arXiv subjects

Hiroshi Koibuchi

Publications and source records attributed to Hiroshi Koibuchi.

At least 19 recordsLinked to original sources

arXiv2026

Turing patterns on non-fluctuating surfaces under mechanical stresses

This paper presents a numerical study of Turing patterns (TPs) governed by reaction diffusion equations for the activator $u$ and the inhibitor $v$ on two- and three-dimensional lattices without vertex fluctuations. In this framework, $u$ and $v$ are fixed at discrete spatial locations, as pigment cells on zebrafish skin or shell patterns. Mechanical effects are incorporated through the Finsler geometry modeling formulation, which introduces an internal degree of freedom, $\vecτ$, representing the direction of mechanical stress. A tensile-stress formula based on the Gaussian bond potential is shown to be well defined on non-fluctuating lattices, enabling the entropy associated with stress relaxation to be evaluated in a manner analogous to that on fluctuating surfaces. The results indicate that biological TPs respond to external mechanical forces in much the same way as TPs on fluctuating membranes. Simulation codes are provided in the Supplementary Material.

nlin.PS↗

arXiv2023

Finsler Geometry Modeling and Monte Carlo Study on Geometrically Confined Skyrmions in Nanodots

Using the Finsler geometry modeling (FG) technique without spontaneous magnetic anisotropy, we numerically study the stability and morphology of geometrically confined skyrmions experimentally observed in nanodots. We find a confinement effect that stabilizes skyrmions for a low external magnetic field without mechanical stresses by decreasing the diameter of the cylindrical lattice and strain effects that cause the sky and vortex to emerge under the zero magnetic field. Moreover, the obtained MC data on the morphological changes are also consistent with the reported experimental data.

cond-mat.mes-hall↗

arXiv2023

Langevin and Navier-Stokes Simulation of Three-Dimensional Protoplasmic Streaming

In this paper, we report the numerical results obtained using the Langevin Navier-Stokes (LNS) simulation of the velocity distribution of three-dimensional (3D) protoplasmic streaming in plant cells, such as those of {\it Nitella flexilis}. The LNS simulations are performed on 3D cylinders discretized by regular cubes in which fluid velocities are activated by boundary velocities parallel and nonparallel to the longitudinal direction and a random Brownian force with strength $D$. We find that, for a finite $D$, the velocity distribution $h(V), V\!=\!|\vec{V}|$, has two different peaks at a small non-zero $V$ and a finite $V$, and the distribution $h(V_z)$ for $|V_z|$ along the longitudinal direction also has a peak at finite $V_z$. These results are in good agreement with the reported velocity distributions observed using laser Doppler velocimetry. Moreover, we study the effects of the Brownian force on biological material mixing and find that mixing along the $\vec{V}$ direction enhanced by the nonparallel circular motion is further improved by the Brownian force in the experimentally relevant region of $D$. In addition, the experimentally relevant $D$ is found to be consistent with the expectation from the fluctuation dissipation relation between the random stress and viscosity in the LNS equation of Landau and Lifschitz for incompressible fluids.

physics.flu-dyn↗

arXiv2023

Numerical study of anisotropic diffusion in Turing patterns based on Finsler geometry modeling

We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system, focusing on anisotropic diffusion by using the Finsler geometry (FG) modeling technique. In the FG modeling prescription, the diffusion coefficients are dynamically generated to be direction dependent owing to an internal degree of freedom (IDOF) and its interaction with the activator and inhibitor under the presence of thermal fluctuations. In this sense, FG modeling contrasts sharply with the standard numerical technique, where direction-dependent diffusion coefficients are assumed in the reaction-diffusion (RD) equations of Turing. To find the solution of the RD equations, we use a hybrid numerical technique as a combination of the metropolis Monte Carlo method for IDOF updates and discrete RD equations for steady-state configurations of activator-inhibitor variables. We find that the newly introduced IDOF and its interaction are one possible origin of spontaneously emergent anisotropic patterns on living organisms such as zebra and fishes. Moreover, the IDOF makes TPs controllable by external conditions if the IDOF is identified with lipids on cells or cell mobility.

