## A01-003 SANO

### Paper | Original Paper

#### 2017

Tomoyuki Mano, *Jean-Baptiste Delfau, Junichiro Iwasawa, and Masaki Sano,
Optimal run-and-tumble based transportation of a Janus particle with active steering,
Proceedings of the National Academy of Sciences 114, in press.

[Summary] Commanding the swimming of micrometric objects subjected to thermal agitation is always challenging both for artificial and living systems. Now, artificial swimmers can be designed whose self-propelling force can be tuned at will. However, orienting such small particles to an arbitrary direction requires counterbalancing the random rotational diffusion. Here, we introduce a simple concept to reorient artificial swimmers, granting them a motion similar to the run-and-tumbling behavior of Escherichia coli. We demonstrate it using Janus particles with asymmetric surface coating and moving under an AC electric field. Moreover, we determine the optimal strategy and compare it with biological swimmers. Our results encourage further investigation into dynamical behavior of colloidal particles, as well as application to microscopic devices.

*Yohsuke T. Fukai and Kazumasa A. Takeuchi,
Kardar-Parisi-Zhang Interfaces with Inward Growth,
Physical Review Letters 119, 030602/1-5 (2017).

[Summary] We study the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an off-lattice Eden model, respectively. To realize the ring initial condition experimentally, we introduce a holography-based technique that allows us to design the initial condition arbitrarily. Then, we find that fluctuation properties of ingrowing circular interfaces are distinct from those for the curved or circular KPZ subclass and, instead, are characterized by the flat subclass. More precisely, we find an asymptotic approach to the Tracy-Widom distribution for the Gaussian orthogonal ensemble and the Airy1 spatial correlation, as long as time is much shorter than the characteristic time determined by the initial curvature. Near this characteristic time, deviation from the flat KPZ subclass is found, which can be explained in terms of the correlation length and the circumference. Our results indicate that the sign of the initial curvature has a crucial role in determining the universal distribution and correlation functions of the KPZ class.

Kazumasa A. Takeuchi,
1/fα power spectrum in the Kardar-Parisi-Zhang universality class,
Journal of Physics A: Mathematical and Theoretical 50, 264006/1-17 (2017).

[Summary] The power spectrum of interface fluctuations in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class is studied both experimentally and numerically. A 1/f-type spectrum is found and characterized through a set of 'critical exponents' for the power spectrum. The recently formulated aging Wiener-Khinchin theorem accounts for the observed exponents. Interestingly, the 1/f-type spectrum in the KPZ class turns out to contain information on a universal distribution function characterizing the asymptotic state of the KPZ interfaces, namely the Baik-Rains universal variance. It is indeed observed in the presented data, both experimental and numerical, and in both circular and flat interfaces in the long time limit.

*Jacopo De Nardis, Pierre Le Doussal, and Kazumasa A. Takeuchi,
Memory and Universality in Interface Growth,
Physical Review Letters 118, 125701/1-5 (2017).

[Summary] Recently, very robust universal properties have been shown to arise in one-dimensional growth processes with local stochastic rules, leading to the Kardar-Parisi-Zhang (KPZ) universality class. Yet it has remained essentially unknown how fluctuations in these systems correlate at different times. Here, we derive quantitative predictions for the universal form of the two-time aging dynamics of growing interfaces and we show from first principles the breaking of ergodicity that the KPZ time evolution exhibits. We provide corroborating experimental observations on a turbulent liquid crystal system, as well as a numerical simulation of the Eden model, and we demonstrate the universality of our predictions. These results may give insight into memory effects in a broader class of far-from-equilibrium systems.

*Daiki Nishiguchi, Ken H. Nagai, Hugues Chate, and Masaki Sano,
Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria,
Physical Review E 95, 020601(R) /1-6 (2017).

[Summary] We study the collective dynamics of elongated swimmers in a very thin fluid layer by devising long, filamentous, non-tumbling bacteria. The strong confinement induces weak nematic alignment upon collision, which, for large enough density of cells, gives rise to global nematic order.　This homogeneous but fluctuating phase, observed on the largest experimentally-accessible scale of millimeters,　 exhibits the properties predicted by standard models for flocking such as the Vicsek-style model of polar particles 　with nematic alignment: true long-range nematic order and non-trivial giant number fluctuations.

#### 2016

Gioia Carinci, Cristiana Giardina, Frank Redig, Tomohiro Sasamoto,
A generalized asymmetric exclusion process with Uq(sl2) stochastic duality,
Probability Theory and Related Fields 166(3), 887-933 (2016).

