On the Stability Analysis of Decoupled Solution Schemes

Many problems in engineering, physics or other disciplines require an integrated treatment of coupled fields. These problems are characterised by a dynamic interaction among two or more physically or computationally distinct components, where the undergoing mathematical model commonly consists of a system of coupled PDE. Considerable progress has been made in the development of appropriate computational schemes to solve such coupled PDE systems. These attempts have resulted in various monolithic and decoupled numerical solution approaches. Despite the unconditional stability offered by implicit monolithic solution strategies, their use is not always recommended. The reason mainly lies in the complexity of the resulting system of equations and the limited flexibility in choosing appropriate time integrators for individual components. This has motivated the elaboration of tailored decoupled solution schemes, which follow the idea of splitting the problem into several sub-problems. But selection of the way of splitting can have a direct influence on the stability of the resulting solution algorithm. This necessitates the stability analysis of such an algorithm. Here, we introduce a general framework for the stability analysis of decoupled solution schemes. The approach is then used to study the stability behaviour of established decoupling strategies applied to typical volume- and surface-coupled problems, namely, coupled problems of thermoelasticity, porous media dynamics and structure-structure interaction. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DIESEL-MP2: a new program to perform large-scale multireference-MP2 computations

This article presents a new MR‐MP2 code (Multi‐Reference Møller–Plesset 2nd order) suitable for the computation MR‐MP2 energies of extended systems with strong near degeneracy effects (e.g., open shell systems). It is based on the DIESEL program package developed by Hanrath and Engels. Due to improved algorithms the new code is able to handle systems with 400–500 basis functions and more than 100 electrons. The code is made for parallel computers with distributed memory, but can also be run on local machines. It possesses two integral interfaces (MOLCAS, TURBOMOLE). The algorithms are briefly introduced and timings for the Neocarzinostatin chromophore are presented. The efficiencies of the codes obtained with Intel or GNU compilers are compared. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1055–1062, 2006     

A 15N-aided artificial atmosphere gas flow technique for online determination of soil N2 release using the zeolite Köstrolith SX6

N2 is one of the major gaseous nitrogen compounds released by soils due to N-transformation processes. Since it is also the major constituent of the earth's atmosphere (78.08% vol.), the determination of soil N2 release is still one of the main methodological challenges with respect to a complete evaluation of the gaseous N-loss of soils. Commonly used approaches are based either on a C2H2 inhibition technique, an artificial atmosphere or a 15N-tracer technique, and are designed either as closed systems (non-steady state) or gas flow systems (steady state). The intention of this work has been to upgrade the current gas flow technique using an artificial atmosphere for a 15N-aided determination of the soil N2 release simultaneously with N2O. A 15N-aided artificial atmosphere gas flow approach has been developed, which allows a simultaneous online determination of N2 as well as N2O fluxes from an open soil system (steady state). Fluxes of both gases can be determined continuously over long incubation periods and with high sampling frequency. The N2 selective molecular sieve K?strolith SX6 was tested successfully for the first time for dinitrogen collection. The presented paper mainly focuses on N2 flux determination. For validation purposes soil aggregates of a Haplic Phaeozem were incubated under aerobic (21 and 6 vol.% O2) and anaerobic conditions. Significant amounts of N2 were released only during anaerobic incubation (0.4 and 640.2 pmol N2 h(-1) g(-1) dry soil). However, some N2 formation also occurred during aerobic incubation. It was also found that, during ongoing denitrification, introduced [NO3]- will be more strongly delivered to microorganisms than the original soil [NO3]-.     

Ion mobility spectrometric investigation of aromatic cations in the gas phase

In this work, ion mobility (IM) spectra of more than 50 aromatic compounds were recorded with a laser-based IM spectrometer at atmospheric pressure. IM spectra of PAH in the laser desorption experiment show a high complexity resulting from the occurrence of monomeric, dimeric, and oligomeric cluster ions. The mobilities of all compounds were determined in helium as drift gas. This allows the calculation of the diffusion cross sections (Omega(calc)) on the basis of the exact hard sphere scattering model and their comparison with the experimentally determined diffusion cross sections (Omega(exp)). Extended Omega(exp)/Omega(calc) and Omega(exp)/mass correlations were performed in order to gain insight into conformational properties of cationic alkyl benzenes and internal rotation of phenyl rings in aromatic ions. This is demonstrated with some examples, such as the evaluation of the dihedral angle of the ions of 9,10-diphenylanthracene, o- and m-terphenyl, and 1,2,3- and 1,3,5-triphenylbenzene. Furthermore, sandwich and T-structures of dimeric PAH cations are discussed. The analysis was extended to oligomeric ions with up to nine monomer units. Experimental evidence is presented suggesting the formation of pi-stacks with a transition toward modified pi-stacks with increasing cluster size. The distance between monomeric units in dimeric and oligomeric ions was obtained.     

