On stochastic non-holonomic systems

Moshchuk, N.K.; Sinitsyn, I. N.

doi:10.1016/0021-8928(90)90030-e

Cited by 3 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

mentioning

confidence: 99%

“…Collectively, rolling particles have different phase behaviours than those that slide [27]. Yet despite their intriguing dynamics, rolling has been considered in stochastic settings only for simple systems such as a rolling ball or sled [28][29][30], or as a noisy relaxation of the rolling constraint itself [31]. This paper studies a natural model of stochastic, rolling particles, with the aim of determining how rolling could affect quantities that are macroscopically measurable.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Stochastic disks that roll

Holmes-Cerfon

2016

Phys. Rev. E

View full text Add to dashboard Cite

We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano-or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible non-trivial system: a linear polymer of three of discs constrained to remain in contact, and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the discs can slide relative to each other, and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or subRiemannian manifold, depending on if the velocity constraints are holonomic or non-holonomic. We use this to compute the trimer's equilibrium distribution both with, and without, the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.Particles that live on the nano-or microscale commonly have short-ranged interactions, so their surfaces come close enough that surface frictional effects may be important. For example, recent experiments and simulations have shown that tangential frictional forces between rough, and otherwise stochastic particles, are probably the origin of the shear-thickening behaviour of many materials [1,2]. Other studies demonstrate that sticky tethers attached to particle surfaces can change their dynamics [3,4]. Since one promising method of creating colloids with programmable interactions is to coat them with strands of DNA [5][6][7][8], which could impede their relative sliding, this could have major implications for their assembly pathways and hence structures that can be formed by selfassembly. On these scales it is extremely difficult to measure the particles' rotational degrees of freedom, so one must resort to indirect methods to determine whether tangential frictional forces are present [9,10]. Therefore, it would be highly desirable to find a simpler way to quantify these forces, via macroscopic measurements of spatial positions only.While the mascroscopic effect of dry friction has been studied in detail i...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Stochastic disks that roll

Holmes-Cerfon

2016

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Equivalently, the ball sits on a table which undergoes a translational Brownian motion. Compare [19]. Alternatively, we can set (F 1 , .…”

Section: C Constrained Brownian Motion and Compressionmentioning

confidence: 99%

“…The latter corresponds to the Chaplygin ball sitting on a table which undergoes a translational Brownian motion. The 3-dimensional version of this case has been considered in [19].…”

Section: Introductionmentioning

confidence: 99%