We studied the mechanical process of seed pods opening in Bauhinia variegate and found a chirality-creating mechanism, which turns an initially flat pod valve into a helix. We studied configurations ...of strips cut from pod valve tissue and from composite elastic materials that mimic its structure. The experiments reveal various helical configurations with sharp morphological transitions between them. Using the mathematical framework of "incompatible elasticity," we modeled the pod as a thin strip with a flat intrinsic metric and a saddle-like intrinsic curvature. Our theoretical analysis quantitatively predicts all observed configurations, thus linking the pod's microscopic structure and macroscopic conformation. We suggest that this type of incompatible strip is likely to play a role in the self-assembly of chiral macromolecules and could be used for the engineering of synthetic self-shaping devices.
The connection between a surface's metric and its Gaussian curvature (Gauss theorem) provides the base for a shaping principle of locally growing or shrinking elastic sheets. We constructed thin gel ...sheets that undergo laterally nonuniform shrinkage. This differential shrinkage prescribes non-Euclidean metrics on the sheets. To minimize their elastic energy, the free sheets form three-dimensional structures that follow the imposed metric. We show how both large-scale buckling and multiscale wrinkling structures appeared, depending on the nature of possible embeddings of the prescribed metrics. We further suggest guidelines for how to generate each type of feature.
Evidence suggests that the perioperative period and the excision of the primary tumour can promote the development of metastases—the main cause of cancer-related mortality. This Review first presents ...the assertion that the perioperative timeframe is pivotal in determining long-term cancer outcomes, disproportionally to its short duration (days to weeks). We then analyse the various aspects of surgery, and their consequent paracrine and neuroendocrine responses, which could facilitate the metastatic process by directly affecting malignant tissues, and/or through indirect pathways, such as immunological perturbations. We address the influences of surgery-related anxiety and stress, nutritional status, anaesthetics and analgesics, hypothermia, blood transfusion, tissue damage, and levels of sex hormones, and point at some as probable deleterious factors. Through understanding these processes and reviewing empirical evidence, we provide suggestions for potential new perioperative approaches and interventions aimed at attenuating deleterious processes and ultimately improving treatment outcomes. Specifically, we highlight excess perioperative release of catecholamines and prostaglandins as key deleterious mediators of surgery, and we recommend blockade of these responses during the perioperative period, as well as other low-risk, low-cost interventions. The measures described in this Review could transform the perioperative timeframe from a prominent facilitator of metastatic progression, to a window of opportunity for arresting and/or eliminating residual disease, potentially improving long-term survival rates in patients with cancer.
The theoretical framework that should be used for describing rotating turbulence1, 2, 3 is the subject of an active debate. It was shown experimentally4, 5 and numerically6, 7 that the formalism of ...2D turbulence is useful in the description of many aspects of rotating turbulence. On the other hand, theoretical and numerical work suggests that the formalism of wave turbulence8, 9, 10 should provide a reliable description of the entire 3D flow field11, 12, 13, 14, 15. The waves that are suggested as the basis for this turbulence are Coriolis-force-driven inertial waves1. Here we present experimental results that suggest the existence of inertial wave turbulence in deep steady rotating turbulence. Our measurements show energy transfer from the injection scale to larger scales, although the energy spectra are concentrated along the dispersion relation of inertial waves. The turbulent fields are, therefore, well described as ensembles of 3D interacting inertial waves.
Self-assembly is an important process by which nontrivial structures are formed on the sub-micron scales. Such processes are governed by chemical and physical principles that dictate how the ...molecular interactions affect the supramolecular geometry. Currently there is no general framework that links between molecular properties and the supramolecular morphology with its size parameters. Here we introduce a new paradigm for the description and analysis of supramolecular structures that self-assemble via short-range interactions. Analysis of molecular interactions determines inputs to the theory of incompatible elasticity, which provides analytic expressions for supramolecular shape and fluctuations. We derive quantitative predictions for specific amphiphiles that self-assembled into chiral nanoribbons. These are quantitatively confirmed experimentally, revealing unique shape evolution, unusual mechanics and statistics, proving that the assemblies are geometrically incompatible. The success in predicting equilibrium and statistics suggests the approach as a new framework for quantitative study of a large variety of self-assembled nanostructures.
