THESIS
2013
xvi, 111 pages : illustrations (some color) ; 30 cm
Abstract
This thesis describes some explorations on complex systems. In particular, it
studies phase transitions in colloids and properties of complex network.
In the first part, we investigated the kinetic path of nucleation with experiments, simulations and theories. In the homogeneous melting of 3D colloidal
crystals, we provided the first direct visualization of melting kinetics with single-particle dynamics utilizing optical microscopies. We found that the precursors
are particle-exchange loops rather than any defects. The superheat limit of our
hard-sphere-like colloidal crystals is at the volume fraction ϕ
s = 47%. This
contributes an important point to the famous hard-sphere phase diagram.
We investigated the solid-solid transitions between □ and △ lattices in colloidal thin films....[
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This thesis describes some explorations on complex systems. In particular, it
studies phase transitions in colloids and properties of complex network.
In the first part, we investigated the kinetic path of nucleation with experiments, simulations and theories. In the homogeneous melting of 3D colloidal
crystals, we provided the first direct visualization of melting kinetics with single-particle dynamics utilizing optical microscopies. We found that the precursors
are particle-exchange loops rather than any defects. The superheat limit of our
hard-sphere-like colloidal crystals is at the volume fraction ϕ
s = 47%. This
contributes an important point to the famous hard-sphere phase diagram.
We investigated the solid-solid transitions between □ and △ lattices in colloidal thin films. The diffusive nucleation process, rather than a martensetic
mechanism, was directly observed with single-particle resolution and follows a
novel two-step nucleation pathway: □-lattice crystal → post-critical liquid nucleus → △-lattice nucleus. We show that it is due to the low solid-liquid interfacial energy and should widely exist in nucleation processes of metals and
alloys.
In the second part, we mapped the phase spaces to complex networks for
several statistical models including six-vertex models and lattice gases. Their
phase-space networks share some common features like Gaussian degree distribution and Gaussian spectral density. Models with long/short-range correlations
in real space exhibit fractal/nonfractal phase spaces.
We discovered new random matrices with novel eigenvalue distributions, such
as square distributions rather than the classical Girko's circular distribution.
Those random matrices are constructed from the adjacency matrices of various
classes of networks, and their eigenvalue distributions exhibit some universal
features, e.g. reflection symmetries about both real and imaginary axes. It's also
found that the eigenvalue distributions are sensitive to the phase transitions in
the networks, and the circular law can also hold for very sparse random matrices.
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