A transport model of the turbulent scalar-velocity

Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables

Higher order turbulence closure models

Theoretical models are developed and numerical studies conducted on various types of flows including both elliptic and parabolic. The purpose of this study is to find better higher order closure models for the computations of complex flows. This report summarizes three new achievements: (1) completion of the Reynolds-stress closure by developing a new pressure-strain correlation; (2) development of a parabolic code to compute jets and wakes; and, (3) application to a flow through a 180 deg turnaround duct by adopting a boundary fitted coordinate system. In the above mentioned models near-wall models are developed for pressure-strain correlation and third-moment, and incorporated into the transport equations. This addition improved the results considerably and is recommended for future computations. A new parabolic code to solve shear flows without coordinate tranformations is developed and incorporated in this study. This code uses the structure of the finite volume method to solve the governing equations implicitly. The code was validated with the experimental results available in the literature

Dispersion Relations in String Theory

We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the graviton multiplet in the Type II Superstring. In particular we obtain explicit double and single dispersion relations, formulas for all the successive branch cuts extending out to plus infinity, as well as for the decay rate of a massive string state of arbitrary mass 2N into two string states of lower mass. We compare our results with the box diagram in a superposition of $\phi^3$-like field theories. The stringy effects are traced to a convergence problem in this superposition.Comment: 17 pages, COLUMBIA-YITP-UCLA/93/TEP/45 (figures fixed up

Persistent Biomechanical Alterations After ACL Reconstruction Are Associated With Early Cartilage Matrix Changes Detected by Quantitative MR.

BackgroundThe effectiveness of anterior cruciate ligament (ACL) reconstruction in preventing early osteoarthritis is debated. Restoring the original biomechanics may potentially prevent degeneration, but apparent pathomechanisms have yet to be described. Newer quantitative magnetic resonance (qMR) imaging techniques, specifically T1ρ and T2, offer novel, noninvasive methods of visualizing and quantifying early cartilage degeneration.PurposeTo determine the tibiofemoral biomechanical alterations before and after ACL reconstruction using magnetic resonance imaging (MRI) and to evaluate the association between biomechanics and cartilage degeneration using T1ρ and T2.Study designCohort study; Level of evidence, 2.MethodsKnee MRIs of 51 individuals (mean age, 29.5 ± 8.4 years) with unilateral ACL injuries were obtained prior to surgery; 19 control subjects (mean age, 30.7 ± 5.3 years) were also scanned. Follow-up MRIs were obtained at 6 months and 1 year. Tibial position (TP), internal tibial rotation (ITR), and T1ρ and T2 were calculated using an in-house Matlab program. Student t tests, repeated measures, and regression models were used to compare differences between injured and uninjured sides, observe longitudinal changes, and evaluate correlations between TP, ITR, and T1ρ and T2.ResultsTP was significantly more anterior on the injured side at all time points (P < .001). ITR was significantly increased on the injured side prior to surgery (P = .033). At 1 year, a more anterior TP was associated with elevated T1ρ (P = .002) and T2 (P = .026) in the posterolateral tibia and with decreased T2 in the central lateral femur (P = .048); ITR was associated with increased T1ρ in the posteromedial femur (P = .009). ITR at 6 months was associated with increased T1ρ at 1 year in the posteromedial tibia (P = .029).ConclusionPersistent biomechanical alterations after ACL reconstruction are related to significant changes in cartilage T1ρ and T2 at 1 year postreconstruction. Longitudinal correlations between ITR and T1ρ suggest that these alterations may be indicative of future cartilage injury, leading to degeneration and osteoarthritis.Clinical relevanceNewer surgical techniques should be developed to eliminate the persistent anterior tibial translation commonly seen after ACL reconstruction. qMR will be a useful tool to evaluate the ability of these newer techniques to prevent cartilage changes

Greater V˙O2peak is correlated with greater skeletal muscle deoxygenation amplitude and hemoglobin concentration within individual muscles during ramp-incremental cycle exercise.

It is axiomatic that greater aerobic fitness (V˙O2peak) derives from enhanced perfusive and diffusive O2 conductances across active muscles. However, it remains unknown how these conductances might be reflected by regional differences in fractional O2 extraction (i.e., deoxy [Hb+Mb] and tissue O2 saturation [StO2]) and diffusive O2 potential (i.e., total[Hb+Mb]) among muscles spatially heterogeneous in blood flow, fiber type, and recruitment (vastus lateralis, VL; rectus femoris, RF). Using quantitative time-resolved near-infrared spectroscopy during ramp cycling in 24 young participants (V˙O2peak range: ~37.4-66.4 mL kg-1 min-1), we tested the hypotheses that (1) deoxy[Hb+Mb] and total[Hb+Mb] at V˙O2peak would be positively correlated with V˙O2peak in both VL and RF muscles; (2) the pattern of deoxygenation (the deoxy[Hb+Mb] slopes) during submaximal exercise would not differ among subjects differing in V˙O2peak Peak deoxy [Hb+Mb] and StO2 correlated with V˙O2peak for both VL (r = 0.44 and -0.51) and RF (r = 0.49 and -0.49), whereas for total[Hb+Mb] this was true only for RF (r = 0.45). Baseline deoxy[Hb+Mb] and StO2 correlated with V˙O2peak only for RF (r = -0.50 and 0.54). In addition, the deoxy[Hb+Mb] slopes were not affected by aerobic fitness. In conclusion, while the pattern of deoxygenation (the deoxy[Hb+Mb] slopes) did not differ between fitness groups the capacity to deoxygenate [Hb+Mb] (index of maximal fractional O2 extraction) correlated significantly with V˙O2peak in both RF and VL muscles. However, only in the RF did total[Hb+Mb] (index of diffusive O2 potential) relate to fitness

Improvement of the Reynolds-stress model by a new pressure-strain correlation

A study is made to improve the predictions of Reynolds stresses in backward facing step flows, through modifications of the pressure-strain correlation. The mean-strain term of the pressure-strain correlation is formulated only in terms of nonisotropic turbulence in order to take the severe nonisotropic effect caused by a separating flow. This model is compared with other models and results are verified with experimental results