for the spherical geometry, which is closer to the shape of a cell, the effect of confinement plays a significant role for the wave generation.
Polarity pattern of stress fibre
       Stress fibres are key elements of mechanical aspects of cells. Main ingredients are actin filaments, myosin II, and a-actinin. Many other proteins have also been found and considered to function. Our purpose in this study is to model stress fibres as assemble of filaments in nonequilibrium systems.
       Actin filaments have polarity, that is, they have plus (barbed) and minus (pointed) ends. Several polarity patterns have been found in cells, for instance graded polarity, alternating polarity, and uniform one. The alternating polarity looks similar to muscle. However, the relation between polarity and mechanical properties are still unknown. We show active stress generated by molecular motors (myosin filaments) determines polarity patterns.

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Publications (Researcher ID: G-3067-2011)


Uyen Tu Lieu and Natsuhiko Yoshinaga
"Dynamic control of self-assembly of quasicrystalline structures through reinforcement learning"
submitted, arXiv

Tatsuro Kai, Takahiro Abe, Natsuhiko Yoshinaga, Shuichi Nakamura, Seishi Kudo, Shoichi Toyabe
"Collective gradient sensing by swimming bacteria without clustering"
submitted, bioRxiv

Satoshi Iihama, Yuya Koike, Shigemi Mizukami, Natsuhiko Yoshinaga
"Universal scaling between wave speed and size enables nanoscale high-performance reservoir computing based on propagating spin-waves"
npj Spintronics, 2, 5 (2024), arXiv

Research News "Giant Leap Towards Neuromorphic Devices: High-performance Spin-wave Reservoir Computing"
Asia Research News:


Saki Nishikawa, Gaku Sato, Sakura Takada, Shunshi Kohyama, Gen Hondac, Miho Yanagisawa, Yutaka Hori, Nobuhide Doi, Natsuhiko Yoshinaga, Kei Fujiwara
"Multimolecular Competition Effect as a Modulator of Protein Localization and Biochemical Networks in Cell-size Space"
Advanced Science, 11, 2308030 (2024) open access

Yueyuan Gao and Natsuhiko Yoshinaga
"Inverse problems of inhomogeneous fracture toughness using phase-field models"
Physica D, 448, 133734 (2023) open access


Natsuhiko Yoshinaga and Satoru Tokuda
"Bayesian Modelling of Pattern Formation from One Snapshot of Pattern"
Physical Review E, 106, 065301 (2022) open access

Uyen Tu Lieu and Natsuhiko Yoshinaga
"Formation and Fluctuation of Two-dimensional Dodecagonal Quasicrystal"
Soft Matter, 18, 7497-7509 (2022) arXiv

Sakura Takada, Natsuhiko Yoshinaga, Nobuhide Doi, and Kei Fujiwara
"Controlling periodicity of a reaction–diffusion wave in artificial cells by a two-way energy supplier"
ACS Nano, 16, 16853–16861 (2022)

Miho Yanagisawa, Chiho Watanabe, Natsuhiko Yoshinaga, and Kei Fujiwara
"Cell-size space regulates behaviors of confined polymers: From Nano- and Micromaterial Science to Biology"
Langmuir, 38, 11811–11827 (2022)

Sakura Takada, Natsuhiko Yoshinaga, Nobuhide Doi, and Kei Fujiwara
"Mode selection mechanism in traveling and standing waves revealed by Min wave reconstituted in artificial cells"
Science Advances, 8, eabm8460 (2022) bioRxiv

Uyen Tu Lieu and Natsuhiko Yoshinaga
"Inverse design of two-dimensional structure by self-assembly of patchy particles"
Journal of Chemcial Physics, 156, 054901 (2022) arXiv


Uyen Tu Lieu and Natsuhiko Yoshinaga
"Topological defects of dipole patchy particles on a spherical surface"
Soft Matter, 16, 7667-7675 (2020) arXiv

Shunshi Kohyama, Kei Fujiwara, Natsuhiko Yoshinaga, Nobuhide Doi
"Conformational equilibrium of MinE regulates the allowable concentration ranges of a protein wave for cell division"
Nanoscale, 12, 11960-11970 (2020)

Akira Kamimaki, Satoshi Iihama, Kazuya Suzuki, Natsuhiko Yoshinaga, and Shigemi Mizukami
"Parametric amplification of magnons in synthetic antiferromagnets"
Physical Review Applied, 13, 044036 (2020)


Shunshi Kohyama, Natsuhiko Yoshinaga, Miho Yanagisawa, Kei Fujiwara, Nobuhide Doi
"Cell-sized confinement controls generation and stability of a protein wave for spatiotemporal regulation in cells"
eLife, 8, e44591 (2019) bioRxiv
Protocol: Kohyama, S., Fujiwara, K., Yoshinaga, N. and Doi, N.
"Self-organization Assay for Min Proteins of Escherichia coli in Micro-droplets Covered with Lipids."
Bio-protocol 10(6): e3561 (2020).

