Active beating modes of two clamped filaments driven by molecular motors

Biological cilia pump the surrounding fluid by asymmetric beating that is driven by dynein motors between sliding microtubule doublets. The complexity of biological cilia raises the question about minimal systems that can re-create similar patterns of motion. One such system consists of a pair of microtubules that are clamped at the proximal end. They interact through dynein motors that cover one of the filaments and pull against the other one. Here, we study theoretically the static shapes and the active dynamics of such a system. Using the theory of elastica, we analyse the shapes of two filaments of different lengths with clamped ends. Starting from equal lengths, we observe a transition similar to Euler buckling leading to a planar shape. When further increasing the length ratio, the system assumes a non-planar shape with spontaneously broken chiral symmetry after a secondary bifurcation and then transitions to planar again. The predicted curves agree with experimentally observed shapes of microtubule pairs. The dynamical system can have a stable fixed point, with either bent or straight filaments, or limit cycle oscillations. The latter match many properties of ciliary motility, demonstrating that a two-filament system can serve as a minimal actively beating model.

Prediction of buckling force in hourglass-shaped specimens

It is important to avoid buckling during low-cycle fatigue testing. The buckling load is dependent on the specimen shape, material properties, and the testing machine. In the present investigation of hourglass-shaped specimens the importance of the diameter to radius of curvature is examined. Diameters of 5 and 7 mm are examined with a ratio of radius of curvature to diameter of 4, 6, and 8. The machine used is an Instron 8800 with elongated rods for a climate chamber. This leads to a reduced stiffness of the machine during compression testing. A finite element model (in Abaqus) is developed to identify the critical buckling force. For hourglass-shaped specimens, buckling means onset of sideways movement, without a drop in the applied load which is typical for conventional Euler buckling. The onset of sideways movement is identified experimentally by analysis of the data from extensometer and the load cell. This model is verified by experiments and fits within 0.6 to − 11% depending on the specimen diameter and diameter to radius of curvature ratio. The smallest deviations are obtained for the 7-mm-diameter specimen with deviation varying from 0.6 to − 3.3% between the model and the experiments. The current investigation is done with a commercially available hot rolled structural steel bar of Ø16 mm.

Elasto-capillary circumferential buckling of soft tubes under axial loading: existence and competition with localised beading and periodic axial modes

We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are as follows: under what loading conditions, if any, can bifurcation into circumferential buckling modes occur, and do such solutions dominate localisation and periodic axial modes? Three distinct boundary conditions are considered: in case 1 the tube’s curved surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. A linear bifurcation analysis is conducted to determine numerically the existence of circumferential mode solutions. In case 1 we focus on the tensile stress regime given the preference of slender compressed tubes towards Euler buckling over axisymmetric periodic wrinkling. We show that tubes under several loading paths are highly sensitive to circumferential modes; in contrast, localised and periodic axial modes are absent, suggesting that the circumferential buckling is dominant by default. In case 2, circumferential mode solutions are associated with negative surface tension values and thus are physically implausible. Circumferential buckling solutions are shown to exist in case 3 for tensile and compressive axial loads, and we demonstrate for multiple loading scenarios their dominance over localisation and periodic axial modes within specific parameter regimes.

Training of a Classifier for Structural Component Failure based on Hybrid Simulation and Kriging

Hybrid simulation is a tool for discovering the inner workings of a tested substructure beyond the linear regime. Hybrid simulation is conducted to reproduce the response of a prototype in scaled or real time using a hybrid model that combines physical and numerical substructures interacting with each other in a feedback loop. As a result, the tested substructure interacts with a realistic assembly subjected to a credible loading scenario. The obtained low-quantity-high-value experimental data is used to conceive and calibrate computational models for nonlinear structural analysis in the current practice. Instead, this paper extends the scope of hybrid simulation to constructing a safe/failure state classifier for the tested substructure by adaptively designing a sequence of parametrized hybrid simulations. Such a classifier is intended to compute the state of any physical-substructure-like component within system-level numerical simulations. The proposed procedure is experimentally validated for a three-degrees-of-freedom hybrid model subjected to Euler buckling.

Inextensibility and Its Effect on the Number of Equilibria of Shallow Buckled Beams

A buckled beam with shallow rise under lateral constraint is considered. The initial rise results from a prescribed end displacement. The beam is modeled as inextensible, and analytical solutions of the equilibria are obtained from a constrained energy minimization problem. For simplicity, the results are derived for the archetypal beam with pinned ends. It is found that there are an infinite number of zero lateral-load equilibria, each corresponding to an Euler buckling mode. A numerical model is used to verify the accuracy of the model and also to explore the effects of extensibility.

Violent buckling benefits galactic bars

ABSTRACT Galactic bars are unstable to a vertical buckling instability which heats the disc and in some cases forms a boxy/peanut shaped bulge. We analyse the buckling instability as an application of classical Euler buckling followed by non-linear gravitational Landau damping in the collisionless system. We find that the buckling instability is dictated by the kinematic properties and geometry of the bar. The analytical result is compared to simulations of isolated galaxies containing the disc and dark matter components. Our results demonstrate that violent buckling does not destroy bars while a less energetic buckling can dissolve the bar. The discs that undergo gentle buckling remain stable to bar formation which may explain the observed bar fraction in the local Universe. Our results align with the results from recent surveys.

Buckling of an Elastic Plate/Layer Along a Rigid Base With Adhesion

An infinitely long elastic plate/layer is under uniaxial compression with its long dimension held by adhesion to a flat rigid base without friction. A prescribed length of the plate/layer is free of adhesion. This configuration is similar to a pre-stressed elastic film for which buckling of an unbonded section is a necessary, but not sufficient, condition for delamination. For that configuration, buckling occurs at the Euler buckling load of a fixed–fixed plate. Although the present study does not include friction or tangential interface stresses, the onset of buckling should be similar for these two cases. For the case of an elastic plate, a cohesive zone is used and it is found that the fixed–fixed buckling load is not attained except for extremely large values of a cohesive zone parameter. For realistic values, the buckling load is about half of that value. For the situation of an elastic layer with adhesion (without a cohesive zone), the buckling load approaches the fixed–fixed value only for very large values of the ratio of the unbonded length to the thickness.