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Register a new userTranslational-Rotational Coupling during the Scattering of a Frictional Sphere from a Flat Surface
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At a macroscopic level, concepts such as top spin, back spin and rolling are commonly used to describe the collision of balls and surfaces. Each term refers to an aspect of the coupling of rotational motion during the collision of a spherical particle with a planar surface. In this paper we explore the mechanisms of energy transfer involving the collision of a rotating sphere and a surface using a model of frictional interactions developed for granular material. We present explicit analytical treatments for the scattering and derive expressions for two important limiting classes: energy conserving collisions and collisions subject to rapid transverse dissipation.
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We consider a measurement of the position of a spot painted on the surface of a trapped nano-optomechanical sphere. The measurement extracts information about the position of the spot and in doing so measures a combination of the orientation and position of the sphere. The quantum back-action of the measurement entangles and correlates these two degrees of freedom. Such a measurement is not available for atoms or ions, and provides a mechanism to probe the quantum mechanical properties of trapped optomechanical spheres. In performing simulations of this measurement process we also test a numerical method introduced recently by Rouchon and collaborators for solving stochastic master equations. This method guarantees the positivity of the density matrix when the Lindblad operators for all simultaneous continuous measurements are mutually commuting. We show that it is both simpler and far more efficient than previous methods.
We present particulate simulation results for translational and rotational friction components of a shish-kebab model of a colloidal rod with aspect ratio (length over diameter) $L/D = 10$ in the presence of a planar hard wall. Hydrodynamic interactions between rod and wall cause an overall enhancement of the friction tensor components. We find that the friction enhancements to reasonable approximation scale inversely linear with the closest distance $d$ between the rod surface and the wall, for $d$ in the range between $D/8$ and $L$. The dependence of the wall-induced friction on the angle $theta$ between the long axis of the rod and the normal to the wall is studied and fitted with simple polynomials in $cos theta$.
Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.
The effects of particle shape on the vibrational properties of colloidal glasses are studied experimentally. Ellipsoidal glasses are created by stretching polystyrene spheres to different aspect ratios and then suspending the resulting ellipsoidal particles in water at high packing fraction. By measuring displacement correlations between particles, we extract vibrational properties of the corresponding shadow ellipsoidal glass with the same geometric configuration and interactions as the source suspension but without damping. Low frequency modes in glasses composed of ellipsoidal particles with major/minor axis aspect ratios $sim$1.1 are observed to have predominantly rotational character. By contrast, low frequency modes in glasses of ellipsoidal particles with larger aspect ratios ($sim$3.0) exhibit a mix of rotational and translational character. All glass samples were characterized by a distribution of particles with different aspect ratios. Interestingly, even within the same sample it was found that small-aspect-ratio particles participate relatively more in rotational modes, while large-aspect-ratio particles tend to participate relatively more in translational modes.
This paper addresses the issue of the determination of the frictional stress distribution from the inversion of the measured surface displacement field for sliding interfaces between a glass lens and a rubber (poly(dimethylsiloxane)) substrate. Experimental results show that high lateral strains are achieved at the periphery of the sliding contacts. As a consequence, an accurate inversion of the displacement field requires that finite strains and non linear response of the rubber substrate are taken into account. For that purpose, a Finite Element (FE) inversion procedure is implemented where the measured displacement field is applied as a boundary condition at the upper surface of a meshed body representing the rubber substrate. Normal pressure is also determined by the same way, if non-diverging values are assumed at the contact edge. This procedure is applied to linearly sliding contacts as well as on twisting contacts.
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