Rafael Monteiro and Natsuhiko Yoshinaga
"The Swift-Hohenberg Equation under directional-quenching: finding heteroclinic connections using spatial and spectral decompositions"
Archive for Rational Mechanics and Analysis, 235, 405-470 (2020)

Natsuhiko Yoshinaga
"Self-propulsion of an active polar drop"
Journal of Chemical Physics, 150, 184904 (2019) arXiv, PDF

Natsuhiko Yoshinaga and Shunsuke Yabunaka
"Theory of active particles and drops driven by chemical reactions: the role of hydrodynamics on self-propulsion and collective behaviours"
"Self-organized Motion: Physicochemical Design based on Nonlinear Dynamics" edited by Satoshi Nakata, Véronique Pimienta, István Lagzi, Hiroyuki Kitahata, Nobuhiko J Suematsu


Hiroyuki Kitahata, Natsuhiko Yoshinaga
"Effective diffusion coefficient including the Marangoni effect"
Journal of Chemical Physics, 148, 134906 (2018) arXiv

Kyongwan Kim, Natsuhiko Yoshinaga, Sanjib Bhattacharyya, Hikaru Nakazawa, Mitsuo Umetsu, and Winfried Teizer
"Large-scale chirality in an active layer of microtubules and kinesin motor proteins"
Soft Matter, 14, 3221-3231 (2018) arXiv

Natsuhiko Yoshinaga, Tanniemola B. Liverpool
"From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers"
European Physical Journal E, 41, 76 (2018) arXiv or Springer Nature Sharing


Natsuhiko Yoshinaga, Tanniemola B. Liverpool
"Hydrodynamic interactions in dense active suspensions:from polar order to dynamical clusters"
Physical Review E Rapid Communications, 96, 020603(R) (2017). arXiv

Natsuhiko Yoshinaga,
"Simple models of self-propelled colloids and liquid drops: from individual motion to collective behaviors"
Journal of the Physical Society of Japan Special Topics "Recent Progress in Active Matter", 86, 101009 (2017)


Shunsuke Yabunaka, Natsuhiko Yoshinaga
"Collision between chemically-driven self-propelled drops"
Journal of Fluid Mechanics, 809, 205-233 (2016) arXiv


Yuki Koyano, Natsuhiko Yoshinaga, Hiroyuki Kitahata
"General Criteria for Determining Rotation or Oscillation in a Two-dimensional Axisymmetric System"
Journal of Chemical Physics , 143, 014117 (2015) arXiv

Tomohiro Matsushita*, Atsushi Kubota, Naohisa Happo, Kazuto Akagi, Natsuhiko Yoshinaga, and Kouichi Hayashi
"Fast Calculation Algorithm Using Barton’s Method for Reconstructing Three-Dimensional Atomic Images from X-ray Fluorescence Holograms"
Zeitschrift für Physikalische Chemie,230, 449-455 (2016)


Natsuhiko Yoshinaga,
"Spontaneous motion and deformation of a self-propelled droplet"
Physical Review E, 89, 012913 (2014) arXiv
Supplementary information


Hiroyuki Kitahata, Natsuhiko Yoshinaga, Ken H. Nagai, Yutaka Sumino,
"Dynamics of Droplets"
in, Pattern Formations and Oscillatory Phenomena edited by Shuichi Kinoshita

Ken H. Nagai, Fumi Takabatake, Yutaka Sumino, Hiroyuki Kitahata, Masatoshi Ichikawa, and Natsuhiko Yoshinaga,
"Rotational motion of a droplet induced by interfacial tension"
Physical Review E, 87, 013009 (2013) arXiv


