155 research outputs found

    Coupled liquid crystalline oscillators in Huygens’ synchrony

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    In the flourishing field of soft robotics, strategies to embody communication and collective motion are scarce. Here we report the synchronized oscillations of thin plastic actuators by an approach reminiscent of the synchronized motion of pendula and metronomes. Two liquid crystalline network oscillators fuelled by light influence the movement of one another and display synchronized oscillations in-phase and anti-phase in a steady state. By observing entrainment between the asymmetric oscillators we demonstrate the existence of coupling between the two actuators. We qualitatively explain the origin of the synchronized motion using a theoretical model and numerical simulations, which suggest that the motion can be tuned by the mechanical properties of the coupling joint. We thus anticipate that the complex synchronization phenomena usually observed in rigid systems can also exist in soft polymeric materials. This enables the use of new stimuli, featuring an example of collective motion by photo-actuation

    Normal resonances in a double Hopf bifurcation

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    We introduce a framework to systematically investigate the resonant double Hopf bifurcation. We use the basic invariants of the ensuing T1-action to analyse the approximating normal form truncations in a unified manner. In this way we obtain a global description of the parameter space and thus find the organising resonance droplet, which is the present analogue of the resonant gap. The dynamics of the normal form yields a skeleton for the dynamics of the original system. In the ensuing perturbation theory both normal hyperbolicity (centre manifold theory) and KAM theory are being used

    Normal-normal resonances in a double Hopf bifurcation

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    We investigate the stability loss of invariant n-dimensional quasi-periodic tori during a double Hopf bifurcation, where at bifurcation the two normal frequencies are in normal-normal resonance. Invariants are used to analyse the normal form approximations in a unified manner. The corresponding dynamics form a skeleton for the dynamics of the original system. Here both normal hyperbolicity and KAM theory are being used.Comment: 22 pages, 6 figure

    A Galilean dance 1:2:4 resonant periodic motions and their librations of Jupiter and his Galilean moons

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    The four Galilean moons of Jupiter were discovered by Galileo in the early 17th century, and their motion was first seen as a miniature solar system. Around 1800 Laplace discovered that the Galilean motion is subjected to an orbital 1:2:4-resonance of the inner three moons Io, Europa and Ganymedes. In the early 20th century De Sitter gave a mathematical explanation for this in a Newtonian framework. In fact, he found a family of stable periodic solutions by using the seminal work of Poincaré, which at the time was quite new. In this paper we review and summarize recent results of Broer, Hanßmann and Zhao on the motion of the entire Galilean system, so including the fourth moon Callisto. To this purpose we use a version of parametrised Kolmogorov-Arnol'd-Moser theory where a family of multi-periodic isotropic invariant three-dimensional tori is found that combines the periodic motions of De Sitter and Callisto. The 3-tori are normally elliptic and excite a family of invariant Lagrangean 8-tori that project down to librational motions. Both the 3- and the 8-tori occur for an almost full Hausdorff measure set in the product of corresponding dimension in phase space and a parameter space, where the external parameters are given by the masses of the moons

    Magnetic Resonance Monitoring of Opaque Temperature-Sensitive Polymeric Scaffolds

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    The monitoring of location and degradation rates of injectable biomaterials is an area of particular interest in the design and implementation of therapeutic scaffolds and carriers for tissue repair and replacement. We describe here the fabrication and characterization of gadolinium (Gd)-labeled temperature-responsive hydrogels that can be detected noninvasively using T1-weight magnetic resonance. Two acrylamide-functionalized GdIIIDOTA-monoamide complexes with either a short n-butylene spacer (GdIII-C4-AA) or a long hydrophilic spacer (GdIII-PEG-AA) were synthesized and incorporated into the hydrogels. At temperatures above the lower critical solution temperature (LCST), 37 °C, these hydrogels have the capacity to enhance relaxivity (r1) due to the hydrophobic interactions of the polyamide chains around the gadolinium chelates. This effect is further accentuated by the presence of the polyethylene glycol groups of the Gd complex GdIII-PEG-AA

    Bifurcations in Volume-Preserving Systems

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    We give a survey on local and semi-local bifurcations of divergence-free vector fields. These differ for low dimensions from ‘generic’ bifurcations of structure-less ‘dissipative’ vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation

    A Global Kam-Theorem: Monodromy in Near-Integrable Perturbations of Spherical Pendulum

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    The KAM Theory for the persistence of Lagrangean invariant tori in nearly integrable Hamiltonian systems is lobalized to bundles of invariant tori. This leads to globally well-defined conjugations between near-integrable systems and their integrable approximations, defined on nowhere dense sets of positive measure associated to Diophantine frequency vectors. These conjugations are Whitney smooth diffeomorphisms between the corresponding torus bundles. Thus the geometry of the integrable torus bundle is inherited by the near-integrable perturbation. This is of intereet in cases where these bundles are nontrivial. The paper deals with the spherical pendulum as a leading example

    Global bifurcation analysis of Topp system

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    In this paper, we study the 3-dimensional Topp model for the dynamics of diabetes. First, we reduce the model to a planar quartic system. In particular, studying global bifurcations, we prove that such a system can have at most two limit cycles. Next, we study the dynamics of the full 3-dimensional model. We show that for suitable parameter values an equilibrium bifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests that near this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arise through period doubling cascades of limit cycles
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