Pressure-volume dependence for the eyeball under an external load

The knowledge for the individual eye of the dependence of the intraocular volume on the intraocular pressure in the presence of a given external load is necessary for obtaining physically correct conclusions from the data of standard measurement procedures used in ophthalmology (tonometry, elastometry, tonography). On the basis of general physical principles, using dimensional theory, restrictions on possible forms of this dependence are formulated on the assumption of elastic behavior of the eye shell and elastic nature of its interaction with surrounding objects. Possible applications of the restrictions obtained to experimental and theoretical investigations are discussed.     

Investigation of the pressure-volume relationship for the eyeball loaded by a thin rod

The static problem of loading the eyeball by a thin cylindrical cornea-deforming rod is solved for obtaining data on the mechanical properties of the eye in clinical examination. The analysis is carried out within the framework of a simple model which treats the cornea as a soft shell and takes into account the elastic properties of the sclera and tissues surrounding it by introducing an elastic constraint between the intraocular pressure and the scleral part of the intraocular volume. The dependence of the intraocular volume on the pressure and the load applied, as well as on the elastic characteristics of the system, is investigated. The problem of relationship between the intraocular pressure and the load at a constant volume is considered. It is shown that loading the same eye by thin rods and flat stamps of different weights makes it possible to find in clinical examination the individual elastic characteristics of the eyeball and the pressure in the unloaded eye.     

In-line measurement of rheological properties of polymer melts

Shear viscosity (), first normal stress difference (N ₁), and extensional viscosity ( _E ) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure , N ₁, and the planar extensional viscosity ( _p ) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure and the uniaxial extensional viscosity ( _u ) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N ₁, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate _E .The hole pressure method was considered better than the exit pressure method to estimate N ₁ (due to the greater susceptibility of the latter to experimental errors). From the hole pressure method N ₁ was obtained from 100 kPa to 500 kPa over a range of shear rates from 40 s^–1 to 700 s^–1. Among the analyses used to estimate the extensional viscosity, Cogswell's is recommended due to its simpler equations without loss of much information compared to the other analyses. The range of extension rates achieved was 1 to 30 s^–1. The combination of the hole pressure and entrance pressure drop methods in a slit rheometer is a feasible design for a process rheometer, allowing the simultaneous measurement of the shear viscosity, first normal stress difference and planar extensional viscosity under processing conditions. Similarly, combining the entrance pressure drop measurements with a tube rheometer is also feasible and convenient.     

Mathematical modeling of Maklakoff’s method for measuring the intraocular pressure

The physical content of Maklakoffs tonometric (based on the loading of the cornea) method of measuring the intraocular pressure, widely used in medical practice, is discussed. For this purpose, we employ both the results of physical modeling of the eye described in the literature and the results of our own mathematical modeling based on the representation of the eyeball as a thin shell. The effect of the physical properties of the shell on the results of the modeling is investigated. Qualitative conclusions that follow from our study and may be of practical interest in measuring the intraocular pressure are discussed.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 24–39. Original Russian Text Copyright © 2005 by Bauer, Lyubimov, and Tovstik.     

All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence

As a type of shock-capturing scheme, the traditional Roe scheme fails in large eddy simulation (LES) because it cannot reproduce important turbulent characteristics, such as the famous k^?5/3 spectral law, as a consequence of the large numerical dissipation. In this work, the Roe scheme is divided into five parts, namely, ξ, δU_p, δp_p, δU_u, and δp_u, which denote basic upwind dissipation, pressure difference-driven modification of interface fluxes, pressure difference-driven modification of pressure, velocity difference-driven modification of interface fluxes, and velocity difference-driven modification of pressure, respectively. Then, the role of each part in the LES of homogeneous decaying turbulence with a low Mach number is investigated. Results show that the parts δU_u, δp_p, and δU_p have little effect on LES. Such minimal effect is integral to computational stability, especially for δU_p. The large numerical dissipation is due to ξ and δp_u, each of which features a larger dissipation than the sub-grid scale model. On the basis of these conditions, an improved all-speed Roe scheme for LES is proposed. This scheme can provide satisfactory LES results even for coarse grid resolutions with usually adopted second-order reconstructions for the finite volume method.     

