37 research outputs found
Dimensional Reduction of Dynamical Systems by Machine Learning: Automatic Generation of a Macroscopic Model
We propose the framework to generate a phenomenological model that extract
the essence of a dynamical system with large degrees of freedom by using
machine learning. For a given microscopic dynamical system, we simultaneously
seek for the suitable projection to a macroscopic variable, which is supposed
to be extensive, and the time proceeding equation that governs them. The
utility of this method is demonstrated by the application to the elementary
cellular automata.Comment: 9 pages, 7 figure
Profile and scaling of the fractal exponent of percolations in complex networks
We propose a novel finite size scaling analysis for percolation transition
observed in complex networks. While it is known that cooperative systems in
growing networks often undergo an infinite order transition with inverted
Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical
simulations to determine the transition point precisely. Since the neighbor of
the ordered phase is not a simple disordered phase but a critical phase,
conventional finite size scaling technique does not work. In our finite size
scaling, the forms of the scaling functions for the order parameter and the
fractal exponent determine the transition point and critical exponents
numerically for an infinite order transition as well as a standard second order
transition. We confirm the validity of our scaling hypothesis through
Monte-Carlo simulations for bond percolations in some network models: the
decorated (2,2)-flower and the random attachment growing network, where an
infinite order transition occurs, and the configuration model, where a second
order transition occurs.Comment: 6 page
Dynamical Study of Polydisperse Hard-Sphere System
We study the interplay between the fluid-crystal transition and the glass
transition of elastic sphere system with polydispersity using nonequilibrium
molecular dynamics simulations. It is found that the end point of the
crystal-fluid transition line, which corresponds to the critical polydispersity
above which the crystal state is unstable, is on the glass transition line.
This means that crystal and fluid states at the melting point becomes less
distinguishable as polydispersity increases and finally they become identical
state, i.e., marginal glass state, at critical polydispersity.Comment: 5 pages, 5 figure
Static and dynamical aspects of the metastable states of first order transition systems
We numerically study the metastable states of the 2d Potts model. Both of
equilibrium and relaxation properties are investigated focusing on the finite
size effect. The former is investigated by finding the free energy extremal
point by the Wang-Landau sampling and the latter is done by observing the
Metropolis dynamics after sudden heating. It is explicitly shown that with
increasing system size the equilibrium spinodal temperature approaches the
bistable temperature in a power-law and the size-dependence of the nucleation
dynamics agrees with it. In addition, we perform finite size scaling of the
free energy landscape at the bistable point.Comment: 8 pages, 6 figures, submitted to Physics Procedia as a proceedings of
the 24th Annual CSP Workshop at the University of Georgi