Yasumasa Nishiura

• Doctor of Science
• Professor Emeritus at Hokkaido University

This study delves into the formation of nanoscale polyhedral block copolymer particles (PBCPs) exhibiting cubic, octahedral, and variant geometries. These structures represent a pioneering class that has never been fabricated previously. PBCP features distinct variations in curvature on the outer surface, aligning with the edges and corners of poly...

In this paper, we focus on annihilation dynamics for the head-on collision of traveling patterns. A representative and well-known example of annihilation is the one observed for one-dimensional traveling pulses of the FitzHugh–Nagumo equations. In this paper, we present a new and completely different type of annihilation arising in a class of three...

In this paper, we focus on annihilation dynamics for the head-on collision of traveling patterns. A representative and well-known example of annihilation is the one observed for 1-dimensional traveling pulses of the FitzHugh-Nagumo equations. In this paper, we present a new and completely different type of annihilation arising in a class of three-c...

The interplay between 1D traveling pulses with oscillatory tails (TPOs) and heterogeneities of the bump type is studied to formulate a generalized three-component FitzHugh–Nagumo system of equations. We present that stationary pulses with oscillatory tails (SPOs) form a “snaky” structure in homogeneous spaces and then TPO branches form a “figure-ei...

In two-dimensional space, we investigate the slow dynamics of multiple localized spots with oscillatory tails in a specific three-component reaction-diffusion system, whose key feature is that the spots attract or repel each other alternatively according to their mutual distances, leading to rather complex patterns. One fundamental pattern is the r...

We study the existence and stability of standing pulse solutions to a singularly perturbed three-component reaction–diffusion system with one activator and two inhibitors. We apply the MAE (matched asymptotic expansion) method to construct solutions and the SLEP (singular limit eigenvalue problem) method to evaluate their stability. This approach i...

The interplay between 1D traveling pulses with oscillatory tails (TPO) and heterogeneities of bump type is studied for a generalized three-component FitzHugh-Nagumo equation. First, we present that stationary pulses with oscillatory tails (SPO) form a ``snaky'' structure in homogeneous spaces, after which TPO branches form a ``figure-eight-like sta...

We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta–Kawasaki model. The projection saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward and upward search algorith...

In this paper, we introduce a three-component Schnakenberg model, whose key feature is that it has a solution consisting of N spikes that undergoes Hopf bifurcations with respect to N distinct modes nearly simultaneously. This results in complex oscillatory dynamics of the spikes, not seen in typical two-component models. For parameter values beyon...

We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta--Kawasaki model. The projected saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward/upward search algorithms....

We study the existence and stability of standing pulse solutions to a singularly perturbed three-component reaction diffusion system with one-activator and two-inhibitor type. We apply the MAE (matched asymptotic expansion) method to the construction of solutions and the SLEP (Singular Limit Eigenvalue Problem) method to their stability properties....

Although the process variables of epoxy resins alter their mechanical properties, recently it was found that the total variation of the X-ray images of these resins is one of the key features that affect the toughness of these materials. However it is still not clear how to visualize such a difference in a clear way. To facilitate the visualization...

Professor Emeritus Yasumasa Nishiura is a mathematician who has dedicated his career to understanding more about the profound impact mathematics has on the world around us. He worked as Research Director at the Alliance for Breakthrough between Mathematics and Sciences (ABMS) (2007–2016) in Japan where he was supporting research activities in mathe...

In this paper, we introduce a three-component Schnakenberg model. Its key feature is that it has a solution consisting of N spikes that undergoes a Hopf bifurcation with respect to N distinct modes nearly simultaneously. This results in complex oscillatory dynamics of the spikes, not seen in typical two-component models. For parameter values above...

Although the process variables of epoxy resins alter their mechanical properties, the visual identification of the characteristic features of X-ray images of samples of these materials is challenging. To facilitate the identification, we approximate the magnitude of the gradient of the intensity field of the X-ray images of different kinds of epoxy...

It is well-known that 10-Hz alpha oscillations in humans observed by electroencephalogram (EEG) are enhanced when the eyes are closed. Toward explaining this, a previous experimental study using manipulation by transcranial magnetic stimulation (TMS) revealed more global propagation of phase resetting in the eyes-open condition than in the eyes-clo...

One of the big challenges in materials science is to bridge microscopic or mesoscopic properties to macroscopic performance such as fracture toughness. This is particularly interesting for the amorphous materials such as epoxy resins because their micro/meso structures are difficult to characterize so that any information connecting different scale...

