U. van Rienen

Influence of Uncertainties in the Material Properties of Brain Tissue on the Probabilistic Volume of Tissue Activated

The aim of this study was to examine the influence of uncertainty of the material properties of brain tissue on the probabilistic voltage response and the probabilistic volume of tissue activated (VTA) in a volume conductor model of deep brain stimulation. To quantify the uncertainties of the desired quantities without changing the deterministic model, a nonintrusive projection method was used by approximating these quantities by a polynomial expansion on a multidimensional basis known as polynomial chaos. The coefficients of this expansion were computed with a multidimensional quadrature on sparse Smolyak grids. The deterministic model combines a finite element model based on a digital brain atlas and a multicompartmental model of mammalian nerve fibers. The material properties of brain tissue were modeled as uniform random parameters using data from several experimental studies. Different magnitudes of uncertainty in the material properties were computed to allow predictions on the resulting uncertainties in the desired quantities. The results showed a major contribution of the uncertainties in the electrical conductivity values of brain tissue on the voltage response as well as on the predicted VTA, while the influence of the uncertainties in the relative permittivity was negligible.

Mechanics and electrostatics of the interactions between osteoblasts and titanium surface.

Due to oxidation and adsorption of chloride and hydroxyl anions, the surface of titanium (Ti) implants is negatively charged. A possible mechanism of the attractive interaction between the negatively charged Ti surface and the negatively charged osteoblasts is described theoretically. It is shown that adhesion of positively charged proteins with internal charge distribution may give rise to attractive interaction between the Ti surface and the osteoblast membrane. A dynamic model of the osteoblast attachment is presented in order to study the impact of geometrically structured Ti surfaces on the osteoblasts attachment. It is indicated that membrane-bound protein complexes (PCs) may increase the membrane protrusion growth between the osteoblast and the grooves on titanium (Ti) surface and thereby facilitate the adhesion of osteoblasts to the Ti surface. On the other hand, strong local adhesion due to electrostatic forces may locally trap the osteoblast membrane and hinder the further spreading of osteointegration boundary. We suggest that the synergy between these two processes is responsible for successful osteointegration along the titanium surface implant.

Comparison of Krylov-type methods for complex linear systems applied to high-voltage problems

Krylov-subspace methods for complex-valued systems are still a present research topic in numerical mathematics. Due to the lack of theoretical results systematic numerical experiments are very important in order to find a sufficiently robust solution method. An important problem in high-voltage power plants are arc-overs on moist or contaminated insulators. A quantitative knowledge of the electric behaviour of layers of water droplets is necessary in order to understand the resulting ageing processes. Discretization of the electro-quasistatic problem leads to large sparse complex systems of linear equations. Comparisons between different Krylov-subspace methods, also in combination with residual smoothing techniques, and parameter studies are presented in this paper.

Extraction of effective permittivity and permeability of metallic powders in the microwave range

In this work, effective electric permittivity and magnetic permeability of metallic‐dielectric mixtures are extracted from electromagnetic full 3D simulation data in the microwave range. The numerical method used here is the finite integration technique with periodic boundary conditions. Simulated mixtureshaveperiodicextendindirectionsperpendiculartothedirectionofthe planewave. Thus, itissufficienttoanalyzeaunitelementinordertoextractthe effective electric and magnetic properties. Using this procedure, the behavior of fine copper powders irradiated by microwaves at a frequency of 2.45GHz is simulated. Then, the relation between particle size and the mixture’s effective properties is studied. By introducing a thin copper oxide or conductive layer it is possible to emulate the effective properties of metallic powder compacts in the early stage of sintering. Thus, this work contributes to improving the insight into the mechanisms of microwave absorption in powders of conductive materials in contrast to non-absorption in bulk metals.

