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Author

Yohsuke T. Fukai

Other affiliations: Tokyo Institute of Technology
Bio: Yohsuke T. Fukai is an academic researcher from University of Tokyo. The author has contributed to research in topics: Ground truth & Initial value problem. The author has an hindex of 3, co-authored 5 publications receiving 45 citations. Previous affiliations of Yohsuke T. Fukai include Tokyo Institute of Technology.

Papers
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Journal ArticleDOI
TL;DR: It is found 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, indicating that the sign of the initial curvature has a crucial role in determining the universal distribution and correlation functions of the KPZ class.
Abstract: 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 ${\text{Airy}}_{1}$ 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.

26 citations

Journal ArticleDOI
TL;DR: In this article, the scaling functions of the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions were determined by simulations of a cluster growth model and experiments with liquid-crystal turbulence, and the universal scaling functions described the height distribution and the spatial correlation of the interfaces growing outward from a ring.
Abstract: We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments with liquid-crystal turbulence, we determine the universal scaling functions that describe the height distribution and the spatial correlation of the interfaces growing outward from a ring. The scaling functions, controlled by a single dimensionless time parameter, show crossover from the statistical properties of the flat interfaces to those of the circular interfaces. Moreover, employing the KPZ variational formula to describe the case of the ring initial condition, we find that the formula, which we numerically evaluate, reproduces the numerical and experimental results precisely without adjustable parameters. This demonstrates that precise numerical evaluation of the variational formula is possible at all, and underlines the practical importance of the formula, which is able to predict the one-point distribution of KPZ interfaces for general initial conditions.

13 citations

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TL;DR: This work generates an initial condition that possesses a long-range property expected for the KPZ stationary state, and identifies finite-time corrections to the KPz scaling laws, which turn out to play a major role in the direct test of the stationary KPZ interfaces.
Abstract: The nonequilibrium steady state of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class has been studied in-depth by exact solutions, yet no direct experimental evidence of its characteristic statistical properties has been reported so far. This is arguably because, for an infinitely large system, infinitely long time is needed to reach such a stationary state and also to converge to the predicted universal behavior. Here we circumvent this problem in the experimental system of growing liquid-crystal turbulence, by generating an initial condition that possesses a long-range property expected for the KPZ stationary state. The resulting interface fluctuations clearly show characteristic properties of the 1D stationary KPZ interfaces, including the convergence to the Baik-Rains distribution. We also identify finite-time corrections to the KPZ scaling laws, which turn out to play a major role in the direct test of the stationary KPZ interfaces. This paves the way to explore unsolved properties of the stationary KPZ interfaces experimentally, making possible connections to nonlinear fluctuating hydrodynamics and quantum spin chains as recent studies unveiled relation to the stationary KPZ.

10 citations

Journal ArticleDOI
09 Nov 2021-Chaos
TL;DR: In this article, the authors show that the perturbation interfaces, defined by the logarithm of the modulus of the components, exhibit the universal, geometry-dependent statistical laws of the Kardar-Parisi-Zhang (KPZ) class despite the deterministic nature of spatiotemporal chaos.
Abstract: Infinitesimal perturbations in various systems showing spatiotemporal chaos (STC) evolve following the power laws of the Kardar–Parisi–Zhang (KPZ) universality class. While universal properties beyond the power-law exponents, such as distributions and correlations and their geometry dependence, are established for random growth and related KPZ systems, the validity of these findings to deterministic chaotic perturbations is unknown. Here, we fill this gap between stochastic KPZ systems and deterministic STC perturbations by conducting extensive simulations of a prototypical STC system, namely, the logistic coupled map lattice. We show that the perturbation interfaces, defined by the logarithm of the modulus of the perturbation vector components, exhibit the universal, geometry-dependent statistical laws of the KPZ class despite the deterministic nature of STC. We demonstrate that KPZ statistics for three established geometries arise for different initial profiles of the perturbation, namely, point (local), uniform, and “pseudo-stationary” initial perturbations, the last being the statistically stationary state of KPZ interfaces given independently of the Lyapunov vector. This geometry dependence lasts until the KPZ correlation length becomes comparable to the system size. Thereafter, perturbation vectors converge to the unique Lyapunov vector, showing characteristic meandering, coalescence, and annihilation of borders of piece-wise regions that remain different from the Lyapunov vector. Our work implies that the KPZ universality for stochastic systems generally characterizes deterministic STC perturbations, providing new insights for STC, such as the universal dependence on initial perturbation and beyond.
Journal ArticleDOI
TL;DR: Laptrack is developed, a LAP-based tracker which allows including arbitrary cost functions and inputs, parallel parameter tuning, and ground-truth track preservation, and analysis of real and artificial datasets demonstrates the advantage of custom metric functions for tracking score improvement.
Abstract: Motivation Particle tracking is an important step of analysis in a variety of scientific fields, and is particularly indispensable for the construction of cellular lineages from live images. Although various supervised machine learning methods have been developed for cell tracking, the diversity of the data still necessitates heuristic methods that require parameter estimations from small amounts of data. For this, solving tracking as a linear assignment problem (LAP) has been widely applied and demonstrated to be efficient. However, there has been no implementation that allows custom connection costs, parallel parameter tuning with ground truth annotations, and the functionality to preserve ground truth connections, limiting the application to datasets with partial annotations. Results We developed LapTrack, a LAP-based tracker which allows including arbitrary cost functions and inputs, parallel parameter tuning, and ground-truth track preservation. Analysis of real and artificial datasets demonstrates the advantage of custom metric functions for tracking score improvement. The tracker can be easily combined with other Python-based tools for particle detection, segmentation, and visualization. Availability and implementation LapTrack is available as a Python package on PyPi, and the notebook examples are shared at https://github.com/yfukai/laptrack. The data and code for this publication are hosted at https://github.com/NoneqPhysLivingMatterLab/laptrack-optimization. Contact ysk@yfukai.net

