- Biophysics: Proteins, Gene regulation network, Computational methods
- Nonlinear Dynamics: Traffic flow, Sand dunes
- Soft Matter: Polymers
- Critical Phenomena: Classical spins, Computational methods
- Quantum Spin Systems: Antiferromagnets, Computational methods
- Miscellaneous: Rare event sampling, Quantum dissipative system

- Tadamune Kaneko and Macoto Kikuchi: Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution, PLoS Comput Biol 18(1): e1009796
The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

- Shintaro Nagata and Macoto Kikuchi: Emergence of cooperative bistability and robustness of gene regulatory networks, PLoS Comput Biol 16(2020) e1007969
Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, “on” and “off”, was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between “on” and “off”. This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.

- Nobu C. Shirai and Macoto Kikuchi: The interplay of intrinsic disorder and macromolecular crowding on alpha-synuclein fibril formation , J. Chem. Phys. Vol.144 (2016) 055101
Alpha-synuclein (alpha-syn) is an intrinsically disordered protein which is considered to be one of the causes of Parkinson's disease. This protein forms amyloid fibrils when in a highly concentrated solution. The fibril formation of alpha-syn is induced not only by increases in alpha-syn concentration but also by macromolecular crowding. In order to investigate the coupled effect of the intrinsic disorder of alpha-syn and macromolecular crowding, we construct a lattice gas model of alpha-syn in contact with a crowding agent reservoir based on statistical mechanics. The main assumption is that alpha-syn can be expressed as coarse-grained particles with internal states coupled with effective volume; and disordered states are modeled by larger particles with larger internal entropy than other states. Thanks to the simplicity of the model, we can exactly calculate the number of conformations of crowding agents, and this enables us to prove that the original grand canonical ensemble with a crowding agent reservoir is mathematically equivalent to a canonical ensemble without crowding agents. In this expression, the effect of macromolecular crowding is absorbed in the internal entropy of disordered states; it is clearly shown that the crowding effect reduces the internal entropy. Based on Monte Carlo simulation, we provide scenarios of crowding-induced fibril formation. We also discuss the recent controversy over the existence of helically folded tetramers of alpha-syn, and suggest that macromolecular crowding is the keytoresolvingthecontroversy.

- Ryo Kanada, Fumiko Takagi and Macoto Kikuchi: Nucleotide-dependent structural fluctuations and regulation of microtubule-binding affinity of KIF1A, Proteins: Structure, Function, and Bioinformatics Vol.83 (2015) p.809-819
Molecular motors such as kinesin regulate affinity to a rail protein during the ATP hydrolysis cycle. The regulation mechanism, however, is yet to be determined. To understand this mechanism, we investigated the structural fluctuations of the motor head of the single-headed kinesin called KIF1A in different nucleotide states using molecular dynamics simulations of a Gō-like model. We found that the helix math formula at the microtubule (MT) binding site intermittently exhibits a large structural fluctuation when MT is absent. Frequency of this fluctuation changes systematically according to the nucleotide states and correlates strongly with the experimentally observed binding affinity to MT. We also showed that thermal fluctuation enhances the correlation and the interaction with the nucleotide suppresses the fluctuation of the helix math formula. These results suggest that KIF1A regulates affinity to MT by changing the flexibility of the helix math formula during the ATP hydrolysis process: the binding site becomes more flexible in the strong binding state than in the weak binding state.

- Nen Saito and Macoto Kikuchi: Robustness leads close to the edge of chaos in coupled map networks: toward the understanding of biological networks, New J. Phys. Vol.15 (2013) 053037
Dynamics in biological networks are, in general, robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems that are robust against phenotypic perturbations (perturbations in dynamics), as well as systems that are robust against mutation (perturbations in network structure). To achieve such a design, we apply a multicanonical Monte Carlo method. Analysis based on the maximum Lyapunov exponent and parameter sensitivity shows that systems with marginal stability, which are regarded as systems at the edge of chaos, emerge when robustness against network perturbations is required. This emergence of the edge of chaos is a self-organization phenomenon and does not need a fine tuning of parameters.