Natsuhiko Yoshinaga, Ken H. Nagai, Yutaka Sumino, Hiroyuki Kitahata
"Drift instability in the motion of a fluid droplet with a chemically reactive surface driven by Marangoni flow"
Physical Review E, 86, 016108 (2012) arXiv
movies are available here

Natsuhiko Yoshinaga and Philippe Marcq
"Contraction of cross-linked actomyosin bundles"
Physical Biology, 9, 046004  (2012) arXiv

Shunsuke Yabunaka, Takao Ohta, and Natsuhiko Yoshinaga
"Self-propelled motion of a fluid droplet under chemical reaction"
Journal of Chemical Physics, 136, 074904 (2012) arXiv

Hiroyuki Kitahata, Natsuhiko Yoshinaga, Ken H. Nagai, Yutaka Sumino
"Spontaneous Motion of a Belousov-Zhabotinsky Reaction Droplet Coupled with a Spiral Wave"
Chemistry Letters , 41, 1052-1054 (2012) arXiv
movies are available here


Hiroyuki Kitahata, Natsuhiko Yoshinaga, Ken H. Nagai, and Yutaka Sumino
"Spontaneous motion of a droplet coupled with a chemical wave"
Physical Review E Rapid Communication, 84, 015101(R) (2011) arXiv
selected by PRE Kaleidoscope Images: July 2011
movies are available here

Philippe Marcq, Natsuhiko Yoshinaga, and Jacques Prost
"Rigidity sensing explained by active matter theory"
Biophysical Journal, 101, L33-L35 (2011) arXiv


Hong-Ren Jiang, Natsuhiko Yoshinaga, and Masaki Sano
"Active Motion of Janus Particle by Self-thermophoresis in Defocused Laser Beam"
Physical Review Letters, 105, 268302 (2010) arXiv
Editor's suggestion and Viewpoint in Physics, 3, 108 (2010) Debut of a hot “fantastic voyager”
movies are available here

Natsuhiko Yoshinaga, Jean-Francois Joanny, Jacques Prost and Pilippe Marcq
"Polarity patterns of stress fibers"
Physical Review Letters, 105, 238103 (2010) arXiv


Takahiro Sakaue and Natsuhiko Yoshinaga
"Dynamics of Polymer Decompression: Expansion, Unfolding and Ejection"
Physical Review Letters, 102, 148302 (2009). arXiv

Hong-Ren Jiang, Hirofumi Wada, Natsuhiko Yoshinaga, and Masaki Sano
"Manipulation of Colloids by Nonequilibrium Depletion Force in Temperature Gradient"
Physical Review Letters, 102, 208301 (2009). arXiv


Natsuhiko Yoshinaga, E.I. Kats and A. Halperin
"On the Adsorption of Two-State Polymers"
Macromolecules, 41, 7744-7751 (2008) arXiv

Natsuhiko Yoshinaga
"Folding and unfolding transition in a single semiflexible polymer "
Physical Review E, 77, 061805 (2008). arXiv


Natsuhiko Yoshinaga and Kenichi Yoshikawa
"Core-shell structures in single flexible-semiflexible block copolymers: Finding the free energy minimum for the folding transition"
Journal of Chemical Physics, 127, 044902 (2007).

N. Yoshinaga, D. J. Bicout, E.I. Kats and A. Halperin
"Dynamic Core Shell Structures in Two State Models of Neutral Water Soluble Polymersr"
Macromolecules, 40(6), 2201-2209 (2007)


N. Yoshinaga
"Transition kinetics of a single semiflexible polymer"
Progress of Theoretical Physics Supplement, 161, 397-402 (2006).


N. Yoshinaga, K. Yoshikawa and T. Ohta
"Different pathways in mechanical unfolding/folding cycle of a single semiflexible polymer"
European Physical Journal E, 17, 485 (2005).

K. Yoshikawa and N. Yoshinaga
"Novel scenario on the folding transition of a single chain"
Journal of Physics: Condensed Matter, 17, S2817-S2823 (2005).


N. Yoshinaga, K. Yoshikawa and S. Kidoaki
"Multiscaling in a Long Semiflexible Polymer Chain in Two Dimension"
Journal of Chemical Physics, 116, 9926 - 9929 (2002).


N. Yoshinaga, T. Akitaya and K. Yoshikawa
“Intercalating Fluorescence Dye YOYO-1 Prevents the Folding Transitionin Giant Duplex DNA”
Biochemical and Biophysical Research Communications, 286, 264-267, (2001).

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