Correction to: On Webs of Maximum Rank (Geom. Dedicata 31 (1989), 19–35)

We correct an error in Example (3.4) in Geom. Dedicata 31 (1989), 19–35.     

Impact of proliferation strategies on food web viability in a model with closed nutrient cycle

A food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The model consists of three trophic levels, each of which is populated by animals of one distinct species. While the species at the intermediate level feeds on the basal species, and is eaten by the predators living at the highest level, the basal species itself uses the detritus of animals from higher levels as the food resource. The individual organisms remain localized, but the species can invade new lattice areas via proliferation. The impact of different proliferation strategies on the viability of the system is investigated. From the phase diagrams generated in the simulations it follows that in general a strategy with the intermediate level species searching for food is the best for the survival of the system. The results indicate that both the intermediate and top level species play a critical role in maintaining the structure of the system.     

Food web model with detritus path

We present and study a lattice (Monte Carlo) model of a food web consisting of three levels. Agents on the lowest level produce food from dead agents (detritus) of the upper levels and are themselves eaten by the first level species, which in turn are prey for the top level species. Agents which do not find food in a given time, die with a given probability, while eating enables them to produce offspring in their neighborhood. This rule applies to species on all levels, including the lowest one. The dynamics is therefore nutrient limited. We are considering two pathways — grazers and detritus (using dead organic matter). We show that the emerging dynamics is more complex than the ordinary predator-prey systems in which bottom species are indestructible. We investigate the viability of our model and we construct appropriate (extinct-alive) phase diagrams. We demonstrate how the temporal fluctuations in the densities of the three populations are correlated. We show also that the density of the middle level agents plays the key role in the viability of the investigated food web.     

Tissus linéaires et théorèmes d'algébrisation de type Abdel-inverse et Reiss-inverse

A d-web in ( ,0) is given by d complex analytic foliations of codimension one in ( ,0) which are in general position. A d-web in ( ,0) is linear if all the leaves are (pieces of) hyperplanes in and is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in of degree d. We characterize linear webs in ( ,0). We give explicit conditions under which a linear d-web in ( ,0) is algebraic and we obtain equations for in this case. Some related problems are discussed and some questions are posed.     

Visible Light Photocatalytic Functional TiO2/PVDF Nanofibers for Dye Pollutant Degradation

The photodegradation of poly(vinylidene fluoride) (PVDF)/titanium oxide (TiO₂) nanofibers under visible light is described, something that has not been previously reported in the literature. Visible light photocatalytic electrospun PVDF/TiO₂ nanofiber webs with anatase TiO₂ concentration varying from 0% to 20% (0%, 1%, 3%, 5%, 10%, and 20%) are produced, and their ability to degrade a toxic pollutant, Rhodamine B (RhB), is studied. Photodegradation study using UV–vis spectroscopy on PVDF/TiO₂ nanofiber webs (with TiO₂ concentration of 20%) shows that 80% of RhB is degraded within 6 h at the wavelength of 546 nm, which clearly falls within the visible spectra. The color of RhB solvent catalyzed by PVDF/TiO₂ nanofiber webs gradually changes from red to orange, then to yellow, further to light yellow till colorless, which suggests the complete photodegradation of RhB under visible light. To estimate the rate of photodegradation, the reaction constant k is calculated. Based on the k value, PVDF/TiO₂ nanofiber webs with 20% TiO₂ concentration show the highest degradation rate compared to other PVDF/TiO₂ nanofiber webs and pure TiO₂ nanoparticles. This study proves the viability of TiO₂‐based nanofibers to have catalytic capabilities under low‐energy visible light.     

A METAPHYSIOLOGICAL POPULATION MODEL OF STORAGE IN VARIABLE ENVIRONMENTS

ABSTRACT. We use mechanistic arguments to generalize a hierarchical metaphysiological approach developed by one of us to modeling biological populations (Getz, [1991, 1993]) and extend the approach to include a storage component in the population. We model the growth of single species and consumer-resource interactions, both with and without storage. Our approach unifies modeling storage across trophic levels and is much simpler and more efficient to implement numerically than individual based approaches or population approaches that include integral, delay, or partial differential equation components in the model. Using intake functions (i.e., functional responses) that include the effects of interference competition, we apply the model to a hypothetical herbivore feeding on a resource that fluctuates seasonally and demonstrate the importance of a flow from storage that buffers the population against periods when resources are scarce or absent. We also apply the model to a hypothetical plant population that is driven by fluctuating resources and demonstrate the importance of a translocation flow from storage at the end of a dormant season, corresponding to periods when resources are most scarce. Finally, we couple these two populations for the case where the herbivore feeds exclusively on non-storage biomass, and demonstrate how the population dynamics can be affected by the rates at which buffering and translocation flows transfer from storage to active tissue in the herbivore and plant populations. In particular, for certain buffering and translocation flow rates, 1-year unimodal, 2-year bimodal, and 2-year unimodal cycles can emerge in the same herbivore population.     

Semiintegrable almost Grassmann structures

In the present paper we study locally semiflat (we also call them semiintegrable) almost Grassmann structures. We establish necessary and sufficient conditions for an almost Grassmann structure to be - or β-semiintegrable. These conditions are expressed in terms of the fundamental tensors of almost Grassmann structures. Since we are not able to prove the existence of locally semiflat almost Grassmann structures in the general case, we give many examples of - and β-semiintegrable structures, mostly four-dimensional. For all examples we find systems of differential equations of the families of integral submanifolds V and V_β of the distributions Δ and Δ_β of plane elements associated with an almost Grassmann structure. For some examples we were able to integrate these systems and find closed form equations of submanifolds V and V_β.     

Computer simulations of history of life: speciation, emergence of complex species from simpler organisms, and extinctions

We propose a generic model of eco-systems, with a hierarchical food web structure. In our computer simulations, we let the eco-system evolve continuously for so long that we can monitor extinctions as well as speciations over geological time scales. Speciation leads not only to horizontal diversification of species at any given trophic level but also to vertical bio-diversity that accounts for the emergence of complex species from simpler forms of life. We find that five or six trophic levels appear as the eco-system evolves for sufficiently long time, starting initially from just one single level. Moreover, the time intervals between the successive collections of ecological data is so short that we could also study “micro”-evolution of the eco-system, i.e., the birth, ageing and death of individual organisms.     

Surface morphology and electrical properties of polyurethane nanofiber webs spray‐coated with carbon nanotubes

Multiwalled carbon nanotubes (MWNTs) were spray‐coated on electrospun polyurethane nanofiber webs for electrical conductive application. For the effective coating of MWNTs, hyperbranched polyurethane (HBPU) was used by blending with linear polyurethane, which was synthesized in the A₂ + B₃ approach using poly(ε‐caprolactone)diol, 4,4′‐methylene bis(phenylisocynate), and castor oil. SEM measurements showed that the MWNTs could be coated well along the surface of nanofibers when the HBPU was blended in the linear polyurethane nanofibers. Blending of HBPU in the nanofibers also affected the electrical conductivity of MWNT‐coated nanofiber webs. The low electrical resistance from 20 to 400 Ω/sq was obtained for MWNT‐coated nanofiber webs and their electrical resistance decreased with an increase of spraying frequency. As a potential application of MWNT‐coated nanofiber webs, the electrical heating effect because of applied voltage was demonstrated. Copyright © 2011 John Wiley & Sons, Ltd.