The Experts below are selected from a list of 225 Experts worldwide ranked by ideXlab platform
George Haller - One of the best experts on this subject based on the ideXlab platform.
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Shearless transport barriers in unsteady two-dimensional flows and maps
Physica D: Nonlinear Phenomena, 2020Co-Authors: Mohammad Farazmand, Daniel Blazevski, George HallerAbstract:We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time interval. This principle reveals that hyperbolic Lagrangian Coherent Structures (LCSs) and parabolic LCSs (or jet cores) are the two main types of shearless barriers in unsteady flows. Based on the boundary conditions they satisfy, parabolic barriers are found to be more observable and robust than hyperbolic barriers, confirming widespread numerical observations. Both types of barriers are special null-geodesics of an appropriate Lorentzian metric derived from the Cauchy--Green Strain Tensor. Using this fact, we devise an algorithm for the automated computation of parabolic barriers. We illustrate our detection method on steady and unsteady non-twist maps and on the aperiodically forced Bickley jet.Comment: Submitted to Physica
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An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows
Chaos, 2016Co-Authors: David Oettinger, George HallerAbstract:Lagrangian coherent structures (LCSs) are material surfaces that shape the finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from different variational principles, solving different equations. Here we observe that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ2(x0), of the Cauchy-Green Strain Tensor. This ξ2-system allows for the detection of LCSs in any unsteady flow by classical methods, such as Poincare maps, developed for autonomous dynamical systems. As examples, we consider both steady and time-aperiodic flows, and use their dual ξ2-system to uncover both hyperbolic and elliptic LCSs from a single computation.
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The Maxey-Riley equation: Existence, uniqueness and regularity of solutions
Nonlinear Analysis-real World Applications, 2015Co-Authors: Mohammad Farazmand, George HallerAbstract:Abstract The Maxey–Riley equation describes the motion of an inertial (i.e., finite-size) spherical particle in an ambient fluid flow. The equation is a second-order, implicit integro-differential equation with a singular kernel, and with a forcing term that blows up at the initial time. Despite the widespread use of the equation in applications, the basic properties of its solutions have remained unexplored. Here we fill this gap by proving local existence and uniqueness of mild solutions. For certain initial velocities between the particle and the fluid, the results extend to strong solutions. We also prove continuous differentiability of the mild and strong solutions with respect to their initial conditions. This justifies the search for coherent structures in inertial flows using the Cauchy–Green Strain Tensor.
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Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2015Co-Authors: Daniel Karrasch, Florian Huhn, George HallerAbstract:Coherent boundaries of Lagrangian vortices in fluid flows have recently been identified as closed orbits of line fields associated with the Cauchy–Green Strain Tensor. Here, we develop a fully automated procedure for the detection of such closed orbits in large-scale velocity datasets. We illustrate the power of our method on ocean surface velocities derived from satellite altimetry.
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Shearless transport barriers in unsteady two-dimensional flows and maps
Physica D: Nonlinear Phenomena, 2014Co-Authors: Mohammad Farazmand, Daniel Blazevski, George HallerAbstract:Abstract We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time interval. This principle reveals that hyperbolic Lagrangian Coherent Structures (LCSs) and parabolic LCSs (or jet cores) are the two main types of shearless barriers in unsteady flows. Based on the boundary conditions they satisfy, parabolic barriers are found to be more observable and robust than hyperbolic barriers, confirming widespread numerical observations. Both types of barriers are special null-geodesics of an appropriate Lorentzian metric derived from the Cauchy–Green Strain Tensor. Using this fact, we devise an algorithm for the automated computation of parabolic barriers. We illustrate our detection method on steady and unsteady non-twist maps and on the aperiodically forced Bickley jet.
Philip V Bayly - One of the best experts on this subject based on the ideXlab platform.
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Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models
Volume 1A: Abdominal Aortic Aneurysms; Active and Reactive Soft Matter; Atherosclerosis; BioFluid Mechanics; Education; Biotransport Phenomena; Bone J, 2013Co-Authors: Ruth J Okamoto, Yuan Feng, Guy M Genin, Philip V BaylyAbstract:Experimental studies [1] have shown that white matter (WM) in the brain is mechanically anisotropic. Based on its fibrous structure, transversely isotropic (TI) material models have been suggested to capture WM behavior. TI hyperelastic material models involve Strain energy density functions that depend on the I4 and I5 pseudo-invariants of the Cauchy-Green Strain Tensor to account for the effects of stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear Strain in planes parallel to the fiber axis. Most, if not all, published models of WM depend on I4 but not on I5.Copyright © 2013 by ASME
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Measurments of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter
Journal of Mech Behav Biomed Maetr, 2013Co-Authors: Yuan Feng, Ravi Namani, Guy M Genin, Ruth J Okamoto, Philip V BaylyAbstract:White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve Strain energy density functions that depend on the I 4 and 5 pseudo-invariants of the Cauchy–Green Strain Tensor to account for the effects of I relatively stiff fibers. The pseudo-invariant 4 is the square of the stretch ratio in the fiber I direction; I 5 contains contributions of shear Strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I 4 but not on 5. Here, we explore the small Strain I limits of these models in the context of experimental measurements that probe these dependencies. Models in which Strain energy depends on I 4 but not 5 can capture differences in Young’s I (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small Strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I 4 and 5 Strain pseudo- I invariants; and (2) behavior in the small Strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.