Cited by
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TL;DR: In this article, the authors studied a random Groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process and showed that shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.
Abstract: We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

1,031 citations

Journal ArticleDOI
TL;DR: The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few as discussed by the authors.
Abstract: The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics — as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.

106 citations

Journal ArticleDOI
TL;DR: This work derives an exact formula for the Green's function as well as for a joint current distribution of the model, and shows that the limiting distribution is a product of theGaussian and the Gaussian unitary ensemble Tracy-Widom distributions.
Abstract: We consider current statistics for a two-species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of the model, and study its long time behavior. For a step-type initial condition, we show that the limiting distribution is a product of the Gaussian and the Gaussian unitary ensemble Tracy-Widom distributions. This is the first analytic confirmation for a multicomponent system of a prediction from the recently proposed nonlinear fluctuating hydrodynamics for one-dimensional systems.

29 citations

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TL;DR: In this article, a field-theoretic thermodynamic uncertainty relation was proposed for the one-dimensional Kardar-parisi-Zhang equation, an extension of the one derived so far for Markovian dynamics on a discrete set of states and for overdamped Langevin equations.
Abstract: We propose a field-theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a Markovian dynamics on a discrete set of states and for overdamped Langevin equations. We first formulate a framework which describes quantities like current, entropy production and diffusivity in the case of a generic field theory. We will then apply this general setting to the one-dimensional Kardar–Parisi–Zhang equation, a paradigmatic example of a non-linear field-theoretic Langevin equation. In particular, we will treat the dimensionless Kardar–Parisi–Zhang equation with an effective coupling parameter measuring the strength of the non-linearity. It will be shown that a field-theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant. The calculations show that the field-theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the Kardar-Parisi-Zhang equation due to an excess term stemming from its non-linearity.

18 citations

Journal ArticleDOI
TL;DR: It is demonstrated that a transient flat statistics is a general feature of systems starting with large initial sizes, regardless of their curvature, which is consistent with their recent observation in ingrowing turbulent liquid crystal interfaces.
Abstract: Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, here we investigate several one-dimensional KPZ models on substrates whose size changes in time as L(t)=L_{0}+ωt, focusing on the case ω 0. Actually, for a given model, L_{0} and |ω|, we observe that a difference between ingrowing (ω 0) systems arises only at long times (t∼t_{c}=L_{0}/|ω|), when the expanding surfaces cross over to the statistics of curved KPZ systems, whereas the shrinking ones become completely correlated. A generalization of the Family-Vicsek scaling for the roughness of ingrowing interfaces is presented. Our results demonstrate that a transient flat statistics is a general feature of systems starting with large initial sizes, regardless of their curvature. This is consistent with their recent observation in ingrowing turbulent liquid crystal interfaces, but it is in contrast with the apparent observation of curved statistics in colloidal deposition at the edge of evaporating drops. A possible explanation for this last result, as a consequence of the very small number of monolayers analyzed in this experiment, is given. This is illustrated in a competitive growth model presenting a few-monolayer transient and an asymptotic behavior consistent, respectively, with the curved and flat statistics.

14 citations