Unique morphologies were found in binary and ternary polymer blended particles, including Ashura-type phase separation, which has three different polymer components on the particle surface. The morphologies of phase-separated structures in the binary polymer blended particles are discussed in terms of the surface tensions of the blended polymers. S...

The large-scale synchronization of neural oscillations is crucial in the functional integration of brain modules, but the combination of modules changes depending on the task. A mathematical description of this flexibility is a key to elucidating the mechanism of such spontaneous neural activity. We present a model that finds the loop structure of...

We analyse pinned front and pulse solutions in a singularly perturbed three-component FitzHugh–Nagumo model with a small jump-type heterogeneity. We derive explicit conditions for the existence and stability of these type of pinned solutions by combining geometric singular perturbation techniques and an action functional approach. Most notably, in...

The article Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model, written by Peter van Heijster, Chao-Nien Chen, Yasumasa Nishiura and Takashi Teramoto, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on August 11, 2018, without open access.

In this manuscript, we combine geometrical singular perturbation techniques and an action functional to revisit—and further study—the existence and stability of stationary localized structures in a singularly perturbed three-component FitzHugh–Nagumo model. In particular, the action functional replaces the Melnikov integral approach used in Doelman...

The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the multiple-scales method to the mixed ODE-PDE system obtained by taking a singular limit of the PDEs. The reduc...

The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the multiple-scales method to the mixed ODE-PDE system obtained by taking a singular limit of the PDEs. The reduc...

Annealing of block copolymers has become a tool of great importance for the reconfiguration of nanoparticles. Here, we present the experimental results of annealing block copolymer nanoparticles and a theoretical model to describe the morphological transformation of ellipsoids with striped lamellae into onionlike spheres. A good correspondence betw...

The response of a traveling pulse to a local external stimulus is considered numerically for a modified three-component Oregonator, which is a model system for the photosensitive Belousov-Zhabotinsky (BZ) reaction. The traveling pulse is traced and constantly stimulated, with the distance between the pulse and the stimulus being kept constant. We a...

Working memory (WM) is known to be associated with synchronization of the theta and alpha bands observed in electroencephalograms (EEGs). Although frontal-posterior global theta synchronization appears in modality-specific WM, local theta synchronization in frontal regions has been found in modality-independent WM. How frontal theta oscillations se...

Correction for 'Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations' by Edgar Avalos et al., Soft Matter, 2016, 12, 5905-5914.

We numerically study a set of coupled Cahn-Hilliard equations as a means to find morphologies of diblock copolymers in three-dimensional spherical confinement. This approach allows us to find a variety of energy minimizers including rings, tennis balls, Janus balls and multipods among several others. Phase diagrams of confined morphologies are pres...

Significance Persistent homology is an emerging mathematical concept for characterizing shapes of data. In particular, it provides a tool called the persistence diagram that extracts multiscale topological features such as rings and cavities embedded in atomic configurations. This article presents a unified method using persistence diagrams for stu...

The ability to continue flowering after loss of inductive environmental cues that trigger flowering is termed floral commitment. Reversible transition involving a switch from floral development back to vegetative development has been found in Arabidopsis mutants and many plant species. Although the molecular basis for floral commitment remains uncl...

This paper presents a detailed analysis of the stability and network structure of thermal convection patterns of mixtures containing two miscible fluids. The stability of steady spatially localized solutions consisting of an even number of convection cells (even-SP) is investigated in detail because even-SPs emerge as transient states resulting fro...

This volume comprises eight papers delivered at the RIMS International Conference "Mathematical Challenges in a New Phase of Materials Science", Kyoto, August 4–8, 2014. The contributions address subjects in defect dynamics, negatively curved carbon crystal, topological analysis of di-block copolymers, persistence modules, and fracture dynamics. Th...

Previous experimental studies have provided evidence that transient large-scale synchronization of neuronal oscillations plays an important role in switching brain states associated with human brain functions. In our previous study, we investigated the behavior of switching between synchronized and desynchronized states induced by inhibitory intera...

Two recent topics arising in pattern dynamics are presented. One is a characterization of amorphous structures by using computational topology, especially persistent diagrams that extract the information of size and shape of various holes embedded in amorphous structures. The other is about an organizing center for the pulse generators arising in r...

Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. The method is c...