Lower critical pressure for dynamic stability of a spherical shell

Dynamic stability of a thin spherical shell is investigated analytically under a uniform normal pressure.The purpose of this paper is to present a dynamic stability criterion which together with the energy method result and the numerical integration of the asymptotic nonlinear shell equations permit to find a closed form analytic expression for the lower critical pressure.The dynamic stability criterion states that the change in kinetic energy is equal to the work of all the forces between the initial and the buckled position after the dynamic stage of buckling.The solution of this nonlinear problem can be interpreted as the trajectory of a material point moving in a nonconservative force field.The resulting lower critical pressure curve lies along all the lowest known experimental data. It determines the boundary for the absolute dynamic stability and can be very useful for the practical shell design to prevent buckling.Nomenclature A constant value 2.2 - dA _s elemental area of the surface of the shell - a, b constants of integration - C elasticity modulus of elastic foundation - C ₁, C ₂, C ₃ constants of integration - D Eh ³/12(1– ²), stiffness of the shell - e base of natural logarithms - E modulus of elasticity - F force vector - F _x , F _y components of the force vector in the x, y directions - h thickness of the shell - H height of a segment of a shell - In *³ A - i imaginary number - I moment of inertia of a beam - K _s , K changes of curvature in the s, and directions - M bending moment in a beam - M _s ,M shell moment resultants - N _s ,N ,N _s shell membrane resultants - N _s ⁰ initial value of the membrane force in the meridional direction - P external uniform normal pressure - p _cl classical value of critical pressure (obtained by Von Kármán from the linear analysis of the shell) - Q shell transverse shear resultant - R initial radius of curvature of the middle surface - r distance from the point on the shell to the axis of symmetry of the shell - S ₀ ⁴ =DR ²/Eh characteristic length of the shell - s distance measured along the meridian of the shell - t= – ^* distance measured from the transition zone - new variables to study the behavior of the shell in the vicinity of x=1 - V velocity vector - Vol total change of volume of the shell - relative change of the curvature in the direction - non-dimensional membrane force - Z=u _x +iu _y complex variable - w deflection of the beam - dW _b bending energy per unit surface of the shell - W _b change of bending energy of the shell - W _c energy of initial uniform compression of the shell - dW _m membrane energy per unit surface of the shell - W _m change of membrane energy - W _p total work done by the external pressure - W _T total work of the buckled shell - _s , membrane deformations - initial angle of the shell - angle of the deformed shell - Poisson's ratio Part of this research was carried out at Princeton University.     

On the number of droplets in aerosols

The number of droplets which may be formed with a supersaturated vapor in presence of a gas cannot exceed a number proportional to (p_v−p_v0)⁴ where p_v and p_v0 denote at the same temperature the pressure of the supersaturated vapor–gas mixture and the pressure of the saturated vapor–gas mixture. The energy necessary to the droplet formation is also bounded by a number proportional to (p_v−p_v0)².     

