A hydrodynamic model of an outer hair cell

On the model it is possible to measure the force and the force direction for each individual hair as a function of the flow direction and velocity. Measurements were made at the man flow velocity .01 m/s, which is equivalent to a flow velocity in the real ear of about 1 micrometer/s. The kinematic viscosity of the liquid used in the model was 10,000 times higher than the viscosity of perilymph to attain hydrodynamic equality. Two different geometries for the sterocilia pattern were tested. First the force distribution for a W-shaped sterocilia pattern was recorded. This is the sterocilia pattern found in all real ears. It is found that the forces acting on the hairs are very regular and perpendicular to the legs of the W when the flow is directed from the outside of the W. When the flow is reversed, the forces are not reversed, but are much more irregular. This can eventually explain the half wave rectification of the nerve signals. As a second experiment, the force distribution for a V-shaped sterocilia pattern was recorded. Here the forces were irregular both when the flow was directed into the V and when it was directed against the edge of the V

Non-Newtonian Fluid Model Incorporated into Elastohydrodynamic Lubrication of Rectangular Contacts

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction

High-speed motion picture camera experiments of cavitation in dynamically loaded journal bearings

A high-speed camera was used to investigate cavitation in dynamically loaded journal bearings. The length-diameter ratio of the bearing, the speeds of the shaft and bearing, the surface material of the shaft, and the static and dynamic eccentricity of the bearing were varied. The results reveal not only the appearance of gas cavitation, but also the development of previously unsuspected vapor cavitation. It was found that gas cavitation increases with time until, after many hundreds of pressure cycles, there is a constant amount of gas kept in the cavitation zone of the bearing. The gas can have pressures of many times the atmospheric pressure. Vapor cavitation bubbles, on the other hand, collapse at pressures lower than the atmospheric pressure and cannot be transported through a high-pressure zone, nor does the amount of vapor cavitation in a bearing increase with time. Analysis is given to support the experimental findings for both gas and vapor cavitation

Elastohydrodynamic lubrication of rectangular contacts

An isothermal elastohydrodynamically lubricated rectangular contact was evaluated numerically. This required the simultaneous solution of the elasticity and Reynolds equations. In the elasticity analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure was applied over each area. The elastohydrodynamic lubrication theory thus developed was used to investigate the influence of the dimensionless speed, load, and materials parameters on minimum film thickness. Ten cases were used in obtaining the minimum film thickness formula. Plots are shown that indicate the details of the pressure distribution, film shape, and flow. The characteristic pressure spike is clearly in evidence as is the parallel film shape through the central portion of the contact, with a minimum film thickness occurring near the outlet of the contact

Vapor Cavitation in Dynamically Loaded Journal Bearings

High speed motion camera experiments were performed on dynamically loaded journal bearings. The length to diameter ratio of the bearing, the speed of the roller and the tube, the surface material of the roller, and the static and dynamic eccentricity of the bearing were varied. One hundred and thirty-four cases were filmed. The occurrence of vapor cavitation was clearly evident in the films and figures presented. Vapor cavitation was found to occur when the tensile stress applied to the oil exceeded the tensile strength of the oil or the binding of the oil to the surface. The physical situation in which vapor cavitation occurs is during the squeezing and sliding motion within a bearing. Besides being able to accurately capture the vapor cavitation on film, an analysis of the formation and collapse of the cavitation bubbles and characteristics of the bubble content are presented

A model for the influence of pressure on the bulk modulus and the influence of temperature on the solidification pressure for liquid lubricants

Two pressure chambers, for compression experiments with liquids from zero to 2.2 GPa pressure, are described. The experimentally measured compressions are then compared to theoretical values given by an isothermal model of equation of state recently introduced for solids. The model describes the pressure and bulk modulus as a function of compression for different types of lubricants with a very high accuracy up to the pressure limit of the high pressure chamber used (2.2 GPa). In addition the influence of temperature on static solidification pressure was found to be a simple function of the thermal expansion of the fluid

The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores

The basic structure of the solar system is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot explain this dichotomy, even if the original surface density of solids increased at the snowline. Instead, the accretion of drifting pebbles by embryos and cores can explain the dichotomy, provided that some assumptions hold true. We propose that the mass-flow of pebbles is two-times lower and the characteristic size of the pebbles is approximately ten times smaller within the snowline than beyond the snowline (respectively at heliocentric distance $r<r_{ice}$ and $r>r_{ice}$, where $r_{ice}$ is the snowline heliocentric distance), due to ice sublimation and the splitting of icy pebbles into a collection of chondrule-size silicate grains. In this case, objects of original sub-lunar mass would grow at drastically different rates in the two regions of the disk. Within the snowline these bodies would reach approximately the mass of Mars while beyond the snowline they would grow to $\sim 20$ Earth masses. The results may change quantitatively with changes to the assumed parameters, but the establishment of a clear dichotomy in the mass distribution of protoplanets appears robust, provided that there is enough turbulence in the disk to prevent the sedimentation of the silicate grains into a very thin layer.Comment: In press in Icaru

Control of nonlinear systems in regions of state space

Control of nonlinear systems in regions of state spac

A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer

Discrete time differential dynamic programming algorithm with application to optimal orbit transfe

Boundary layer stability on a yawed spinning body of revolution and its effect on the magnus force and moment

The parameters are established which are important to the stability of a boundary layer flow over a yawed spinning cylinder in a uniform stream. It is shown that transition occurs asymmetrically in general and this asymmetry can be important for the prediction of aerodynamic forces and moments (e.g., the Magnus effect). Instability of the steady-state boundary layer flow is determined using small disturbance theory. Although the approach is strictly valid only for the calculation of the conditions for stability in the small, experimental data indicate that in many problems, it provides a good estimate for the transition to turbulence