Mohammad Farazmand - One of the best experts on this subject based on the ideXlab platform.
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Shearless transport barriers in unsteady two-dimensional flows and maps
Physica D: Nonlinear Phenomena, 2020Co-Authors: Mohammad Farazmand, Daniel Blazevski, George HallerAbstract:We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time interval. This principle reveals that hyperbolic Lagrangian Coherent Structures (LCSs) and parabolic LCSs (or jet cores) are the two main types of shearless barriers in unsteady flows. Based on the boundary conditions they satisfy, parabolic barriers are found to be more observable and robust than hyperbolic barriers, confirming widespread numerical observations. Both types of barriers are special null-geodesics of an appropriate Lorentzian metric derived from the Cauchy--Green Strain Tensor. Using this fact, we devise an algorithm for the automated computation of parabolic barriers. We illustrate our detection method on steady and unsteady non-twist maps and on the aperiodically forced Bickley jet.Comment: Submitted to Physica
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The Maxey-Riley equation: Existence, uniqueness and regularity of solutions
Nonlinear Analysis-real World Applications, 2015Co-Authors: Mohammad Farazmand, George HallerAbstract:Abstract The Maxey–Riley equation describes the motion of an inertial (i.e., finite-size) spherical particle in an ambient fluid flow. The equation is a second-order, implicit integro-differential equation with a singular kernel, and with a forcing term that blows up at the initial time. Despite the widespread use of the equation in applications, the basic properties of its solutions have remained unexplored. Here we fill this gap by proving local existence and uniqueness of mild solutions. For certain initial velocities between the particle and the fluid, the results extend to strong solutions. We also prove continuous differentiability of the mild and strong solutions with respect to their initial conditions. This justifies the search for coherent structures in inertial flows using the Cauchy–Green Strain Tensor.
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Shearless transport barriers in unsteady two-dimensional flows and maps
Physica D: Nonlinear Phenomena, 2014Co-Authors: Mohammad Farazmand, Daniel Blazevski, George HallerAbstract:Abstract We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time interval. This principle reveals that hyperbolic Lagrangian Coherent Structures (LCSs) and parabolic LCSs (or jet cores) are the two main types of shearless barriers in unsteady flows. Based on the boundary conditions they satisfy, parabolic barriers are found to be more observable and robust than hyperbolic barriers, confirming widespread numerical observations. Both types of barriers are special null-geodesics of an appropriate Lorentzian metric derived from the Cauchy–Green Strain Tensor. Using this fact, we devise an algorithm for the automated computation of parabolic barriers. We illustrate our detection method on steady and unsteady non-twist maps and on the aperiodically forced Bickley jet.
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The Maxey-Riley Equation: Existence, Uniqueness and Regularity of Solutions
arXiv: Dynamical Systems, 2013Co-Authors: Mohammad Farazmand, George HallerAbstract:The Maxey--Riley equation describes the motion of an inertial (i.e., finite-size) spherical particle in an ambient fluid flow. The equation is a second-order, implicit integro-differential equation with a singular kernel, and with a forcing term that blows up at the initial time. Despite the widespread use of the equation in applications, the basic properties of its solutions have remained unexplored. Here we fill this gap by proving local existence and uniqueness of weak solutions. For certain initial velocities between the particle and the fluid, the results extend to strong solutions. We also prove continuous differentiability of the weak and strong solutions with respect to their initial conditions. This justifies the search for coherent structures in inertial flows using the Cauchy--Green Strain Tensor.
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Attracting and repelling Lagrangian coherent structures from a single computation.
Chaos, 2013Co-Authors: Mohammad Farazmand, George HallerAbstract:Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling or most attracting material surfaces in a finite-time dynamical system. To identify both types of hyperbolic LCSs at the same time instance, the standard practice has been to compute repelling LCSs from future data and attracting LCSs from past data. This approach tacitly assumes that coherent structures in the flow are fundamentally recurrent, and hence gives inconsistent results for temporally aperiodic systems. Here, we resolve this inconsistency by showing how both repelling and attracting LCSs are computable at the same time instance from a single forward or a single backward run. These LCSs are obtained as surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green Strain Tensor.
Yuan Feng - One of the best experts on this subject based on the ideXlab platform.