We consider the mixed ODE-PDE system called a hybrid system, in which the two interfaces interact with each other through a continuous medium and their equations of motion are derived in a weak interaction frame- work. We study the bifurcation property of the resulting hybrid system and construct an unstable standing pulse solution, which plays the...

A potential energy landscape (PEL) gives rise to diverse non-equilibrium dynamics in complex systems. In this study, we visualize the topological landscape of a steady-state flow under shear deformation in a model metallic glass. We use the “state space network” as the best predictor of state transitions in terms of statistical model selection. The...

The photo-sensitive Belousov-Zhabotinsky (BZ) reaction system was investigated to understand the response of wave propagation to a local pulse stimulation on an excitable field. When the chemical wave was irradiated with a bright pulse or a dark pulse, the speed of wave propagation decreased or increased. The timing of pulse irradiation that signif...

The description of amorphous structures has been a long-standing problem, and conventional methods are insufficient for revealing intrinsic structures. In this Letter, we propose a computational homological approach that provides indicators of amorphous structures. We found curves in the persistence diagram (PD), which describes shapes and scales o...

In this study, we propose a continuous model for a pathfinding system. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified vertices, and the path is represented by a stable solution of the proposed model. The system has a self-recovery property, i.e.,...

Heterogeneity is one of the most important and ubiquitous types of external perturbations. We study a spontaneous pulse-generating mechanism in an excitable medium with jump-type heterogeneity. Such a pulse generator (PG) has attracted considerable interest due to the computational potential of pulse waves in physiological signal processing. We fir...

We propose a network of excitable systems that spontaneously initiates and completes loop searching against the removal and attachment of connection links. Network nodes are excitable systems of the FitzHugh-Nagumo type that have three equilibrium states depending on input from other nodes. The attractors of this network are stationary solutions th...

This study propose a continuous pathfinding system based on coupled oscillator systems. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified vertices, and the path is represented by phase-synchronized oscillatory solutions. To develop a system capable...

We consider the dynamics of two interfaces that interact through a continuous medium with spatial heterogeneity. The dynamics of interface positions is governed by ordinary differential equations (ODEs), whereas that of the continuous field by a partial differential equation. The resulting mixed ODE-PDE system, which we call a hybrid system (HS), i...

Heterogeneity is one of the most important and ubiquitous types of external perturbations. We study a spontaneous pulse generating mechanism caused by the heterogeneity of jump type. Such a pulse generator (PG) has attracted much interest in relation to potential computational abilities of pulse waves in physiological signal processing. Exploring t...

We study spontaneous pattern formation and its asymptotic behaviour in binary fluid flow driven by a temperature gradient. When the conductive state is unstable and the size of the domain is large enough, finitely many spatially localized time-periodic travelling pulses (PTPs), each containing a certain number of convection cells, are generated spo...

Spatially localized patterns form a representative class of patterns in dissipative systems. We study how the dynamics of traveling spots in two-dimensional space change when heterogeneities are introduced in the media. The simplest but fundamental one is a line heterogeneity of jump type. When spots encounter the jump, they display various outputs...

A cascade process involving stripe splitting in reaction–diffusion systems with isotropically growing one-dimensional domains is studied. Such cascades, propagating from a smaller domain to a larger domain, have been proposed as an answer to the criticism that the Turing mechanism lacks robustness because many stable patterns can coexist on a large...

It has recently been reported that even single-celled organisms appear to be "indecisive" or "contemplative" when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly b...

Spatially localized patterns are ubiquitous such as chemical blobs, discharge patterns, morphological spot, and binary convection cells. When they are moving in space, it is unavoidable that they collide each other, interact strongly and emit various outputs depending on incident angle and parameters. Moving localized spots in dissipative systems h...

1 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA 2 Mathematisch Instituut, Universiteit Leiden, PO Box 9512, 2300 RA Leiden, Netherlands 3 Department of Mathematics and Center for BioDynamics, Boston University, 111 Cummington Street, Boston, MA 02215, USA 4 Laboratory of Nonlinear Studies and Comput...

We study the mathematical structure of localized convection cell solutions in a binary fluid mixture, some of which are not observed in Rayleigh-Benard convection in a pure fluid. In particular, a solution representing time-periodic traveling localized convection cells (periodic traveling pulse, PTP) has not been obtained even numerically because t...

