Optimal Mathematical Models for Nonlinear Dynamical Systems

We propose a new method for the optimal causal representation of nonlinear systems. The proposed approach is based on the best constrained approximation of mappings in probability spaces by operators constructed from matrices of special form so that the approximant preserves the causality property. It is supposed that the observable input is contaminated with noise. The approximant minimises the mean-square difference between a desired output signal and the output signal of the approximating model. The method provides a numerically realisable mathematical model of the system. An analysis is given of the error associated with this representation.     

Numerical and experimental validation of a hybrid finite element-statistical energy analysis method

The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.     

Recent developments in the high-performance chelation ion chromatography of trace metals

There have been a number of significant developments in the high-performance chelation ion chromatography (HPCIC) of trace metals in recent years. This review focuses on these developments, while giving important information on the fundamental parameters controlling the chelation sorption mechanism, including type of chelating group, stability constants, kinetics, and column temperature. The discussion pays particular attention to the types and properties of efficient chelating stationary phases which have been fabricated for certain groups of metals. The review also describes a number of major improvements in postcolumn reaction detection including the use of the latest reagents and noise reduction strategies to improve sensitivity and reduce LOD. In the final section, an indication of the applicability of HPCIC to a range of complex sample types is given with some key examples and chromatograms using the latest high-efficiency chelating phases.     

Statistical mechanical theory for steady state systems. VII. Nonlinear theory

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics.     

Acid-base titrations of functional groups on the surface of the thermophilic bacterium Anoxybacillus flavithermus: comparing a chemical equilibrium model with ATR-IR spectroscopic data

Acid-base functional groups at the surface of Anoxybacillus flavithermus (AF) were assigned from the modeling of batch titration data of bacterial suspensions and compared with those determined from in situ infrared spectroscopic titration analysis. The computer program FITMOD was used to generate a two-site Donnan model (site 1: pKa = 3.26, wet concn = 2.46 x 10(-4) mol g(-1); site 2: pKa = 6.12, wet concn = 6.55 x 10(-5) mol g(-1)), which was able to describe data for whole exponential phase cells from both batch acid-base titrations at 0.01 M ionic strength and electrophoretic mobility measurements over a range of different pH values and ionic strengths. In agreement with information on the composition of bacterial cell walls and a considerable body of modeling literature, site 1 of the model was assigned to carboxyl groups, and site 2 was assigned to amino groups. pH difference IR spectra acquired by in situ attenuated total reflection infrared (ATR-IR) spectroscopy confirmed the presence of carboxyl groups. The spectra appear to show a carboxyl pKa in the 3.3-4.0 range. Further peaks were assigned to phosphodiester groups, which deprotonated at slightly lower pH. The presence of amino groups could not be confirmed or discounted by IR spectroscopy, but a positively charged group corresponding to site 2 was implicated by electrophoretic mobility data. Carboxyl group speciation over a pH range of 2.3-10.3 at two different ionic strengths was further compared to modeling predictions. While model predictions were strongly influenced by the ionic strength change, pH difference IR data showed no significant change. This meant that modeling predictions agreed reasonably well with the IR data for 0.5 M ionic strength but not for 0.01 M ionic strength.     

Enantioselective total syntheses of (-)-palau'amine, (-)-axinellamines, and (-)-massadines

Dimeric pyrrole-imidazole alkaloids represent a rich and topologically unique class of marine natural products. This full account will follow the progression of efforts that culminated in the enantioselective total syntheses of the most structurally ornate members of this family: the axinellamines, the massadines, and palau'amine. A bio-inspired approach capitalizing on the pseudo-symmetry of the members of this class is recounted, delivering a deschloro derivative of the natural product core. Next, the enantioselective synthesis of the chlorocyclopentane core featuring a scalable, catalytic, enantioselective Diels-Alder reaction of a 1-siloxydiene is outlined in detail. Finally, the successful divergent conversion of this core to each of the aforementioned natural products, and the ensuing methodological developments, are described.     

Scalable synthesis of cortistatin A and related structures

Full details are provided for an improved synthesis of cortistatin A and related structures as well as the underlying logic and evolution of strategy. The highly functionalized cortistatin A-ring embedded with a key heteroadamantane was synthesized by a simple and scalable five-step sequence. A chemoselective, tandem geminal dihalogenation of an unactivated methyl group, a reductive fragmentation/trapping/elimination of a bromocyclopropane, and a facile chemoselective etherification reaction afforded the cortistatin A core, dubbed "cortistatinone". A selective Δ(16)-alkene reduction with Raney Ni provided cortistatin A. With this scalable and practical route, copious quantities of cortistatinone, Δ(16)-cortistatin A (the equipotent direct precursor to cortistatin A), and its related analogues were prepared for further biological studies.     

Trifluoromethanesulfonic acid catalyzed isomerization of kinetic enol derivatives to the thermodynamically favored isomers

Trifluoromethanesulfonic acid catalyzed isomerization of kinetic enol derivatives to the thermodynamically favored isomers was developed. Under the present conditions, kinetic enol phosphates, enol acetates and benzoates, and enol sulfonates were smoothly isomerized to produce the corresponding thermodynamically favored isomers in good to excellent yields.