[Summary] In the studies of one-dimensional asymmetric simple exclusion process(ASEP), the existence of self-duality is very useful but it has not been well understood what type of stochastic models with current have self-duality. In this paper we present a general scheme to construct stochastic processes with self-duality related to quantum group symmetries. As an example we constructed a model with multi-particle occupancy at a site related to higher spin representation of the quantum algebra Uq(sl2).

*Kazumasa A. Takeuchi and Takuma Akimoto,
Characteristic Sign Renewals of Kardar-Parisi-Zhang Fluctuations,
Journal of Statistical Physics 164, 1167-1182 (2016).

[Summary] Tracking the sign of fluctuations governed by the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called the renewal process, studied in the context of aging and ergodicity breaking. Although KPZ and the renewal process are fundamentally different in many aspects, we find remarkable agreement in some of the time correlation properties, such as the recurrence time distributions and the persistence probability, while the two systems can be different in other properties. Moreover, we find inequivalence between long-time and ensemble averages in the fraction of time occupied by a specific sign of the KPZ-class fluctuations. The distribution of its long-time average converges to nontrivial broad functions, which are found to differ significantly from that of the renewal process, but instead be characteristic of KPZ. Thus, we obtain a new type of ergodicity breaking for such systems with many-body interactions. Our analysis also detects qualitative differences in time-correlation properties of circular and flat KPZ-class interfaces, which were suggested from previous experiments and simulations but still remain theoretically unexplained.

*Xiong Ding, Hugues Chate, Predrag Cvitanovic, Evangelos Siminos, and Kazumasa A. Takeuchi,
Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits,
Physical Review Letters 117, 024101/1-5 (2016).

[Summary] We provide numerical evidence that a finite-dimensional inertial manifold on which the dynamics of a chaotic dissipative dynamical system lives can be constructed solely from the knowledge of a set of unstable periodic orbits. In particular, we determine the dimension of the inertial manifold for the Kuramoto-Sivashinsky system and find it to be equal to the “physical dimension” computed previously via the hyperbolicity properties of covariant Lyapunov vectors.

*J.-B. Delfau, John J. Molina and M. Sano,
Collective behavior of strongly confined suspensions of squirmers,
Europhysics Letters 114, 24001/1-5 (2016).

[Summary] We run numerical simulations of strongly confined suspensions of model spherical swimmers called “squirmers”. Because of the confinement, the Stokeslet dipoles generated by the particles are quickly screened and the far-field flow is dominated by the source dipole for all the different kinds of squirmers. However, we show that the collective behavior of the suspension still depends on the self-propelling mechanism of the swimmers as polar states can only be observed for neutral squirmers. We demonstrate that the near-field hydrodynamic interactions play a crucial role in the alignment of the orientation vectors of spherical particles. Moreover, we point out thatthe enstrophy and the fluid fluctuations of an active suspension also depend on the nature of the squirmers.

*Takao Ohta, Mitsusuke Tarama and Masaki Sano,
Simple model of cell crawling,
Physica D 318, 3-11 (2016).

[Summary] Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of the cell on a substrate. For time-independent forces we show that not only a stationary motion but also a limit cycle oscillation of the migration velocity and the shape occurs as a result of nonlinear coupling between different deformation modes. Time-dependent forces are generated in a stochastic manner by utilizing the so-called coherence resonance of an excitable system. The present coarse-grained model has a flexibility that it can be applied, e.g., both to keratocyte cells and to View the MathML source cells, which exhibit quite different dynamics from each other. The key factors for the motile behavior inherent in each cell type are identified in our model.

*John J. Molina, Kotaro Otomura, Hayato Shiba, Hideki Kobayashi, Masaki Sano, and Ryoichi Yamamoto,
Rheological evaluation of colloidal dispersions using the smoothed profile method: formulation and applications,
Journal of Fluid Mechanics 792, 590-619 (2016).

[Summary] The smoothed profile method is extended to study the rheological behaviour of colloidal dispersions under shear flow by using the Lees–Edwards boundary conditions. We start with a reformulation of the smoothed profile method, a direct numerical simulation method for colloidal dispersions, so that it can be used with the Lees–Edwards boundary condition, under steady or oscillatory-shear flow. By this reformulation, all the resultant physical quantities, including local and total shear stresses, become available through direct calculation. Three simple rheological simulations are then performed for (1) a spherical particle, (2) a rigid bead chain and (3) a collision of two spherical particles under shear flow. Quantitative validity of these simulations is examined by comparing the viscosity with that obtained from theory and Stokesian dynamics calculations. Finally, we consider the shear-thinning behaviour of concentrated colloidal dispersions.

