A multiphase finite element simulation of biological conversion processes in landfills

Worldwide, landfills are the most common way to dispose of waste, but have an impact on the environment as a result of harmful gas and leachate production. Estimating the long-term behaviour of a landfill in regard to this gas production and organic degrading, as well as to settlement and waste water production, is of high importance. Therefore, a model has been developed to simulate these processes. This constitutive model is based on the multiphase Theory of Porous Media. The body under investigation consists of an organic and an inorganic phase as well as a liquid and a gas phase. The equations of the model are developed on the basis of a consistent thermo-mechanical approach including the momentum balance for the solid phase and the mixture, the energy balance for the mixture and the mass balance for the gas phase. All interactions between the constituents such as mass transfers, interaction forces and energy fluxes are taken into consideration. The strongly coupled set of partial differential equations is implemented in the finite element code FEAP. The theoretical framework and the results of meantime successfully performed simulation of a real landfill body will be shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient kinetic Monte Carlo simulation

This paper concerns kinetic Monte Carlo (KMC) algorithms that have a single-event execution time independent of the system size. Two methods are presented—one that combines the use of inverted-list data structures with rejection Monte Carlo and a second that combines inverted lists with the Marsaglia–Norman–Cannon algorithm. The resulting algorithms apply to models with rates that are determined by the local environment but are otherwise arbitrary, time-dependent and spatially heterogeneous. While especially useful for crystal growth simulation, the algorithms are presented from the point of view that KMC is the numerical task of simulating a single realization of a Markov process, allowing application to a broad range of areas where heterogeneous random walks are the dominate simulation cost.     

Microvascular oxygen quantification using two-photon microscopy

An instrument is demonstrated that is capable of three-dimensional (3D) vasculature imaging and pO(2) quantification with high spatial resolution. The instrument combines two-photon (2P) microscopy with phosphorescence quenching to measure pO(2). The instrument was demonstrated by performing depth-resolved microvascular pO(2) measurements of rat cortical vessels down to 120 microm below the surface. 2P excitation of porphyrin was confirmed, and measured pO(2) values were consistent with previously published data for normoxic and hyperoxic conditions. The ability to perform 3D pO(2) measurements using optical techniques will allow researchers to overcome existing limitations imposed by polarographic electrodes, magnetic resonance techniques, and surface-only pO(2) measurement techniques.     

The Scenery Flow for Hyperbolic Julia Sets

We define the scenery flow space at a point z in the Julia setJ of a hyperbolic rational map T : C C with degree at least2, and more generally for T a conformal mixing repellor. We prove that, for hyperbolic rational maps, except for a fewexceptional cases listed below, the scenery flow is ergodic.We also prove ergodicity for almost all conformal mixing repellors;here the statement is that the scenery flow is ergodic for therepellors which are not linear nor contained in a finite unionof real-analytic curves, and furthermore that for the collectionof such maps based on a fixed open set U, the ergodic casesform a dense open subset of that collection. Scenery flow ergodicityimplies that one generates the same scenery flow by zoomingdown towards almost every z with respect to the Hausdorff measureH^d, where d is the dimension of J, and that the flow has a uniquemeasure of maximal entropy. For all conformal mixing repellors, the flow is loosely Bernoulliand has topological entropy at most d. Moreover the flow atalmost every point is the same up to a rotation, and so as acorollary, one has an analogue of the Lebesgue density theoremfor the fractal set, giving a different proof of a theorem ofFalconer. 2000 Mathematical Subject Classification: 37F15, 37F35, 37D20.     

Taxol Inclusion Complexes with a Cyclodextrin Dimer: Possibilities to Detoxify Chemotherapeutics and to Target Drugs Specifically to Tumors?

The natural drug, paclitaxel (taxol), is highly effectiveas a tumor chemotherapeuticwith a low probability of inducing chemoresistance,but shows severe toxic side effectsat the therapeutic dose. How can this toxicitybe overcome? Here we report the synthesisof cyclodextrin dimers connected at thesecondary face by amide-bonded aliphatic spacers. The spacer length of one of the dimers referred to asdiβCD(2N-A4C5A4) or dimer 7cmatches the distance between the twobenzoic acid residues of paclitaxel. We investigated the physical inclusion of taxol into this dimer using the TNS-label competition method. Affinity constants with the dimer in comparison to free β-cyclodextrin are found to be of the order of 10⁷ l/mole.When included into the cyclodextrin dimer, the drug shows a considerable time delay of incorporation into human tumor cell cultures (OAT SCLC cells) or a total exclusion from the cells. This is the prerequisite to avoid intoxication of other organs of a patient. Possibilities are discussed to detoxify chemotherapeutics and to target their inclusioncomplexes specifically to tumors using specific biological signals.     

Triads, Flocks of Conics and Q -(5,q)

We show that if an ovoid of Q (4,q),q even, admits a flock of conics then that flock must be linear. It follows that an ovoid of PG (3,q),q even, which admits a flock of conics must be an elliptic quadric. This latter result is used to give a characterisation of the classical example Q ^-(5,q) among the generalized quadrangles T ₃( ), where is an ovoid of PG (3q) and q is even, in terms of the geometric configuration of the centres of certain triads.     

Structure in the classical knot concordance group

We provide new information about the structure of the abelian group of topological concordance classes of knots in $S^3$. One consequence is that there is a subgroup of infinite rank consisting entirely of knots with vanishing Casson-Gordon invariants but whose non-triviality is detected by von Neumann signatures.