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Nowadays I'm interested in applying Reinforcement Learning (RL) -- the most current research in the field of machine learning -- to complex systems.
My main research area centers on statistical and computational physics as I work on non-linear, non-equilibrium and complex systems, especially self-organized systems, growth processes, granular materials, and network systems. One of my main goals is to find a connection between these complicated systems and the solvable models (Ising, Potts and percolation models) by means of universality-class concepts.
I use analytical (statistical and conformal field theories, stochastic processes) and computational (classical and quantum Monte Carlo, stochastic non-linear differential equation, molecular dynamics, data analysis, quantum annealing, machine learning) frameworks.
Research Fellow
Statistical and Computational Physics
Australian Institute for Bioengineering and Nanotechnology (AIBN)
The University of Queensland
Australia
In what follows, I will mention some of my recent projects.
Percolation transition in the shear-driven granular systems
We investigate the criticality of the jamming transition for the shear-driven systems in two dimensions. Here you can see the force chain configurations related to a snapshot.
Effect of geometrical constraints on Abelian, non-Abelian self-organized critical system
We are interested to study the competition between the Abelian and non-Abelian processes in the sandpile models (which may live on a lattice or network) to find out which one is more dominant in terms of self-organized criticality. It seems that it depends on the topology of the systems. I try to get a phenomenological interpretation of my results.
Self-Repelling Bipedal Exploration Process
We study the systems of self-repelling two-leg (biped) spider walk where the local stochastic movements are governed by two independent control parameters T_d and T_h, so that the former controls the distance ( d ) between the legs positions, and the latter controls the statistics of self-crossing of the traversed paths; this backs to the fact that the traces that traversed by the legs of the spider matter, i.e. the traces are self-repulsive in the sense that in each time step t, the random walkers drop a unit of debris at the point that they stand on, say the site i, so that the height of the site increases by one: h_i(t) → h_i(t)+1.
In the classical extreme value theory, one concerned with the uncorrelated random variables. It is shown that there exist universal limit laws for the distribution of the maximum M for the case of IID variables. For those systems, one gets three different universality classes (shown in above fig). Here p(x) is the parent distribution and f(z) is PDF of M.
For weakly correlated variables, one can provide a general renormalization group type of argument to study the EVS. This technique does not work for strongly correlated and one has to study case by case different models (one-dimensional Brownian motion, branching Brownian motion, random walks, Levy flights, 1/f^alpha signals are examples of solvable models). For strongly correlated variables, the issue of universality is wide open.
In this study, we seek some universal laws for EVS of various types of correlated temporal networks.
Extreme Value Statistics (EVS) of Correlated Temporal Networks
Two-dimensional super-roughening in the three-dimensional Ising model
A random-interface representation of the 3D Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model (a) and its 2D cross section (b) are shown.
A geometric spin cluster is defined as a set of connected nearest-neighbor sites of like-sign spins which is identified by the clustering algorithm.
We show that the global interfacial width as a function of temperature for different lattice sizes which is shown to signal the criticality of the model at Tc by forming a size-independent cusp in 3D, along with an emergent super-roughening at its 2D cross section.
We find that the super-rough state is accompanied by an intrinsic anomalous scaling behavior in the local properties characterized by a set of geometric exponents which are the same as those for a pure 2D Ising model.
Universality of Non-Equilibrium Growth Models at Crossing Points
(Left) We study the universality of height fluctuations at the crossing point of two interacting interfaces (subjected to non-equilibrium growth processes).
(Right) Snapshots for the time evolution of the height profiles on the flat-wedge geometry.
Each substrate supposedly follow the Tracy Wisdom distributions. At a specific condition where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in non-equilibrium transport and traffic flow.
Classification of boundary curves using Schramm-Loewner evolution (SLE)
The positive-height clusters shown in different colors, and the corresponding spanning iso-height lines (solid lines) are shown. We show that theses curves can be classified by SLE.
Sandpile on uncorrelated site-diluted percolation lattice; from three to two dimensions
The BTW sandpile model is considered on the three dimensional percolation lattice which is tuned by the occupation parameter p. Along with the three-dimensional avalanches, we study the avalanches in two-dimensional cross-sections.
Avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections
In many situations we are interested in the propagation of energy in some portions of a three-dimensional system with dilute long-range links. In this project, a sandpile model is defined on the three-dimensional small-world network with real dissipative boundaries and the energy propagation is studied in three dimensions as well as the two-dimensional cross-sections. Two types of cross-sections are defined in the system, one in the bulk and another in the system boundary. The motivation of this is to make clear how the statistics of the avalanches in the bulk cross-section tend to the statistics of the dissipative avalanches, defined in the boundaries as the concentration of long range links (α) increases.This trend is numerically shown to be a power law.
Random walks on intersecting geometries
We present an analytical approach to study simple symmetric random walks on a crossing geometry consisting of a plane square lattice crossed by n_l number of lines that all meet each other at a single point (the origin) on the plane