- Nobu C. Shirai, and Macoto Kikuchi: Structural flexibility of intrinsically disordered proteins induces stepwise target recognition, J.Chem.Phys. Vol.139 (2013) 225103
An intrinsically disordered protein (IDP) lacks a stable three-dimensional structure, while it folds into a specific structure when it binds to a target molecule. In some IDP-target complexes, not all target binding surfaces are exposed on the outside, and intermediate states are observed in their bind- ing processes. We consider that stepwise target recognition via intermediate states is a characteristic of IDP binding to targets with “hidden” binding sites. To investigate IDP binding to hidden target binding sites, we constructed an IDP lattice model based on the HP model. In our model, the IDP is modeled as a chain and the target is modeled as a highly coarse-grained object. We introduced motion and internal interactions to the target to hide its binding sites. In the case of unhidden binding sites, a two-state transition between the free states and a bound state is observed, and we consider that this represents coupled folding and binding. Introducing hidden binding sites, we found an inter- mediate bound state in which the IDP forms various structures to temporarily stabilize the complex. The intermediate state provides a scaffold for the IDP to access the hidden binding site. We call this process multiform binding. We conclude that structural flexibility of IDPs enables them to ac- cess hidden binding sites and this is a functional advantage of IDPs.

- Katsuyoshi Matsushita and Macoto Kikuchi: Frustration-induced protein intrinsic disorder, J.Chem.Phys. Vol.130 (2013) 105101
Spontaneous folding into a specific native structure is the most important property of protein to perform their biological functions within organisms. Spontaneous folding is understood on the basis of an energy landscape picture based on the minimum frustration principle. Therefore, frustration seemingly only leads to protein functional disorder. However, frustration has recently been suggested to have a function in allosteric regulation. Functional frustration has the possibility to be a key to our deeper understanding of protein function. To explore another functional frustration, we theoretically examined structural frustration, which is designed to induce intrinsic disorder of a protein and its function through the coupled folding and binding. We extended the Wako-Saitô-Muñoz-Eaton model to take into account a frustration effect. With the model, we analyzed the binding part of neuron-restrictive silencer factor and showed that designed structural frustration in it induces intrinsic disorder. Furthermore, we showed that the folding and the binding are cooperative in interacting with a target protein. The cooperativity enables an intrinsically disordered protein to exhibit a sharp switch-like folding response to binding chemical potential change. Through this switch-like response, the structural frustration may contribute to the regulation function of interprotein interaction of the intrinsically disordered protein.

- Hiroo Kenzaki and Macoto Kikuchi: Free-energy landscape of kinesin by a realistic lattice model, Proteins: Structure, Function, and Bioinformatics Vol.71 (2008) p.389-395
Structural fluctuations in the thermal equilibrium of the kinesin motor domain are studied using a lattice protein model with Gō interactions. By means of the multi-self-overlap ensemble Monte Carlo method and the principal component analysis, the free-energy landscape is obtained. It is shown that kinesins have two subdomains that exhibit partial folding/unfolding at functionally important regions: one is located around the nucleotide binding site and the other includes the main microtubule binding site. These subdomains are consistent with structural variability that was reported recently based on experimentally-obtained structures. On the other hand, such large structural fluctuations have not been captured by B-factor or normal mode analyses. Thus, they are beyond the elastic regime, and it is essential to take into account chain connectivity for studying the function of kinesins.

- Fumiko Takagi and Macoto Kikuchi: Structural Change and Nucleotide Dissociation of Myosin Motor Domain: Dual Go Model Simulation, Biophys.J. Vol.93 (2007) p.3820-3827
We investigated the structural relaxation of myosin motor domain from the pre-power stroke state to the near-rigor state using molecular dynamics simulation of a coarse-grained protein model. To describe the spontaneous structural change, we propose a dual Gō-model—a variant of the Gō-like model that has two reference structures. The nucleotide dissociation process is also studied by introducing a coarse-grained nucleotide in the simulation. We found that the myosin structural relaxation toward the near-rigor conformation cannot be completed before the nucleotide dissociation. Moreover, the relaxation and the dissociation occurred cooperatively when the nucleotide was tightly bound to the myosin head. The result suggested that the primary role of the nucleotide is to suppress the structural relaxation.

- Hiroo Kenzaki and Macoto Kikuchi: Diversity in free energy landscape and folding pathway of proteins with the same native topology, Chem.Phys.Lett. Vol.427 (2006) p.414-417
To elucidate the role of relative stability of subdomains in folding processes of multi-domain proteins, we have studied a free-energy landscape of c-type lysozyme by Monte Carlo simulations using a realistic lattice model with a Gō-like interaction. By varying the relative interaction strength of two subdomains as a parameter, we obtained a variety of the free-energy landscapes. Experimentally-observed diversity in folding processes of c-type lysozymes can then be described by this Gō-like model with only one variable parameter. The result demonstrates that folding of multi-domain proteins can be understood in the framework of the energy landscape theory.

