The biomechanics of skin and underlying tissues plays a fundamental role in the human sense of touch. It governs the mechanics of contact between the skin and an object, the transmission of the mechanical signals through the skin, and their transduction into neural signals by the mechanoreceptors. To better understand the mechanics of touch, it is necessary to establish quantitative relationships between the loads imposed on the skin by an object, the state of stresses/strains at mechanoreceptor locations, and the resulting neural response. Towards this goal, 3-D finite-element models of human and monkey fingertips with realistic external geometries were developed. By computing fingertip model deformations under line loads, it was shown that a multi-layered model was necessary to match previously obtained in vivo data on skin surface displacements. An optimal ratio of elastic moduli of the layers was determined through numerical experiments whose results were matched with empirical data. Numerical values of the elastic moduli of the skin layers were obtained by matching computed results with empirically determined force-displacement relationships for a variety of indentors. Finally, as an example of the relevance of the model to the study of tactile neural response, the multilayered 3-D finite-element model was shown to be able to predict the responses of the slowly adapting type I (SA-I) mechanoreceptors to indentations by complex object shapes.

Tactile information about an object in contact with the skin surface is contained in the spatio-temporal load distribution on the skin, the corresponding stresses and strains at mechanosensitive receptor locations within the skin, and the associated pattern of electrical impulses produced by the receptor population. At present, although the responses of the receptors to known stimuli can be recorded, no experimental techniques exist to observe either the load distribution on the skin or the corresponding stress-state at the receptor locations. In this paper, the role of mechanics in the neural coding of tactile information is investigated using simple models of the primate fingertip. Four models that range in geometry from a semi-infinite medium to a cylindrical finger with a rigid bone, and composed of linear elastic media, are analyzed under plane strain conditions using the finite element method. The results show that the model geometry has a significant influence on the surface load distribution as well as the subsurface stress and strain fields for a given mechanical stimulus. The elastic medium acts like a spatial low pass filter with the property that deeper the receptor location, the more blurred the tactile information. None of the models predicted the experimentally observed surface deflection profiles under line loads as closely as a simple heterogeneous waterbed model that treated the fingerpad as a membrane enclosing an incompressible fluid (Srinivasan, 1989). This waterbed model, however, predicted a uniform state of stress inside the fingertip and thus failed to explain the spatial variations observed in the neural response. For the cylindrical model indented by rectangular gratings, the maximum compressive strain and strain energy density at typical receptor locations emerged as the two strain measures that were directly related to the electrophysiologically recorded response rate of slowly adapting type I (SAI) mechanoreceptors. Strain energy density is a better candidate to be the relevant stimulus for SAIs, since it is a scalar that is invariant with respect to receptor orientations and is a direct measure of the distortion of the receptor caused by the loads imposed on the skin.

Turbulent flame-speed data for premixed flames of methane-air, propane-air, and ethylene-air mixtures stabilized in grid turbulence are reported and discussed. It is shown that turbulence effects on flame speed cannot be correlated fully by the turbulence length scale and rms velocity in the cold flow. Rather there appear to be significant flame-flow turbulence interactions affecting both turbulence level in the reaction zone and measured flame speeds. Results of detailed velocity measurements, including autocorrelations, by laser velocimetry are used to elucidate the nature of these interactions. It is concluded that flame-speed experiments must be designed and conducted to provide sufficient information (e.g., boundary conditions) to allow for reconstruction of the flowfield and these interactions by modelers if the data are to be of value in turbulent combustion model development and evaluation. Nomenclature ? = integral scale of turbulence P = pressure R ( = turbulence Reynolds number, uV/v R x = microscale turbulence Reynolds number, u\/v S L = laminar flame speed S T = turbulent flame speed u = rms velocity, = vw 77 u" = U-U U = instantaneous velocity U = Favre average velocity U = Reynolds average velocity e = Favre average energy dissipation rate X =Tay lor's microscale p = gas density p(r) = autocorrelation coefficient, =

Results of density measurements by Rayleigh scattering from an unconfined, V-shaped, methane-air flame stabilized in grid turbulence are reported and discussed. Data for mean and root-mean-square (rms) density, power spectra, and for probability density functions (pdf's) are presented along with velocity data obtained by laser velocimetry and hot-wire anemometry. Profiles of mean density and rms fluctautions show that the flame thickens with distance from the flame stabilizer but there is no significant change in rms fluctuation magnitude with distance. The pdf's are biniodal but cannot be represented adequately by two delta functions. Normalized spectra do not vary significantly across the flame and exhibit similarities to velocity spectra in the reactant flow.

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