nlin.PS↗

arXiv2022

Langevin Navier-Stokes simulation of protoplasmic streaming by 2D MAC method

We study protoplasmic streaming in plant cells such as chara brauni by simplifying the flow field to a two-dimensional Couette flow with Brownian random motion inside parallel plates. Protoplasmic streaming is receiving a lot of attention in many areas, such as agriculture-technology and biotechnology. The plant size depends on the velocity of streaming and the driving force originating in molecular motors. Therefore, it is interesting to study detailed information on the velocity of streaming. Recently, experimentally observed peaks in the velocity distribution have been simulated by a 2D Langevin Navier-Stokes (LNS) equation for vortex and flow function. However, to simulate actual 3D flows, we have to use the NS equation for velocity, which, in the case of 2D flows, is not always equivalent to that for vorticity and stream function. In this paper, we report that a 2D LNS equation for velocity and pressure successfully simulates protoplasmic streaming by comparing the results with the experimental data and those obtained by 2D LNS simulations for vortex and flow function. Moreover, a dimensional analysis clarifies the dependence of numerical results on the strength $D$ of Brownian random force and physical parameters such as kinematic viscosity and cell size. We find from this analysis how the peak position in normalized velocity distribution moves depending on these parameters.

physics.flu-dyn↗

arXiv2022

The stability of 3D skyrmions under mechanical stress studied via Monte Carlo calculations

Using Monte Carlo (MC) simulations, we study the skyrmion stability/instability as a response to uniaxial mechanical stresses. Skyrmions emerge in chiral magnetic materials as a stable spin configuration under external magnetic field $\vec{B}$ with the competition of ferromagnetic interaction and Dzyaloshinskii-Moriya interaction (DMI) at low temperature $T$. Skyrmion configurations are also known to be stable (unstable) under a compressive stress applied parallel (perpendicular) to $\vec{B}$. To understand the origin of such experimentally confirmed stability/instability, we use the Finsler geometry modeling technique with a new degree of freedom for strains, which plays an essential role in DMI being anisotropic. We find from MC data that the area of the skyrmion state on the $B$-$T$ phase diagram increases (decreases) depending on the direction of applied stresses, in agreement with reported experimental results. This change in the area of the skyrmion state indicates that skyrmions become more (less) stable if the tensile strain direction is parallel (perpendicular) to $\vec{B}$. From the numerical data in this paper, we find that the so-called magneto-elastic effect is suitably implemented in the effective DMI theory with the strain degree of freedom without complex magneto-elastic coupling terms for chiral magnetic materials. This result confirms that experimentally-observed skyrmion stability and instability are caused by DMI anisotropy.

cond-mat.str-el↗

arXiv2021

Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

Skyrmions in chiral magnetic materials are topologically stable and energetically balanced spin configurations appearing under the presence of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI). Much of the current interest has focused on the effects of magneto-elastic coupling on these interactions under mechanical stimuli, such as uniaxial stresses for future applications in spintronics devices. Recent studies suggest that skyrmion shape deformations in thin films are attributed to an anisotropy in the coefficient of DMI, such that $D_{x}\!\not=\!D_{y}$, which makes the ratio $λ/D$ anistropic, where the coefficient of FMI $λ$ is isotropic. It is also possible that $λ_{x}\!\not=\!λ_{y}$ while $D$ is isotropic for $λ/D$ to be anisotropic. In this paper, we study this problem using a new modeling technique constructed based on Finsler geometry (FG). Two possible FG models are examined: In the first (second) model, the FG modeling prescription is applied to the FMI (DMI) Hamiltonian. We find that these two different FG models' results are consistent with the reported experimental data for skyrmion deformation. We also study responses of helical spin orders under lattice deformations corresponding to uniaxial extension/compression and find a clear difference between these two models in the stripe phase, elucidating which interaction of FMI and DMI is deformed to be anisotropic by uniaxial stresses.

cond-mat.mtrl-sci↗

arXiv2020

Stochastic Fluid Dynamics Simulations of the Velocity Distribution in Protoplasmic Streaming

Protoplasmic streaming in plant cells is directly visible in the cases of \textit{Chara corallina} and \textit{Nitella flexilis}, and this streaming is understood to play a role in the transport of biological materials. For this reason, related studies have focused on molecular transportation from a fluid mechanics viewpoint. However, the experimentally observed distribution of the velocity along the flow direction $x$, which exhibits two peaks at $V_x\!=\!0$ and at a finite $V_x(\not=\!0)$, remains to be studied. In this paper, we numerically study whether this behavior of the flow field can be simulated by a 2D stochastic Navier-Stokes (NS) equation for Couette flow, in which random Brownian force is assumed. We present the first numerical evidence that these peaks are reproduced by the stochastic NS equation, which implies that the Brownian motion of the fluid particles plays an essential role in the emergence of these peaks in the velocity distribution. We also find that the position of the peak at $V_x(\not=\!0)$ moves with the variation in the strength $D$ of the random Brownian force, which also changes depending on physical parameters such as the kinematic viscosity, boundary velocity and diameter of the plant cells.

