181 research outputs found
Numerical solution of two-dimensional navier stokes equations
Get PDFAn attempt has been made to develop a convergent iterative method to obtain two-dimensional steady state solutions of the Navier-Stokes equations. In the last few years, various successful attempts have been made to apply numerical methods to obtain both the time dependent and steady state solutions of the Navier-Stokes equations for different types of boundary configurations. The non-linearity of the differential equations makes the convergence of the iterative method difficult. The limitations on the storage capacity of the available computing machines makes it impracticable to obtain solutions having any predetermined accuracy. In addition, the imposition of the natural boundary conditions which prescribe the velocities on the boundaries, also contributes to the complexity of the problem. A brief survey of some representative work done on the numerical solution of Navier-Stokes equations has been given here.
The Navier-Stokes equations have been reduced to a system of two second order coupled differential equations which are then solved numerically. Some finite difference schemes have recently been suggested which guarantee the convergence of the iterations for solving the two difference equations. However, these schemes require a certain number of parameters which have to be determined by numerical experimentation. Our aim here is to develop a procedure which would be economical and would require a minimum of numerical experimentation.
We have succeeded in showing that only one parameter besides the optimum over-relaxation factors is sufficient for convergence. Different criteria for convergence are studied and the one, which appears to be most efficient, has been used to obtain numerical solutions for the steady flow of a viscous fluid in a two-dimensional cavity flow. Another problem for which the numerical solutions have been obtained is the separating flow due to a thin plate of finite length placed at the point of symmetry of an otherwise two-dimensional stagnation point flow. A non-uniform mesh has been used for this problem and the numerical results for different values of Reynolds number have been obtained. These are given in the form of stream lines and equi-vorticity curves. We have also extended the difference schemes to problem of axisymmetric flows although no numerical results have been obtained.
The results obtained in this thesis may be considered as qualitatively satisfactory in the sense that they exhibit the characteristics of the fluid flow. These results can not be considered quantitatively reliable unless some insight is gained about the convergence of the numerical solution of the discretized problem to that of the differential equations. This can partly be done by repeating the calculations using smaller mesh sizes. However, this would require a considerable amount of computing time. It would be interesting to investigate the possibilities of improving the results using some higher order stable difference schemes or finer mesh sizes in the boundary layer only without unduly increasing the computing time
Convergence and stability of finite difference schemes for some elliptic equations
Get PDFThe problem of convergence and stability of finite difference schemes used for solving boundary value problems for some elliptic partial differential equations has been studied in this thesis. Generally a boundary value problem is first replaced by a discretized problem whose solution is then found by numerical computation.
The difference between the solution of the discretized problem and the exact solution of the boundary value problem is called the discretization error. This error is a measure of the accuracy of the numerical solution, provided the roundoff error is negligible. Estimates of the discretization error are obtained for a class of elliptic partial differential equations of order 2m (M ≥ 1) with constant coefficients in a general n-dimensional domain. This result can be used to define finite difference approximations with an arbitrary order of accuracy.
The numerical solution of a discretized problem is usually obtained by solving the resulting system of algebraic equations by some iterative procedure. Such a procedure must be stable in order to yield a numerical solution. The stability of such an iteration scheme is studied in a general setting and several sufficient conditions of stability are obtained.
When a higher order differential equation is solved numerically, roundoff error can accumulate during the computations. In order to reduce this error the differential equation is sometimes replaced by several lower order differential equations. The method of splitting is analyzed for the two-dimensional biharmonic equation and the convergence of the discrete solution to the exact solution is discussed. An iterative procedure is presented for obtaining the numerical solution. It is shown that this method is also applicable to non-rectangular domains.
