A fourth‐order method for numerical integration of age‐ and size‐structured population models

In many applications of age‐ and size‐structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth‐order method based on composite Newton‐Cotes quadratures for a size‐structured population model. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Synthesis and liquid crystalline properties of low molecular mass compounds containing the 1,4-bis(5-phenyl-1,3,4-oxadiazolyl)benzene unit

The synthesis and characterization of low molecular mass compounds containing 1,4-bis(5-phenyl-1,3,4-oxadiazolyl)benzene is reported. All compounds are fluorescent in solution. Due to the flat shape of the conjugated unit, smectic-like packing is observed at high temperatures for some of the synthesized compounds. Moreover the insertion of a lateral flexible alkoxy unit strongly destabilizes the smectic order whilst promoting the appearance of a nematic phase in the case of the shortest methoxy unit. The mesogenic character of this unit may be of interest in the synthesis of liquid crystalline polymeric systems, taking advantage of both the fluorescent properties and the peculiar molecular structure of the liquid crystalline state.     

Synthesis and liquid crystalline properties of low molecular mass compounds containing the 1,4-bis(5-phenyl-1,3,4-oxadiazolyl)benzene unit

The synthesis and characterization of low molecular mass compounds containing 1,4-bis(5-phenyl-1,3,4-oxadiazolyl)benzene is reported. All compounds are fluorescent in solution. Due to the flat shape of the conjugated unit, smectic-like packing is observed at high temperatures for some of the synthesized compounds. Moreover the insertion of a lateral flexible alkoxy unit strongly destabilizes the smectic order whilst promoting the appearance of a nematic phase in the case of the shortest methoxy unit. The mesogenic character of this unit may be of interest in the synthesis of liquid crystalline polymeric systems, taking advantage of both the fluorescent properties and the peculiar molecular structure of the liquid crystalline state.     

Two-sex age structured dynamics in a fixed sex-ratio population

An age structured model is considered in order to analyze the growth of a two sex population with a fixed age-specific sex ratio. The model is intended to give an insight into the dynamics of a population where the mating process takes place at random and the proportion between females and males is not influenced by environmental or social factors, but only depends on a differential mortality or on a possible transition from one sex to the other (e.g. in sequential hermaphrodite species).First a basic model, asymptotically linear, is considered and its ergodicity is studied. Survival thresholds and their dependence on the sex ratio are then analyzed, in connection with the optimal sex ratio to guarantee survival.A further model including logistic effect is also considered and discussed in connection with existence and stability of steady states.     

Liquid crystal behaviour of linear copolymers—I

The molar volumes of some mesophasic linear homo- and copolymers have been measured as a function of temperature. Both the liquid crystal phase (nematic) and the isotropic liquid have been examined. The polymer chain is characterized by an alternating sequence of rigid groups and flexible spacers. The molar volumes measured for the liquid crystal phase give evidence for a substantially disordered conformation taken by the flexible spacers in the nematic phase. Analogies between homo- and copolymers are discussed.     

Mesophasic properties of low molecular weight analogues of nematogenic polycarbonates

The mesophasic behaviour of the following compounds has been investigated by DSC, X-ray diffraction and optical microscopy methods: CH₃(CH₂)₄-CO-R-A _n -R-CO-(CH₂)₄-CH₃,n=9 14, 16 CH₃(CH₂)₄-CO-R-B _n -R-CO-(CH₂)₄-CH₃,n=2, 3A _n=-CO-O-(CH₂)_n–4-O-CO-,B _n =-CO-(OCH₂CH₂) _n -O-CO-,R=-O-Ø-C(CH₃)=N-N=(CH₃)C-Ø-O-,Ø=-C₆H₄ They have been assumed to be low molecular weight models of homologous nematogenic polymers.All the examined compounds exhibit nematic mesomorphism. On complete analogy with the corresponding polymers, the thermodynamic data relative to the nematic-isotropic phase transition show a very reduced, if any, odd-even fluctuation. These data are compared with those obtained for very similar compounds, both polymeric and non-polymeric, containing ester linkages between the rigid and flexible groups, to provide evidence of the reliability of the dimeric compounds as models of the polymeric homologues.