*Masaki Sano and Keiichi Tamai,
A Universal Transition to Turbulence in Channel Flow,
Nature Physics 12, 249-253 (2016).

[Summary] Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag properties of fluids, yet when and how turbulence emerges is elusive even for simple flow within pipes and rectangular channels1,2. Unlike the onset of temporal disorder, which is identified as the universal route to chaos in confined flows3,4, characterization of the onset of spatio-temporal disorder has been an outstanding challenge because turbulent domains irregularly decay or spread as they propagate downstream. Here, through extensive experimental investigation of channel flow, we identify a distinctive transition with critical behavior. Turbulent domains continuously injected from an inlet ultimately decayed, or in contrast, spread depending on flow rates. Near a transition point, critical behavior was observed. We investigate both spatial and temporal dynamics of turbulent clusters, measuring four critical exponents, a universal scaling function and a scaling relation, all in agreement with the (2+1) dimensional directed percolation universality class.

#### 2015

Alexei Borodin, Ivan Corwin, Leonid Petrov, Tomohiro Sasamoto,
Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz,
Communications in Mathematical Physics 339(3), 1167-1245 (2015).

[Summary] In recent studies of KPZ systems, stochastic particle systems called the q-TASEP and the q-boson zero range process have been playing important roles. In this paper we have introduced a generalized process related to the orthogonal weight of the q-Hahn polynomials. We have given a formula for the moments of the currents.

*Daiki Nishiguchi and Masaki Sano,
Mesoscopic turbulence and local order in Janus particles self-propelling under an ac electric field,
Physical Review E 92, 052309/1-11 (2015).

[Summary] To elucidate mechanisms of mesoscopic turbulence exhibited by active particles, we experimentally study turbulent states of nonliving self-propelled particles. We realize an experimental system with dense suspensions of asymmetrical colloidal particles (Janus particles) self-propelling on a two-dimensional surface under an ac electric field. Velocity fields of the Janus particles in the crowded situation can be regarded as a sort of turbulence because it contains many vortices and their velocities change abruptly. Correlation functions of their velocity field reveal the coexistence of polar alignment and antiparallel alignment interactions, which is considered to trigger mesoscopic turbulence. Probability distributions of local order parameters for polar and nematic orders indicate the formation of local clusters with particles moving in the same direction. A broad peak in the energy spectrum of the velocity field appears at the spatial scales where the polar alignment and the cluster formation are observed. Energy is injected at the particle scale and conserved quantities such as energy could be cascading toward the larger clusters.

*Shoichi Toyabe, Masaki Sano,
Nonequilibrium Fluctuations in Biological Strands, Machines, and Cells,
Journal of the Physical Society of Japan 84, 102001/1-17 (2015).

[Summary] Can physics provide a quantitative methodology and unified view to elucidate rich and diverse biological phenomena? Nonequilibrium fluctuations are key quantities. These fluctuations have universal symmetries, convey essential information about systems’ behaviors, and are experimentally accessible in most systems. We review experimental developments to extract information from the nonequilibrium fluctuations of biological systems. In particular, we focus on the three major hierarchies in small scales: strands, molecular machines, and cells.

Tomohiro Sasamoto, Herbert Spohn,
Point-interacting Brownian motions in the KPZ universality class,
Electronic Journal of Probability 20, 1-28 (2015).

[Summary] We constructed an interacting Brownian motion model in the KPZ class. In particular the model has self-duality by which we could show that the current distribution tends to the Tracy-Widom distribution. This could be used as model for colloidal particle system which shows KPZ behaviors.

*Timothy Halpin-Healy, Kazumasa A. Takeuchi,
A KPZ Cocktail: Shaken, not stirred… -Toasting 30 years of kinetically roughened surfaces,
Journal of Statistical Physics 160, 794-814 (2015).

[Summary] The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we i) pay debts to heroic predecessors, ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of $d = \infty$ KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.

*Hiroyuki Ebata and Masaki Sano,
Swimming droplets driven by a surface wave,
Scientific Reports 5, 8546/1-7 (2015).

