Over the past four decades in the United States, there has been a divergent trend in mortality rates between African-Americans and Caucasians with colorectal cancer (CRC). Rates among Caucasians have been steadily declining, whereas rates among African-Americans have only started a gradual decline in recent years. We reviewed epidemiologic studies of CRC racial disparities between African-Americans and Caucasians, including studies from SEER and population-based cancer registries, Veterans Affairs (VA) databases, healthcare coverage databases, and university and other medical center data sources. Elevated overall and stage-specific risks of CRC mortality and shorter survival for African-Americans compared with Caucasians were reported across all data sources. The magnitude of racial disparities varied across study groups, with the strongest associations observed in university and non-VA hospital-based medical center studies, while an attenuated discrepancy was found in VA database studies. An advanced stage of disease at the time of diagnosis among African-Americans is a major contributing factor to the racial disparity in survival. Several studies, however, have shown that an increased risk of CRC death among African-Americans remains even after controlling for tumor stage at diagnosis, socioeconomic factors, and comorbidity. Despite advances in treatment, improvements in the standard of care, and increased screening options, racial differences persist in CRC mortality and survival. Therefore, continued research efforts are necessary to disentangle the clinical, social, biological, and environmental factors that constitute the racial disparity. In addition, results across data sources should be considered when evaluating racial differences in cancer outcomes.
The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential de¯ection formulation. The way in which the differential de¯ection is incorporated into the overall solution method for a point contact is discussed. A range of spatial and temporal discretization methods are incorporated and compared. The method is validated under transient conditions by a detailed comparison with published work produced using a different, independent method incorporating a moving roughness feature.A comparison of the results with different discretization methods leads to the conclusion that spatial central differencing with a Crank±Nicolson temporal discretization is the most effective ®nite difference scheme, and this is generally equivalent to the ®nite element discretization given in detail in the paper. A comparison of the results produced for moving rough surfaces suggests that the ®nite element formulation is preferred. NOTATIONheight of the surface feature de®ned by equation (12) (m) E 0 effective modulus of elasticity (Pa) f i, j pressure coef®cient in the differential de¯ection equation (m ¡1 ) F factor determining timestepˆU UDt=Dx h ®lm thickness (m) h 0 constant in the ®lm thickness equation (3) (m) L Moes and Bosma non-dimensional parameterˆaE 0 ‰2Z 0 U U=…E 0 R R †Š 1=4 M Moes and Bosma non-dimensional parameterˆ‰w=…E 0 R R 2 †Š‰E 0 R R=…2Z 0 U U †Š 3=4 n c number of neighbouring mesh points in discretization N i shape function p pressure (Pa) p hz maximum pressure in Hertzian contact (Pa) Pˆp=p hz in Figs 4 to 7 R x , R y radii of relative curvature in axis directions (m) R R 2R x R y =…R x ‡ R y † (m) u total de¯ection of the surfaces perpendicular to the xy plane (m) U U, V V mean surface velocities in axis directions (m/s) w load (N) W b width of surface feature de®ned by equation (12) (m) x, y coordinates in the contact plane (m) x b x coordinate of the centre of the ridge feature (m) Z parameter in the viscosity equation (5) a=‰w ln…Z 0 =k †Š a pressure viscosity coef®cient (Pa ¡1 ) g coef®cient in the density equation (6) (Pa ¡1 ) Dt timestep (s) Dx, Dy mesh spacing in coordinate directions (m) Z viscosity (Pa s) The MS was Downloaded from Z 0 viscosity at ambient pressure (Pa s) k coef®cient in the viscosity equation (5) (Pa s) l coef®cient in the density equation (6) (Pa ¡1 ) x slide±roll ratio r density (kg/m 3 ) r 0 density at ambient pressure (kg/m 3 ) s x , s y¯o w coef®cients in axis directions (m s) t 0 non-Newtonian shear stress parameter (Pa) f surface roughness feature (m) w coef®cient in the viscosity equation (5) (Pa ¡1 )
The paper presents a procedure for evaluating the Laplacian of the de¯ection of a semiin®nite body subject to pressure loading using suitable quadrature expressions. Both line contact and point contact situations are considered. The validity of the treatments is veri®ed by consideration of the Hertzian pressure distributions, and it is shown for each case that the de¯ection can be obtained numerically by solution of the resulting dierential equation. The eect of the pressure distribution in this`dierential de¯ection' method is shown to be extremely localized in comparison with direct evaluation of the de¯ection. A companion paper clari®es how this important property can be exploited to enable a fully coupled approach to the elastohydrodynamic problem to be constructed without the need to consider the solution of the fully populated matrix that has hitherto been thought to be necessary. The technique developed in this paper thus forms the key to exploiting the acknowledged bene®ts of full coupling in these problems.
This paper describes how a dierential de¯ection technique for determining the de¯ection due to pressure acting on a semi-in®nite body can be incorporated into solution schemes for the elastohydrodynamic lubrication (EHL) line contact problem. The method allows a fully coupled approach to be used without the full matrix penalty usually associated with that technique. This is achieved by the dierential de¯ection method which speci®es the de¯ection in a distributed implicit way rather than a speci®c explicit way. The dierential de¯ection method is shown to give unchanged results with a radical reduction in the computing time required. It thus makes the inherent bene®ts of full coupling of the elastic and hydrodynamic equations available to EHL solution schemes without the computational penalty that has hitherto been associated with that approach.
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