Initial motion disks

The second notable feature of these evolution curves is the pronounced shoulder effect seen on short time scales, particularly for the case where the flow is initiated from a site farthest removed from the reaction center. The appearance of shoulders is related to the fact that, for a particle initiating its motion at a specific site somewhere in the lattice, there is a minimum time required for the coreactant to reach the reaction center this time is proportional to the length of the shortest path, and hence the reactive event cannot occur until (at least) that interval of time has expired. This effect is analogous to the one observed in computer simulations of Boltzmann s H function calculated for two-dimensional hard disks [27]. Starting with disks on lattice sites with an isotropic velocity distribution, there is a time lag (a horizontal shoulder) in the evolution of the system owing to the time required for the first collision between two hard particles to occur. 

How, you ask, does this result in oscillating deformation Well, the easiest way to see is to follow the motion of a point on the upper disk (point 2), relative to one on the lower disk (point 1) as the disks rotate. Here, we choose point 1 on the axis of rotation (center) of the lower disk and point 2 directly above it at the start of the analysis, cot = Q. This is the simplest choice, because point 1 remains stationary, but the same result will be obtained for any pair of points initially at the same values of x and y (you can prove this with a compass, ruler, and protractor). Figure 16.10a shows the relative displacement vector in the xy plane. 

A related effect for spiral waves inside small disks of excitable medium has been recently investigated [18]. The numerical simulations of a reaction-diffusion system showed that the dynamical regime with a spiral wave steadily rotating around the centre of the disk is unstable in small disks. A slight shift of the initial position of the spiral wave leads to the motion of the wave s core towards the boundary of the disk and then the spiral waves begins to migrate along this boundary at a certain distance from it. 

What therefore has allowed this quantity of oil to enter die contact It might be speculated that the rig dynamics causes a rapid reduction in load at start of motion. This would reduce the contact area and cause lubricant to be drawn into the gap between the surfaces. Rapid re-imposition of the load would entrap this lubricant and could lead to films thicker than the steady state value. If the load fell to zero, the quantity of oil enclosed by the contacting bodies within the radius a would be equivalent to a uniform film of 0.47 pm over the Hertzian area. This mechanism (of transient load reduction) could therefore quite easily provide means for a film of 0.16 pm to develop. However the simplest explanation is (hat die kinematic configuration is somehow different to that measured. The disk used in the experiments is itself clamped to ensure it remains at rest [13]. Friction in the dry contact may be sufficient to cause stick between the surfaces initially, which gives way suddenly when sufficient torque is developed. This could result in an initial overspeed of the ball when motion commences and subsequent damped torsional vibration. This mechanism has, however, been considered and discounted by Glovnea and Spikes [1]. For such a speed variation mechanism to explain the variation in he shown in Figure 2 for the 50 m/s case, the ball velocity corresponding to the first peak would need to be 0.7 m/s compared to its final stearfy state value of 0.4 m/s. 

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