cond-mat.stat-mech↗

arXiv2019

Skyrmions on 2D Elastic Surfaces with Fixed Boundary Frame

We report simulation results of skyrmions on fluctuating 2D lattices, where the vertices ${\bf r}_i (\in {\bf R}^3)$ are treated as a dynamical variable and, hence, there is no crystalline structure. On the fluctuating surfaces, an external magnetic field perpendicular to the surface, Dzyaloshinskii-Moriya and ferromagnetic interactions are assumed in addition to the Helfrich-Polyakov Hamiltonian for membranes. The surface (or frame) tension $τ$ is calculated under both isotropic and uniaxial strain conditions, and this calculation clarifies a non-trivial dependence of $τ$ on the skyrmion, stripe, and ferromagnetic phases. We find that the variation of $τ$ with respect to the applied magnetic field in the skyrmion phase is accompanied by a variation of the total number of skyrmions. Moreover, we find that this total number variation is qualitatively consistent with a recent experimental result for the creation/annihilation of skyrmions of 3D crystalline material under uniaxial stress conditions. It is also found that the stripe phase is significantly influenced by uniaxial strains, while the skyrmion phase remains unchanged. These results allow us to conclude that the skyrmion phase is stable even on fluctuating surfaces.

cond-mat.str-el↗

arXiv2019

Surface tension of membranes depending on the boundary shape

In this paper, we study the boundary effect on the surface (or frame) tension of elastic membrane surface models. The frame tension generally depends only on the projected area of the boundary over which the surface spans. However, from a spin model analogy, the frame tension is expected to be dependent also on the boundary shape at the continuous transition point. We confirm this expectation using the following fixed-connectivity and tethered surface models: the surface model of Helfrich and Polyakov and a surface model with deficit angle term. We also discuss the reason why this expectation is worthwhile to study.

cond-mat.soft↗

arXiv2017

Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling

We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping ${\bf r}$ from a two dimensional parameter space $M$ to the three dimensional Euclidean space ${\bf R}^3$. The metric variable $g_{ab}$, which is always fixed to the Euclidean metric $δ_{ab}$, can be extended to a more general non-Euclidean metric on $M$ in the continuous model. The problem we focus on in this paper is whether such an extension is well-defined or not in the discrete model. We find that a discrete surface model with nontrivial metric becomes well-defined if it is treated in the context of Finsler geometry (FG) modeling, where triangle edge length in $M$ depends on the direction. It is also shown that the discrete FG model is orientation assymetric on invertible surfaces in general, and for this reason, the FG model has a potential advantage for describing real physical membranes, which are expected to have some assymetries for orientation changing transformations.

cond-mat.soft↗

arXiv2017

J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

We present Monte Carlo data of the stress-strain diagrams obtained using two different triangulated surface models. The first is the canonical surface model of Helfrich and Polyakov (HP), and the second is a Finsler geometry (FG) model. The shape of the experimentally observed stress-strain diagram is called J-shaped. Indeed, the diagram has a plateau for the small strain region and becomes linear in the relatively large strain region. Because of this highly non-linear behavior, the J-shaped diagram is far beyond the scope of the ordinary theory of elasticity. Therefore, the mechanism behind the J-shaped diagram still remains to be clarified, although it is commonly believed that the collagen degrees of freedom play an essential role. We find that the FG modeling technique provides a coarse-grained picture for the interaction between the collagen and the bulk material. The role of the directional degrees of freedom of collagen molecules or fibers can be understood in the context of FG modeling. We also discuss the reason for why the J-shaped diagram cannot (can) be explained by the HP (FG) model.

cond-mat.soft↗

arXiv2017

Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer

We study a three-dimensional ($3D$) liquid crystal elastomer (LCE) in the context of Finsler geometry (FG) modeling, where FG is a mathematical framework for describing anisotropic phenomena. The LCE is a $3D$ rubbery object and has remarkable properties, such as the so-called soft elasticity and elongation, the mechanisms of which are unknown at present. To understand these anisotropic phenomena, we introduce a variable $σ$, which represents the directional degrees of freedom of a liquid crystal (LC) molecule. This variable $σ$ is used to define the Finsler metric for the interaction between the LC molecules and bulk polymers. Performing Monte Carlo (MC) simulations for a cylindrical body between two parallel plates, we numerically find the soft elasticity in MC data such that the tensile stress and strain are consistent with reported experimental results. Moreover, the elongation is also observed in the results of MC simulations of a spherical body with free boundaries, and the data obtained from the MC simulations are also consistent with existing experimental results.