Our subject is the diblock copolymer problem in a three-dimensional space. Using numerical simulations, the double gyroid and orthorhombic morphologies are obtained as energy minimizers. By investigating the geometric properties of these bicontinuous morphologies, we demonstrate the underlying mechanism affecting the triply periodic energy minimize...

What is the origin of rotational motion? An answer is presented through the study of the dynamics for spatially localized spots near codimension 2 singularity consisting of drift and peanut instabilities. The drift instability causes a head-tail asymmetry in spot shape, and the peanut one implies a deformation from circular to peanut shape. Rotatio...

Heterogeneity is one of the most important and ubiquitous types of external perturbations in dissipative systems. To know the behaviors of pulse waves in such media is closely related to studying the collision process between the pulse and the heterogeneity-induced-ordered pattern. In particular, we focus on unidirectional propagation of pulses in...

In light water commercial reactors, extensive change of grain structure was found at high burnup ceramic fuels. The mechanism is driven by bombardment of fission energy fragments and studies were conducted by combining accelerator based experiments and computer-science. Specimen of CeO2 was used as simulation material of fuel ceramics. With swift h...

We study the collision processes of spatially localized convection cells (pulses) in a binary fluid mixture by the extended complex Ginzburg–Landau equations. Both counter- and co-propagating pulse collisions are examined numerically. For counter-propagating pulse collision, we found a special class of unstable time-periodic solutions that play a c...

We studied the migration dynamics of oxygen point defects in UO2 which is the primary ceramic fuel for light-water reactors. Temperature accelerated dynamics simulations are performed for several initial conditions. Though the migration of the single interstitial is much slower than that of the vacancy, clustered interstitial shows faster migration...

Pulse wave is one of the main careers of information and the effect of heterogeneity of the media in which it propagates is of great importance for the understanding of signaling processes in biological and chemical systems. A typical one dimensional heterogeneity is a spatially localized bump or dent, which creates associated defects in the media....

MI: Global COE Program Education-and-Research Hub for Mathematics-for-Industry グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」 The dynamics of a pulse for reaction-diffusion systems in 1D is considered in the neighborhood of the bifurcation point with codimension two, at which both of saddle-node and drift bifurcations occur at the same time. It is theoreticall...

We study intermittent switching behaviors in a system with three identical oscillators coupled diffusively and repulsively, to clarify a bifurcation scenario which generates such intermittent switching behaviors. We use the Stuart-Landau oscillator, which is a general form of Hopf bifurcation, and can describe both cases: limit cycle and inactive (...

One of the fundamental issues of pulse dynamics in dissipative systems is clarifying how the heterogeneity in the media influences the propagating manner. Heterogeneity is the most important and ubiquitous type of external perturbation. We focus on a class of one-dimensional traveling pulses, the associated parameters of which are close to drift an...

When two food sources are presented to the slime mold Physarum in the dark, a thick tube for absorbing nutrients is formed that connects the food sources through the shortest route. When the light-avoiding organism is partially illuminated, however, the tube connecting the food sources follows a different route. Defining risk as the experimentally...

International Symposium on "Topological Aspects of Critical Systems and Networks". 13-14 February 2006. Hokkaido University, Sapporo, JAPAN. We report here a new kind of behavior that seems to be 'indecisive' in an amoeboid organism, the Physarum plasmodium of true slime mold. The plasmodium migrating in a narrow lane stops moving for a period of t...

We consider the dynamics when traveling pulses encounter heterogeneities in a three-component reaction diffusion system of one-activator-two-inhibitor type, which typically arises as a qualitative model of a gas-discharge system. We focused on the case where one of the kinetic coefficients changes similar to a smoothed step function, which is basic...

We study pulse dynamics in one-dimensional heterogeneous media. In particular we focus on the case where the pulse is close to the singularity of codim 2 type consisting of drift and saddle-node instabilities in a parameter space. We assume that the heterogeneity is of jump type, namely one of the coefficients of the system undergoes an abrupt chan...

To improve understanding of radiation damage and recovery process, especially under condition of high energy and high fluence irradiation, is currently studied at the new cross-over project (NXO). Most severe irradiation is realized by fission fragments in nuclear fuel. A guiding experiment is taken from experience in power generating Light Water R...

Scattering process between traveling breathers (TBs) is studied for the complex Ginzburg-Landau equations (CGLE) with a parametric forcing term. The phase-dependency of the input-output relation can be explained from the scattor's viewpoint. In this note, we especially focus on the issue for the asymmetric head-on collisions, i.e., the phases of tw...

