A MICROFOUNDATION OF PREDATOR‐PREY DYNAMICS

ABSTRACT. Predator‐prey relationships account for an important part of all interactions betweenspecies. In this paper we provide a microfoundation for such predator‐prey relations in afood chain. Basic entities of our analysis are representative organisms of species modeled similar to economic households. With prices as indicators of scarcity, organisms are assumed to behave as if they maximize their net biomass subject to constraints which express the organisms' risk of being preyed upon during predation. Like consumers, organisms face a ‘budget constraint’ requiring their expenditure on prey biomass not to exceed their revenue from supplying own biomass. Short‐run ecosystem equilibria are defined and derived. The net biomass acquired by the representative organism in the short term determines the positive or negative population growth. Moving short‐run equilibria constitute the dynamics of the predator‐prey relations that are characterized in numerical analysis. The population dynamics derived here turn out to differ significantly from those assumed in the standard Lotka‐Volterra model.     

Curcumin: A naturally occurring long‐wavelength photosensitizer for diaryliodonium salts

Curcumin, a naturally occurring, intensely yellow dye extracted from the spice turmeric, is an efficient photosensitizer for diaryliodonium salt photoinitiators at wavelengths ranging from 340 to 535 nm. With curcumin as a photosensitizer, it is possible to carry out the cationic photopolymerization of a wide variety of epoxide, oxetane, and vinyl monomers with long‐wavelength UV and visible light. An example of the photopolymerization of an epoxide monomer with ambient solar irradiation is provided. Several other curcumin analogues were synthesized, and their use as photosensitizers is examined. With such photosensitizers, the range of spectral sensitivity can be extended well into the visible region of the electromagnetic spectrum. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5217–5231, 2005     

Poly(L‐lysine) and clay nanocomposite with desired matrix secondary structure: Effects of polypeptide molecular weight

Nanocomposites (NC) were formed using cationic poly(L ‐lysine) (PLL), a semicrystalline polypeptide, that was reinforced by sodium montmorillonite (MMT) clay via solution intercalation technique. By varying solution conditions such as pH, temperature, and polypeptide concentration in the presence of clay platelets, the secondary structure of PLL was controllably altered into α‐helical, β‐sheet, and random coil. The high molecular weight polypeptide shows a strong propensity to fold into the β‐sheet structure when cast as films, irrespective of the initial secondary structure in solution. Nanocomposite local morphology confirms intercalated MMT platelets with PLL over a wide range of compositions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 239–252, 2007.     

Influence of organic modifiers on morphology and crystallization of poly(ϵ‐caprolactone)/synthetic clay intercalated nanocomposites

ε‐caprolactone was polymerized in the presence of neat montmorillonite or organomontmorillonites to obtain a variety of poly(ε‐caprolactone) (PCL)‐based systems loaded with 10 wt % of the silicates. The materials were thoroughly investigated by different X‐ray scattering techniques to determine factors affecting structure of the systems. For one of the nanocomposites it was found that varying the temperature in the range corresponding to crystallization of PCL causes reversible changes in the interlayer distance of the organoclay. Extensive experimental and literature studies on this phenomenon provided clues indicating that this effect might be a result of two‐dimensional ordering of PCL chains inside the galleries of the silicate. Small angle X‐ray scattering and wide angle X‐ray scattering investigation of filaments oriented above melting point of PCL revealed that polymer lamellae were oriented perpendicularly to particles of unmodified silicate, while in PCL/organoclay systems they were found parallel to clay tactoids. Calorimetric and microscopic studies shown that clay particles are effective nucleating agents. In the nanocomposites, PCL crystallized 20‐fold faster than in the neat polymer. The crystallization rate in nanocomposites was also significantly higher than in microcomposite. Further research provided an insight how the presence of the filler affects crystalline fraction and spherulitic structure of the polymer matrix in the investigated systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2350–2367, 2007     

Novel UV‐induced photografting process for preparing poly(tetrafluoroethylene)‐based proton‐conducting membranes

A novel process comprising the UV‐induced photografting of styrene into poly(tetrafluoroethylene) (PTFE) films and subsequent sulfonation has been developed for preparing proton‐conducting membranes. Although under UV irradiation the initial radicals were mainly generated on the surface of the PTFE films by the action of photosensitizers such as xanthone and benzoyl peroxide, the graft chains were readily propagated into the PTFE films. The sulfonation of the grafted films was performed in a chlorosulfonic acid solution. Fourier transform infrared and scanning electron microscopy were used to characterize the grafted and sulfonated membranes. With a view to use in fuel cells, the proton conductivity, water uptake, and mechanical properties of the prepared membranes were measured. Even through the degree of grafting was lower than 10%, the proton conductivity in the thickness direction of the newly prepared membranes could reach a value similar to that of a Nafion membrane. In comparison with γ‐ray radiation grafting, UV‐induced photografting is very simple and safe and is less damaging to the membranes because significant degradation of the PTFE main chains can be avoided. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2624–2637, 2007     

Application of N,N‐bis(diphenylphosphino)aniline palladium(II) complexes as pre‐catalysts in Heck coupling reactions

Palladium(II) complexes with N,N‐bis(diphenylphosphino)aniline ligands catalyse the Heck reaction between styrene and aryl bromides, affording stilbenes in good yield. The structures of two of the complexes used as pre‐catalysts have been determined by single‐crystal X‐ray diffraction. Copyright © 2007 John Wiley & Sons, Ltd.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Isothermal crystallization kinetics of poly(3‐hydroxybutyrate)/layered double hydroxide nanocomposites

Poly(3‐hydroxybutyrate) (PHB)/layered double hydroxides (LDHs) nanocomposites were prepared by mixing PHB and poly(ethylene glycol) phosphonates (PEOPAs)‐modified LDH (PMLDH) in chloroform solution. Both X‐ray diffraction data and TEM micrographs of PHB/PMLDH nanocomposites indicate that the PMLDHs are randomly dispersed and exfoliated into the PHB matrix. In this study, the effect of PMLDH on the isothermal crystallization behavior of PHB was investigated using a differential scanning calorimeter (DSC) and polarized optical microscopy. Isothermal crystallization results of PHB/PMLDH nanocomposites show that the addition of 2 wt % PMLDH into PHB induced more heterogeneous nucleation in the crystallization significantly increasing the crystallization rate and reducing their activation energy. By adding more PMLDH into the PHB probably causes more steric hindrance of the diffusion of PHB, reducing the transportation ability of polymer chains during crystallization, thus increasing the activation energy. The correlation among crystallization kinetics, melting behavior and crystalline structure of PHB/PMLDH nanocomposites can also be discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3337–3347, 2006     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003