The wake flow control behind a circular cylinder using ion wind

Active and passive flow control methods have been studied for decades, but there have been only a few studies of flow control methods using ion wind, which is the bulk motion of neutral molecules driven by locally ionized air from a corona discharge. This paper describes an experimental study of ion wind wake control behind a circular cylinder. The experimental conditions consisted of a range of electrohydrodynamic numbers—the ratio of an electrical body force to a fluid inertial force—from 0 to 2 and a range of Reynolds numbers from 4×10³ to 8×10³. Pressure distributions over the cylinder surface were measured and flow visualizations were carried out using a smoke-wire method. The flow visualizations confirmed that ion wind significantly affects the wake structure behind a circular cylinder, and that the pressure drag can be dramatically reduced by superimposing ion wind.List of symbols BR blockage ratio - C _d coefficient of the pressure drag - C _p coefficient of the surface pressure, 2(p–p ₀)/(U ₀ ²) - C _pb coefficient of the base surface pressure, 2(p _b–p ₀)/(U ₀ ²) - D diameter of the cylinder - D _P pressure drag - d _p diameter of particle - E the electric field - F _e Coulombian force (qE) - F _v viscous force - H wire-to-cylinder spacing - I total electric current (A) - L the axial length of cylinder (m) - N _EHD electrohydrodynamic number - p _b base pressure of cylinder at =180° - p ₀ reference static pressure at 10D upstream - q the charge on the particle - R radius of the cylinder - V applied voltage (kV) - U ₀ mean flow velocity (m/s) - ion mobility in air (m²/(s V)) - ₀ permittivity of free space - viscosity of fluid (kg/ms) - density of fluid (kg/m³) - installation angle of a wire electrode (°)     

On the use of neural networks for identification of linear and nonlinear systems

A procedure based on neural networks for the classification of linear and nonlinear systems is presented, using excitation and response data under swept sine excitation. Special attention is paid to the classification and identification of linear and bilinear systems, the latter being considered since they exhibit typical characteristics of cracked systems. The computer simulations show that: (1) using the procedure presented in this paper the trained classification network can reliably classify a linear system and different nonlinear systems; (2) the output of the trained identification neural network for a linear system and a bilinear system can be used as a quantitative indicator of characteristics of bilinear systems having different stiffness ratios (k _(x>0)/k _(x<0)) with respect to the bilinear system used in the training stage; (3) for two-degree-of-freedom systems, the trained network can not only determine the existence of a bilinear stiffness and the magnitude of its stiffness ratio, but also specify which stiffness is bilinear, i.e. indicate its position. These results provide a possibility of using the trained neural networks to detect and locate structural cracks which have the characteristics of bilinear systems.Visiting scholar, from People's Republic of China.     

A method for determining the frictional velocity in a turbulent channel flow with roughness on the bottom wall

A method is proposed for determining the frictional velocity U on both walls of a fully developed turbulent channel flow, one smooth and the other rough. This should aid experimentalists in obtaining a reliable estimate of U with knowledge of only the pressure drop and location where the Reynolds shear stress is zero. The method is general and does not depend on the roughness geometry that is used. It has been validated against direct estimates of the wall stress using DNS databases for two types of two-dimensional roughness. Results for a surface composed of staggered cubes are also in accord with the method.     

Note on the cancellation of contaminating noise in the measurement of turbulent wall pressure fluctuations

A method is presented for the cancellation of wide band contaminating noise occurring within internal flow configurations such as rectangular channels and pipes. Facility generated noise within these flow systems contaminates the turbulent wall pressure signature at low frequencies thus preventing the possible extraction of useful information. The proposed methodology utilizes the signals from two flush mounted wall pressure transducers. A first estimate for the one-point spectral density is obtained using a least mean square algorithm. A secondary correction to this estimate is obtained by taking advantage of the planar homogeneity of the turbulence. The application of the technique is demonstrated in a fully developed turbulent channel flow for which a more than 40 dB cancellation is obtained at low frequencies. In this low frequency range, the power spectral density is shown to have an approximate quadratic dependence, substantiating past theoretical predictions reported in the literature.List of symbols d transducer diameter - d ⁺ non-dimensional transducer diameter, - f frequency (Hz) - h channel half-height - l spanwise separation of transducers - p _N (t) signal due to contaminating noise - p _q (t) system output signal - p _R (t) turbulent wall pressure signal at reference transducer - p ₁(t) turbulent wall pressure signal at primary transducer - R _h channel Reynolds number, - s _R (t) pressure signal from reference transducer - s ₁ (t) pressure signal from primary transducer - t time - U channel centerline velocity, (maximum velocity) - u ^* shear velocity, - W(f) optimized filter function used for cancellation (Fourier transform) - correction factor, (noise to signal ratio) - ² coherence function - _z lateral turbulence macro-scale - _N correlation length scale of contaminating noise - v kinematic viscosity - fluid density - _wall wall shear stress - _pN (f) auto spectral density of p _N (t) - _pR (f) auto spectral density of p _R (t) - ₁ p auto spectral density of p ₁(t) - _sR (f) auto spectral density of s _R (t) - ₁ s(f) auto spectral density of s ₁(t) - _1ssr cross spectral density of s ₁ (t) with s _R (t)     

