Superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders

A mathematical model of superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders is constructed. The macroscopic stresses of the reinforced material are additively determined by matrix stresses and by tensile or constrained compression stresses in the reinforcing fibers. The model is based on the numerical solution of two boundary-value problems, one of which corresponds to the butt-end torsion and the other to the coaxial torsion and axial shear. The boundary-value problem on joint deformations is solved with the use of the displacement field determined from the solution to the boundary-value problem on butt-end torsion. The results obtained by applying this method to homogeneous and axially-radially reinforced thick-wall cylinders subjected to butt-end torsion with subsequent coaxial torsion and axial shear are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 465–492, July–August, 2007.     

The application of a Gauss-Eyring model to predict the behavior of thermoplastics in tensile experiments

The Gaussian expression for the isothermal tensile deformation of thermoplastics including the proposed strain hardening constant G_p, has been combined with the Eyring flow equation to provide a new relation describing the rate of strain of a thermoplastic in terms of the true stress and the extension ratio under isothermal conditions. In conventional mechanical tests this model can be used to quantify the tendency to strain localization, to predict the natural draw ratio and the inversion point where the true engineering stress passes through a minimum. The latter is expected to correlate with the value of the extension ratio where crazes do not propagate under tension. The equation is most easily demonstrated in constant load experiments where they agree well with published work. However, for a more precise evaluation of the theory the constant G_p should be measured separately and the calculated results compared with other tests on the same material. Where necking occurs it is possible to use a simplified plug flow model to calculate neck profiles. These show that no special assumptions are required to account for necking which results directly from the interaction of geometric thinning and strain hardening, even where true strain softening is absent. The procedure makes it possible to illustrate the way in which the form of the neck can be affected by the rate of extension or in a constant load experiment by the applied load. ©1995 John Wiley & Sons, Inc.     

On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

We prove dimension formulas for the cotangent spaces T ¹ and T ² for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity X does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term c (X ) is zero for rational determinantal surface singularities. In particular our result implies that c (X ) is zero for Riemenschneiders quasi‐determinantal rational surface singularities, and this also generalizes results for quotient singularities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Instanton in the Field of a Pointlike Source of a Euclidean Non-Abelian Field

We consider the behavior of an (anti)instanton in the field of a pointlike source of a Euclidean non-Abelian field and investigate (anti)instanton deformations described by variations of its characteristic parameters. We formulate the variational problem of seeking the corresponding “crumpled” topological configurations and solve it algebraically using the Ritz method (of multipole decomposition of deformation fields). We investigate the domain of parameters specific for the instanton liquid model. We propose a simple method of taking contributions of such configurations in the functional integral into account approximately. In the framework of superposition analysis, we obtain an estimate for the mean energy of the source in the instanton liquid, and the estimate increases linearly with distance. In the case of a dipole in the color-singlet state, the energy is a linear function of the distance between the sources with the “strength” coefficient agreeing well with the known model and lattice estimates. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 267–298, February, 2006.     

Deforming subdivisions

Subdivisions are continuously deformed subject to three local conditions and shown to retain the global property of being a subdivision. Cell maps, which are introduced, enable elementary arguments.This research is supported in part by the National Science Foundation Grant DMS-8902662.     

Remarks on the r and Δ convolutions

In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive. Partially sponsored with KBN grant no 2P03A00723 and RTN HPRN-CT-2002-00279.     

Deformations of the canonical commutation relations

Deformations of the canonical commutation relations which have the effect of altering the spectrum of a standard Hamiltonian, bilinear in creation and annihilation operators are described. The problem of going over from an eigenvalue situation, as is the case in the vast majority of papers in the literature, to a theory with time evolution is discussed, and a special example with deformation parameter an Nth root of unity is constructed which possesses a consistent time evolution. This work is an account of some recent studies of associative deformations of the Heisenberg algebra of several creation and annihilation algebras, with Jean Nuyts of the University of Mons, Hainaut, together with some observations of my own concerning the difficulty of implementing time evolution in a quantum group context. It builds on earlier work with Cosmas Zachos (Argonne National Laboratory, USA), which in turn is re;ated to work of Manin, and Wess, Zumino and collaborators. The main idea is that, if quantum groups have any role in physics, then they must manifest themselves at the level of the basic rules of quantisation.     

Finite element simulation for dynamic large elastoplastic deformation in metal powder forming

In this paper, a transient dynamic analysis of the powder compaction process is simulated by a large displacement finite element method based on a total and updated Lagrangian formulation. A combination of the Mohr–Coulomb and elliptical yield cap model, which reflects the stress state and degree of densification, is applied to describe the constitutive model of powder materials. A Coulomb friction law and a plasticity theory of friction in the context of an interface element formulation are employed in the constitutive modelling of the frictional behaviour between the die and powder. Finally, the powder behaviour during the compaction of a plain bush, a rotational flanged and a shaped tip component are analysed numerically. It is shown that the updated Lagrangian formulation, using a combination of the Mohr–Coulomb and elliptical cap model, can be effective in simulating metal powder compaction.     

The quadrupole plus pairing interaction model in large configuration space for W,Os and Pt nuclei

The equilibrium deformations of tungsten, osmium and platinum nuclei are studied with the self-consistent quadrupole plus pairing interaction model by considering all the nucleons in nucleus explicitly. It is shown that similar results can be obtained by performing calculations with or without the assumption of an inert core. The only difference is in the strength of the quadrupole and pairing interactions to be employed in the respective calculations. The experimental static quadrupole moments and theB (E2) values are correctly reproduced by performing calculations with bare nucleon charge for all the nucleons.