- Kazuki Nakanishi and Macoto Kikuchi: Thermodynamics of Aggregation of Two Proteins, J.Phys.Soc.Jpn. Vol.75 (2006) 064803
We investigate aggregation mechanism of two proteins in a thermodynamically unambiguous manner by considering the finite size effect of free energy landscape of HP lattice protein model. Multi-self-overlap-ensemble Monte Carlo method is used for numerical calculations. We find that a dimer can be formed spontaneously as a thermodynamically stable state when the system is small enough. It implies the possibility that the aggregation of proteins in a cell is triggered when they are confined in a small region by, for example, being surrounded by other macromolecules. We also find that the dimer exhibits a transition between unstable state and metastable state in the infinite system.

- George Chikenji and Macoto Kikuchi: What is the role of non-native intermediates of beta-lactoglobulin in protein folding? ,
Proc.Natl.Acad.Sci. Vol.97 (2000) p.14273-14277
The mechanism of α→β transition in folding of β-lactoglobulin is discussed based on free energy landscape analysis of a long lattice model. It is found that helical propensity of β-lactoglobulin is driven by conformational entropy and is intrinsically coded in its native structure. We propose a view on a role of folding intermediate, which is “on-pathway” but rich in non-native structures. The present results suggest that the native structure topology plays an important role in α→β transition.

- George Chikenji, Macoto Kikuchi, and Yukito Iba: Multi-Self-Overlap Ensemble for protein folding: ground state search and thermodynamics, Phys.Rev.Lett. Vol.83 (1999) p.1886-1889
Long chains of the HP lattice protein model are studied by the multi-self-overlap ensemble Monte Carlo method, which was developed recently by Iba, Chikenji, and Kikuchi. This method successfully finds the lowest energy states reported before for sequences of the chain length N=42–100 in two and three dimensions. Moreover, the method realizes the lowest energy state that was ever found in a case of N=100. Finite-temperature properties of these sequences are also investigated by this method. Two successive transitions are observed between the native and random coil states. Thermodynamic analysis suggests that the ground state degeneracy is relevant to the order of the transitions.

- Shin-ichi Tadaki, Macoto Kikuchi, Akihiro Nakayama, Akihiro Shibata, Yuki Sugiyama and Satoshi Yukawa:
Characterizing and distinguishing free and jammed traffic flows from the distribution and correlation of experimental speed data,
New J. Phys., vol.18 083022 (2016).
From a physics point of view, the emergence of a traffic jam is considered to be a dynamical phase transition. To verify this, we performed a series of circuit experiments. In previous work, Tadaki et al (2013 New J. Phys 15 103034), we confirmed the occurrence of this phase transition and estimated the critical density between free and jammed flows by analyzing the fundamental diagram. In this paper, we characterize and distinguish free and jammed flows, beyond the analyses of fundamental diagrams, according to the distribution and correlation of experimental speed data. We find that the speed in free flow does not correlate and its distribution has a narrow single peak at the average. The distribution of speed in jammed flow has two peaks or a single broad peak. The two peaks indicate the car speeds inside and outside of jam clusters. The broad single peak appears as a result of the appearance and disappearance of jam clusters. We also find that the formation of jam clusters induces a long correlation in speed. We can identify the size of jam clusters and the relative distance between coexisting jam clusters from this speed correlation.

- Akihiro Nakayama, Macoto Kikuchi, Akihiro Shibata, Yuki Sugiyama, Shin-ichi Tadaki, Satoshi Yukawa:
Quantitative explanation of circuit experiments and real traffic using the optimal velocity model,
New J. Phys., vol.18 043040 (2016).
We have experimentally confirmed that the occurrence of a traffic jam is a dynamical phase transition (Tadaki et al 2013 New J. Phys. 15 103034, Sugiyama et al 2008 New J. Phys. 10 033001). In this study, we investigate whether the optimal velocity (OV) model can quantitatively explain the results of experiments. The occurrence and non-occurrence of jammed flow in our experiments agree with the predictions of the OV model. We also propose a scaling rule for the parameters of the model. Using this rule, we obtain critical density as a function of a single parameter. The obtained critical density is consistent with the observed values for highway traffic.

