Shear-band bifurcation of an isotropic compressible hyperelastic solid

This paper concerns shear-band bifurcations from the homogeneous finite plane deformation of an isotropic compressible hyperelastic solid. The governing equations for the incremental plane deformation superposed on the initial finite deformation are derived and then the equilibrium equations in terms of incremental displacements are classified into the elliptic type, parabolic type, etc. From this classification follows a restriction which should be placed on the strain-energy function in order that the equilibrium equations may be either elliptic or parabolic for all principal stretches. For the hyperelastic solid complying with this restriction, the condition for the shear-band bifurcation is obtained. Finally, the incremental displacement field of an infinite series of shear bands in a slab sandwiched between slippery rigid layers is established.     

Extended implementation of canonical transformation theory: parallelization and a new level-shifted condition

The canonical transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies.     

Finite deformations of an area-preserving material

A continuum theory of finite deformations of an area-preserving material is proposed. The material is assumed to deform preserving both volume and the area on the surfaces defined by unit normal vector field in the material; that is, the material has the internal constraints of incompressibility and inexpansibility. After a brief discussion of plane deformations, basic equations for axisymmetric deformations of rotationally symmetric bodies are derived; deformation gradients are explicitly expressed, and compatibility conditions and equilibrium equations are obtained. To illustrate the calculation of deformation and stress, a simple problem of forming a spherical cap from a circular disc is solved.

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Zusammenfassung Es wird eine Kontinuumtheorie für finite Verformungen eines flächenbewahrenden Materials vorgeschlagen. Es wird angenommen, daß das Material sich verformt, während es das Volumen und die Oberfläche wie durch das Einheitsnormalvektorfeld im Material definiert beibehält, d. h. das Material hat den inneren Zwang der Nichtzusammendrückbarkeit und der Nichtausdehnbarkeit. Nach einer kurzen Diskussion der Ebenenverformungen werden grundlegende Gleichungen für achsensymmetrische Verformungen von rotationssymmetrischen Körpern abgeleitet, die Verformungsgradienten werden explizit ausgedrückt, Kompatibilitätsbedingungen und Gleichgewichtsgleichungen werden erhalten. Um die Berechnung von Verformung und Spannung zu illustrieren, wird das einfache Problem der Formung einer sphärischen Kappe aus einer kreisförmigen Scheibe gelöst.

     

Acid/base-regulated reversible electron transfer disproportionation of N–N linked bicarbazole and biacridine derivatives

Regulation of electron transfer on organic substances by external stimuli is a fundamental issue in science and technology, which affects organic materials, chemical synthesis, and biological metabolism. Nevertheless, acid/base-responsive organic materials that exhibit reversible electron transfer have not been well studied and developed, owing to the difficulty in inventing a mechanism to associate acid/base stimuli and electron transfer. We discovered a new phenomenon in which N–N linked bicarbazole (BC) and tetramethylbiacridine (TBA) derivatives undergo electron transfer disproportionation by acid stimulus, forming their stable radical cations and reduced species. The reaction occurs through a biradical intermediate generated by the acid-triggered N–N bond cleavage reaction of BC or TBA, which acts as a two electron acceptor to undergo electron transfer reactions with two equivalents of BC or TBA. In addition, in the case of TBA the disproportionation reaction is highly reversible through neutralization with NEt₃, which recovers TBA through back electron transfer and N–N bond formation reactions. This highly reversible electron transfer reaction is possible due to the association between the acid stimulus and electron transfer via the acid-regulated N–N bond cleavage/formation reactions which provide an efficient switching mechanism, the ability of the organic molecules to act as multi-electron donors and acceptors, the extraordinary stability of the radical species, the highly selective reactivity, and the balance of the redox potentials. This discovery provides new design concepts for acid/base-regulated organic electron transfer systems, chemical reagents, or organic materials.