On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis

In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We show the existence of an exponential attractor and, hence, of a finite-dimensional global attractor under certain 'balance conditions' on the order of the degeneracy and the growth of the chemotactic function

Coordination of Cu(II) and Ni(II) in polymers imprinted so as to optimize amine chelate formation

Molecular imprinting has become an established technique. However, little was done on direct investigation of the sorbents produced. In the present work, en ESR method was used for the investigation of the complex formation processes within the sorbents imprinted with copper(II) and nickel(II). The sorbents were synthesized from a mixture of linear low molecular weight polyethyleneimine oligomers. The composition, structure and distribution of complexes in the resin phase were investigated. The effects of the synthesis conditions, loading degree and water content were examined. The presence of certain copper complexes was found to be a convenient characteristic of the imprinting efficiency. The optimum synthesis conditions for obtaining sorbents imprinted with copper(II) or nickel(II) were identified. The imprinting results in the improvement of the stability of the complexes and the selectivity and working capacity of the sorbents. The imprinted samples are also characterized by a more even distribution of chelating sites. The synthesis conditions and loading by ions allow for the regulation of the ratio between individual complexes and magnetic associates in the resin phase. This is a critical point on the future use of the metal containing imprinted sorbents as catalysts. (C) 2003 Published by Elsevier Science Ltd

Linearly constrained evolutions of critical points and an application to cohesive fractures

We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material

Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems

In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps efficiently coupling coarse and microscopic state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov Chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.Comment: 37 page

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

This article has been made available through the Brunel Open Access Publishing Fund.A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments

Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast

We consider divergence-form scalar elliptic equations and vectorial equations for elasticity with rough ($L^\infty(\Omega)$, $\Omega \subset \R^d$) coefficients $a(x)$ that, in particular, model media with non-separated scales and high contrast in material properties. We define the flux norm as the $L^2$ norm of the potential part of the fluxes of solutions, which is equivalent to the usual $H^1$-norm. We show that in the flux norm, the error associated with approximating, in a properly defined finite-dimensional space, the set of solutions of the aforementioned PDEs with rough coefficients is equal to the error associated with approximating the set of solutions of the same type of PDEs with smooth coefficients in a standard space (e.g., piecewise polynomial). We refer to this property as the {\it transfer property}. A simple application of this property is the construction of finite dimensional approximation spaces with errors independent of the regularity and contrast of the coefficients and with optimal and explicit convergence rates. This transfer property also provides an alternative to the global harmonic change of coordinates for the homogenization of elliptic operators that can be extended to elasticity equations. The proofs of these homogenization results are based on a new class of elliptic inequalities which play the same role in our approach as the div-curl lemma in classical homogenization.Comment: Accepted for publication in Archives for Rational Mechanics and Analysi

Quasistatic crack growth based on viscous approximation: a model with branching and kinking.

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking

SIK1/SOS2 networks: decoding sodium signals via calcium-responsive protein kinase pathways

Changes in cellular ion levels can modulate distinct signaling networks aimed at correcting major disruptions in ion balances that might otherwise threaten cell growth and development. Salt-inducible kinase 1 (SIK1) and salt overly sensitive 2 (SOS2) are key protein kinases within such networks in mammalian and plant cells, respectively. In animals, SIK1 expression and activity are regulated in response to the salt content of the diet, and in plants SOS2 activity is controlled by the salinity of the soil. The specific ionic stress (elevated intracellular sodium) is followed by changes in intracellular calcium; the calcium signals are sensed by calcium-binding proteins and lead to activation of SIK1 or SOS2. These kinases target major plasma membrane transporters such as the Na+,K+-ATPase in mammalian cells, and Na+/H+ exchangers in the plasma membrane and membranes of intracellular vacuoles of plant cells. Activation of these networks prevents abnormal increases in intracellular sodium concentration

A modeling and simulation study of siderophore mediated antagonism in dual-species biofilms

<p>Abstract</p> <p>Background</p> <p>Several bacterial species possess chelation mechanisms that allow them to scavenge iron from the environment under conditions of limitation. To this end they produce siderophores that bind the iron and make it available to the cells later on, while rendering it unavailable to other organisms. The phenomenon of siderophore mediated antagonism has been studied to some extent for suspended populations where it was found that the chelation ability provides a growth advantage over species that do not have this possibility. However, most bacteria live in biofilm communities. In particular <it>Pseudomonas fluorescens </it>and <it>Pseudomonas putida</it>, the species that have been used in most experimental studies of the phenomenon, are known to be prolific biofilm formers, but only very few experimental studies of iron chelation have been published to date for the biofilm setting. We address this question in the present study.</p> <p>Methods</p> <p>Based on a previously introduced model of iron chelation and an existing model of biofilm growth we formulate a model for iron chelation and competition in dual species biofilms. This leads to a highly nonlinear system of partial differential equations which is studied in computer simulation experiments.</p> <p>Conclusions</p> <p>(i) Siderophore production can give a growth advantage also in the biofilm setting, (ii) diffusion facilitates and emphasizes this growth advantage, (iii) the magnitude of the growth advantage can also depend on the initial inoculation of the substratum, (iv) a new mass transfer boundary condition was derived that allows to a priori control the expect the expected average thickness of the biofilm in terms of the model parameters.</p