- Shin-ichi Tadaki, Macoto Kikuchi, Minoru Fukui, Akihiro Nakayama, Katsuhiro Nishinari, Akihiro Shibata, Yuki Sugiyama, Taturu Yosida and Satoshi Yukawa:
Phase transition in traffic jam experiment on a circuit, New J. Phys. Vol.15 (2013) 103034.
The emergence of a traffic jam is considered to be a dynamical phase transition in a physics point of view; traffic flow becomes unstable and changes phase into a traffic jam when the car density exceeds a critical value. In order to verify this view, we have been performing a series of circuit experiments. In our previous work (2008 New J. Phys. 10 033001), we demonstrated that a traffic jam emerges even in the absence of bottlenecks at a certain high density. In this study, we performed a larger indoor circuit experiment in the Nagoya Dome in which the positions of cars were observed using a high-resolution laser scanner. Over a series of sessions at various values of density, we found that jammed flow occurred at high densities, whereas free flow was conserved at low densities. We also found indications of metastability at an intermediate density. The critical density is estimated by analyzing the fluctuations in speed and the density-flow relation. The value of this critical density is consistent with that observed on real expressways. This experiment provides strong support for physical interpretations of the emergence of traffic jams as a dynamical phase transition.

- Atsunari Katsuki and Macoto Kikuchi: Simulation of barchan dynamics with inter-dune sand streams, New J. Phys. Vol.13 (2011) 063049
A group of barchans, crescent sand dunes, exhibit a characteristic flying-geese pattern in deserts on Earth and Mars. This pattern implies that an indirect interaction between barchans, mediated by an inter-dune sand stream, which is released from one barchan's horns and caught by another barchan, plays an important role in the dynamics of barchan fields. We used numerical simulations of a recently proposed cell model to investigate the effects of inter-dune sand streams on barchan fields. We found that a sand stream from a point source moves a downstream barchan laterally until the head of the barchan is finally situated behind the stream. This final configuration was shown to be stable by a linear stability analysis. These results indicate that flying-geese patterns are formed by the lateral motion of barchans mediated by inter-dune sand streams. By using simulations we also found a barchan mono-corridor generation effect, which is another effect of sand streams from point sources.

- A.Katsuki, M.Kikuchi, H.Nishimori, N.Endo, and K.Taniguchi: Cellular model for sand dunes with saltation, avalanche and strong erosion: collisional simulation of barchans, Earth Surface Processes and Landforms Vol.36 (2011) 372
Barchans are crescent-shaped dunes that form under unidirectional wind in areas of limited sand supply. The recent development of flume experiments and computer simulations has renewed interest in the interaction dynamics of two or more barchans. From the flume experiment, four distinguishable types of collision patterns between two barchans have been observed: coalescence, ejection, split and reorganization. We have proposed a simple cellular model for numerical simulations of dune dynamics, in which saltation and avalanche are elementary processes. In the present paper, we first describe the model in detail. The model reproduces three types of collision patterns: coalescence, ejection, and reorganization. The largest reason for a split pattern not to occur is the lack of an effect of the flow separation at the brink line of dunes and the recirculation bubble that it produces. We then model the effect of the recirculation bubble by assuming that strong erosion occurs at the reattachment point of the separation flow. The strong-erosion model successfully reproduces all the collision patterns. Thus, three elementary processes – saltation, avalanche and strong-erosion – are sufficient for a phenomenological description of the interaction dynamics of aqueous barchans. It is also shown that the type of collision is determined by competition between the filling-up of the interdune between two barchans and the change in height of each dune.

- Yuki Sugiyama, Minoru Fukui, Macoto Kikuchi, Katsuya Hasebe, Akihiro Nakayama, Katsuhiro Nishinari, Shin-ichi Tadaki and Satoshi Yukawa: Traffic jam without bottleneck - Experimental evidence for the physical mechanism of forming a jam, New J. Phys. Vol.10 (2008) 033001
A traffic jam on a highway is a very familiar phenomenon. From the physical viewpoint, the system of vehicular flow is a non-equilibrium system of interacting particles (vehicles). The collective effect of the many-particle system induces the instability of a free flow state caused by the enhancement of fluctuations, and the transition to a jamming state occurs spontaneously if the average vehicle density exceeds a certain critical value. Thus, a bottleneck is only a trigger and not the essential origin of a traffic jam. In this paper, we present the first experimental evidence that the emergence of a traffic jam is a collective phenomenon like 'dynamical' phase transitions and pattern formation in a non-equilibrium system. We have performed an experiment on a circuit to show the emergence of a jam with no bottleneck. In the initial condition, all the vehicles are moving, homogeneously distributed on the circular road, with the same velocity. The average density of the vehicles is prepared for the onset of the instability. Even a tiny fluctuation grows larger and then the homogeneous movement cannot be maintained. Finally, a jam cluster appears and propagates backward like a solitary wave with the same speed as that of a jam cluster on a highway.