On the difficulties and remedies in enforcing the div = 0 condition in the finite element analysis of thermal plumes with strongly temperature-dependent viscosity

A finite element (FE) analysis of experimentally observed creeping thermal plumes in a medium whose viscosity is strongly temperature-dependent is performed. Such plumes are considered to play an important role in numerous geological processes and numerical modelling is often the only option to study their physics. Initial simulations by means of the general-purpose Galerkin finite element package NACHOS-II demonstrated serious deficiencies of the method in modelling plumes with large viscosity contrasts, in spite of several options for the solution (mixed or penalty formulation) and the elements (continuous or discontinous pressure). In agreement with observations from FE simulations of isothermal Stokes flow in other studies, we have isolated the violation of the div = 0 or incompressibility constraint as the major culprit in the failure of the FE method. It is demonstrated that the a posteriori computed discrete divergence (DDIV) can be used as a diagnostic tool to evaluate the reliability of the FE solution and to rank the solution and element options provided in the NACHOS code. On the basis of these considerations, the combination of the mixed method with a Q₂-P₁ (discontinuous pressure) element turns out to be the most suitable for the present plume problem but is still unable to sufficiently enforce the div = 0 condition. With a goal to remedy this detrimental behaviour, several FE modifications and new approaches have been taken. These include: (i) use of a new scaling option for the governing equations which has the effect of equilbrating the stiffness matrices and thus improving their condition; (ii) implementation of several iterative solution techniques such as the iterated penalty and the Uzawa algorithm for the augmented Langrangian to better accommodate the dual role of the pressure; (iii) use of a multistep Newton method to better handle the high non-linearity of the coupled flow/transport problem. Although each of these options (or a combination of them) is able to improve on the quality of FE solution, the most startling amelioration has been gained with option (iii). Use of the latter resulted in very satisfactory modelling of the experimentally observed plumes.     

On the viscosity-temperature behavior of polymer melts

Based on the free volume concept and the equation by Doolittle, an empirical equation is offered for the flow activation energy, E ^*, for polymer melts for the range of over 150°C above glass transition temperature, T _g. This E ^* represents the temperature coefficient of viscosity for the Newtonian region which is also equal to the value measured at constant shear stress for non-Newtonian flow. Data show that the E ^* of linear polymers approaches a constant value for a temperature range above T _g+150°C. Data on 17 polymers are correlated. The proposed equation for this region predicts the E ^* of polymer melts from the volume expansion coefficient, _l, above T _g and also from the T _g.Correlations have also been developed between E ^* and _l and between E ^* and T _g by simplifying the equation by use of the Simha-Boyer expression. A polymer having a lower _l or higher T _g generally has a higher E ^*. However, more satisfactory results are obtained by calculating E ^* from both _l and T _g. The E ^* calculated is found to agree with measurements within the experimental precision of about ±1 Kcal/mole.The effects of polymer composition, molecular weight, branching and microstructure on E ^* are also discussed. These factors influence E ^* in the way in which they effect _l and T _g.     

