Optimal Motion of a Scallop: Some Case Studies

Maggistro, Rosario; Zoppello, Marta

doi:10.1109/lcsys.2019.2919751

Cited by 7 publications

(4 citation statements)

References 23 publications

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“…In consequence, the slow motion caused by a relatively small but long-lasting force is more effective than the fast one. The effect is similar to the slow-open, fast-close actuation mechanism of the scallop motion, the molecular motors-driven internal sliding of polymeric filaments in singly flagellated eukaryotes [57,58]; however, instead of the inertia or viscous effects being the cause of scallop or eukaryote motion, the motion of the analyzed copolymer is due to its energetic asymmetry. The forces exerted by part P2 on P1 of the chain computed as partial derivatives of the free Helmholtz energy (Figure 17) and averaged for positions of the chain mass center are collected in Figure 19.…”

Section: Mechanism Of Unidirectional Motionmentioning

confidence: 66%

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

Nowicki

2020

Polymers

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The structure and dynamic properties of polymer chains in a confined environment were studied by means of the Monte Carlo method. The studied chains were represented by coarse-grained models and embedded into a simple 3D cubic lattice. The chains stood for two-block linear copolymers of different energy of bead–bead interactions. Their behavior was studied in a nanotube formed by four impenetrable surfaces. The long-time unidirectional motion of the chain in the tight nanopore was found to be correlated with the orientation of both parts of the copolymer along the length of the nanopore. A possible mechanism of the anomalous diffusion was proposed on the basis of thermodynamics of the system, more precisely on the free energy barrier of the swapping of positions of both parts of the chain and the impulse of temporary forces induced by variation of the chain conformation. The mean bead and the mass center autocorrelation functions were examined. While the former function behaves classically, the latter indicates the period of time of superdiffusive motion similar to the ballistic motion with the autocorrelation function scaling with the exponent t5/3. A distribution of periods of time of chain diffusion between swapping events was found and discussed. The influence of the nanotube width and the chain length on the polymer diffusivity was studied.

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Section: Mechanism Of Unidirectional Motionmentioning

confidence: 66%

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

Nowicki

2020

Polymers

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“…The minimal time optimal control problem seeks the optimal solution to move from a given configuration to another given one in the shortest possible time, whereas optimisation of the power expended deals with minimising the power expended to achieve the motion (this is useful in view in presence of limited amount of resources). Similar optimal control problems have been tackled in [7,9,19] for the power expended of a filament moving on a plane, for the minimal time of a planar Purcell swimmer, and for the minimal time ad quadratic cost for a scallop subject to a switching dynamics, respectively.…”

Section: Introductionmentioning

confidence: 99%

The $N$-link swimmer in three dimensions: controllability and optimality results

Roberto¹,

Morandotti²,

Shum³

et al. 2019

Preprint

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The controllability of a fully three-dimensional N -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2 -link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2 -link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all six linearly independent directions in the configuration space; every direction and orientation can be achieved by operating on the two shape variables. The result is subsequently extended to the N -link swimmer. Finally, the minimal time optimal control problem and the minimisation of the power expended are addressed and a qualitative description of the optimal strategies is provided.

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“…The minimal time optimal control problem seeks the optimal solution to move from a given configuration to another given one in the shortest possible time, whereas optimization of the power expended deals with minimizing the power expended to achieve the motion (this is useful in consideration of a limited amount of resources). Similar optimal control problems have been tackled in [ 9 , 13 , 17 , 30 , 32 ] for the power expended of a filament moving on a plane, for the minimal time of a planar Purcell swimmer, and for the minimal time ad quadratic cost for a scallop subject to a switching dynamics, respectively.…”

Section: Introductionmentioning

confidence: 99%

The $N$-Link Swimmer in Three Dimensions: Controllability and Optimality Results

et al. 2022

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The controllability of a fully three-dimensional $N$ N -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the $N$ N -link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided.

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Optimal Motion of a Scallop: Some Case Studies

Cited by 7 publications

References 23 publications

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

The Longitudinal Superdiffusive Motion of Block Copolymer in a Tight Nanopore

The $N$-link swimmer in three dimensions: controllability and optimality results

The $N$-Link Swimmer in Three Dimensions: Controllability and Optimality Results

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