# Computational Mathematics

 How many ways can a virus vibrate? Normal Coordinate Analysis (NCA) yields vibrational modes (eigenmodes), but until recently was only feasible for small systems with just a few thousand atoms. ORNL's new large-scale NCA capability will soon allow study of molecules of even greater size and complexity (~1,000,000 atoms).

 Innovations in Algorithm Design By combining new large-scale eigensolver techniques with new methods for calculation of the Hessian matrix, ORNL has raised the bar for Normal Coordinate Analysis from the previous record of about 3,000 atoms to a polymer system of 100,000 atoms. Research applications include optimized drug design, fabrication of nanoscale devices, and better understanding of basic biological processes such as photosynthesis. more info image Computational Solid Dynamics Boundary Integral Methods are used in analysis of stresses that affect the lifespan of coatings in metallic and ceramic materials. ORNL researchers have significantly improved the accuracy of computed crack stress intensity factors by incorporating the ORNL-developed "modified quarter-point" element (MQP) into boundary integral fracture codes. This improvement in accuracy makes it feasible to reliably model real problems, particularly those where cracks follow curved paths. Research applications include studying failures in thermal barrier coatings on turbine blades and increasing the lifespan of coatings on components of Direction and Attitude Control Systems. more info Computational Fluid Dynamics Computational scientists at ORNL have recently verified that fluid can be pumped without the presence of valves in the system. Specifically, the computational model, using the immersed boundary method, produces net flow in an oval tube with periodic forcing applied to a flexible membrane that forms part of the tube. A startling result is that the direction and magnitude of the flow depends upon the frequency of the forcing function. The research will now be applied to model cardiopulmonary resuscitation. During CPR, it is not yet known whether the heart acts as a pump (through cardiac pumping), or as a passive conduit for valveless pumping (thoracic pumping). There is some echocardiographic evidence to suggest that the mitral valve remains open during CPR in the thoracic pump model. The immersed boundary method will be applied to a heart model to help understand the mechanism of blood flow during CPR and to provide insight into the development of more effective CPR techniques. more info

## Researchers:

Innovations in Algorithm Design

 ORNL: Chao Yang, Chuck Romine, Don Noid, Bobby Sumpter. CalTech: Rudolph Marcus, Bryan Hathorne.

Computational Solid Dynamics

 ORNL: Lenny Gray, Ted Kaplan, Joe Richardson, Anh-Vu Phan, Ted Besmann. Berkeley: Jamie Sethian. Univ. of Illinois U.-C.: Glaucio Paulino. Colo. School of Mines: John Berger.

Computational Fluid Dynamics

 ORNL: Eunok Jung NYU/Courant: Charles Peskin.

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Updated: Friday, 27-Oct-2000 17:11:35 EDT
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