饱和两相介质动力固结问题时域求解的精细时程积分方法

针对u-p形式的饱和两相介质波动方程,采用精细时程积分方法计算固相位移u,采用向后差分算法求解流体压力p,建立了饱和两相介质动力固结问题时域求解的精细时程积分方法。针对标准算例,对该方法的计算精度进行了校核。开展了该方法相关算法特性的研究,对采用不同数值积分方法计算非齐次波动方程特解项计算精度的差异进行了对比研究,并对采用不同积分点数目的高斯积分法计算特解项条件下计算精度的差异进行了对比研究。研究结果表明,(1)该方法具有良好的计算精度。(2)计算非齐次波动方程特解项的数值积分方法中,梯形积分法的计算精度最差,高斯积分法、辛普生积分法和科茨积分法都具有较好的计算精度。(3)增加高斯积分点数目对于提高计算精度的作用并不显著。     

Cryogenic transonic wind tunnels and the condensation of nitrogen

A brief tutorial on the need for Reynolds number similarity and the advent of cryogenic transonic wind tunnels is presented. Experimental results of nitrogen condensation in nozzles are collected and related to the flow in the wind tunnels. New theoretical approaches to a solution of the condensation problem in the supersaturated state are proposed.List of symbols a speed of sound - A area - {ovc} wing area/wing span - c _p pressure coefficient, Eq. (12) - G ^* energy of formation of a critical droplet, Eq. (14) - h altitude - J homogeneous nucleation rate, Eq. (13) - k Boltzmann constant - l characteristic length - M Mach number, Eq. (2) - n ^* number of molecules in a critical droplet, Eq. (14) - p static pressure - p ₀ wind tunnel supply pressure - p ⁰ standard pressure - p equilibrium vapor pressure - P wind tunnel fan power - q dynamic pressure - Re Reynolds number, Eq. (1) - t time - T temperature - T ₀ wind tunnel supply temperature - molecular volume - V air speed - ratio of specific heats - dynamic viscosity - v kinematic viscosity - density - surface tension This paper is dedicated to my old friend Eberhard Berger upon his retirement from the Föttinger Institut of the Technical University of Berlin     

A new method for measuring static pressure fluctuations with application to wind-wave interaction

A new technique for in stream static pressure fluctuations sensing is presented. The higher capability of the method with regard the classical one, particularly over laboratory wind wave, is proved. First measurements have been done in a turbulent boundary layer above the air-water interface during the wave generation stage. The results show that, for pure laboratory wind waves at short fetches, a strong coupling exists between air and water motions and that the energy transfer from wind to the waves seems mainly due to the work done by the wave induced pressure fluctuations.List of symbols C wave phase celerity - C _g wave group celerity - Coh coherency function - C _ps pressure coefficient for a static pressure sensing head - C _pt pressure coefficient for a total pressure sensing head - g gravitational acceleration - n frequency - p instantaneous static pressure - p _m measured instantaneous static pressure - p _t instantaneous total pressure - p _tm measured instantaneous total pressure - p (t) static pressure fluctuation - Q _pn quadspectrum between static pressure fluctuations and water level deflections - S _p static pressure fluctuations spectrum - S _pt total pressure fluctuations spectrum - S _n wave spectrum - u instantaneous air velocity vector - U air velocity outside the boundary layer - X fetch - instantaneous incidence angle of the air velocity - instantaneous water level - phase shift - wave energy amplification ratio - ^p non dimensional energy transfer ratio by pressure work - _M non dimensional energy transfer ratio predicted by Miles theory - _a air density - _w water density A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, September 22–24, 1986     

Instantaneous density measurement in two-dimensional gas flow by high speed differential interferometry

The aim of this paper is to present an experimental set-up using a Wollaston prism differential interferometer producing up to twenty successive short exposure white light interferograms at a high framing rate. It is shown that, through optical component calibration, the interferograms can be analysed to yield the instantaneous density field. This method has been successfully tested in the two-dimensional unsteady flow generated by the interaction of a mixing layer and a cavity.List of symbols h height of the downstream edge of the cavity - H height of backward facing step - M Mach number - t time - t time interval between two successive frames - N frequency - double-prism median plane - birefringence angle - _p pressure fluctuation - C _p pressure coefficient - biprism abscissa corresponding to any colour - ₀ biprism reference abscissa corresponding to background colour - _y deviation of light rays - R radius of curvature of spherical mirror - L virtual distance from the middle of the test section to the spherical mirror - E optical thickness - E _e optical thickness corresponding to background colour - d _E difference of optical thickness - d _x abscissa difference - gas density - ₀ stagnation gas density - _e gas density of background colour     