MAFIA version 4

MAFIA Version 4.0 is an almost completely new version of the general purpose electromagnetic simulator known since 13 years. The major improvements concern the new graphical user interface based on state of the art technology as well as a series of new solvers for new physics problems. MAFIA now covers heat distribution, electro-quasistatics, S-parameters in frequency domain, particle beam tracking in linear accelerators, acoustics and even elastodynamics. The solvers that were available in earlier versions have also been improved and/or extended, as for example the complex eigenmode solver, the 2D–3D coupled PIC solvers. Time domain solvers have new waveguide boundary conditions with an extremely low reflection even near cutoff frequency, concentrated elements are available as well as a variety of signal processing options. Probably the most valuable addition are recursive sub-grid capabilities that enable modeling of very small details in large structures.

Simulation of low-frequency fields on high-voltage insulators with light contaminations

This paper deals with the numerical solution of the linear complex Poisson equation. The practical background of posing this problem are arc-overs on moist or contaminated insulators in high-voltage power plants. The electrostatic field of the charge-free space prevails; essentially below a critical voltage U/sub k/. However, the dielectric material loses its insulating characteristics above U/sub k/. It becomes the carrier of a discharge which builds up a conducting connection along the insulator. It is a matter of slowly varying fields (50 Hz), for which the displacement current is a significant quantity. These slowly varying fields can be determined by solving a complex potential problem. Discretization leads to a complex system of linear equations with symmetric matrix. This system is solved by various modern conjugate gradient-type methods. Numerical simulations for test and real life problems are presented.

Attachment of Rod-Like (BAR) Proteins and Membrane Shape

Previous studies have shown that cellular function depends on rod-like membrane proteins, among them Bin/Amphiphysin/Rvs (BAR) proteins may curve the membrane leading to physiologically important membrane invaginations and membrane protrusions. The membrane shaping induced by BAR proteins has a major role in various biological processes such as cell motility and cell growth. Different models of binding of BAR domains to the lipid bilayer are described. The binding includes hydrophobic insertion loops and electrostatic interactions between basic amino acids at the concave region of the BAR domain and negatively charged lipids. To shed light on the elusive binding dynamics, a novel experiment is proposed to expand the technique of single-molecule AFM for the traction of binding energy of a single BAR domain.

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin–Poisson–Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin–Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson–Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field.

Multigrid Solvers for Poisson’s Equation in Computational Electromagnetics

Complex real life problems, as they appear with the simulation of electromagnetic fields, demand the construction of efficient and robust solvers for the related equations. In the present paper we investigate multigrid algorithms for the solution of static problems on adaptive discretizations. Two multigrid strategies are compared: algebraic multigrid, which performs the adaption to the discretization automatically and geometric multigrid with semi-coarsening, which has fast convergence if the discretization fits the coarsening strategy.

Frequency Domain Analysis of Waveguides and Resonators With Fit On Non-Orthogonal Triangular Grids- Abstract

The focus of this paper is on the solution of Maxwells equations for time-harmonic fields on triangular, possibly non-orthogonal meshes. The method is based on the well-known Finite Integration Technique (FIT) [?, ?] which is a proven consistent discretization method for the computation of electromagnetic fields. FIT on triangular grids was first introduced in [?, ?] for eigenvalue problems arising in the design of accelerator components and dielectric loaded waveguides. For many technical applications the 2D simulation on a triangular grid combines the advantages of FIT, as e.g. the consistency of the method or the numerical advantage of banded system matrices, with the geometrical flexibility of non-coordinate grids. The FIT-discretization on non-orthogonal 2D grids has close relations [?] to the Nédélec elements [?, ?] or edge elements in the Finite Element Method.The focus of this paper is on the solution of Maxwells equations for time-harmonic fields on triangular, possibly non- orthogonal meshes. The method is based on the well-known Finite Integration Technique (FIT) (33, 35) which is a proven consistent discretization method for the computation of electromagnetic fields. FIT on triangular grids was first introduced in (29, 31) for eigenvalue problems arising in the design of accelerator components and dielectric loaded waveguides. For many technical applications the 2D simulation on a triangular grid combines the advantages of FIT, as e.g. the consistency of the method or the numerical advantage of banded system matrices, with the geometrical flexibility of non-coordinate grids. The FIT-discretization on non-orthogonal 2D grids has close relations (26) to the Nedelec elements (14, 15) or edge elements in the Finite Element Method.