cond-mat.soft↗

arXiv2016

Finsler geometry modeling of phase separation in multi-component membranes

Finsler geometric surface model is studied as a coarse-grained model for membranes of three-component such as DOPC, DPPC and Cholesterol. To understand the phase separation of liquid ordered (DPPC rich) $L_o$ and the liquid disordered (DOPC rich) $L_d$, we introduce a variable $σ(\in \{1,-1\})$ in the triangulated surface model. We numerically find that there appear two circulars and stripe domains on the surface and that these two morphologies are separated by a phase transition. The morphological change from the one to the other with respect to the variation of the area fraction of $L_o$ is consistent with existing experimental results. This gives us a clear understanding of the origin of the line tension energy, which has been used to understand those morphological changes in the three-component membranes. In addition to these two circulars and stripe domains, raft-like domain and budding domain are also observed, and the corresponding several phase diagrams are obtained. Technical details of the Finsler geometry modeling are also shown.

cond-mat.soft↗

arXiv2016

Dependence of the surface tension on the shape of surface boundary

We numerically check that the surface tension of membranes is independent of the shape of surface boundary. The surface tension is calculated by means of the Monte Carlo simulation technique on two types of cylinders made of rubans of size $L_1$ and $L_2$, where the rubans are the same for the projected area and different in the ratio $L_1/L_2$. The difference of the surface tension disappears in the thermodynamic limit in both models of Helfrich-Polyakov and Landau-Ginzburg.

cond-mat.soft↗

arXiv2015

Parallel tempering Monte Carlo simulations of spherical fixed-connectivity model for polymerized membranes

We study the first order phase transition of the fixed-connectivity triangulated surface model using the Parallel Tempering Monte Carlo (PTMC) technique on relatively large lattices. From the PTMC results, we find that the transition is considerably stronger than the reported ones predicted by the conventional Metropolis MC (MMC) technique and the flat histogram MC technique. We also confirm that the results of the PTMC on relatively smaller lattices are in good agreement with those known results. This implies that the PTMC is successfully used to simulate the first order phase transitions. The parallel computation in the PTMC is implemented by OpenMP, where the speed of the PTMC on multi-core CPUs is considerably faster than that on the single-core CPUs.

cond-mat.soft↗

arXiv2015

Surface tension and Laplace pressure in triangulated surface models for membranes without fixed boundary

A Monte Carlo (MC) study is performed to evaluate the surface tension $γ$ of spherical membranes that may be regarded as the models of the lipid layers. We use the canonical surface model defined on the self-avoiding triangulated lattices. The surface tension $γ$ is calculated by keeping the total surface area $A$ constant during the MC simulations. In the evaluation of $γ$, we use $A$ instead of the projected area $A_p$, which is unknown due to the fluctuation of the spherical surface without boundary. The pressure difference ${\itΔ}p $ between the inner and the outer sides of the surface is also calculated by maintaining the enclosed volume constant. Using ${\itΔ}p $ and the Laplace formula, we obtain the tension, which is considered to be equal to the frame tension $τ$ conjugate to $A_p$, and check whether or not $γ$ is consistent with $τ$. We find reasonable consistency between $γ$ and $τ$ in the region of sufficiently large bending rigidity $κ$ or sufficiently large $A/N$. It is also found that $τ$ becomes constant in the limit of $A/N\to \infty$ both in the tethered and fluid surfaces.

cond-mat.soft↗

arXiv2015

Internal phase transition induced by external forces in Finsler geometric model for membranes

We numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three dimensional unit vector $σ$ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of $σ$ with the interaction coefficient $λ$. For large (small) $λ$, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate $λ$, the surface becomes planar. Conversely, fixing the surface with the boundary of area $A$ or with the two point boundaries of distance $L$, we find that the variable $σ$ changes from random to aligned state with increasing of $A$ or $L$ for the intermediate region of $λ$. This implies that an internal phase transition for $σ$ is triggered not only by the thermal fluctuations but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to $A/N$ ($L/N$) at the intermediate region of $A$ ($L$) where the $σ$ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension $γ$ at sufficiently large $λ$ is considerably smaller than that at small $λ$. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.

cond-mat.soft↗