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Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models
Volume 1A: Abdominal Aortic Aneurysms; Active and Reactive Soft Matter; Atherosclerosis; BioFluid Mechanics; Education; Biotransport Phenomena; Bone J, 2013Co-Authors: Ruth J Okamoto, Yuan Feng, Guy M Genin, Philip V BaylyAbstract:Experimental studies [1] have shown that white matter (WM) in the brain is mechanically anisotropic. Based on its fibrous structure, transversely isotropic (TI) material models have been suggested to capture WM behavior. TI hyperelastic material models involve Strain energy density functions that depend on the I4 and I5 pseudo-invariants of the Cauchy-Green Strain Tensor to account for the effects of stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear Strain in planes parallel to the fiber axis. Most, if not all, published models of WM depend on I4 but not on I5.Copyright © 2013 by ASME
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Measurments of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter
Journal of Mech Behav Biomed Maetr, 2013Co-Authors: Yuan Feng, Ravi Namani, Guy M Genin, Ruth J Okamoto, Philip V BaylyAbstract:White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve Strain energy density functions that depend on the I 4 and 5 pseudo-invariants of the Cauchy–Green Strain Tensor to account for the effects of I relatively stiff fibers. The pseudo-invariant 4 is the square of the stretch ratio in the fiber I direction; I 5 contains contributions of shear Strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I 4 but not on 5. Here, we explore the small Strain I limits of these models in the context of experimental measurements that probe these dependencies. Models in which Strain energy depends on I 4 but not 5 can capture differences in Young’s I (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small Strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I 4 and 5 Strain pseudo- I invariants; and (2) behavior in the small Strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.
Giuseppe Saccomandi - One of the best experts on this subject based on the ideXlab platform.
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Quasistatic anti-plane motion in the simplest theory of nonlinear viscoelasticity
Nonlinear Analysis-real World Applications, 2008Co-Authors: Ramón Quintanilla, Giuseppe SaccomandiAbstract:Abstract We consider a very simple model in the framework of differential viscoelastic materials which are isotropic and incompressible. In this model the Cauchy stress Tensor is split in an elastic part and a dissipative part. The elastic part is derived from a Strain-energy density function only of the first invariant of the Cauchy–Green Strain Tensor. The dissipative part is like the Navier–Stokes equations: linear in the stretching Tensor with a constant viscosity parameter. For this model we provide some time and spatial estimates in the quasistatic approximations for the equations governing anti-plane shear motions. Several explicit examples for specific form of the Strain energy are produced. Our results impose analytical restrictions on the mathematical properties of the Strain energy to ensure a physical behavior in the creep and recovery experiments. Moreover, we show polynomial decay for the spatial behavior in the class of stress-hardening (or Strain-stiffening) materials. For stress-softening materials a Phragmen–Lindelof alternative is proved.
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Finite-amplitude inhomogeneous waves in Mooney–Rivlin viscoelastic solids
Wave Motion, 2004Co-Authors: Michel Destrade, Giuseppe SaccomandiAbstract:New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finite-amplitude, transverse, linearly polarized, inhomogeneous motions superposed upon a finite homogeneous static deformation. The viscoelastic body is composed of a Mooney–Rivlin viscoelastic solid, whose constitutive equation consists in the sum of an elastic part (Mooney–Rivlin hyperelastic model) and a viscous part (Newtonian viscous fluid model). The analysis shows that the results are similar to those obtained for the purely elastic case; inter alia, the normals to the planes of constant phase and to the planes of constant amplitude must be orthogonal and conjugate with respect to the B-ellipsoid, where B is the left Cauchy–Green Strain Tensor associated with the initial large static deformation. However, when the constitutive equation is specialized either to the case of a neo-Hookean viscoelastic solid or to the case of a Newtonian viscous fluid, a greater variety of solutions arises, with no counterpart in the purely elastic case. These solutions include travelling inhomogeneous finite-amplitude damped waves and standing damped waves. © 2004 Elsevier B.V. All rights reserved.
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A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity
Journal of Elasticity, 2002Co-Authors: Cornelius O. Horgan, Giuseppe SaccomandiAbstract:Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical Strain-hardening at large Strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The Strain-energy density in the Gent model depends only on the first invariant I1 of the Cauchy–Green Strain Tensor, is a simple logarithmic function of I1 and involves just two material parameters, the shear modulus μ and a parameter Jm which measures a limiting value for I1−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Pade approximant for this function. The constants μ and Jm in the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function.
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Finite Amplitude Transverse Waves in Special Incompressible Viscoelastic Solids
Journal of Elasticity, 2000Co-Authors: Michael Hayes, Giuseppe SaccomandiAbstract:We consider the propagation of finite amplitude plane transverse waves in a class of homogeneous isotropic incompressible viscoelastic solids. It is assumed that the Cauchy stress may be written as the sum of an elastic part and a dissipative viscoelastic part. The elastic part is of the form of the stress corresponding to a Mooney–Rivlin material, whereas the dissipative part is a linear combination of A1, A12 and A2, where A1, A2 are the first and second Rivlin–Ericksen Tensors. The body is first subject to a homogeneous static deformation. It is seen that two finite amplitude transverse plane waves may propagate in every direction in the deformed body. It is also seen that a finite amplitude circularly polarized wave may propagate along either n+ or n−, where n+, n− are the normals to the planes of the central circular section of the ellipsoid x⋅B−1x=1. Here B is the left Cauchy–Green Strain Tensor corresponding to the finite static homogeneous deformation.