The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Microscopic Theory of Blue Phases Ⅰ and Ⅱ of Liquid Crystal

The microscopic theory of the blue phases of chiral liquid crystal is proposed. Beginning with the potential between two molecules, by using the cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. By using variational approach and zero-order approximation, the differential equation that the order parameter tensor of the blue phase can satisfy is obtained. Then we change the differential equation to the eigenequation problem in quantum mechanics. Considering the symmetry of the blue phases,the order parameter tensors of blue phases Ⅰ and Ⅱ can be made up of the eigenvectors. Our results are the same as the results of Ginzberg-Landau‘s phenomenological theory. The parameters in the order parameter tensors that we calculate in the located system are close to the predecessors‘ results.     

Synthesis of optically active poly(N‐propargylsulfamides) with helical conformation

A novel chiral N‐propargylsulfamide monomer ( 1a ) and its enantiomer ( 1b ) were synthesized and polymerized with (nbd)Rh⁺B^?(C₆H₅)₄ as a catalyst providing poly(1) (poly( 1a ) and poly( 1b )) in high yields (≥99%). Poly(1) could take stable helices in less polar solvents (chloroform and THF), demonstrated by strong circular dichroism signals and UV–vis absorption peaks at about 415 nm and the large specific rotations; but in more polar solvents including DMF and DMSO, poly(1) failed to form helix. Quantitative evaluation with anisotropy factor showed that the helical screw sense had a relatively high thermal stability. These results together with the IR spectra measured in solvents showed that hydrogen bonding between the neighboring sulfamide groups is one of the main driving forces for poly(1) to adopt stable helices. In addition, copolymerization of monomer 1a and monomer 2 was conducted, the solubility of poly(1) was improved drastically. However, the copolymerization had adverse effects on the formation of stable helices in the copolymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 500–508, 2007     

A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Chiral discrimination of a helically organized crown ether array parallel to the helix axis of polyisocyanate

The asymmetric polymerization of 4′‐isocyanatobenzo‐18‐crown‐6 with the lithium amide of (S)‐(2‐methoxymethyl)pyrrolidine successfully proceeded to afford end‐functionalized poly(4′‐isocyanatobenzo‐18‐crown‐6) with (S)‐(2‐methoxymethyl)pyrrolidine (polymer 2 ). In the circular dichroism (CD) spectrum of 2 , a clear positive Cotton effect was observed in the range of 240–350 nm corresponding to the absorption of the polymer backbone, indicating that 2 partially formed a one‐handed helical structure, which was preserved by the chirality of (S)‐(2‐methoxymethyl)pyrrolidine bonding to the terminal end in 2 . In the titration experiments for the CD intensity of 2 in the presence of D ‐ and L ‐Phe·HClO₄ (where Phe is phenylalanine), a small but remarkable difference was observed in the amount of the chiral guest needed for saturation of the CD intensity and in the saturated CD intensity, indicating that the extremely stable, one‐handed helical part should exist in the main chain of 2 , which was not inverted even when the unfavorable chiral guest for the predominant helical sense, L ‐Phe·HClO₄, was added. In addition, helical polymer 2 exhibited a chiral discrimination ability toward racemic guests; that is, the guests were extracted from the aqueous phase into the organic phase with enantiomeric excess. The driving force of the chiral discrimination ability of 2 should certainly be attributed to the one‐handed helical structure in 2 . © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 325–334, 2006     

Stimuli‐responsive polymers. VIII. Polyesters and poly(ester amides) containing azobenzene and chiral binaphthylene segments: Highly adaptive materials endowed with light‐, heat‐, and solvent‐regulated optical rotatory power

Azobenzene‐modified polyesters and poly(ester amide)s fitted with chiral, atropisomeric binaphthylene segments were prepared by a series of low‐temperature polycondensation reactions carried out in polar solvent media. When compared with their polyaramide counterparts studied earlier, these materials had significantly improved solubility behaviors and were readily dissolved by a wide range of organic solvents. In solution, each of these constructs underwent photoinduced oscillations in optical rotatory power when subjected to multiple UV‐light/visible‐light illumination cycles that drove trans?cis isomerization reactions along their polymer chains. Light‐regulated chiroptical perturbations were dependent on polymer backbone structures and were further modulated by well‐coordinated temperature fluctuations and by the nature of the solvent medium employed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 207–218, 2006     

Preparation and characterization of optically active polystyrene via a chiral nitroxide‐mediated polymerization

2,2,6,6‐Tetramethyl‐4‐[d‐(+)‐10‐camphorsulfonyl]‐1‐piperidinyloxy was synthesized and used as a chiral nitroxide for the bulk polymerizations of styrene initiated with benzoyl peroxide (BPO), tetraethylthiuram disulfide (TETD), and thermal initiation. The results showed that the polymerizations proceeded in a controlled/living way; that is, the kinetics presented approximately first‐order plots, and the number‐average molecular weights of the polymers with narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight) increased with the monomer conversion linearly. The molecular weight distributions in the case of thermal initiation were narrower than those in the case of BPO and TETD, whereas the polymerization rate with BPO or TETD as an initiator was obviously faster than that with thermal initiation. In addition, successful chain‐extension reactions were carried out, and the structures of the obtained polymers were characterized by gel permeation chromatography and ¹H NMR. The specific rotations of the polymers were also measured by polarimetric analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1522–1528, 2006     

Chiral soluble polymers and microspheres for enantioselective crystallization

A series of chiral polymers based on poly(N‐acryl) amino acids was synthesized using a convergent synthetic approach. These chiral polymers have been used as chiral additives to induce enantioselective crystallization of racemic or conglomerate amino acids in solutions. These polymeric additives showed strong capabilities to enhance highly enantioselective resolution during the crystallization of amino acids. In addition, these polymers caused unusual modifications of amino acid crystal morphologies. Furthermore, spherical microparticles of those same chiral polymers were also shown active in similar chiral discriminations during amino acid crystallizations occurring on microparticle surfaces. Our study demonstrates the high potential of chiral polymers and microparticles to resolve amino acids throughout crystallization processes. High enantiomeric excesses in one targeted enantiomer of amino acids can also be maximized via time‐dependent kinetic control of crystallizations. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3009–3017, 2006     

USING A SYSTEM DYNAMICS APPROACH TO MODEL SUSTAINABILITY INDICATORS FOR IRRIGATION SYSTEMS IN AUSTRALIA

ABSTRACT. An indicator defined as a function of the total water diversion through the Coleambally canal and the potential irrigation demand is selected to represent the sustainability of the irrigation water system in the Coleambally irrigation area, Australia. A simulation procedure using a system dynamics approach was developed to evaluate the indicator. The procedure includes water diversion assessment, potential crop water demand and total gross margin. Three cases of water supply options (surface water, ground water pumping and water trading), two cases of changes in the total agricultural area and three cropping pattern scenarios were simulated to better understand their impact on sustainability. The simulated results indicate that increasing the agricultural area reduces the sustainability of the irrigation system because the demand of water increased despite increase in the gross margin. The scenarios show that imposed water trading and ground water pumping would considerably increase the supply system having a positive impact on the sustainability. The paper concludes that a multi‐objective sustainability indicator taking account of economic and environmental issues could be more useful.     

Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.