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Liquid Crystalline Elastomers (LCEs) are active materials that are of interest due to their programmable response to various external stimuli such as light and heat. When exposed to these stimuli,...

 

We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.

 

Scientific applications, especially legacy applications, contain a wealth of scientific knowledge. As hardware changes, applications need to be ported to new architectures and extended to include scientific advances. As a result, it is common to encounter problems like performance bottlenecks and dead code. A visual representation of the dataflow can help performance experts identify and debug such problems. The Computation API of the sparse polyhedral framework (SPF) provides a single entry point for tools to generate and manipulate polyhedral dataflow graphs, and transform applications. However, when viewing graphs generated for scientific applications there are several barriers. The graphs are large, and manipulating their layout to respect execution order is difficult. This paper presents a case study that uses the Computation API to represent a scientific application, GeoAc, in the SPF. Generated polyhedral dataflow graphs were explored for optimization opportunities and limitations were addressed using several graph simplifications to improve their usability. 

Many important applications including machine learning, molecular dynamics, and computational fluid dynamics, use sparse data. Processing sparse data leads to non-affine loop bounds and frustrates the use of the polyhedral model for code transformation. The Sparse Polyhedral Framework (SPF) addresses limitations of the Polyhedral model by supporting non-affine constraints in sets and relations using uninterpreted functions. This work contributes an object-oriented API that wraps the SPF intermediate representation (IR) and integrates the Inspector/Executor Generation Library and Omega+ for precise set and relation manipulation and code generation. The result is a well-specified definition of a full computation using the SPF IR. The API provides a single entry point for tools to interact with the SPF, generate and manipulate polyhedral data flow graphs, and transform sparse applications. 

Contactless actuation powered using light is shown to generate torque densities approaching 10 N.m/kg at angular velocities ~10 2 rad/s: metrics that compare favorably against tethered electromechanical systems. This is possible even though the extinction of actinic light limits the characteristic thickness of photoresponse in polymers to tens of μm. Confinement of molecularly patterned developable shells fabricated from azobenzene-functionalized liquid crystalline polymers encodes torque-dense photoactuation. Photostrain gradients from unstructured irradiation segment this geometry into two oppositely curved regions connected by a curved crease. A monolithic curved shell spontaneously bifurcates into a jointed, arm-like mechanism that generates flexure over sweep angles exceeding a radian. Strain focusing at the crease is hierarchical: an integral crease nucleates at smaller magnitudes of the prebiased curvature, while a crease decorated with point-like defects emerges at larger curvatures. The phase-space of morphogenesis is traceable to the competition between stretch and bending energies and is parameterizable as a function of the geometry. The framework for generating repetitive torque-dense actuation from slender light-powered actuators holds broader implications for the design of soft, remotely operated machines. Here, it is harnessed in illustrative mechanisms including levers, lifters and grabbers that are powered and regulated exclusively using light. 

The effect of chain extender structure and composition on the thermomechanical properties of liquid crystal elastomers (LCE) synthesized using thiol-acrylate Michael addition is presented. The intrinsic molecular stiffness of the thiol chain extender and its relative molar ratio to acrylate-based host mesogens determine the magnitudes of the thermomechanical strains, temperatures at which they are realized and the mechanical work-content. A non-linear structure-property relationship emerges, wherein higher concentrations of flexible extenders first magnify the thermomechanical sensitivity, but a continued increase leads to weaker actuation. Understanding this interplay leads to a composite material platform, enabling a peak specific work production of ~2 J/kg using ~115 mW of electrical power supplied at 2 V. Composites of LCE with eGaIn liquid metal (LM) are prepared, which act as heaters, while being capable of actuation themselves. The thermomechanically active electrodes convert the electrical power into Joule heat, which they efficiently couple with the neat LCE to which they are bound. This system harnesses the nascent responsiveness of the LCE using electrodes that work with them, instead of fighting against them (or passively standing in the way). Specific work generated increases when subjected to increasing levels of load, reaching a peak at loads 260x the actuator weight. These ideas are extended to tri-layered actuators, where LCE films with orthogonal molecular orientations sandwich LCE-LM composite heaters. Torsional actuation modes are harnessed to twist under load.