arXiv subjects

Keiichi Tamai

Publications and source records attributed to Keiichi Tamai.

5 recordsLinked to original sources

arXiv2026

Universal interface fluctuations in absorbing-state phase transitions

Despite similarities between models exhibiting absorbing phase transitions (APTs) and those showing Kardar-Parisi-Zhang (KPZ) growth, the relationship between these universal fluctuations has remained elusive. We numerically study (1+1)-dimensional interfaces of (2+1)-dimensional models showing APTs of directed percolation (DP) and compact directed percolation (CDP) classes with an active boundary, finding a universal crossover from short-time APT-governed fluctuations to long-time KPZ fluctuations. Upon rescaling time and length by the APT correlation time and length, the cumulants of the interface height distributions collapse onto a single scaling function. The fluctuation properties of the discrete Domany-Kinzel model and the continuum stochastic Fisher-Kolmogorov-Petrovsky-Piskunov (sFKPP) equation coincide, indicating that the KPZ growth parameters are determined solely by fundamental properties of the APT. For the CDP sFKPP equation, a dimensionless parameter tunes both the critical interface distribution and the KPZ parameters, with the interface properties of the biased voter model recovered in a limiting case. These results uncover a universal crossover in which KPZ fluctuations emerge from APT fluctuations at long times, linking paradigmatic universality classes of nonequilibrium scale-invariant phenomena.

cond-mat.stat-mech↗

arXiv2025

Universal Scaling Laws of Absorbing Phase Transitions in Artificial Deep Neural Networks

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in non-equilibrium statistical mechanics. We exploit the fully deterministic nature of the propagation dynamics to elucidate an analogy between a signal collapse in the neural networks and an absorbing state (a state that the system can enter but cannot escape from). Our numerical results indicate that the multilayer perceptrons and the convolutional neural networks belong to the mean-field and the directed percolation universality classes, respectively. Also, the finite-size scaling is successfully applied, suggesting a potential connection to the depth-width trade-off in deep learning. Furthermore, our analysis of the training dynamics under the gradient descent reveals that hyperparameter tuning to the phase boundary is necessary but insufficient for achieving optimal generalization in deep networks. Remarkably, nonuniversal metric factors associated with the scaling laws are shown to play a significant role in concretizing the above observations. These findings highlight the usefulness of the notion of criticality for analyzing the behavior of artificial deep neural networks and offer new insights toward a unified understanding of the essential relationship between criticality and intelligence.

stat.ML↗

arXiv2020

Data Assimilation Method for Experimental and First-Principles Data: Finite-Temperature Magnetization of (Nd,Pr,La,Ce)$_{2}$(Fe,Co,Ni)$_{14}$B

We propose a data-assimilation method for evaluating the finite-temperature magnetization of a permanent magnet over a high-dimensional composition space. Based on a general framework for constructing a predictor from two data sets including missing values, a practical scheme for magnetic materials is formulated in which a small number of experimental data in limited composition space are integrated with a larger number of first-principles calculation data. We apply the scheme to (Nd$_{1-α-β-γ}$Pr$_α$La$_β$Ce$_γ$)$_{2}$(Fe$_{1-δ-ζ}$Co$_δ$Ni$_ζ$)$_{14}$B. The magnetization in the whole $(α, β, γ, δ, ζ)$ space at arbitrary temperature is obtained. It is shown that the Co doping does not enhance the magnetization at low temperatures, whereas the magnetization increases with increasing $δ$ above 320 K.

cond-mat.mtrl-sci↗

arXiv2018

How to experimentally probe universal features of absorbing phase transitions using steady state

We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of duration/length of intervals of local inactive state in quasi-steady state, which has been very commonly used in experiments, in a case of the contact process. We show that the distributions obey the universal scaling ansatz expected from phenomenological scaling argument, but that care must be taken in order to suppress a bias caused by censoring due to a finite observation window. To demonstrate the latter point, we compare the distributions for the temporal intervals estimated through conventional histograms with those through the estimator which properly takes account of censoring and sampling bias. On the other hand, we also propose that, if a system is subject to uniform advection as is often the case with flowing systems, a correlation length and a correlation time near the transition point can be easily quantified by supplying the system with an active boundary condition. In order to support our proposal, we introduce a new model whose advection strength can be arbitrarily controlled. The results of numerical simulations on our model suggest that a correlation time, which is difficult to measure through the interval distributions without the aforementioned bias, can be measured through characteristic decay length of an order parameter. Crossovers between two different power-law behaviors are also identified in this case, and the universal scaling ansätze associated with the crossovers are discussed.

cond-mat.stat-mech↗

arXiv2015

A Universal Transition to Turbulence in Channel Flow

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 channels. Unlike the onset of temporal disorder, which is identified as the universal route to chaos in confined flows, 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.

cond-mat.stat-mech↗