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Zusammenfassung Das mesophasische Verhalten der folgenden Verbindungen wurde mittels DSC, Röntgendiffraktion und optischer Mikroskopie untersucht: CH₃(CH₂)₄-CO-R-A _n -R-CO-(CH₂)₄-CH₃;n=914, 16 CH₃(CH₂)₄-CO-R-B _n -R-CO-(CH₂)₄-CH₃;n=2, 3A _n =-CO-O-(CH₂)_n-4-O-CO-;B _n =-CO-(OCH₂CH₂)_n-O-CO-;R=-O-C₆H₄-C(CH₃)=N-N=(CH₃)C-C₆H₄-O-. Die Verbindungen wurden als Modelle homologer nematogener Polymere mit niedrigem Molekulargewicht angesehen. Alle untersuchten Verbindungen zeigen einen nematischen Mesomorphismus. Analog zu den entsprechenden Polymeren zeigen die sich auf den nematisch-isotropen Phasenübergang beziehenden thermodynamischen Daten eine, wenn überhaupt, sehr reduzierte ungerade-gerade Fluktuation. Diese Daten werden mit denen verglichen, die für sehr ähnliche, sowohl polymère als auch nicht-polymere Verbindungen mit Esterbindungen zwischen den starren und flexiblen Gruppen erhalten wurden, um Beweise für die Zuverlässigkeit der auf dimeren Verbindungen aufbauenden Modelle für polymère Homologe zu erhalten.

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, : CH₃(CH₂)₄-CO-R-A _n -R-CO-(CH₂)₄-CH₃ n=914,16 CH₃(CH₂)₄-CO-R-B _n -R-CO-(CH₂)₄-CH₃ n=2, 3A _n =-CO-O-(CH₂) _n–4-O-CO-;B _n =-CO-(OCH₂CN₂) _n -O-COR =-O--C(CH₃)=N-N=(CH₃)C--O- =C₆H₄ , . . — , , , - . , , ,

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The financial assistance of the Ministero Pubblica Istruzione is acknowledged.     

Derivation and characteristics analysis of an acoustics–convection upstream resolution algorithm for the two‐dimensional Euler and Navier–Stokes equations

The first of a two‐paper series, this paper introduces a new decomposition not of the hyperbolic flux vector but of the flux vector Jacobian. The paper then details for the Euler and Navier–Stokes equations an intrinsically infinite directional upstream‐bias formulation that rests on the mathematics and physics of multi‐dimensional acoustics and convection. Based upon characteristic velocities, this formulation introduces the upstream bias directly at the differential equation level, before the spatial discretization, within a characteristics‐bias governing system. Through a decomposition of the Euler flux divergence into multi‐dimensional acoustics and convection–acoustics components, this characteristics‐bias system induces consistent upstream bias along all directions of spatial wave propagation, with anisotropic variable‐strength upstreaming that correlates with the spatial distribution of characteristic velocities. Copyright © 2005 John Wiley & Sons, Ltd.     

A CFD Euler solver from a physical acoustics–convection flux Jacobian decomposition

This paper introduces a continuum, i.e. non‐discrete, upstream‐bias formulation that rests on the physics and mathematics of acoustics and convection. The formulation induces the upstream‐bias at the differential equation level, within a characteristics‐bias system associated with the Euler equations with general equilibrium equations of state. For low subsonic Mach numbers, this formulation returns a consistent upstream‐bias approximation for the non‐linear acoustics equations. For supersonic Mach numbers, the formulation smoothly becomes an upstream‐bias approximation of the entire Euler flux. With the objective of minimizing induced artificial diffusion, the formulation non‐linearly induces upstream‐bias, essentially locally, in regions of solution discontinuities, whereas it decreases the upstream‐bias in regions of solution smoothness. The discrete equations originate from a finite element discretization of the characteristic‐bias system and are integrated in time within a compact block tridiagonal matrix statement by way of an implicit non‐linearly stable Runge–Kutta algorithm for stiff systems. As documented by several computational results that reflect available exact solutions, the acoustics–convection solver induces low artificial diffusion and generates essentially non‐oscillatory solutions that automatically preserve a constant enthalpy, as well as smoothness of both enthalpy and mass flux across normal shocks. Copyright © 1999 John Wiley & Sons, Ltd.