Complexity Research Group

Broadly speaking, complex systems are those consisting of many simple elements that interact with each other. The most interesting aspect of complex systems is the cooperative behaviors of the elements as a result of their nonlinear interactions. Such cooperative behaviors are manifested in the spatial and/or temporal patterns, which give rise to novel structures and functions. In our institute, there are nine faculty members and a number of postdocs and graduate students working in this field. Areas of studies include the followings:

(1). Physics of granular gas, granular flow and granular chain

Vibrated granular materials are out of thermal equilibrium and characterized by strong dissipations. Due to the interplay of energy input and dissipation in the system, many novel spatial temporal patterns can be observed. Major achievements are:

1. Understanding the mechanism of a granular clock;
2. Understanding the mechanism of the stretching of DNA by the viscoelastic properties of the flow field (Chi-Keung Chan).

We have also investigated the diffusive dynamics of a quasi-two-dimensional granular gas (Q2DGS) composed of plastic balls confined in a vertically vibrating thin box. The motion of the particles in the Q2DGS was found to follow the Langevin equation with the top and bottom of the box acting as an effective viscous fluid. Surprisingly, we found that both the granular temperature T_g and the diffusion constant D increased with the number of ball (N) in the box for small N as shown on the right of the figure below. Based on the velocity distributions and the two different kinds of horizontal motions observed in the experiments, we proposed a simple two-state model to explain the unusual diffusion behavior. We also studied the dynamics of mono-dispersed granular gas in a box with two connected partitions by molecular dynamic simulations. We found that oscillations could happen even in granular gas consisting of one kind of molecule. We also continued our research on the jamming probability of metal spheres flowing through a two-dimensional silo inclined at different angle to the horizontal plane. Surprisingly, we found that the jamming probability was insensitive to the value of the angle (Kiwing To).

Using cyclically sheared two-dimensional grains, we have set up an experimental system for the purpose of investigating the transitions between different regimes, among which the idealized collisional dynamics (like molecular gases) and the so-called quasi-static behaviors (like stationary sands or soil) are believed to be the two extreme cases. Experimental results have demonstrated the importance of dissipation, which leads to clustering and consequently the coexistence of the two different states at low density. These findings have motivated us to extend the studies into using photoelastic materials to further investigation of the force distribution inside the clusters and other possible scenarios when the clusters might have been removed by imposing mechanical vibrations to the substrate. Parallel studies using photo-elastic materials, or foams, may supplement our understandings of the rheological changes as the transitions occur (Jih-Chiang Tsai).

(2). Statistical and Computational Physics Approach to Complex Systems

Laboratory of Statistical and Computational Physics (LSCP, website: http://www.sinica.edu.tw/~statphys/) at our institute is devoted to frontier research in statistical and computational physics (SCP), applications of SCP to problems in physical, biological, and social sciences, sponsoring meetings in SCP, and promoting education and research of SCP in developing countries. Recent results completed at LSCP include (Chin-Kun Hu and Ming-Chya Wu): 1. Solved a puzzle about finite-size corrections for the dimer model on N×∞ square lattice and calculated finite-size scaling function for the dimer on the triangular lattice. 2. Found scaling and universal behavior in transition to synchronous chaos with local-global interactions and routes to synchronization for coupled map lattice on scale-free networks. 3. Developed general algorithm and computer packages ARVO and CAVE to calculate volume, surface area, and properties of cavities in macromolecules (e.g. protein, DNA, RNA, etc). 4. Used GROMOS96 force field to simulate C-terminal β-hairpin of protein G and found that the free energy landscape of the beta-hairpin is consistent with a two-state behavior with a broad transition state. 5. Used Go-like model and MD simulations to study unfolding and refolding of immunoglobulin domain I27 and ubiquitin upon force quench and found that the dependence of the refolding time on quenched force is consistent with that observed in experiments; predicted the unfolding pathways. 6. Studied molecular models of biological evolution to obtain related phase diagrams for very general fitness functions; studied asexual and diploid models with general smooth fitness landscapes and recombination. 7. Proposed temporal transfer entropy (TTE) to analyze causality between two time series and used TTE to construct a scheme for chaotic communications. 8. Used replicators in a fine-grained environment to establish a theory of polymorphism.. 9. We found that velocity distribution of monomers in the system of non-equilibrium polymer chains follows q-statistics. 10. We used phase statistics to classify human ventricular fibrillation signals into three types and found that one of them is fatal.

(3). Biology-Inspired Physics

Biological organisms are likely the most complex and the least understood systems that one can imagine, due to their intricate biochemical and physical interactions among macromolecules. Because all biological processes operate in a thermal environment, statistical physics is an indispensable tool in studying them. Experimentally, we try to understand the rich dynamics in networks of excitable and oscillatory systems. Such systems are the BZ reactions, neuronal networks, cardiac tissues and slime mould. We are studying the pattern formation, synchronization and effects of external stimuli on the dynamics of the system, specifically, the effects of heterogeneities. Major achievements include 1) Discovery of the difference in firing patterns in neuronal network with and without glia; 2) Understanding of the synchronization of cardiac cells in the presence of fibroblast (Chi-Keung Chan). Theoretically, we address the problem of biological flocking. By means of particle-based simulations, we obtain the phase diagram that separates the occurrence of marching, rotating and swamping state. Vortices are found to split into 2, 3 or more subgroups depending on the density and speed of the particles. Such a splitting is seen as the driving force behind a vortex-to-marching transition (Kwan-tai Leung).

