Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Transverse orthotropic elastic moduli of bundled coated thin elliptical tubes

Light weight structures with tailored mechanical properties have evolved beyond regular hexagonal/circular honeycomb topology. For applications which demand anisotropic mechanical properties, elliptical-celled structures offer interesting features. This paper characterizes the anisotropic in-plane elastic response of coated thin elliptical tubes in different array patterns viz, close-packed, diagonal and rectangular patterns under compression. This paper also extends earlier works on elliptical close-packed structure to a more general case of coated tubes. Theoretical framework using thin ring theory provides formulae in terms of geometric and material parameters. These are compared with a series of FE simulations using contact elements. The FE results are presented as graphs to aid in design. (C) 2014 Elsevier Ltd. All rights reserved.

Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Alvarez-Consul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Gamma-schemes, for a finite group Gamma. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Alvarez-Consul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

Moduli spaces of vector bundles on a singular rational ruled surface

We study moduli spaces M-X (r, c(1), c(2)) parametrizing slope semistable vector bundles of rank r and fixed Chern classes c(1), c(2) on a ruled surface whose base is a rational nodal curve. We showthat under certain conditions, these moduli spaces are irreducible, smooth and rational (when non-empty). We also prove that they are non-empty in some cases. We show that for a rational ruled surface defined over real numbers, the moduli space M-X (r, c(1), c(2)) is rational as a variety defined over R.

Effective elastic moduli of two-dimensional solids with multiple cracks

An accurate method which directly accounts for the interactions between different microcracks is used for analyzing the elastic problem of multiple cracks solids. The effective elastic moduli for randomly oriented cracks and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks.

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

The Surface- And Size-Dependent Elastic Moduli Of Nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional tyro-phase composites.

The surface- and size-dependent elastic moduli of nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

Prediction of Effective Moduli of Carbon Nanotube-Reinforced Composites with Waviness and Debonding

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. However, the waviness of the CNTs and the interfacial bonding condition between them and the matrix are two key factors that influence the reinforcing efficiency. In this paper, the effects of the waviness of the CNTs and the interfacial debonding between them and the matrix on the effective moduli of CNT-reinforced composites are studied. A simple analytical model is presented to investigate the influence of the waviness on the effective moduli. Then, two methods are proposed to examine the influence of the debonding. It is shown that both the waviness and debonding can significantly reduce the stiffening effect of the CNTs. The effective moduli are very sensitive to the waviness when the latter is small, and this sensitivity decreases with the increase of the waviness. (C) 2008 Elsevier Ltd. All rights reserved.

Investigation of Chemical Bond Characteristics, Thermal Expansion Coefficients and Bulk Moduli of alpha-R2MoO6 and R2Mo2O7 (R = rare earths) by Using a Dielectric Chemical Bond Method

Theoretical researches are performed on the alpha-R2MoO6 (R = Y, Gd, Tb Dy, Ho, Er, Tm and Yb) and pyrochlore-type R2Mo2O7 (R = Y, Nd, Sm, Gd, Tb and Dy) rare earth molybdates by using chemical bond theory of dielectric description. The chemical bonding characteristics and their relationship with thermal expansion property and compressibility are explored. The calculated values of linear thermal expansion coefficient (LTEC) and bulk modulus agree well with the available experimental values. The calculations reveal that the LTECs and the bulk moduli do have linear relationship with the ionic radii of the lanthanides: the LTEC decreases from 6.80 to 6.62 10(-6)/K and the bulk modulus increases from 141 to 154 GPa when R goes in the order Gd, Tb Dy, Ho, Er, Tm, and Yb in the alpha-R2MoO6 series; while in the R2Mo2O7 series, the LTEC ranges from 6.80 to 6.61 10(-6)/K and the bulk modulus ranges from 147 to 163 GPa when R varies in the order Nd, Sm, Gd, Tb and Dy.

Influence of inherent structure shear stress of supercooled liquids on their shear moduli

Configurations of supercooled liquids residing in their local potential minimum (i.e. in their inherent structure, IS) were found to support a non-zero shear stress. This IS stress was attributed to the constraint to the energy minimization imposed by boundary conditions, which keep size and shape of the simulation cell fixed. In this paper we further investigate the influence of these boundary conditions on the IS stress. We investigate its importance for the computation of the low frequency shear modulus of a glass obtaining a consistent picture for the low- and high frequency shear moduli over the full temperature range. Hence, we find that the IS stress corresponds to a non-thermal contribution to the fluctuation term in the Born-Green expression. This leads to an unphysical divergence of the moduli in the low temperature limit if no proper correction for this term is applied. Furthermore, we clarify the IS stress dependence on the system size and put its origin on a more formal basis.

On moduli spaces for abelian categories

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.

Dynamical Elastic Moduli of the Ti-13Nb-13Zr biomaterial alloy by mechanical spectroscopy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Storage moduli, loss moduli and damping factor of GaAs and Ga1-xMnxAs thin films using DMA 2980

The spin injector part of spintronic FET and diodes suffers from fatigue due to rising heat on the depletion layer. In this study the stiffness of Ga1-xMnxAs spin injector in terms of storage modulus with respect to a varying temperature, 45 degrees C <= T <= 70 degrees C was determined. It was observed that the storage modulus for MDLs (Manganese Doping Levels) of 0%, 1% and 10% decreased with increase in temperature while that with MDLs of 20% and 50% increase with increase in temperature. MDLs of 20% and 50% appear not to allow for damping but MDLs <= 20% allow damping at temperature range of 45 degrees C <= T <= 70 degrees C. The magnitude of storage moduli of GaAs is smaller than that for ferromagnetic Ga1-xMnxAs systems. The loss moduli for GaAs were found to reduce with increase in temperature. Its magnitude of reducing gradient is smaller than Ga1-xMnxAs systems. The two temperature extremes show a general reduction in loss moduli for different MDLs at the study temperature range. From damping factor analysis, damping factors for ferromagnetic Ga1-xMnxAs was found to increase with decrease in MDLs contrary to GaAs which recorded the largest damping factor at 45 degrees C <= T <= 70 degrees C Hence, MDL of 20% shows little damping followed by 50% while MDL of 0% has the most damping in an increasing trend with temperature. (C) 2013 Elsevier Ltd. All rights reserved.