Polymer Fluid Dynamics: Continuum and Molecular Appoaches

To solve problems in polymer fluid dynamics, one needs the equation of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (1) one can write a continuum expression for the stress tensor in terms of kinematic tensors, or (2) one can select a molecular model that represents the polymer molecule, and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. In this review, we restrict the discussion primarily to the simplest stress tensor expressions or “constitutive equations” containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. The virtue of studying the simplest models is that we can discover some general notions as to which types of empiricisms or which types of molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows. These are the flows that are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

An Agricultural continuum : a descriptive study of the farmworker population and the settling-out process : based on information collected under Contract no. HEW-OS-72-217.

"Jointly funded by the Department of Health, Education & Welfare and the Office of Economic Opportunity."

A new continuum model for traffic flow. Final report.

Transportation Department, Office of University Research, Washington, D.C.

A new continuum model for traffic flow /

"Final report under contract DOT-RD-82018."

Rural-urban continuum codes for metro and nonmetro counties /

"April 1990"--P. iii.

The ALMACA continuum of services : alcohol and drug abuse in the workplace.

Shipping list no.: 87-243-P.

Training continuum for civil service employees : a guide to training and professional development.

Shipping list no.: 2004-0121-P.

Identifying sequence regions undergoing conformational change via predicted continuum secondary structure

Motivation: Conformational flexibility is essential to the function of many proteins, e.g. catalytic activity. To assist efforts in determining and exploring the functional properties of a protein, it is desirable to automatically identify regions that are prone to undergo conformational changes. It was recently shown that a probabilistic predictor of continuum secondary structure is more accurate than categorical predictors for structurally ambivalent sequence regions, suggesting that such models are suited to characterize protein flexibility. Results: We develop a computational method for identifying regions that are prone to conformational change directly from the amino acid sequence. The method uses the entropy of the probabilistic output of an 8-class continuum secondary structure predictor. Results for 171 unique amino acid sequences with well-characterized variable structure (identified in the 'Macromolecular movements database') indicate that the method is highly sensitive at identifying flexible protein regions, but false positives remain a problem. The method can be used to explore conformational flexibility of proteins (including hypothetical or synthetic ones) whose structure is yet to be determined experimentally.

Prediction of protein continuum secondary structure with probabilistic models based on NMR solved structures

Background: The structure of proteins may change as a result of the inherent flexibility of some protein regions. We develop and explore probabilistic machine learning methods for predicting a continuum secondary structure, i.e. assigning probabilities to the conformational states of a residue. We train our methods using data derived from high-quality NMR models. Results: Several probabilistic models not only successfully estimate the continuum secondary structure, but also provide a categorical output on par with models directly trained on categorical data. Importantly, models trained on the continuum secondary structure are also better than their categorical counterparts at identifying the conformational state for structurally ambivalent residues. Conclusion: Cascaded probabilistic neural networks trained on the continuum secondary structure exhibit better accuracy in structurally ambivalent regions of proteins, while sustaining an overall classification accuracy on par with standard, categorical prediction methods.