The accuracy of numerical solutions of a nonselfadjoint elliptic differential equation is discussed when it is solved with a finite non-zero mesh size. This equation contains a parameter which may take large values. Some extensions to the two-dimensional Navier-Stokes equations are also presented
Pulmonary vascular pressures of exercising Thoroughbred horses with and without endoscopic evidence of EIPH
No full text Manohar, Murli, and Thomas E. Goetz. Pulmonary vascular pressures of exercising Thoroughbred horses with and without endoscopic evidence of EIPH. J. Appl. Physiol.81(4): 1589–1593, 1996.—Exercise-induced pulmonary hemorrhage (EIPH) is a common occurrence in racehorses. The objective of this study was to compare pulmonary vascular pressures of healthy Thoroughbred horses with and without postexertion endoscopically detectable fresh blood in the trachea. The nasopharynx, larynx, and trachea (down to the carina) of horses were examined weekly with an endoscope 55–60 min postexertion, and the diagnosis of EIPH was confirmed by the presence of fresh blood in the trachea. Measurements of heart rate and right atrial, pulmonary arterial, and pulmonary arterial wedge pressures were made during quiet rest and during treadmill exercise performed at 14.5 m/s on a 5% uphill grade. This workload elicited maximal heart rate of the horses. Mean pulmonary capillary pressure was estimated to be halfway between the mean pulmonary arterial pressure and the mean pulmonary arterial wedge pressure. These data from 7 healthy sound exercise-trained horses that were positive on 12 consecutive occasions (at 1-wk intervals) for the postexercise presence of fresh blood in the trachea were compared with those in 8 healthy horses that were consistently negative for the evidence of fresh blood in the trachea on postexercise endoscopic examination over 12–16 wk. The heart rate and the right heart and/or pulmonary vascular pressures in the two groups of horses were similar at rest. Exercise was attended by a large significant ( P < 0.05) increase in these pressures and heart rate in both groups. However, statistically significant differences between endoscopically EIPH-positive and endoscopically EIPH-negative horses for heart rate and right atrial and pulmonary vascular pressures were not found during exercise. Thus these data revealed that the magnitude of exercise-induced right atrial as well as pulmonary arterial, capillary, and venous hypertension in endoscopically EIPH-positive horses that are otherwise healthy is quite similar to that in endoscopically EIPH-negative horses during comparable exertion. </jats:p
Equine Epistaxis Research
Get PDFMurli Manohar, B.V.Sc., Ph.D., of the University of Illinois College of Veterinary Medicine, estimates that as many as 70 to 80 percent of Thoroughbred racehorses are "bleeders." After exercise - often even a mild warmup (breezing) - blood Hows from their nostrils or can be seen in the bronchial tubes with special scopes. "When 80 percent of animals have a condition, usually you would consider it to be normal and wonder what was wrong with the other 20 per cent that they didn't have it;' Dr. Manohar said. Dr. Manohar is studying bleeders at the University of Illinois through a grant from Morris Animal Foundation, Englewood, Colorado. The non-profit Foundation funds studies of the health problems of horses, dogs, cats and zoo animals.</p
Functional and Structural Characterization of Cation/H+ Antiporters
Get PDFInorganic cations play decisive roles in many cellular and physiological processes and are essential components of plant nutrition. Therefore, the uptake of cations and their redistribution must be precisely controlled. Vacuolar antiporters are important elements in mediating the intracellular sequestration of these cations. CAXs (for CAtion eXchanger) are members of a multigene family and appear to predominately reside on vacuoles. Defining CAX regulation and substrate specificity have been aided by utilizing yeast as an experimental tool. Studies in plants suggest CAXs regulate apoplastic Ca2+ levels in order to optimize cell wall expansion, photosynthesis, transpiration and plant productivity. CAX studies provide the basis for making designer transporters that have been used to develop nutrient enhanced crops and plants for remediating toxic soils.
In my second study, I have characterized and defined autoinhibitory domain of Arabidopsis CAX3. Several CAX transporters, including CAX1, appear to contain an approximately 40 amino acid N-terminal regulatory regions (NRR) that modulates transport through N-terminal autoinhibition. Deletion of the NRR from several CAXs (sCAX) enhances function in plant and yeast expression assays; however, to date, there are no functional assays for CAX3. In this report, we create a series of truncations in the CAX3 NRR and demonstrate activation of CAX3 in both yeast and plants by truncating a large portion of the NRR. Experiments on endomembrane-enriched vesicles isolated from yeast expressing activated CAX3 demonstrate that the gene encodes Ca2+/H+ exchange with properties distinct from CAX1. These studies demonstrate shared and unique aspects of CAX1 and CAX3 transport and regulation.
My third study is to express and purify CAX proteins for X-ray crystallographic analysis. In this study, I initiated crystallization of vacuolar membrane localized CAX protein from eukaryotes. Membrane proteins continue to be challenging targets for structural biology because of their hydrophobic nature. We have demonstrated here that eukaryotic Ca2+/H+ exchanger can be successfully expressed in E. coli based expression system. Collectively, our findings suggest that CAX protein can be successfully expressed, detergent solublized and purified from E. coli with a yield sufficient for functional and structural studies
Anti-fibrotic role of IL-15 in chronic pancreatitis
No full textAnti-fibrotic role of IL-15 in chronic pancreatiti
The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics, edited by G. W. Gibbons, E.P.S. Shellard and S.J. Rankin
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