Influence of the initial boundary layer on base pressure

The base pressure p_b, for an initial turbulent boundary layer, is determined for supersonic nonisothermal flow about a two-dimensional backward-facing step. This problem has been considered previously. In solving it in [1, 2], use was made of the Korst condition [3], which assumes equality of the total pressure p_j ^* on the line of constant mass to the pressure behind the closing oblique shock. However the pressure at the reattachment section p_* is lower than that behind the closing shock by 30–40% [4], and consequently the Korst condition is inaccurate. Therefore in the references cited only qualitative agreement with experiment was obtained. In contrast with [1, 3], Nash [5] introduces p_*; however, it is defined by an empirical coefficient. In the present study, to find p_b we make use of the condition of conservation of mass in the base region, written in the form of the equality p_j ^*=p_*, where p_* is defined from the assumption of minimum thickness of the dissipative layer at the reattachment section.Satisfactory agreement with the available experimental data is obtained without the use of correction factors. In the simplest case, when the thickness of the oncoming boundary layer ₁=0, the proposed method is no more complex than that of Korst. The determination of the base pressure with ₁=0 is considered in §1, and the determination with ₁>0 is considered in §2.     

First results of simplified analysis of second order effects in a cylindrical shell subjected to wind loading

Summary This work investigates the stability of an upright cylindrical shell, simply supported at the bottom and free at the top when it is exposed to a horizontal wind which creates a non-uniform pressure on the outside of the shell. The special case of the wind pressure p=p₀ cos 0 and the cylinder with elastic foundation are investigated, too. First results show that the analysis provides the linear part of the deflection fairly accurately, but significant non-linear effects do not appear, on account of the employed approximations, unless the wind velocity is excessively high.

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Sommario Si studia la stabilità di una voltina cilindrica retta, semplicemente appoggiata alla base e libera in sommità, quando è esposta all'azione del vento che, spirando orizzontalmente, crea una pressione non uniforme sul bordo esterno della voltina. E' esaminato pure il caso particolare che la pressione del vento sia rappresentabile da una distribuzione p=p₀ cos 0 e quello della voltina cilindrica su fondazione elastica. I primi risultati mostrano che l'analisi fatta fornisce, abbastanza accuratamente, la parte lineare della deformazione, epperò, a causa delle ipotesi introdotte, non appaiono effetti non lineari a meno che la velocità del vento non risulti eccessivamente alta.

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This work was done in the Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, U.S.A.     

On the viscosity of suspensions of solid spheres

A cell theory is used to derive the dependence of the zero-shear-rate viscosity on volume concentration for a suspension of uniform, solid, neutrally buoyant spheres. This result reduces to Einstein's solution at infinite dilution and to Frankel and Acrivos's expression in the limit as the concentration approaches its maximum value. Good agreement is found between the solution and the available data for the entire concentration range, provided that the maximum concentration is determined from the viscosity data themselves.Nomenclature a radius of sphere - d the distance separating the sphere surfaces measured parallel to the line connecting the sphere centers - E energy dissipation rate in one-half the liquid volume separating the spheres - E _cell total energy dissipation rate in the cell - E _homogeneous energy dissipation rate in the cell of a hypothetical one phase fluid - E _interaction energy dissipation rate in the cell due to sphere interactions - E _sphere energy dissipation rate in the cell due to the sphere at the cell center - F force on one sphere - h minimum separation distance between two spheres - J (1/2)d = one-half the distance separating the sphere surfaces measured parallel to the line connecting the sphere centers - p pressure - W velocity of one sphere in squeezing flow between two spheres relative to the midpoint of the line connecting the sphere centers - _i unit vectors in thei-th direction - elongation rate - viscosity of the suspending fluid - _r */ = relative viscosity - * viscosity of the suspension - the total stress tensor - the part of the total stress tensor that vanishes at equilibrium - volume fraction of spheres