- Atsunari Katsuki, Macoto Kikuchi, and Noritaka Endo: Emergence of a Barchan Belt in a Unidirectional Flow: Experiment and Numerical Simulation, J.Phys.Soc.Jpn. Vol.74 (2005) p.878-881
We observed the time evolution of dune fields in a water tank experiment and simulated it by using a simple model without taking complex fluid dynamics into account. The initial sand bed changed its form to transverse ripples, that is, dunes with straight crest lines perpendicular to the flow direction. Then crescentic dunes, called barchans, evolved from transverse ripples.

- Shin-ichi Tadaki, Macoto Kikuchi, Yuki Sugiyama, and Satoshi Yukawa: Coupled map traffic flow simulator Based on Optimal Velocity Functions, J.Phys.Soc.Jpn. Vol.67 (1998) p.2270-2276
A coupled map traffic flow model is introduced, based on optimal velocity functions. The model is simulated under open boundary conditions. Effects of noises in velocity are investigated. The average car density increases with the noise level. The high throughput flow is realized when the noise level is sufficiently large, and power law behavior appears in temporal spectra of density fluctuations at the same time. By introducing traffic bottlenecks, a hysteresis loop, which indicates the emergence of traffic jams, is observed in the headway-velocity plane. Temporal spectra of density fluctuations also obey a power law in this case, whose exponent is independent of the noise level.

- Satoshi Yukawa and Macoto Kikuchi: Coupled-Map Modeling of One-Dimensional Traffic Flow, J.Phys.Soc.Jpn. Vol.64 (1995) p.35-38
We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle properly, and the maps are coupled to each other through the headway distance. By simulating the model, we obtain a plot of the flow against the concentration similar to the observed data in real traffic flows. Realistic traffic jam regions are observed in space-time trajectories.

- Satoshi Yukawa, Macoto Kikuchi, and Shin-ichi Tadake: Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage, J.Phys.Soc.Jpn. Vol.63 (1994) p.3609-3618
Effects of a bottleneck in a linear trafficway is investigated using a simple cellular automaton model. Introducing a blockage site which transmit cars at some transmission probability into the rule-184 cellular automaton, we observe three different phases with increasing car concentration: Besides the free phase and the jam phase, which exist already in the pure rule-184 model, the mixed phase of these two appears at intermediate concentration with well-defined phase boundaries. This mixed phase, where cars pile up behind the blockage to form a jam region, is characterized by a constant flow. In the thermodynamic limit, we obtain the exact expressions for several characteristic quantities in terms of the car density and the transmission rate. These quantities depend strongly on the system size at the phase boundaries; We analyse these finite size effects based on the finite-size scaling.

- Yukito Iba, George Chikenji, and Macoto Kikuchi: Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble, J.Phys.Soc.Jpn. Vol.67 (1998) p.3327-3330
A novel family of dynamical Monte Carlo algorithms for lattice polymers is proposed. Our central idea is to simulate an extended ensemble in which the self-avoiding condition is systematically weakened. The degree of self-overlap is controlled in a similar manner as the multicanonical ensemble. As a consequence, the ensemble ― the multi-self-overlap ensemble ― contains adequate portions of self-overlapping conformations as well as higher energy ones. It is shown that the multi-self-overlap ensemble algorithm correctly reproduces the canonical averages at finite temperatures of the HP model of lattice proteins. Moreover, it is superior in performance to the standard multicanonical algorithm when applied to a complicated problem of a polymer with eight-stickers. An alternative algorithm based on the exchange Monte Carlo method is also discussed.

