Biomimetic Synthesis of Materials for Technology

In a world with ever decreasing natural reserves, researchers are striving to find sustainable methods of producing components for technology. Bioinspired, biokleptic and biomimetic materials can be used to form a wide range of technologically relevant materials under environmentally friendly conditions. Here we investigate a range of biotemplated and bioinspired materials that can be used to develop components for devices, such as optics, photonics, photovoltaics, circuits and data storage.     

A finite element method for interface problems in domains with smooth boundaries and interfaces

This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite element method to the perturbed problem on the approximate polygonal domains. It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation. As such the method is robust in the regularity of the data in the original problem.     

A new approximation technique for div-curl systems

In this paper, we describe an approximation technique for div-curl systems based in where is a domain in . We formulate this problem as a general variational problem with different test and trial spaces. The analysis requires the verification of an appropriate inf-sup condition. This results in a very weak formulation where the solution space is and the data reside in various negative norm spaces. Subsequently, we consider finite element approximations based on this weak formulation. The main approach of this paper involves the development of ``stable pairs" of discrete test and trial spaces. With this approach, we enlarge the test space so that the discrete inf-sup condition holds and we use a negative-norm least-squares formulation to reduce to a uniquely solvable linear system. This leads to optimal order estimates for problems with minimal regularity which is important since it is possible to construct magnetostatic field problems whose solutions have low Sobolev regularity (e.g., with ). The resulting algebraic equations are symmetric, positive definite and well conditioned. A second approach using a smaller test space which adds terms to the form for stabilization will also be mentioned. Some numerical results are also presented.

     

Regularity estimates for solutions of the equations of linear elasticity in convex plane polygonal domains

The Dirichlet problem for the plane elasticity problem on a convex polygonal domain is considered and it is proved that for data in L ² the H ² regularity estimate holds with constants independent of the Lamé coefficients.     

The approximation of the Maxwell eigenvalue problem using a least-squares method

In this paper we consider an approximation to the Maxwell's eigenvalue problem based on a very weak formulation of two div-curl systems with complementary boundary conditions. We formulate each of these div-curl systems as a general variational problem with different test and trial spaces, i.e., the solution space is and components in the test spaces are in subspaces of , the Sobolev space of order one on the computational domain . A finite-element least-squares approximation to these variational problems is used as a basis for the approximation. Using the structure of the continuous eigenvalue problem, a discrete approximation to the eigenvalues is set up involving only the approximation to either of the div-curl systems. We give some theorems that guarantee the convergence of the eigenvalues to those of the continuous problem without the occurrence of spurious values. Finally, some results of numerical experiments are given.

     

A sphere theorem for the equations of elasticity

Zusammenfassung In dieser Arbeit werden Ausdrücke für das Verschiebungsfeld in einer elastischen Kugel angegeben, deren Oberfläche a) elastisch gelagert, b) eingespannt, c) frei ist. Die Verschiebungen werden durch diejenigen Verschiebungen und Spannungen ausgedrückt, die in einem unendlichen Körper unter derselben Verteilung von Singularitäten entstehen.     

A least-squares approach based on a discrete minus one inner product for first order systems

The purpose of this paper is to develop and analyze a least-squares approximation to a first order system. The first order system represents a reformulation of a second order elliptic boundary value problem which may be indefinite and/or nonsymmetric. The approach taken here is novel in that the least-squares functional employed involves a discrete inner product which is related to the inner product in (the Sobolev space of order minus one on ). The use of this inner product results in a method of approximation which is optimal with respect to the required regularity as well as the order of approximation even when applied to problems with low regularity solutions. In addition, the discrete system of equations which needs to be solved in order to compute the resulting approximation is easily preconditioned, thus providing an efficient method for solving the algebraic equations. The preconditioner for this discrete system only requires the construction of preconditioners for standard second order problems, a task which is well understood.

     

Self-assembled layers based on isomerizable stilbene and diketoarylhydrazone moieties

The ability to form self-assembled layers on gold (Au) using five organosulfur compounds that contain isomerizable groups has been investigated. The isomerizable groups are either stilbene or diketoarylhydrazone derivatives. To anchor them on a gold surface, the isomerizable groups have been combined with sulfur-containing groups (disulfide, 1,2-dithiolane, and thiophene). The resulting thin films assembled on gold were characterized by X-ray photoelectron spectroscopy (XPS), infrared (FTIR) reflectance spectroscopy, ellipsometry, and water contact angle measurements. Though all substances have the potential to form self-assembled monolayers (SAMs), only two of them, disulfanediyl-bis(ethane-2,1-diyl) bis(4-styrylbenzoate) (1) and 4-[(2,4-dioxo-3-pentylidene)diazane-2,2,1-triyl]phenyl thioctate (4), yield the expected structure, the latter one showing the possibility to incorporate diarylketohydrazone moieties into SAMs. The compound 4-[(2,4-dioxo-3-pentylidene)diazane-2,2,1-triyl]phenyl thiophene-2-carboxylate (5) does not self-assemble on gold, but 4-styrylphenyl thioctate (3) presumably forms multilayers. In the case of disulfanediyl-bis(ethane-2,1-diyl) bis[4-(p-nitrostyryl)benzoate] (2), we propose a structure with a fraction of the molecules bound to gold via the nitro group. The results show that the propensity of organosulfur compounds to self-assemble on gold not only is determined by the sulfur-containing group but also is affected by the complete molecule.     

Ferrous Iron Binding Key to Mms6 Magnetite Biomineralisation: A Mechanistic Study to Understand Magnetite Formation Using pH Titration and NMR Spectroscopy

Formation of magnetite nanocrystals by magnetotactic bacteria is controlled by specific proteins which regulate the particles’ nucleation and growth. One such protein is Mms6. This small, amphiphilic protein can self‐assemble and bind ferric ions to aid in magnetite formation. To understand the role of Mms6 during in vitro iron oxide precipitation we have performed in situ pH titrations. We find Mms6 has little effect during ferric salt precipitation, but exerts greatest influence during the incorporation of ferrous ions and conversion of this salt to mixed‐valence iron minerals, suggesting Mms6 has a hitherto unrecorded ferrous iron interacting property which promotes the formation of magnetite in ferrous‐rich solutions. We show ferrous binding to the DEEVE motif within the C‐terminal region of Mms6 by NMR spectroscopy, and model these binding events using molecular simulations. We conclude that Mms6 functions as a magnetite nucleating protein under conditions where ferrous ions predominate.