Enhancing dependency pair method using strong computability in simply-typed term rewriting

We enhance the dependency pair method in order to prove termination using recursive structure analysis in simply-typed term rewriting systems, which is one of the computational models of functional programs. The primary advantage of our method is that one can exclude higher-order variables which are difficult to analyze theoretically, from recursive structure analysis. The key idea of our method is to analyze recursive structure from the viewpoint of strong computability. This property was introduced for proving termination in typed λ-calculus, and is a stronger condition than the property of termination. The difficulty in incorporating this concept into recursive structure analysis is that because it is defined inductively over type structure, it is not closed under the subterm relation. This breaks the correspondence between strong computability and recursive structure. In order to guarantee the correspondence, we propose plain function-passing as a restriction, which is satisfied by many non-artificial functional programs.     

Electrodialysis plant at Hatsushima

A commercial multistage batch system electrodialysis plant for desalination of brackish groundwater was installed at Hatsushima, Atami City in April 1973. The plant has three stages each of which is operated at a constant voltage. Each stage has a dialyzer which is provided with 150 pairs of ion exchange membranes having an effective area of 1 m² each. This plant is used for drinking water supply and has a capacity of 200 m³/day when the raw water has a saline concentration of 6,000 ppm TDS. The operation was very stable and easy, and it was possible to produce water of constant quality at all times regardless of fluctuations in the raw water concentration. The dialyzer was chemically cleaned for removal of deposits on membranes thereby reducing the maintenance cost by 62% without adversely influencing ion exchange membranes.     

Temperature-swing adsorption of proteins in water using N-isopropylacrylamide copolymer gel particles

The adsorption and desorption behaviors of bovine serum albumin (BSA) in water for temperature-responsive polymer gel particles have been investigated by the temperature-swing operation between 298 and 313 K, where the cationic N-isopropylacrylamide (NIPA) gels copolymerized with vinylbenzyl trimethylammonium chloride (VBTA) or 2-(dimethylamino)ethyl methacrylate (DMAEMA) were used. The NIPA-VBTA and the NIPA-DMAEMA copolymer gels adsorbed BSA while the NIPA homopolymer gel hardly adsorbed BSA, indicating that the copolymer gels adsorb BSA through the electrostatic attraction between the positively charged groups in the gels and the negatively charged BSA. The adsorption amounts for the NIPA-DMAEMA gels were smaller than those for the NIPA-VBTA gels. This may be because almost every VBTA group, which is a quaternary ammonium salt, can be positively charged in water, while only some of the tertiary amine DMAEMA groups are protonated in water. Moreover, it was found that both the copolymer gels with a large mesh size of the polymer network repeatedly adsorbed BSA at 298 K and desorbed some of pre-adsorbed BSA at 313 K by the temperature-swing operation. This BSA desorption may result from the decrease of the number of the positively charged groups accessible to BSA due to the shrinking of the constituent polymer chains.     

Experiments and FE-analysis of 2-D root-soil contact problems based on node-to-segment approach

Accurate predictions of the mechanical response of root-soil systems are required for assessing and reducing the risk of landslides, surface erosions, and lodging. The present paper proposes the use of the node-to-segment (NTS) approach with the finite element method for predicting contact phenomena between roots and soils, such as collision, sliding, and separation. To obtain reliable predictions for the deformation of such geometrically complex problems, a stabilizing algorithm within the NTS approach is proposed and implemented here. The proposed algorithm prevents the well-known non-uniqueness problem of the pairing algorithm in the NTS approach, which has been an obstacle to applying the approach to root-soil systems. The current method is employed for two numerical examples. The first is an example of validation, in which pullout experiments are re-analyzed to examine the applicability of the method to a geometrically simple root-soil contact problem. It is shown that the current method provides a reasonable prediction of the pullout response, and that both the friction and the cohesion can also be accurately estimated with it. The second is an example of a realistic problem, in which a 2-D lodging experiment, analogous to pile-loading problems, is conducted and simulated to demonstrate the accuracy and applicability of the NTS approach in plant-scale problems with complex root geometries. The relationship between the displacement and the reaction force of the simulation is consistent with that of the experiment, and it enables the visualization of the stress contour and deformation of the rhizosphere.