Vacuum moulding of a superplastic in two dimensions

A mathematical model is proposed for the process of vacuum superplasticforming. The model exploits the fact that in most industrialapplications the sheet aspect ratio (thickness/sheet width)is small. After an initial consideration of some of the moregeneral properties and the literature of superplastic materials,the elastic/plastic deformation of an internally-inflated thin-walledcylinder is examined. Plates of arbitrary geometry are thenconsidered. A quasisteady model in which the sheet moves througha sequence of steady states is developed. Some simplified closed-formsolutions are examined, but for general cases a system of nonlinearpartial differential equations must be solved numerically. Anefficient and accurate semi-explicit numerical scheme is proposedand a simplified stability analysis is presented; the methodis then used to compute properties of superplastic vacuum mouldedsheets in a number of practically motivated cases.     

Structural instability of one-dimensional systems as a physical principle underlying the functioning of molecular electronic devices

Structural instability of one-dimensional conducting molecular systems is suggested as a physical principle underlying the operation of molecular electronic devices, and its potential application in such devices is analyzed. The theoretical basis of this effect is discussed. The conditions and parameters determining its characteristics are analyzed from the viewpoint of molecular electronics. Data on one-dimensional molecular structures which are of interest for the design of electronic devices are given. Peculiarities of structural instability are discussed, and potential static and dynamic control over the conductivity of one-dimensional systems is analyzed. Molecular structures are given as examples of hypothetical electronic devices. The possibilities and prospects of this approach in the development of molecular electronics are discussed.     

The true potential energy curves for different states of SiO and SiS molecules

The true potential energy curves forX ¹ Σ ⁺, a³ π _r,A ¹ π,e ³ Σ ⁻,E ¹ Σ ⁺,c ³ π _i states of astrophysically important molecule SiO, whose spectra were observed in the sunspots, have been constructed using the method of Lakshman and Rao. Dissociation energy and ionization potential have been estimated as 65,350 cm⁻¹ and 92,854 cm⁻¹ respectively and found to be in good agreement with the values cited in literature. The true potential energy curves forX ¹ Σ ⁺,D ¹ π andE ¹ Σ ⁺ states of SiS molecule have been constructed by the same method and its dissociation energy in the ground state has been estimated using Hulburt-Hirschfelder potential function as 54,765 cm⁻¹ in good agreement with 53,250.9 cm⁻¹ given by Herzberg.     

A Notion of Synchronization of Symbolic Dynamics and a Class of C ∗-Algebras

We discuss a synchronization property for subshifts, that we call λ-synchronization. Under an irreducibility assumption we associate to a λ-synchronizing subshift a simple C ^?-algebra.