- Macoto Kikuchi and Kurt Binder: Microphase separation in Thin Films of the Symmetric Diblock-Copolymer Melt, J.Chem.Phys. Vol.101 (1994) p.3367-3377
By means of Monte Carlo simulations of a lattice model, microphase separation transition of symmetric diblock‐copolymer melts confined in the thin‐film geometry between parallel hard walls is studied. We impose a surface field which acts repulsively only on one of the two species, to stabilize lamellar order parallel to the surfaces. However, interplay between two characteristic lengths, that is, the natural thickness of the lamellar l and the thickness of the film D, causes complicated behavior. In case that the two lengths are compatible with each other, clear lamellar order parallel to the surfaces is observed at temperatures lower than the bulk transition temperature, as expected. On the other hand, tilted or deformed lamellar structure, or even coexistence of lamellae in different orientations are found in cases of strong conflict. In both cases, lamellae are fully established. Even at temperature higher than the bulk transition temperature, weak order is induced by the surface field, and a gradual transition between such surface‐induced order and bulklike order is observed. Film thickness and temperature dependence of the ordered structure is discussed, as well as a density reduction near the walls and in the interfaces between the segregated regions.

- Tomotoshi Nishino, Koichi Okunishi, and Macoto Kikuchi: Numerical Renormalization Group at Criticality, Phys. Lett. A213 (1996) p.69-72
We apply a recently developed numerical renormalization group, the corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice models at their critical temperatures. It is shown that the combination of CTMRG and the finite-size scaling analysis gives two independent critical exponents.

- Macoto Kikuchi and Yutaka Okabe: Multispin Coding of the Monte Carlo Simulation of the Three-State Random Potts Model and the Block-Spin Transformation, Intntl.J.Mod.Phys. C6 (1995) p.747-763
The multi-spin coding of the Monte Carlo simulation of the three-state Potts model on the simple cubic lattice is presented. The ferromagnetic (F) model, the antiferromagnetic (AF) model, and the random mixture of the F and AF couplings are treated. The multispin coding technique is also applied to the block-spin transformation. The block-spin transformation of the F Potts model is simply realized by the majority rule, whereas the AF three-state Potts model is transformed to the block spin having a six-fold symmetry.

- Macoto Kikuchi and Nobuyasu Ito: Statistical Dependence Time and Its Application to the Dynamical Critical Exponent, J.Phys.Soc.Jpn. Vol.62 (1993) p.3052-3061
A new method for studying dynamical correlation of temporal sequence is proposed. We introduce a new quantity named statistical dependence time τ dep as an estimator for the equilibrium relaxation time. The calculation of τ dep does not require calculation of any time-displaced correlation function nor numerical fitting in extracting the relaxation time; as a result, the estimation of τ dep and statistical analysis such as the error estimation are quite straightforward and simple. We apply this method to the critical dynamics of 3D Ising model, and estimate the dynamical critical exponent z as 2.030±0.004, provided K c =0.221654 (if possible error in K c is taken into account, the error in z becomes 0.01).

- Hikaru Kawamura and Macoto Kikuchi: Free-vortex formation and topological phase transitions of two-dimensionsal spin systems, Phys.Rev. B47 (1993) p.1134-1137
A numerical method to study defect-mediated phase transitions is proposed, which combines a standard Monte Carlo technique with a particular type of boundary conditions. The method is applied to the two-dimensional XY (plane rotator) model as well as to the two-dimensional SO(3) Heisenberg model which models a triangular-lattice Heisenberg antiferromagnet. Our results give a direct numerical support for the occurrence of a topological transition in these systems driven by the vortex binding-unbinding.

- Macoto Kikuchi and Yutaka Okabe: A Scaling Approach to Monte Carlo Renormalization Group, Prog.Theor.Phys. Vol.78 (1987) 540-551
We propose a simple method of Monte Carlo renormalization group. Thermodynamic quantities of the block-spin system are analyzed phenomenologically on the basis of scaling concept. The field exponent yH is obtained from the square of block-spin magnetization at the fixed point, while the temperature exponent yT is obtained as a consequence of nonlinearity of the scaling fields. In order to check the effectiveness of the method, we perform calculation on the three-dimensional Ising model. The critical temperature and the two critical exponents are estimated precisely. Finite-size effect is shown to be weak, whose origin is the regular part of the free energy density. Statistical errors of the ratios of the block-spin quantities are proved to be surprisingly small compared to those of the block-spin quantities themselves.

- Macoto Kikuchi and Yutaka Okabe: Renormalization, Self-Similarity, and Relaxation of Order-Parameter Structure in Critical Phenomena, Phys.Rev. B35 (1987) p.5382-5384
We present a new method for studying the temporal evolution of order-parameter structure. The relaxation of the block-spin magnetization ratio of the three-dimensional kinetic Ising model is investigated by use of a Monte Carlo simulation with a block-spin transformation. We find that the short-range structure relaxes very fast and is statistically stable even at the critical point.

