More Like this

1. “Morphogenetic Action” Principle for 3D Shape Formation by the Growth of Thin Sheets

   https://doi.org/10.1103/PhysRevX.15.021068  

   Cislo, Dillon J; Pavlopoulos, Anastasios; Shraiman, Boris I (May 2025, Physical Review X)

   How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In particular, growth profiles may differ in their degree of spatial variation and growth anisotropy; however, the criteria that distinguish observed patterns of growth from other possible alternatives are not understood. Here we exploit the mathematical formalism of quasiconformal transformations to formulate the problem of “growth pattern selection” quantitatively in the context of 3D shape formation by growing 2D epithelial sheets. We propose that nature settles on growth patterns that are the “simplest” in a certain way. Specifically, we demonstrate that growth pattern selection can be formulated as an optimization problem and solved for the trajectories that minimize spatiotemporal variation in areal growth rates and deformation anisotropy. The result is a complete prediction for the growth of the surface, including not only a set of intermediate shapes, but also a prediction for cell displacement along those surfaces in the process of growth. Optimization of growth trajectories for both idealized surfaces and those observed in nature show that relative growth rates can be uniformized at the cost of introducing anisotropy. Minimizing the variation of programmed growth rates can therefore be viewed as a generic mechanism for growth pattern selection and may help us to understand the prevalence of anisotropy in developmental programs. Published by the American Physical Society2025 

   more » « less
2. Variational Surface Cutting

   Sharp, Nicholas; Crane, Keenan (July 2018, ACM transactions on graphics)

   This paper develops a global variational approach to cutting curved surfaces so that they can be flattened into the plane with low metric distortion. Such cuts are a critical component in a variety of algorithms that seek to parameterize surfaces over flat domains, or fabricate structures from flat materials. Rather than evaluate the quality of a cut solely based on properties of the curve itself (e.g., its length or curvature), we formulate a flow that directly optimizes the distortion induced by cutting and flattening. Notably, we do not have to explicitly parameterize the surface in order to evaluate the cost of a cut, but can instead integrate a simple evolution equation defined on the cut curve itself. We arrive at this flow via a novel application of shape derivatives to the Yamabe equation from conformal geometry. We then develop an Eulerian numerical integrator on triangulated surfaces, which does not restrict cuts to mesh edges and can incorporate user-defined data such as importance or occlusion. The resulting cut curves can be used to drive distortion to arbitrarily low levels, and have a very different character from cuts obtained via purely discrete formulations. We briefly explore potential applications to computational design, as well as connections to space filling curves and the problem of uniform heat distribution. 

   more » « less
3. Kirigami‐Inspired Inflatables with Programmable Shapes

   https://doi.org/10.1002/adma.202001863  

   Jin, Lishuai; Forte, Antonio_Elia; Deng, Bolei; Rafsanjani, Ahmad; Bertoldi, Katia (July 2020, Advanced Materials)

   Abstract Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, kirigami principles are exploited to design inflatables that can mimic target shapes upon pressurization. The system comprises a kirigami sheet embedded into an unstructured elastomeric membrane. First, it is shown that the inflated shape can be controlled by tuning the geometric parameters of the kirigami pattern. Then, by applying a simple optimization algorithm, the best parameters that enable the kirigami inflatables to transform into a family of target shapes at a given pressure are identified. Furthermore, thanks to the tessellated nature of the kirigami, it is shown that we can selectively manipulate the parameters of the single units to allow the reproduction of features at different scales and ultimately enable a more accurate mimicking of the target. 

   more » « less
4. Swelling as a stabilizing mechanism in irradiated thin films: II. Effect of swelling rate

   https://doi.org/10.1088/1361-648X/ac75a3  

   Evans, Tyler; Norris, Scott (June 2022, Journal of Physics: Condensed Matter)

   Abstract It has long been observed experimentally that energetic ion-beam irradiation of semiconductor surfaces may lead to spontaneous nanopattern formation. For most ion/target/energy combinations, the patterns appear when the angle of incidence exceeds a critical angle, and the models commonly employed to understand this phenomenon exhibit the same behavioral transition. However, under certain conditions, patterns do not appear for any angle of incidence, suggesting an important mismatch between experiment and theory. Previous work by our group (Swenson and Norris 2018 J. Phys.: Condens. Matter 30 304003) proposed a model incorporating radiation-induced swelling, which is known to occur experimentally, and found that in the analytically-tractable limit of small swelling rates, this effect is stabilizing at all angles of incidence, which may explain the observed suppression of ripples. However, at that time, it was not clear how the proposed model would scale with increased swelling rate. In the present work, we generalize that analysis to the case of arbitrary swelling rates. Using a numerical approach, we find that the stabilization effect persists for arbitrarily large swelling rates, and maintains a stability profile largely similar to that of the small swelling case. Our findings strongly support the inclusion of a swelling mechanism in models of pattern formation under ion beam irradiation, and suggest that the simpler small-swelling limit is an adequate approximation for the full mechanism. They also highlight the need for more—and more detailed—experimental measurements of material stresses during pattern formation. 

   more » « less
5. Physics-aware differentiable design of magnetically actuated kirigami for shape morphing

   https://doi.org/10.1038/s41467-023-44303-x  

   Wang, Liwei; Chang, Yilong; Wu, Shuai; Zhao, Ruike Renee; Chen, Wei (December 2023, Nature Communications)

   Abstract Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook the underlying physics. This study introduces a differentiable inverse design framework that considers the physical interplay between geometry, materials, and stimuli of active kirigami, made by soft material embedded with magnetic particles, to realize target shape-morphing upon magnetic excitation. We achieve this by combining differentiable kinematics and energy models into a constrained optimization, simultaneously designing the cuts and magnetization orientations to ensure kinematic and physical feasibility. Complex kirigami designs are obtained automatically with unparalleled efficiency, which can be remotely controlled to morph into intricate target shapes and even multiple states. The proposed framework can be extended to accommodate various active systems, bridging geometry and physics to push the frontiers in shape-morphing applications, like flexible electronics and minimally invasive surgery. 

   more » « less