(4). Macroporous 3D Ordered Structures for Tissue Engineering Scaffolds

We invented a simple, inexpensive and fast microfluidic method to fabricate three-dimensional ordered macroporous gel and use it as tissue engineering scaffolds. The microfluidic device consists of two concentric micropipettes where one is nested inside the other. Nitrogen gas and aqueous alginate solution with Pluronic F127 are pumped through the inner and the outer channel respectively. The bubble flow exhibit interesting dynamic patterns at different flow rate and gas pressure. Under appropriate conditions, bubbles of a uniform size are generated within the device at few thousand Hz. Monodisperse bubbles are collected and self-assemble into crystal structures as wet foam. The alginate solution between bubbles is crosslinked by divalent calcium ions and turns into 3D ordered macroporous gel where the pores are highly interconnected. Chondrocytes are successfully cultured in the 3D ordered foam for more than a month (Keng-hui Lin).

(a)	(b)	(c)	(d)
(a) and (b), flow patterns at different air pressure and liquid flow rate. (c) 3D confocal image of scaffold. (d) chondrocytes cultured on the 3D scaffolds.

(5). Single Molecule Studies of Highly Confined Biological Macromolecules

The idea of confining long-chain macromolecules to surfaces has always intrigued polymer scientists. Although lots of efforts have been made in the studies of bulk characters of confined polymer chains, our knowledge on these molecules at microscopic level is still very limited. Our research interests are mainly focused on understanding the static and dynamic behaviors of highly confined polymer molecules. Two model systems, the densely end-tethered polymer brushes and the fully adsorbed polymers on glass-supported lipid membranes, have been intensively studied from the single molecule aspect for past years. A novel assay has been developed to construct high density end-grafted polymer layers on solid-liquid interface through end-tethering DNA molecules at grafting density above 25 molecules/ R_g². We have demonstrated the first single molecule study of polymer brushes with the fluorescent microscopy technique. We are able to visualize the conformation and the dynamics of individual polymer molecule in this model polymer coated layer, and understand the detailed response of the polymer brush to the shear flow. Our very recent finding also shows the diffusivity of small molecules in such an entropy-driven brush layer could be strongly retarded. This finding might be relevant to how this tailor-made surface protects the substrate. Through monitoring the adsorption and the relaxation of DNA molecules on the glass-supported charged lipid membranes, the response of individual chain-like macromolecule to the sudden variation of the system geometry has been studied. Following a rapid adsorption, a multi-stage anomalous swelling governed by the interplay between the polymer topology and the dynamics of the charged lipid molecules on the membrane has been observed for the first time. Our analysis also shows a novel spatial-temporal pattern of the adsorbed DNA molecule at scales of a few Kuhn steps and a few seconds. This new finding may have implications in stretching biopolymers into locally straight segments using different confined geometries (Wen-Tau Juan).

(a) Dye labeled DNA brushes and the corresponding monomer density distribution.

(b) Typical conformation of individual molecules inside the brush layer.

(c) The swelling process of the DNA molecule after the adsorption. The scale bar is 2 microns.

(6). Dynamics of Biological Macromolecules and Complex Fluids

The dynamics and conformation of soft particles such as DNA, proteins, and cells in highly confined systems are of interest to microfluidic applications, nano-material design, and biophysical processes. Theoretical and computer modeling have allowed us to investigate the dynamics of large, micron-sized, DNA and soft particles undergoing flow in microchannels. Our investigation into the effects of electrostatic, hydrodynamic, and entropic on soft particle dynamics could reveal new methods for DNA/protein/cell manipulation in small systems (Yeng-Long Chen).

(7). Hydrodynamics and Atmospheric Physics

Dispersion of emitted airborne pollutants in urban environment is mainly affected by the buildings density and wind attack angles on the buildings. Due to the complexity of the buildings arrangements in the urban region, it is difficult to predict precisely the dispersion of pollutant by the numerical model. Field study can achieve the goal in a more precision status. But works of the field investigation cost much. Wind tunnel experimental simulation is therefore a feasible alternative. Experiments of wind tunnel study on the dispersion of pollution in urban environment of cubic building array in-line configuration for different wind attack angles were conducted in cooperation with the Environmental Wind Tunnel Laboratory of National Taiwan Ocean University (NTOU). Results indicate that as decreasing the ratio of building gap and width, G/H, the pollution concentrations spread wider in lateral. It means that the higher building density arrangement in urban region favors the dispersion and transport of pollution (Bao-Shi Shiau).

Fig. 1. View of the Environmental Wind Tunnel (Total length 22.6 m, and test section: 12.6m (L) x 2 m (W) x 1.4~1.6 m (H); speed range 0~20 m/s; Motor power of the 10-blade axial fan: 75 HP)

Fig. 2. Schematic diagram of the arrangement of the cubic buildings and location of the source; wind attack angle θ=0⁰, G=H

(a)	(b)
(c)	(d)

Fig. 3. Dimensionless concentration contours in horizontal plane for different building array gap at Z/H=0.5, θ=0^o; (a)open terrain, (b)G/H=3, (c)G/H=2, (d)G/H=1