[Summary] Self-propelling motion is ubiquitous for soft active objects such as crawling cells, ac-tive filaments, and liquid droplets moving on surfaces. Deformation and energy dissi-pation are required for self-propulsion of both living and non-living matter. From the perspective of physics, searching for universal laws of self-propelled motions in a dis-sipative environment is worthwhile, regardless of the objects’ details. In this article, we propose a simple experimental system that demonstrates spontaneous migration of a droplet under uniform mechanical agitation. As we vary control parameters, sponta-neous symmetry breaking occurs sequentially, and cascades of bifurcations of the mo-tion arise. Equations describing deformable particles and hydrodynamic simulations successfully describe all of the observed motions. This system should enable us to im-prove our understanding of spontaneous motions of self-propelled objects.

*Takaki Yamamoto, Masafumi Kuroda, and Masaki Sano,
Three-dimensional analysis of thermo-mechanically rotating cholesteric liquid crystal droplets under a temperature gradient,
EPL 109, 46001/1-6 (2015).

[Summary] We studied the rotational motion of cholesteric liquid crystal droplets under a temperaturegradient (the Lehmann effect). We found that different surface treatments, planar andhomeotropic anchoring, provided three types of droplets with different textures and geometries.The rotational velocity of these droplets depends differently on their size. Determining the threedimensionalstructures of these droplets by the fluorescence confocal polarizing microscopy, wepropose a phenomenological equation to explain the rotational behavior of these droplets. Thisresult shows that the description by the Ericksen-Leslie theory should be valid in the bulk of thedroplet, but we need to take into account the surface torque induced by temperature gradient tofully understand the Lehmann effect.

Alexei Borodin, Ivan Corwin, Leonid Petrov, and Tomohiro Sasamoto,
Spectral theory for the q-boson particle system,
Compositio Mathematica 151, 1-67 (2015).

[Summary] We develop spectral theory for the generator of the q-Boson particle system. Our cen- tral result is a Plancherel type isomorphism theorem for this system. This theorem has various implications. It proves the completeness of the Bethe ansatz for the q-Boson generator and con- sequently enables us to solve the Kolmogorov forward and backward equations for general initial data. Owing to a Markov duality with q-TASEP, this leads to moment formulas which characterize the fixed time distribution of q-TASEP started from general initial conditions. The theorem also implies the biorthogonality of the left and right eigenfunctions.We consider limits of our q-Boson results to a discrete delta Bose gas considered previously by van Diejen, as well as to another discrete delta Bose gas that describes the evolution of moments of the semi-discrete stochastic heat equation (or equivalently, the O’Connell-Yor semi-discrete directed polymer partition function). A further limit takes us to the delta Bose gas which arises in studying moments of the stochastic heat equation / Kardar-Parisi-Zhang equation.

#### 2014

Tomohiro Sasamoto, and Lauren Williams,
Combinatorics of the asymmetric exclusion process on a semi-infinite lattice,
Journal of Combinatorics 5(4), 419-434 (2014).

[Summary] We develop spectral theory for the generator of the q-Boson particle system. Our cen- tral result is a Plancherel type isomorphism theorem for this system. This theorem has various implications. It proves the completeness of the Bethe ansatz for the q-Boson generator and con- sequently enables us to solve the Kolmogorov forward and backward equations for general initial data. Owing to a Markov duality with q-TASEP, this leads to moment formulas which characterize the fixed time distribution of q-TASEP started from general initial conditions. The theorem also implies the biorthogonality of the left and right eigenfunctions.We consider limits of our q-Boson results to a discrete delta Bose gas considered previously by van Diejen, as well as to another discrete delta Bose gas that describes the evolution of moments of the semi-discrete stochastic heat equation (or equivalently, the O’Connell-Yor semi-discrete directed polymer partition function). A further limit takes us to the delta Bose gas which arises in studying moments of the stochastic heat equation / Kardar-Parisi-Zhang equation.

Ismael S. S. Carrasco, Kazumasa A. Takeuchi, Silvio da Costa Ferreira Junior, and *Tiago José Oliveira,
Interface fluctuations for deposition on enlarging flat substrates,
New Journal of Physics 16, 123057/1-20 (2014).

