Disordered hyperuniform quantum materials

Disordered hyperuniform systems and materials (DHU) are a new, exotic class of amorphous matter that lie between crystal and liquid states: they behave like crystals in the way that they possess completely suppressed density/volume-fraction fluctuations at large length scales, and yet they are statistically isotropic and do not display diffraction Bragg peaks, which are similar to liquids. We have been extending the concept of DHU to a wide range of atomic-scale low-dimensional quantum materials such as graphene, silica, boron nitride, to name a few. Interestingly, certain such materials are found to be endowed with exotic electronic, transport, and mechanical properties. For example, while according to the well-known "Anderson localization", provided that the degree of randomness (disorder) in a lattice is sufficiently large, the system could undergo a transition from metallic to insulating behavior, we find that adding disorder in a "hyperuniform" manner could result in a transition from insulating to metallic behavior.

Block copolymer melts

Block copolymers is a class of soft-matter systems of particular interest since their key design parameters can be predicted by theory and carefully controlled during synthesis, and they can form a wide variety of ordered and disordered mesophases at convenient experimental conditions. At mesoscale, the structures formed by block copolymer melts can be essentially viewed as spatially-varying scalar density elds associated with the constituent monomers. We have been employing and generalizing various theoretical machinery from statistical mechanics, heterogeneous materials as well as state-of-the-art field-theoretical simulations to explore the process-structure-property relationships in this context, which will shed light on the rational design of novel functional polymeric materials with targeted physical properties.

Colloids and polymer–colloid complexes

Colloids and polymer-colloid complexes are widely used in food, pharmaceutical, and information technology industries. We have been employing the self-assembly of these building blocks to design and fabricate a wide range of ordered and disordered target structures with desirable physical properties. These structures include two-dimensional low-coordinated crystal structures that are defect-free, as well as disordered hyperuniform materials. We will continue to tap into the potential of these systems as platform for the design of novel functional materials.

Granular materials

Granular materials are widely used in applications such as pharmaceutical industry, agriculture, and energy production, and are also relevant in many geomechanical contexts. The morphology of the granular media plays an important role in determining the macroscopic behaviors of these systems. In particular, the packing density of the grains in these systems are critical to the mechanical, transport, and fluid flow properties, as well as fabrication cost of these materials, and much research effort has been devoted to developing novel high-density (or low-porosity) functional granular materials. We have been employing a wide range of analytical, simulation and data-driven techniques to establish the relations between a set of nontrivial lower-order structural descriptors and the mechanical, transport, and fluid flow properties of these materials. Moreover, guided by these structure-property relations, we tune the grain size and shape distributions, and boundary conditions to inversely design and realize novel ultra low-porosity granular materials with high mechanical strength and other desirable physical properties.

Statistical-mechanical models of pattern formation in biosystems

Progression of dormant tumors

Pattern formation of skin cells

Soft-matter systems, in particular biosystems, often span orders of magnitude in length and time scales. Moreover, these systems undergo constant deformations under external forces or thermal fluctuations, and are known to possess no single well-defined state. These complexities make it very challenging to understand the pattern formation in biosystems, and a range of theoretical and simulation techniques have been developed to strengthen our understanding from different perspectives. We have been developing statistical-mechanical models for a variety of biosystems. The identification of simple effective interaction between cells and mechanisms that can account for pattern formation in different settings will strengthen our understanding of the morphogenesis, wound healing, and disease-progression processes in different tissues, and shed light on the development of novel functional bio-inspired materials.