A short, abrupt increase in energy injection rate into steady strongly driven rotating turbulent flow is used as a probe for energy transfer in the system. The injected excessive energy is localized ...in time and space and its spectra differ from those of the steady turbulent flow. This allows measuring energy transfer rates, in three different domains: In real space, the injected energy propagates within the turbulent field, as a wave packet of inertial waves. In the frequency domain, energy is transferred nonlocally to the low, quasigeostrophic modes. In wave number space, energy locally cascades toward small wave numbers, in a rate that is consistent with two-dimensional (2D) turbulence models. Surprisingly however, the inverse cascade of energy is mediated by inertial waves that propagate within the flow with small, but nonvanishing frequency. Our observations differ from measurements and theoretical predictions of weakly driven turbulence. Yet, they show that in strongly driven rotating turbulence, inertial waves play an important role in energy transfer, even in the vicinity of the 2D manifold.A short, abrupt increase in energy injection rate into steady strongly driven rotating turbulent flow is used as a probe for energy transfer in the system. The injected excessive energy is localized in time and space and its spectra differ from those of the steady turbulent flow. This allows measuring energy transfer rates, in three different domains: In real space, the injected energy propagates within the turbulent field, as a wave packet of inertial waves. In the frequency domain, energy is transferred nonlocally to the low, quasigeostrophic modes. In wave number space, energy locally cascades toward small wave numbers, in a rate that is consistent with two-dimensional (2D) turbulence models. Surprisingly however, the inverse cascade of energy is mediated by inertial waves that propagate within the flow with small, but nonvanishing frequency. Our observations differ from measurements and theoretical predictions of weakly driven turbulence. Yet, they show that in strongly driven rotating turbulence, inertial waves play an important role in energy transfer, even in the vicinity of the 2D manifold.
Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the ...violation of Gauss’s Theorema Egregium. Such “Gauss frustration” exhibits rich phenomenology; it may lead to mechanical instabilities, anomalous mechanics, and shape-morphing abilities that can be harnessed in engineering systems. Here we report a new type of geometrical frustration, one that is as general as Gauss frustration. We show that its origin is the violation of Mainardi-Codazzi-Peterson compatibility equations and that it appears in Euclidean sheets. Combining experiments, simulations, and theory, we study the specific case of a Euclidean ribbon with radial and geodesic curvatures. Experiments, conducted using different materials and techniques, reveal shape transitions, symmetry breaking, and spontaneous stress focusing. These observations are quantitatively rationalized using analytic solutions and geometrical arguments. We expect this frustration to play a significant role in natural and engineering systems, specifically in slender 3D printed sheets.
While living organisms have mastered the dynamic control of residual stresses within sheets to induce shape transformation and locomotion, man-made implementations are rudimentary. We present the ...first autonomously shape-shifting sheets made of a gel that shrinks and swells in response to the phase of an oscillatory chemical (Belousov-Zhabotinsky) reaction. Propagating reaction-diffusion fronts induce localized deformation of the gel. We show that these localized deformations prescribe a spatiotemporal pattern of Gaussian curvature, leading to time-periodic global shape changes. We present the computational tools and experimental protocols needed to control this system, principally the relationship between the Gaussian curvature and the reaction phase, and optical imprinting of the wave pattern. Together, our results demonstrate a route for developing fully autonomous soft machines mimicking some of the locomotive capabilities of living organisms.
Although Nature has always been a common source of inspiration in the development of artificial materials, only recently has the ability of man-made materials to produce complex three-dimensional ...(3D) structures from two-dimensional sheets been explored. Here we present a new approach to the self-shaping of soft matter that mimics fibrous plant tissues by exploiting small-scale variations in the internal stresses to form three-dimensional morphologies. We design single-layer hydrogel sheets with chemically distinct, fibre-like regions that exhibit differential shrinkage and elastic moduli under the application of external stimulus. Using a planar-to-helical three-dimensional shape transformation as an example, we explore the relation between the internal architecture of the sheets and their transition to cylindrical and conical helices with specific structural characteristics. The ability to engineer multiple three-dimensional shape transformations determined by small-scale patterns in a hydrogel sheet represents a promising step in the development of programmable soft matter.
Self‐morphing of thin plates could greatly impact the life if used in architectural context. Yet, so far, its realizations are limited to small‐scale structures made of model materials. Here, new ...fabrication techniques are developed that turn two conventional construction materials—clay and fiber composites (FRP)—into smart, self‐morphing materials, compatible with architectural needs. Controlled experiments verify the quantitative connection between the prescribed small‐scale material structure and the global 3D surface, as predicted by the theory of incompatible elastic sheets. Scaling up of desired structures is demonstrated, including a method that copes with self‐weight effects. Finally, a method for the construction of FRP surfaces with complex curvature distribution is presented, together with a software interface that allows the computation of the 3D surface for a given fiber pattern (the forward problem), as well as the fiber distribution required for a desired 3D shape (the inverse problem). This work shows the feasibility of large‐scale self‐morphing surfaces for architecture.
Self‐shaping by material frustration is demonstrated for the first time at an architectural scale and in structural materials, typical of the construction field. Quantitative comparison with theoretical predictions, as well as scaling‐up and gravitation effect are presented. Together with a flexible design interface, it suggests a future mold‐less architectural application.
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