Non-linear interactions in imperfect beams at veering

Non-linear interactions in a hinged-hinged uniform moderately curved beam with a torsional spring at one end are investigated. The two-mode interaction is a one-to-one autoparametric resonance activated in the vicinity of veering of the frequencies of the lowest two modes and results from the non-linear stretching of the beam centerline. The excitation is a base acceleration that is involved in a primary resonance with either the first mode only or with both modes. The ensuing non-linear responses and their stability are studied by computing force- and frequency-response curves via bifurcation analysis tools. Both the sensitivity of the internal resonance detuning—the gap between the veering frequencies—and the linear modal structure are investigated by varying the rise of the beam half-sinusoidal rest configuration and the torsional spring constant. The internal and external resonance detunings are varied accordingly to construct the non-linear system response curves. The beam mixed-mode response is shown to undergo several bifurcations, including Hopf and homoclinic bifurcations, along with the phenomenon of frequency island generation and mode localization.     

Simulations of Redox Mediation within Bioactive Hydrogels of Amperometric Biosensors

Highly hydrated bioactive hydrogels containing immobilized oxidoreductase enzymes and immobilized redox mediators were simulated as the biorecognition layer of amperometric biosensors. The linear dynamic range of the amperometric response of mediated biosensors increases and moves to higher concentration brackets with an increase in the concentration of mediator. This informs the design of biosensors that target the same analyte but possesses several independently addressable electrodes modified with hydrogels that contain different concentrations of mediator. Increases in enzyme concentration increase the linear dynamic range but does not alter the sensitivity of amperometric biosensors. Both sensitivity and linear dynamic range of mediated amperometric enzyme biosensors may be “tuned” by varying the concentrations of the enzyme and the mediator. Simulations effectively guide the initial domains of study of complex systems such as implantable biosensors.     

Correction to: Sub-range Jacobi polynomials

Numerical Algorithms - The first equation in Eq. (2.9) should read     

Uncertainty,economics and optimization: recent developments

Computational Management Science -     

Actinide Organometallic Complexes with π-Ligands

Recent developments and results from the organometallic chemistry of the actinides are reviewed. In the last one and a half years the structural data of about 15 organometallic complexes of transuranium actinides (Np or Pu) have been published, all involving π-ligands in the coordination sphere of the metal ion. On the basis of these data, a comparison of these molecules is presented. Depending on the steric demands of the ligands, effects like the actinide contraction seem to be stronger or weaker in the structural features. This indicates that the interplay between the actinide ion and the π-ligand is rather flexible, enabling the formation of stable bonds over a broad range of actinide ion oxidation states.     

The Electronic Nature of the 1,4‐β‐Glycosidic Bond and Its Chemical Environment: DFT Insights into Cellulose Chemistry

The molecular understanding of the chemistry of 1,4‐β‐glucans is essential for designing new approaches to the conversion of cellulose into platform chemicals and biofuels. In this endeavor, much attention has been paid to the role of hydrogen bonding occurring in the cellulose structure. So far, however, there has been little discussion about the implications of the electronic nature of the 1,4‐β‐glycosidic bond and its chemical environment for the activation of 1,4‐β‐glucans toward acid‐catalyzed hydrolysis. This report sheds light on these central issues and addresses their influence on the acid hydrolysis of cellobiose and, by analogy, cellulose. The electronic structure of cellobiose was explored by DFT at the BB1 K/6‐31++G(d,p) level. Natural bond orbital (NBO) analysis was performed to grasp the key bonding concepts. Conformations, protonation sites, and hydrolysis mechanisms were examined. The results for cellobiose indicate that cellulose is protected against hydrolysis not only by its supramolecular structure, as currently accepted, but also by its electronic structure, in which the anomeric effect plays a key role.     

Synthesis of Glycosyl Azides by the Addition of Phenylselenenyl Azide to Glycals

Abstract

The addition of phenylselenenyl azide to glycals is carried out under conditions that give 2-deoxy-2-phenylselenoglycosyl azides. This regiochemistry is opposite to that obtained under free-radical conditions, which are known to produce 2-azido-2-deoxyselenoglycosides. The addition reaction is carried out with phenylselenenyl chloride and sodium azide in dimethylformamide, and is stereoselective for trans addition. Tri-O-benzyl-d-glucal and di-O-benzyl-l-rhamnal each gave two addition products, in which the phenylselenyl and azido groups were either trans diaxial or trans diequatorial. Tri-O-benzyl-d-galactal gave only the trans diaxial addition product.