From conservation of energy to the principle of least action: A story line

Hanč, Jozef; Taylor, Edwin F.

doi:10.1119/1.1645282

Cited by 28 publications

(23 citation statements)

References 10 publications

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“…During the filling phase, the formation of a vortex ring aids in preserving the kinetic energy of the incoming flow through fast rotating motion [33] and induces blood exchange to prevent flow stagnation [31]. As the vortex ring rotates around its center of mass while translating from the base to the apex, the total kinetic energy of the incoming blood flow is converted into rotational and translational energy [34]. The translational energy allows penetration of the vortex ring to the stagnant flow region at the apex, while blood mixing is enhanced by the rotational energy.…”

Section: Discussionmentioning

confidence: 99%

Sensitivity Analysis of Left Ventricle with Dilated Cardiomyopathy in Fluid Structure Simulation

et al. 2013

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Dilated cardiomyopathy (DCM) is the most common myocardial disease. It not only leads to systolic dysfunction but also diastolic deficiency. We sought to investigate the effect of idiopathic and ischemic DCM on the intraventricular fluid dynamics and myocardial wall mechanics using a 2D axisymmetrical fluid structure interaction model. In addition, we also studied the individual effect of parameters related to DCM, i.e. peak E-wave velocity, end systolic volume, wall compliance and sphericity index on several important fluid dynamics and myocardial wall mechanics variables during ventricular filling. Intraventricular fluid dynamics and myocardial wall deformation are significantly impaired under DCM conditions, being demonstrated by low vortex intensity, low flow propagation velocity, low intraventricular pressure difference (IVPD) and strain rates, and high-end diastolic pressure and wall stress. Our sensitivity analysis results showed that flow propagation velocity substantially decreases with an increase in wall stiffness, and is relatively independent of preload at low-peak E-wave velocity. Early IVPD is mainly affected by the rate of change of the early filling velocity and end systolic volume which changes the ventriculo:annular ratio. Regional strain rate, on the other hand, is significantly correlated with regional stiffness, and therefore forms a useful indicator for myocardial regional ischemia. The sensitivity analysis results enhance our understanding of the mechanisms leading to clinically observable changes in patients with DCM.

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Section: Discussionmentioning

confidence: 99%

Sensitivity Analysis of Left Ventricle with Dilated Cardiomyopathy in Fluid Structure Simulation

et al. 2013

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“…While rigorous justification of the variational view of the Lagrange multiplier only appeared in the 1970s, the basic idea can be traced back to early developments of the calculus of variations and is associated with the names of Euler, Hamilton, Lagrange, Legendre and many others (see [3][4][5]). Besides the explicit use of a Lagrange multiplier in calculus of variations problems involving isoperimetric or similar constraints, also very influential are the ideas of (i) imbedding an optimization problem in a related class of problems, of (ii) using optimal value functions and of (iii) decoupling.…”

Section: Introductionmentioning

confidence: 99%

“…Explicitly named only in the last century by Feynman and others, the principle states that the path taken in a mechanical system will be the one which is stationary with respect to the action (which of course must be specified)[3,5].…”

mentioning

confidence: 99%

A Variational Approach to Lagrange Multipliers

Borwein

Zhu

2015

J Optim Theory Appl

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“…[12][13][14][15] This literature was the foundation on which we built our instruction. Resources to support instruction are also available, 7,16 including assignments and computational laboratories in the supplemental material.…”

Section: 5mentioning

confidence: 99%

Action physics

McGinness

Savage

2016

American Journal of Physics

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More than a decade ago Edwin Taylor issued a "call to action" that presented the case for basing introductory university mechanics teaching around the principle of stationary action. 1 We report on our response to that call in the form of an investigation of the teaching and learning of the stationary action formulation of physics in a first-year university course. Our action physics instruction proceeded from the many-paths approach to quantum physics through to ray optics, classical mechanics, and relativity. Despite the challenges presented by action physics, students reported it to be accessible, interesting, motivational and valuable.

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From conservation of energy to the principle of least action: A story line

Cited by 28 publications

References 10 publications

Sensitivity Analysis of Left Ventricle with Dilated Cardiomyopathy in Fluid Structure Simulation

Sensitivity Analysis of Left Ventricle with Dilated Cardiomyopathy in Fluid Structure Simulation

A Variational Approach to Lagrange Multipliers

Action physics

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