Traveling Waves

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Dennis M Freeman - One of the best experts on this subject based on the ideXlab platform.

  • effects of geometry and cochlear loads on tectorial membrane Traveling Waves
    13th Mechanics of Hearing Workshop: To the Ear and Back Again - Advances in Auditory Biophysics MoH 2017, 2018
    Co-Authors: Jonathan B Sellon, Roozbeh Ghaffari, Dennis M Freeman
    Abstract:

    It has been suggested that the decay constants of tectorial membrane (TM) Traveling Waves contribute to differences in the tuning of Tectb −/– mutant mice, wild-type mice, and humans. However, the experiments underlying these results were obtained in vitro, in the absence of cochlear loads. In this work, we analyze effects of cochlear loads on TM Traveling Waves using a viscoelastic model. Results demonstrate that hair bundle stiffness has little effect on TM Waves, the limbal attachment tends to increase the wavelength of TM Waves, and viscous loss to subtectorial fluid tends to decrease the wave decay constant. To understand how the TM is able to support Traveling Waves despite these loads we examined how TM wave decay constants depend on thickness of the TM. We observe that increasing TM thickness tends to moderate all effects of cochlear loads and that as TM thickness increases, the wave decay constant approaches an asymptotic limit that is independent of cochlear loads. For material properties corres...

  • longitudinally propagating Traveling Waves of the mammalian tectorial membrane
    Proceedings of the National Academy of Sciences of the United States of America, 2007
    Co-Authors: Roozbeh Ghaffari, Alexander J Aranyosi, Dennis M Freeman
    Abstract:

    Sound-evoked vibrations transmitted into the mammalian cochlea produce Traveling Waves that provide the mechanical tuning necessary for spectral decomposition of sound. These Traveling Waves of motion that have been observed to propagate longitudinally along the basilar membrane (BM) ultimately stimulate the mechano-sensory receptors. The tectorial membrane (TM) plays a key role in this process, but its mechanical function remains unclear. Here we show that the TM supports Traveling Waves that are an intrinsic feature of its visco-elastic structure. Radial forces applied at audio frequencies (2–20 kHz) to isolated TM segments generate longitudinally propagating Waves on the TM with velocities similar to those of the BM Traveling wave near its best frequency place. We compute the dynamic shear storage modulus and shear viscosity of the TM from the propagation velocity of the Waves and show that segments of the TM from the basal turn are stiffer than apical segments are. Analysis of loading effects of hair bundle stiffness, the limbal attachment of the TM, and viscous damping in the subtectorial space suggests that TM Traveling Waves can occur in vivo. Our results show the presence of a Traveling wave mechanism through the TM that can functionally couple a significant longitudinal extent of the cochlea and may interact with the BM wave to greatly enhance cochlear sensitivity and tuning.

Xiaoqiang Zhao - One of the best experts on this subject based on the ideXlab platform.

  • Traveling Waves for monotone semiflows with weak compactness
    Siam Journal on Mathematical Analysis, 2014
    Co-Authors: Jian Fang, Xiaoqiang Zhao
    Abstract:

    This paper is devoted to the study of Traveling Waves for monotone semiflows of monostable type with weak compactness. To weaken the compactness condition imposed in previous works, we construct a compact set in the kinetic phase space and use an abstract variant of Helly's theorem. The obtained result is then applied to three prototypical noncompact (even non-$\alpha$-contractive) evolution systems.

  • bistable Traveling Waves for monotone semiflows with applications
    arXiv: Analysis of PDEs, 2011
    Co-Authors: Jian Fang, Xiaoqiang Zhao
    Abstract:

    This paper is devoted to the study of Traveling Waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable Traveling Waves for discrete and continuous-time monotone semiflows. This result is then extended to the cases of periodic habitat and weak compactness, respectively. We also apply the developed theory to four classes of evolution systems.

  • spreading speeds and Traveling Waves for abstract monostable evolution systems
    Journal of Functional Analysis, 2010
    Co-Authors: Xing Liang, Xiaoqiang Zhao
    Abstract:

    Abstract This paper is devoted to the development of the theory of spreading speeds and Traveling Waves for abstract monostable evolution systems with spatial structure. Under appropriate assumptions, we show that the spreading speeds coincide with the minimal wave speeds for monotone Traveling Waves in the positive and negative directions. Then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the Dirichlet boundary condition, a reaction–diffusion model with a quiescent stage, a porous medium equation in a tube, and a lattice system in a periodic habitat.

  • spreading speeds and Traveling Waves for nonmonotone integrodifference equations
    Siam Journal on Mathematical Analysis, 2008
    Co-Authors: Szebi Hsu, Xiaoqiang Zhao
    Abstract:

    The spreading speeds and Traveling Waves are established for a class of nonmonotone discrete-time integrodifference equation models. It is shown that the spreading speed is linearly determinate and coincides with the minimal wave speed of Traveling Waves.