- Macoto Kikuchi and Yutaka Okabe: Critical Relaxation of Three-Dimensional Kinetic Ising Model, J.Phys.Soc.Jpn. Vol.55 (1986) p.1359-1363
We report a Monte Carlo study on the critical relaxation of the three-dimensional kinetic Ising model from a nonequilibrium initial state. It is shown that the details of the method, namely, a choice of the sampling procedure and a functional form of the transition probability do not affect an asymptotic power-law relaxation. The finite-size effects on the critical relaxation is also studied. Cross-over from the power-law relaxation to the exponential one is found, which is discussed in view of the dynamical finite-size scaling theory.

- Macoto Kikuchi and Yutaka Okabe: Monte Carlo Study of the Surface Critical Phenomena of the Ising Model, Prog.Theor.Phys. Vol.73 (1985) p.32-40
Monte Carlo technique is applied to the three-dimensional Ising model with free surface. The critical behavior of the layer magnetization, the layer susceptibility and the local susceptibility near the ordinary transition point is investigated. The universal properties of the surface critical exponents and the surface critical amplitude ratios are confirmed. The scaling of magnetization profile is studied, and the bulk amplitude ratio for the correlation length ξ0h / ξ0- is calculated

- Macoto Kikuchi and Yutaka Okabe: Monte Carlo Study of Critical Relaxation Near a Surface, Phys.Rev.Lett. Vol.55 (1985) p.1220-1222
We report the first Monte Carlo simulation on the critical relaxation of the three-dimensional kinetic Ising model with free surfaces. The surface-layer magnetization is shown to relax as t^{−β1/νz} at T=Tc, while the bulk magnetization relaxes as t^{−β/νz}. The dynamic bulk-to-surface crossover is discussed in view of the dynamic scaling theory.

- Macoto Kikuchi, Yutaka Okabe, and Seiji Miyashita: On the Ground-State Phase Transition of the Spin 1/2 $XXZ$ Model on the Square Lattice, J.Phys.Soc.Jpn. Vol.59 (1990) p.492-496
We study the effect of anisotropy for the ground state of the spin 1/2 antiferromagnet on the square lattice by diagonalizing the Hamiltonian numerically. The symmetry change of the ground state at the isotropic point is discussed.

- Yutaka Okabe and Macoto Kikuchi: Quantum Monte Carlo Simulation of the Spin 1/2 $XXZ$ Model on the Square Lattice, J.Phys.Soc.Jpn. Vol.57 (1988) p.4351-4358
We systematically study the spin 1/2 quantum XXZ model on the square lattice using a quantum Monte Carlo method. The temperature dependence of the energy, specific heat and order parameter is calculated for the systems of sizes up to 16×16. Investigating the size dependence carefully, we exarnine the ground-state energy and the existence of the long-range order.

- Akimasa Kitajima and Macoto Kikuchi: Numerous but Rare: An Exploration of Magic Squares, PLOS ONE, vol.10 (2015) e0125062
How rare are magic squares? So far, the exact number of magic squares of order n is only known for n<=5. For larger squares, we need statistical approaches for estimating the number. For this purpose, we formulated the problem as a combinatorial optimization problem and applied the Multicanonical Monte Carlo method (MMC), which has been developed in the field of computational statistical physics. Among all the possible arrangements of the numbers 1; 2,..., n^2 in an n*n square, the probability of finding a magic square decreases faster than the exponential of n. We estimated the number of magic squares for n<=30. The number of magic squares for n = 30 was estimated to be 6.56(29)*10^2056 and the corresponding probability is as small as 10^-212. Thus the MMC is effective for counting very rare configurations.

- Gen Tatara, Macoto Kikuchi, Satoshi Yukawa, and Hiroshi Matsukawa: Dissipation Enhanced Asymmetric Transport in Quantum Ratchets, J.Phys.Soc.Jpn. Vol.67 (1998) p.1090-1093
Quantum mechanical motion of a particle in a periodic asymmetric potential is studied theoretically at zero temperature. It is shown based on a semi-classical approximation that the tunneling probability from one local minimum to the next becomes asymmetric in the presence of a weak oscillating field, even though there is no average macroscopic field gradient. Dissipation enhances this asymmetry, and leads to a steady unidirectional current, resulting in a quantum ratchet system.