Kibble-Zurek mechanism in curved elastic surface crystals

Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their validity for discontinuous first-order transitions in curved and topologically nontrivial systems still poses an open question. Here, we use recent experimentally confirmed theory to investigate topological defect formation in curved elastic surface crystals formed by stress-quenching a bilayer material. Studying both spherical and toroidal crystals, we find that the defect densities follow KZ-type power laws independent of surface geometry and topology. Moreover, the nucleation sequences agree with recent experimental observations for spherical colloidal crystals. These results suggest that KZ scaling laws hold for a much broader class of dynamical phase transitions than previously thought, including non-thermal first-order transitions in non-planar geometries.Comment: 8 pages, 3 figures; introduction and typos correcte

Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.Comment: 20 pages, 5 figure

Geometry of wave propagation on active deformable surfaces

Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between surface geometry and contraction wave dynamics remains poorly understood, but will be essential for the future design of chemically-driven soft robots and active materials. Here, we couple prototypical chemical wave and reaction-diffusion models to non-Euclidean shell mechanics to identify and characterize generic features of chemo-mechanical wave propagation on active deformable surfaces. Our theoretical framework is validated against recent data from contractile wave measurements on ascidian and starfish oocytes, producing good quantitative agreement in both cases. The theory is then applied to illustrate how geometry and preexisting discrete symmetries can be utilized to focus active elastic surface waves. We highlight the practical potential of chemo-mechanical coupling by demonstrating spontaneous wave-induced locomotion of elastic shells of various geometries. Altogether, our results show how geometry, elasticity and chemical signaling can be harnessed to construct dynamically adaptable, autonomously moving mechanical surface wave guides.Comment: text changes abstract and intro, new results on self-propelled elastic shells added; 5 pages, 3 figures; videos available on reques

Subdivision Shell Elements with Anisotropic Growth

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl

Curvature-Induced Instabilities of Shells

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains still poorly understood. Via a combination of precision experiments on elastomeric spherical bilayer shells, simulations, and theory, we show a spontaneous curvature-induced rotational symmetry-breaking as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities and their dependence on geometry are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike bulk term and a torquelike boundary term, allowing scaling predictions for the instabilities in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.Comment: 12 pages, 9 figures (including Supporting Information

Bimodal rheotactic behavior reflects flagellar beat asymmetry in human sperm cells

Successful sperm navigation is essential for sexual reproduction, yet we still understand relatively little about how sperm cells are able to adapt their swimming motion in response to chemical and physical cues. This lack of knowledge is owed to the fact that it has been difficult to observe directly the full 3D dynamics of the whip-like flagellum that propels the cell through the fluid. To overcome this deficiency, we apply a new algorithm to reconstruct the 3D beat patterns of human sperm cells in experiments under varying flow conditions. Our analysis reveals that the swimming strokes of human sperm are considerably more complex than previously thought, and that sperm may use their heads as rudders to turn right or left.Swiss National Science Foundation (Grant 148743)Solomon Buchsbaum AT&T Research Fun

Curvature-Controlled Defect Localization in Elastic Surface Crystals

We investigate the influence of curvature and topology on crystalline dimpled patterns on the surface of generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal, and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling, or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test bed for exploring the effects of geometrically induced forces on assemblies of topological charges.MIT Masdar ProgramSwiss National Science Foundation (148743)Solomon Buchsbaum AT&T Research FundAlfred P. Sloan Foundation (Sloan Research Fellowship)National Science Foundation (U.S.) (CAREER CMMI-1351449

Universality in the firing of minicolumnar-type neural networks

An open question in biological neural networks is whether changes in firing modalities are mainly an individual network property or whether networks follow a joint pathway. For the early developmental period, our study focusing on a simple network class of excitatory and inhibitory neurons suggests the following answer: Networks with considerable variation of topology and dynamical parameters follow a universal firing paradigm that evolves as the overall connectivity strength and firing level increase, as seen in the process of network maturation. A simple macroscopic model reproduces the main features of the paradigm as a result of the competition between the fundamental dynamical system notions of synchronization vs chaos and explains why in simulations the paradigm is robust regarding differences in network topology and largely independent from the neuron model used. The presented findings reflect the first dozen days of dissociated neuronal in vitro cultures (upon following the developmental period bears similarly universal features but is characterized by the processes of neuronal facilitation and depression that do not require to be considered for the first developmental period). A key element for explaining processes in nature by physics has been the art of choosing the optimal level of description for the effects to be described. In our current challenge to explain important aspects of our brain by means of physics, we still largely miss such a handle at many levels: To what detail, e.g., is it necessary to model neurons and their connectivity to understand what their neural network is doing? For simple small-size networks of minicolumnar type (by many considered as a potential module underlying the function of the cortex), we show that all networks from this large network class follow the same—universal—behavior, as their overall connectivity strength is enhanced. Moreover, the paradigm that they follow can be explained in terms of low-dimensional dynamical systems theory, which reveals the origin of the universal behavior. Our findings suggest that other network classes could be treated in a similar manner. The uncovered universality permits us to substantially limit the degree of details required to model cortical computation, which opens up a novel perspective toward more effective simulations of and investigations into close-to-biology neural networks and sheds a novel perspective on biological multiscale information processing. From the practical side, our findings imply that biological neural networks with strong parallels to the increase of a connectivity strength will develop closely along the uncovered paradigm. Examples are neuronal cultures at the early stage of their development or biochemical processes that globally enhance the connectivity strength among the elements of the neural network