We analyze the effect of periodic forcing on a chain of FitzHugh-Nagumo elements in an excitable regime. The element at the end of chain is coupled unidirectional to a single pacemaker, limit cycle oscillator. With a suitable pacemaker's frequency, we find that the suppression of the pulse propagation occurs in some parameter regime, while the isol...

One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there...

This paper presents a new method for effectively searching all global minima of a multimodal function. The method is based on particle swarm optimizer, particles are dynamically divided into serval subgroups of different size in order to explore variable space using various step size simultaneously. In each subgroup, a new scheme is proposed to upd...

We analyze the effect of additive periodic stimuli in one-dimensional FitzHugh-Nagumo equations in an excitable regime. With a suitable stimulus interval, the suppression of the pulse propagation occurs in some parameter regime. This propagation failure comes from the formation of the "death spot" where successive pulses annihilate. In the paramete...

We study the appearance and the relevance of edge bifurcations in the stability problem associated to a front pattern in a certain class of (singularly perturbed) bi-stable reaction-diffusion equations.

Existence and dynamics of chaotic pulses on a one-dimensional lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh–Nagumo equations. Such pulses annihilate when they collide with each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic b...

We can access a lot of information and data through networks anywhere and at any time. In order to provide fast-changing data that is useful to users as soon as possible, and to stop malicious data, we need to understand the characteristics of data dissemination dynamics. In this paper, we consider a mobile P2P network and investigate the effect of...

Existence and stability of stationary internal layered solutions to a rescaled diblock copolymer equation are studied in higher dimensional space. Rescaling is necessary since the characteristic domain size of any stable pattern eventually vanishes in an appropriate singular limit. A general sufficient condition for the existence of singularly pert...

Even though the field of nonequilibrium thermodynamics has been popular and its importance has been suggested by Demirel and Sandler [J. Phys. Chem. B 108, 31 (2004)], there are only a few investigations of reaction-diffusion systems from the aspect of thermodynamics. A possible reason is that model equations are complicated and difficult to analyz...

To evaluate performance in a complex survival task, we studied the morphology of the Physarum plasmodium transportation network when presented with multiple separate food sources. The plasmodium comprises a network of tubular elements through which chemical nutrient, intracellular signals and the viscous body are transported and circulated. When th...

We consider the Gray-Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to ex...

Scattering process between one-dimensional traveling breathers (TBs), i.e., oscillatory traveling pulses, for the complex Ginzburg-Landau equation (CGLE) with external forcing and a three-component activator-substrate-inhibitor model are studied. The input-output relation depends in general on the phase of two TBs at collision point, which makes a...

In this article, we consider a class of bistable reaction-diffusion equations in two components on the real line. We assume that the system is singularly perturbed, i.e., that the ratio of the diffusion coefficients is (asymptotically) small. This class admits front solutions that are asymptotically close to the (stable) front solution of the “triv...

We present a model of motion and evaporation of a droplet of a solute along with precipitation. It is demonstrated that the model can simulate the formation of stripe patterns parallel to the droplet edge resulting from periodic precipitation.

Scattering of particle-like patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision where traveling pulses or spots interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of unsta...

Addition of hydrophobic guest molecule (C12H26) into the nonionic surfactant/water system (C16E7/D2O) system modifies the phase behavior between the lamellar and column phases. The distribution of the added guest molecule in the microstructure and the interfacial structure is examined by using a small angle neutron scattering technique. The charact...

We report that various geometric patterns can be formed upon mechanical deformation of hexagonal micro polymer mesh. The patterning of micromesh can be applied to the fabrication of micropatterned soft-materials for cell culturing. A microporous film was prepared from a viscoelastic polymer, poly(ε-caprolactone). The film was a hexagonal mesh of 4...

Scattering of particlelike patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision in the one-dimensional(1D) space where traveling pulses interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that...

We study the limiting behavior as e tends to zero of the solution of a second order nonlocal parabolic equation of conservative type which models the micro-phase separation of diblock copolymers. We consider the case of spherical symmetry and prove that as the reaction coefficient tends to infinity the problem converges to a free boundary problem w...

Three typical transient dynamics in dissipative systems are discussed, namely self-replication, self-destruction, and scattering among spatially localized patterns. The difficulty lies in the fact that patterns are deformed a lot and the associated orbits behave globally in the phase space. A conventional treatment in general does not work and need...