  • spreading speeds and Traveling Waves for periodic evolution systems
    Journal of Differential Equations, 2006
    Co-Authors: Xing Liang, Xiaoqiang Zhao
    Abstract:

    Abstract The theory of spreading speeds and Traveling Waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case. Then these abstract results are applied to a periodic system modeling man–environment–man epidemics, a periodic time-delayed and diffusive equation, and a periodic reaction–diffusion equation on a cylinder.

Taro Toyoizumi - One of the best experts on this subject based on the ideXlab platform.

  • Learning poly-synaptic paths with Traveling Waves.
    arXiv: Neurons and Cognition, 2021
    Co-Authors: Yoshiki Ito, Taro Toyoizumi
    Abstract:

    Traveling Waves are commonly observed across the brain. While previous studies have suggested the role of Traveling Waves in learning, the mechanism is still unclear. We adopted a computational approach to investigate the effect of Traveling Waves on synaptic plasticity. Our results indicate that Traveling Waves facilitate the learning of poly-synaptic network-paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that Traveling Waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as exclusive or (XOR) function.

  • Learning poly-synaptic paths with Traveling Waves.
    PLoS computational biology, 2021
    Co-Authors: Yoshiki Ito, Taro Toyoizumi
    Abstract:

    Traveling Waves are commonly observed across the brain. While previous studies have suggested the role of Traveling Waves in learning, the mechanism remains unclear. We adopted a computational approach to investigate the effect of Traveling Waves on synaptic plasticity. Our results indicate that Traveling Waves facilitate the learning of poly-synaptic network paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that Traveling Waves expedite finding the shortest paths and learning nonlinear input/output mapping, such as exclusive or (XOR) function.

  • Learning distant paths with Traveling Waves
    arXiv: Neurons and Cognition, 2019
    Co-Authors: Yoshiki Ito, Taro Toyoizumi
    Abstract:

    Traveling Waves are commonly observed across the brain. While previous studies have suggested the role of Traveling Waves in learning, the mechanism is still unclear. We adopted a computational approach to investigate the effect of Traveling Waves on synaptic plasticity. Our results indicate that Traveling Waves facilitate learning of distant and indirectly connected network-paths when combined with a reward-based local synaptic plasticity rule. We demonstrate that Traveling Waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as the XOR function.

Bruno Eckhardt - One of the best experts on this subject based on the ideXlab platform.

  • Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow
    Science (New York N.Y.), 2004
    Co-Authors: Björn Hof, Bruno Eckhardt, Frans T. M. Nieuwstadt, Jerry Westerweel, Casimir W. H. Van Doorne, Holger Faisst, Håkan Wedin, Richard R Kerswell, Fabian Waleffe
    Abstract:

    Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable Traveling Waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these Traveling Waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.

  • Traveling Waves in pipe flow
    Physical Review Letters, 2003
    Co-Authors: Holger Faisst, Bruno Eckhardt
    Abstract:

    : A family of three-dimensional Traveling Waves for flow through a pipe of circular cross section is identified. The Traveling Waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.

Yoshiki Ito - One of the best experts on this subject based on the ideXlab platform.

  • Learning poly-synaptic paths with Traveling Waves.
    arXiv: Neurons and Cognition, 2021
    Co-Authors: Yoshiki Ito, Taro Toyoizumi
    Abstract:

    Traveling Waves are commonly observed across the brain. While previous studies have suggested the role of Traveling Waves in learning, the mechanism is still unclear. We adopted a computational approach to investigate the effect of Traveling Waves on synaptic plasticity. Our results indicate that Traveling Waves facilitate the learning of poly-synaptic network-paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that Traveling Waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as exclusive or (XOR) function.

  • Learning poly-synaptic paths with Traveling Waves.
    PLoS computational biology, 2021
    Co-Authors: Yoshiki Ito, Taro Toyoizumi
    Abstract:

    Traveling Waves are commonly observed across the brain. While previous studies have suggested the role of Traveling Waves in learning, the mechanism remains unclear. We adopted a computational approach to investigate the effect of Traveling Waves on synaptic plasticity. Our results indicate that Traveling Waves facilitate the learning of poly-synaptic network paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that Traveling Waves expedite finding the shortest paths and learning nonlinear input/output mapping, such as exclusive or (XOR) function.

  • Learning distant paths with Traveling Waves
    arXiv: Neurons and Cognition, 2019
    Co-Authors: Yoshiki Ito, Taro Toyoizumi
    Abstract:

    Traveling Waves are commonly observed across the brain. While previous studies have suggested the role of Traveling Waves in learning, the mechanism is still unclear. We adopted a computational approach to investigate the effect of Traveling Waves on synaptic plasticity. Our results indicate that Traveling Waves facilitate learning of distant and indirectly connected network-paths when combined with a reward-based local synaptic plasticity rule. We demonstrate that Traveling Waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as the XOR function.