Bryan Gin-ge Chen

Topological modes bound to dislocations in mechanical metamaterials

Mechanical metamaterials are artificial structures whose properties originate from their geometry. In such structures, it is now shown that topological modes can exist that are robust against a range of structural deformations.

Colloquium: Disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, we review and expound upon the classification of defects in uniaxial nematic liquid crystals. Particular attention is paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet.

Nonlinear conduction via solitons in a topological mechanical insulator

Significance Mechanisms are zero-energy motions that are key to the operation of mechanical devices, from windshield wipers to robotic arms. We built and studied chain-like mechanisms of coupled rigid rotors that are topologically protected, which means that they are not affected by smooth changes in material parameters like their quantum analogues. These prototypes are examples of mechanical structures that we dub topological metamaterials. Their mechanical excitations are nonlinear solitary waves which are topologically protected and yet tunable by changing the geometry of the unit cell. Although the left and right edges of the sample are equivalent in terms of local constraint counting, the solitary waves can start propagating only from the edge singled out by the topological polarization of the chain. Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built of folding components. Here, we investigate a chain-like linkage that, according to linear elasticity, behaves like a topological mechanical insulator whose zero-energy modes are localized at the edge. Simple experiments we performed using prototypes of the chain vividly illustrate how the soft motion, initially localized at the edge, can in fact propagate unobstructed all of the way to the opposite end. Using real prototypes, simulations, and analytical models, we demonstrate that the chain is a mechanical conductor, whose carriers are nonlinear solitary waves, not captured within linear elasticity. Indeed, the linkage prototype can be regarded as the simplest example of a topological metamaterial whose protected mechanical excitations are solitons, moving domain walls between distinct topological mechanical phases. More practically, we have built a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another. Our work paves the way toward adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures.

The Wetting Agent Required for Swarming in Salmonella enterica Serovar Typhimurium Is Not a Surfactant

We compared the abilities of media from agar plates surrounding swarming and nonswarming cells of Salmonella enterica serovar Typhimurium to wet a nonpolar surface by measuring the contact angles of small drops. The swarming cells were wild type for chemotaxis, and the nonswarming cells were nonchemotactic mutants with motor biases that were counterclockwise (cheY) or clockwise (cheZ). The latter strains have been shown to be defective for swarming because the agar remains dry (Q. Wang, A. Suzuki, S. Mariconda, S. Porwollik, and R. M. Harshey, EMBO J. 24:2034-2042, 2005). We found no differences in the abilities of the media surrounding these cells, either wild type or mutant, to wet a low-energy surface (freshly prepared polydimethylsiloxane); although, their contact angles were smaller than that of the medium harvested from the underlying agar. So the agent that promotes wetness produced by wild-type cells is not a surfactant; it is an osmotic agent.

Topological Mechanics of Origami and Kirigami.

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.

Mechanical Weyl Modes in Topological Maxwell Lattices.

We show that two-dimensional mechanical lattices can generically display topologically protected bulk zero-energy phonon modes at isolated points in the Brillouin zone, analogs of massless fermion modes of Weyl semimetals. We focus on deformed square lattices as the simplest Maxwell lattices, characterized by equal numbers of constraints and degrees of freedom, with this property. The Weyl points appear at the origin of the Brillouin zone along directions with vanishing sound speed and move away to the zone edge (or return to the origin) where they annihilate. Our results suggest a design strategy for topological metamaterials with bulk low-frequency acoustic modes and elastic instabilities at a particular, tunable finite wave vector.

Helical Packings and Phase Transformations of Soft Spheres in Cylinders

The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of the volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as the particle volume fraction is reduced, consistent with recent hard-sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter psi6. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase-transition-like behavior in quasi-one-dimensional systems.

Symmetry breaking in smectics and surface models of their singularities

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, whereas disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need to add compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, while disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need for compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.

The role of rigidity in controlling material failure

Significance As a solid approaches a rigidity transition, its failure behavior changes dramatically: cracks become wider and wider until their width reaches the system size. In this regime, bonds initially break at apparently random positions until they produce a percolating cluster spanning across the sample. Because the spatial extent of the failure process zone depends on material toughness, varying the rigidity can be used as a lens to examine the nonlinear response that would otherwise be observable only on a microscopic scale in a rigid material. We investigate how material rigidity acts as a key control parameter for the failure of solids under stress. In both experiments and simulations, we demonstrate that material failure can be continuously tuned by varying the underlying rigidity of the material while holding the amount of disorder constant. As the rigidity transition is approached, failure due to the application of uniaxial stress evolves from brittle cracking to system-spanning diffuse breaking. This evolution in failure behavior can be parameterized by the width of the crack. As a system becomes more and more floppy, this crack width increases until it saturates at the system size. Thus, the spatial extent of the failure zone can be used as a direct probe for material rigidity.

Nematic films and radially anisotropic Delaunay surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.