[Summary] We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate. Despite the null global curvature, we show that all investigated models have asymptotic height distributions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In 1+1 dimensions, the height distribution and covariance are given by the GUE Tracy-Widom distribution and the Airy2 process instead of the GOE and Airy1 foreseen for flat interfaces. These results imply that when the KPZ class splits into curved and flat subclasses, as conventionally considered, the expanding substrate may play a role equivalent to, or perhaps more important than, the global curvature. Moreover, the translational invariance of the interfaces evolving on growing domains allowed us to accurately determine, in 2+1 dimensions, the analog of the GUE Tracy-Widom distribution for height distribution and that of the Airy2 process for spatial covariance. Temporal covariance is also calculated and shown to be universal in each dimension and in each of the two subclasses. A logarithmic correction associated with the duplication of columns is observed and theoretically elucidated. Finally, crossover between regimes with fixed-size and enlarging substrates is also investigated.

Alexei Borodin, *Ivan Corwin, Tomohiro Sasamoto,
From duality to determinants for q-TASEP and ASEP,
Annals of Probability 42, 2314-2382 (2014).

[Summary] We prove duality relations for two interacting particle systems: the q-deformed totally asymmetric simple exclusion process (q-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents, respectively. Duality implies that they solve systems of ODEs. These systems are integrable and for particular step and half- stationary initial data we use a nested contour integral ansatz to provide ex- plicit formulas for the systems’ solutions, and hence also the moments.

*Kazumasa A. Takeuchi,
Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments,
Journal of Statistical Mechanics: Theory and Experiment P01006/1-28 (2014).

[Summary] This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where nontrivial universality classes have been identified theoretically: absorbing-state phase transitions and growing interfaces. First the paper summarizes the main results obtained for electrically driven turbulent liquid crystals, which exhibited the scaling laws for the directed percolation class at the transition between two turbulent regimes, and those for the Kardar-Parisi-Zhang class in the supercritical phase where one turbulent regime invades the other. Other experimental investigations on these universality classes and related situations are then overviewed and discussed. Some remarks on analyses of these scaling laws are also given from the practical viewpoint.

*Hirokazu Tanimoto and Masaki Sano,
A simple force-motion relation for migrating cells revealed by multipole analysis of traction stress,
Biophysical Journal 106, 16-25 (2014).

[Summary] For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.

#### 2013

*Hiroyuki Ebata and Masaki Sano,
Bifurcation from stable holes to replicating holes in vibrated dense suspensions,
Physical Review E 88, 053007/1-8 (2013).

[Summary] In vertically vibrated starch suspensions, we observe bifurcations from stable holes to replicating holes. Abovea certain acceleration, ﬁnite-amplitude deformations of the vibrated surface continue to grow until void penetratesﬂuid layers, and a hole forms. We studied experimentally and theoretically the parameter dependence of the holesand their stabilities. In suspensions of small dispersed particles, the circular shapes of the holes are stable. However,we ﬁnd that larger particles or lower surface tension of water destabilize the circular shapes; this indicates theimportance of capillary forces acting on the dispersed particles. Around the critical acceleration for bifurcation,holes show intermittent large deformations as a precursor to hole replication. We applied a phenomenologicalmodel for deformable domains, which is used in reaction-diffusion systems. The model can explain the basicdynamics of the holes, such as intermittent behavior, probability distribution functions of deformation, and timeintervals of replication. Results from the phenomenological model match the linear growth rate below criticalitythat was estimated from experimental data.

*Patrik L. Ferrari, Tomohiro Sasamoto, Herbert Spohn,
Coupled Kardar-Parisi-Zhang Equations in One Dimension,
Journal of Statistical Physics 153, 377-399 (2013).

[Summary] Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case of coupled KPZ equations in one dimension. We establish equivalence with nonlinear fluctuating hydrodynamics for multi-component driven stochastic lattice gases. To check the predictions of the theory, we perform Monte Carlo simulations of the two-component AHR model. Its steady state is computed using the matrix product ansatz. Thereby all coefficients appearing in the coupled KPZ equations are deduced from the microscopic model. Time correlations in the steady state are simulated and we confirm not only the scaling exponent, but also the scaling function and the non-universal coefficients.

Takashi Imamura, *Tomohiro Sasamoto, Herbert Spohn,
On the equal time two-point distribution of the one-dimensional KPZ equation by replica,
Journal of Physics A: Mathematical and Theoretical 46, 355002/1-9 (2013).

[Summary] In a recent contribution, Dotsenko establishes a Fredholm determinant formula for the two-point distribution of the Kardar–Parisi–Zhang equation in the long time limit and starting from narrow wedge initial conditions. We establish that his expression is identical to the Fredholm determinant resulting from the Airy2 process.