By Pardalos P.M. (ed.)

ISBN-10: 9810214154

ISBN-13: 9789810214159

Modern-day high-performance pcs are making to be had suggestions to rheological stream difficulties of ever-increasing complexity. Computational rheology is a fast-moving topic - difficulties which was intractable, resembling 3D temporary flows of polymeric drinks, non-isothermal non-Newtonian flows or flows of hugely elastic beverages via complicated geometries, at the moment are being tackled because of the provision of parallel pcs, adaptive equipment and advances in constitutive modelling. This paintings strains the advance of numerical tools for non-Newtonian flows from the overdue 1960's to 2001. It starts with vast assurance of non-Newtonian fluids, together with their mathematical modelling and research, earlier than particular computational innovations are mentioned. the appliance of those suggestions to a few very important rheological circulation difficulties of educational and business curiosity is then handled in a close exposition. eventually, the reader is stored abreast of issues on the innovative of study in computational utilized arithmetic, reminiscent of adaptivity and stochastic partial differential equations. all of the subject matters during this booklet are handled from an uncomplicated point

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1991) , "Non-deterministic exponential time has two-prover interactive protocols," Computation al Complexity 1, 3-40. [6] Bellare, M. (1992), "Interactive proofs and approximation," IBM Research Report RC 17969. Also Proceedings of the second Israel Symposium on theory of computing and systems, 1993. , Goldwasser, S-, Lund, C , and Russell, A. (1993), "Efficient probabilistically checkable proofs and applications to approximation," Proceedings of the 25th AnnuaJ ACM Symposium on the Theory of Computing, ACM.

Acknowledgments We are grateful to Peter Hammer, who, during a visit to Dartmouth College, described the work in [12] which inspired our initial results. We thank Stephen Vavasis for much helpful information on the subject of nonlinear optimization, and especially for explaining to us the importance of using the right definition of a p-approximation. We thank Rajeev Motwani for drawing our attention to [3). We thank an anonymous referee for various helpful comments. References [1] Arora, S. and Safra, S.

This would mean that the result of [26] mentioned above is essentially optimal. To improve our theorems in this manner we would need new and more efficient two prover, one round proof systems for NP (cf. Section 4). 3 Techniques from Interactive Proofs Our results rely on recent advances in the theory of interactive proof systems and the connection of these to approximation problems. We give a brief summary of relevant work in this area. Interactive proofs were introduced by Goldwasser, Micati and Rackoff [16] and Babai [4].

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