Synthesis of cyclic peroxides containing the Si-gem-bisperoxide fragment. 1,2,4,5,7,8-Hexaoxa-3-silonanes as a new class of peroxides

A method was developed for the synthesis of the previously unknown class of organic peroxides, 1,2,4,5,7,8-hexaoxa-3-silonanes, based on the reaction of dialkyldichlorosilanes with 1,1'-dihydroperoxyperoxides. 1,2,4,5,7,8-Hexaoxa-3-silonanes are rather stable under ambient conditions and were characterized by NMR spectroscopy, X-ray diffraction, and elemental analysis. Their yields are in a range of 59-96%. The attempts were made to prepare 1,2,4,5-tetraoxa-3-silinanes by the reaction of dialkyldichlorosilanes with gem-bishydroperoxides. 1,2,4,5-Tetraoxa-3-silinanes were detected by NMR spectroscopy; these compounds rapidly decompose upon isolation.     

Multivariate subexponential distributions and their applications

We propose a new definition of a multivariate subexponential distribution. We compare this definition with the two existing notions of multivariate subexponentiality, and compute the asymptotic behaviour of the ruin probability in the context of an insurance portfolio, when multivariate subexponentiality holds. Previously such results were available only in the case of multivariate regularly varying claims.     

Examining ligand-protein interactions with binding-energy landscapes

Binding-energy landscapes are used to investigate the thermodynamics of molecular recognition for the pteridine ring, a recognition anchor in binding with dihydrofolate reductase, and two molecules with the same shape but different heteroatom substitutions. The relative importance of hydrogen bonding and hydrophobic interactions in this system is analyzed by comparing these three different decorations of the pteridine scaffold. Received: 5 May 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Generalized trajectory surface hopping method based on the Zhu-Nakamura theory

We present a generalized formulation of the trajectory surface hopping method applicable to a general multidimensional system. The method is based on the Zhu-Nakamura theory of a nonadiabatic transition and therefore includes the treatment of classically forbidden hops. The method uses a generalized recipe for the conservation of angular momentum after forbidden hops and an approximation for determining a nonadiabatic transition direction which is crucial when the coupling vector is unavailable. This method also eliminates the need for a rigorous location of the seam surface, thereby ensuring its applicability to a wide class of chemical systems. In a test calculation, we implement the method for the DH(2) (+) system, and it shows a remarkable agreement with the previous results of C. Zhu, H. Kamisaka, and H. Nakamura, [J. Chem. Phys. 116, 3234 (2002)]. We then apply it to a diatomic-in-molecule model system with a conical intersection, and the results compare well with exact quantum calculations. The successful application to the conical intersection system confirms the possibility of directly extending the present method to an arbitrary potential of general topology.     

Localised knife waves in a structured interface

We consider a Mode III lattice with an interface layer where the dynamic crack growth is caused by a localised sinusoidal wave. In the wave–fracture scenario, the ‘feeding wave’ (here also called the knife wave) delivers energy to the moving crack front, while the dissipative waves carry a part of this energy away from the front. The questions addressed here are:

• What are the conditions of existence of the localised knife wave?

• What is the lower bound of the amplitude of the feeding wave, which supports the crack propagation, for a given deformational fracture criterion?

• How does the crack speed depend on the amplitude of the feeding wave?

• What are the dissipative waves? How much energy is irradiated by these waves and what is the total dissipation?

• What are the conditions of existence of the steady-state regime for the propagating crack?

We consider analytically two established regimes: the steady-state regime, where the motion of neighbouring masses (along the interface) differs only by a constant shift in time, and an alternating-strain regime, where the corresponding amplitudes differ by sign. We also present the numerical simulation results for a model of a high-contrast interface structure. Along with the energy of the feeding and dissipative waves, an energy radiated to the bulk of the lattice is identified.