Dynamics of a Bouncing Dimer

Dorbolo, Stéphane; Volfson, Dmitri; Tsimring, Lev S.; Kudrolli, Arshad

doi:10.1103/physrevlett.95.044101

Cited by 84 publications

(92 citation statements)

References 13 publications

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“…In this paper, the numerical simulation for the bouncing dimer is implemented by using the theory developed in part I. Comparisons between the numerical and experimental results presented in Dorbolo et al (2005) will be carried out to illustrate and validate the scheme.…”

Section: Introductionmentioning

confidence: 99%

“…In §2, we present a brief summary for the basic equations of the bouncing dimer. In terms of the dynamical equations of the bouncing dimer and the correlative coefficient defined for stick mode as well as the experimental findings in Dorbolo et al (2005), the static coefficient of friction between the dimer and the oscillated plate is estimated in §3. In §4, we present a qualitative analysis for the origins of the formation of the positive and negative drift motions in the bouncing dimer, in which the double impacts and the stick mode at contact points are found to play a significant role for the complex behaviour of the dimer.…”

Section: Introductionmentioning

confidence: 99%

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Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

2009

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The objective of this paper is to implement and test the theory presented in a companion paper for the non-smooth dynamics exhibited in a bouncing dimer. Our approach revolves around the use of rigid body dynamics theory combined with constraint equations from the Coulomb's frictional law and the complementarity condition to identify the contact status of each contacting point. A set of impulsive differential equations based on Darboux-Keller shock dynamics is established that can deal with the complex behaviours involved in multiple collisions, such as the frictional effects, the local dissipation of energy at each contact point, and the dispersion of energy among various contact points. The paper will revisit the experimental phenomena found in Dorbolo et al. (Dorbolo et al. 2005 Phys. Rev. Lett. 95, 044101), and then present a qualitative analysis based on the theory proposed in part I. The value of the static coefficient of friction between the plate and the dimer is successfully estimated, and found to be responsible for the formation of the drift motion of the bouncing dimer. Plenty of numerical simulations are carried out, and precise agreements are obtained by the comparisons with the experimental results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

2009

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“…We suggest experimental realizations and tests of the model. Directed motion without an imposed external gradient in a homogeneous, isotropic environment is seen not only in living systems [1] but also in agitated granular matter [2,3]. Can these apparently diverse systems be understood in a unified manner?…”

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confidence: 99%

Active elastic dimers: Self-propulsion and current reversal on a featureless track

2008

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We present a Brownian inchworm model of a self-propelled elastic dimer in the absence of an external potential. Nonequilibrium noise together with a stretch-dependent damping form the propulsion mechanism. Our model connects three key nonequilibrium features -position-velocity correlations, a nonzero mean internal force, and a drift velocity. Our analytical results, including striking current reversals, compare very well with numerical simulations. The model unifies the propulsion mechanisms of DNA helicases, polar rods on a vibrated surface, crawling keratocytes and Myosin VI. We suggest experimental realizations and tests of the model. While not losing sight of the application to particular organisms or devices, our focus is on the general principles governing propulsion by rectification of an unbiased input active noise in a homogeneous medium.In all the systems mentioned above, macroscopic directed motion of the center-of-mass (CM) arises via a coupling to internal coordinates, as a result of two crucial features -an asymmetrical environment for the internal coordinates and external energy input. Unlike in traditional "Brownian ratchet models" [8] of directed motion, the asymmetry of interest in the above systems is internal to the motile objects, and does not lie in an external periodic potential. Our approach is distinct from that of [9] where the external potential plays a central role, and also differs from the dynamical systems approach of [10]. The present model is similar in spirit to [11,12] but simpler, and differs in several important details as seen below. We find an unexpected range of possible behaviors, especially in the dependence of the motion on the details of the nonequilibrium noise.Our model self-propelled object is a dimer whose two heads are coupled by a spring, in a homogeneous, dissipative, noisy environment. The damping coefficients of the heads depend on the relative coordinate or strain. The noise on the particles is made of two parts -a thermal part whose strength is determined by a fluctuationdissipation relation with the strain-dependent damping, and a nonequilibrium or active part, with strength independent of the damping, which represents the external energy input.Our results are as follows: (i) The steady-state average of the CM velocity is in general nonzero and exhibits counter-intuitive reversals of direction as a function of the strengths and characteristics of the drive and the dampings. (ii) The steady state displays two other key nonequilibrium features: the mean internal force as well as the the equal-time correlation of the relative coordinate to the CM velocity are both nonzero. (iii) Active noise alone will not result in propulsion, even in the presence of an asymmetric internal potential; the straindependent damping is an essential ingredient. (iv) The preceding results, obtained by perturbative analytical solution of our model Langevin equations, with the coefficient of the stretch-dependent damping as a small parameter, are confirmed in detail by direct numerica...

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“…This work has been done in collaboration with experimental groups of Arshad Kudrolli (Clark University) and Igor Aranson (Argonne). This work has been published in [13,6,5,8].…”

Section: Modeling Of Anisotropic Granular Dynamicsmentioning

confidence: 99%

Modeling for Process Control: High-Dimensional Systems

Tsimring¹

2008

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Dynamics of a Bouncing Dimer

Cited by 84 publications

References 13 publications

Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

Active elastic dimers: Self-propulsion and current reversal on a featureless track

Modeling for Process Control: High-Dimensional Systems

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