Decay of eigenfunctions of elliptic PDE's,I

We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on R^d${\mathbb{R}}^d$. We show that the possible (global) critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying eigenfunctions and a refined exponential upper bound.     

Neutral gas free molecular flow algorithm including ionization and walls for use in plasma simulations

Several plasma devices, including Hall and ion thrusters, operate by ionizing a low density neutral gas for which the mean free path between collisions of gas molecules is greater than typical device dimensions. In general, the discrete-particle algorithms used to calculate the neutral gas ignore velocity changes due to collisions between gas molecules. However, particle algorithms are a source of unphysical statistical noise that may detract from the study of the plasma physics, the prime purpose of most simulations. In this paper we present a new neutral gas algorithm for use in plasma simulation codes that exploits the fact that very few collisions change the velocity of neutral gas molecules. The algorithm assumes that the particle velocity distribution function for neutrals emitted from a given surface remains unchanged except for a scale factor that reflects the loss of neutrals to ionization. The sources of neutrals may be gas inlets, and isotropic, thermally accommodated, gas molecules coming off chamber surfaces including recombined ions. The algorithm is implemented in two dimensions (R–Z) with emitting surfaces represented as surfaces of revolution. The advantage of this algorithm over the conventional particle approach is the absence of statistical noise.     

Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant λ. We show that the ground-state energy is an analytic function of λ and that the corresponding ground state can also be chosen to be an analytic function of λ. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground-state energy can be calculated using regular analytic perturbation theory.     

Damage simulation of brittle heterogeneous materials at the grain size level

Microstructure models at the grain size level open new potentials for the numerical investigation of micromechanical damage and fracturing. This paper presents a strategy to model heterogeneous brittle structures composed of binder and aggregate using the Discrete Element Method (DEM). A discretisation concept for both components was developed and implemented using spherical particles as discrete elements. The aggregate grains were modelled by clusters of these particles. Special routines were developed to generate specimens, to simulate laboratory tests and to analyse these simulations. Methods were developed to calibrate homogeneous and heterogeneous material by the determination of appropriate constitutive laws and their corresponding parameters. The simulation strategy allows to distinguish in detail between inter- and intra-granular microfracturing, between shear- and tensile-cracking and between microcracks within or between the different components of the heterogeneous material. Exemplarily, selected simulation results are presented for MgO-concrete.     

Crystal structure and hydrogen bonding study of (10E)-2,2-dimethyl-3,4-dihydro-2H-benzo[g]chromene-5,10-dione 10-oxime derived from α-lapachone

The compound (10E)-2,2-dimethyl-3,4-dihydro-2H-benzo[g]chromene-5,10-dione-10-oxime (1) was synthesized from a-lapachone and hydroxylamine chloride in alkaline medium. Single-crystals suitable for X-ray diffraction measurements were grown from an ethanol solution, and the crystal structure of the title molecule is reported for the first time. The title molecule was also characterized by 1H- and 13C-NMR in CDCl? solution, FTIR and MS. The crystal structure of 1 shows an E stereochemistry and dimers formed through classical hydrogen bonds.     

Structural insights into calmodulin/adenylyl cyclase 8 interaction

Calmodulin (CaM) is a highly conserved intracellular Ca²⁺-binding protein that exerts important functions in many cellular processes. Prominent examples of CaM-regulated proteins are adenylyl cyclases (ACs), which synthesize cAMP as a central second messenger. The interaction of ACs with CaM represents the link between Ca²⁺-signaling and cAMP-signaling pathways. Thereby, different AC isoforms stimulated by CaM, comprise diverse mechanisms of regulation by the Ca²⁺ sensor. To extend the structural information about the detailed mechanisms underlying the regulation of AC8 by CaM, we employed an integrated approach combining chemical cross-linking and mass spectrometry with two peptides representing the CaM-binding regions of AC8. These experiments reveal that the structures of CaM/AC8 peptide complexes are similar to that of the CaM/skeletal muscle myosin light chain kinase peptide complex where CaM is collapsed around the target peptide that binds to CaM in an antiparallel orientation. Cross-linking experiments were complemented by investigating the binding of AC8 peptides to CaM thermodynamically with isothermal titration calorimetry. There were no hints on a complex, in which both AC8 peptides bind simultaneously to CaM, refining our current understanding of the interaction between CaM and AC8.

Disease extinction in the presence of random vaccination

We investigate disease extinction in an epidemic model described by a birth-death process. We show that, in the absence of vaccination, the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed random vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters.     

Termination processes in group transfer polymerization

Two major termination processes in the GTP of methacrylates and acrylates have been studied. For methacrylates, intramolecular cyclization is the dominant, if not sole, termination reaction. Both cyclization and O/C-silyl isomerization of the chain end are observed for acrylates. Oligomerization experiments were used to study the relative rates of cyclization and propagation and the influence of temperature, catalyst and dp. Under typical GTP conditions for methacrylates, cyclization is at least two orders of magnitude slower than monomer addition.