Influence of phosphonation and phosphation on surface acid-base and morphological properties of CaO as investigated by in situ FTIR spectroscopy and electron microscopy

Pure, phosphated, and phosphonated CaO samples were prepared and characterized by X-ray powder diffractometry, FTIR spectroscopy, scanning electron microscopy, and energy-dispersive X-ray microprobing. Surface acid-base properties were probed by in situ FTIR spectroscopy of adsorbed CO (at 85 K), CDCl3 (at RT), CO2 (at RT), and methyl butynol decomposition reactions (at 473 K). Results obtained have shown phosphate and, to a larger extent, phosphonate additives to enhance the strength of Lewis acid sites exposed on CaO surfaces, at the expense of the Lewis base site strength. The phosphonation has been found, moreover, to make CaO particles grow in a preferential direction and be less susceptible to rehydration. These findings may establish surface chemical attributes for the application of the methylene bisphosphonate (MBP) class of drugs to hamper acid-induced resorption of bone materials (osteoporosis).     

Asymmetric synthesis of highly substituted azapolycyclic compounds via 2-alkenyl sulfoximines: potential scaffolds for peptide mimetics

The application of metalated, enantiomerically pure acyclic and cyclic 2-alkenyl sulfoximines for the synthesis of highly substituted aza(poly)cyclic ring systems is described. The method relies on a one-pot combination of a reagent-controlled allyl transfer reaction to alpha- or beta-amino aldehydes, followed by a Michael-type cyclization of the intermediate vinyl sulfoximines generated in the first step. The sulfur-free target compounds are preferentially obtained by samarium iodide treatment of the sulfonimidoyl substituted heterocycles. In addition to this methodological work, initial results on the biological activity of selected examples are reported. Furthermore, a concept for the transformation of peptidic lead structures into non-peptide mimetics is described, and the relevance of the new approach to highly substituted azaheterocycles in this context is discussed.     

The conformation of cyclo(-D-Pro-Ala4-) as a model for cyclic pentapeptides of the DL4 type

The conformation of the cyclic pentapeptide cyclo(-D-Pro-Ala(4)-) in solution and in the solid state was reinvestigated using modern NMR techniques. To allow unequivocal characterization of hydrogen bonds, relaxation behavior, and intramolecular distances, differently labeled isotopomers were synthesized. The NMR results, supported by extensive MD simulations, demonstrate unambiguously that the preferred conformation previously described by us, but recently questioned, is indeed correct. The validation of the conformational preferences of this cyclic peptide is important given that this system is a template for several bioactive compounds and for controlled "spatial screening" for the search of bioactive conformations.     

Finite reservoir replica exchange to enhance canonical sampling in rugged energy surfaces

A "finite reservoir" replica exchange method is presented to further enhance sampling upon the regular replica exchange method (REM) in a rugged energy surface. The present method can facilitate important sampling more efficiently by exchanging structures with configurations randomly selected from a finite-sized reservoir; this finite reservoir is pregenerated and updated by a mechanism of replica exchange with neighboring "temperature" simulations. In practice, this proposal revises exchange schedule in REM simulations in order to make productive exchange for conformational "tunneling" more frequent.     

The algebraic degree of semidefinite programming

Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices. We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes.     

Dynamic Wave Propagation in Porous Media Semi-Infinite Domains

The problem of dynamic wave propagation in semi-infinite domains is of great importance, especially, in subjects of applied mechanics and geomechanics, such as the issues of earthquake wave propagation in an infinite half-space and soil-structure interaction under seismic loading. In such problems, the elastic waves are supposed to propagate to infinity, which requires a special treatment of the boundaries in initial boundary-value problems (IBVP). Saturated porous materials, e. g. soil, basically represent volumetrically coupled solid-fluid aggregates. Based on the continuum-mechanical principles and the established macroscopic Theory of Porous Media (TPM) [1, 2], the governing balance equations yield a coupled system of partial differential equations (PDE). Restricting the discussion to the isothermal and geometrically linear case, this system comprises the solid and fluid momentum balances and the overall volume balance, and can be conveniently treated numerically following an implicit monolithic approach [3]. Therefore, the equations are firstly discretised in space using the mixed Finite Element Method (FEM) together with quasi-static Infinite Elements (IE) at the boundaries that represent the extension of the domain to infinity [4], and secondly in time using an appropriate implicit time-integration scheme. Additionally, a stable implementation of the Viscous Damping Boundary (VDB) method [5] for the simulation of transient waves at infinity is presented, which implicitly treats the damping boundary terms in a weakly imposed sense. The proposed algorithm is implemented into the FE tool PANDAS and tested on a two-dimensional IBVP. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)