Equi-biaxial tension tests on magneto-rheological elastomers

A bespoke test rig has been designed to facilitate testing of magneto-rheological (MR) elastomers (MREs) under equi-biaxial tension using a standard universal test machine. Tests were performed up to 10% strain on both isotropic and anisotropic MREs with and without the application of an external magnetic field. Assumptions regarding the material's response were used to analyse stress–strain results in the two stretching directions. The assumptions have been verified previously by uniaxial tension tests and by simulations of the magnetic flux distribution performed using a commercial multi-physics finite element software. The MR effect, which is defined as the increase in tangent modulus at a given strain, has been studied versus engineering strain. The latter was measured optically in the experiments using a digital image correlation system. Relative MR effects up to 74% were found when the particle alignment of anisotropic MREs was oriented parallel to an applied magnetic induction of just 67.5 mT

Chiral Symmetry Breaking for Domain Wall Fermions in Quenched Lattice QCD

The domain wall fermion formulation exhibits full chiral symmetry for finite lattice spacing except for the effects of mixing between the domain walls. Close to the continuum limit these symmetry breaking effects should be described by a single residual mass. We determine this mass from the conservation law obeyed by the conserved axial current in quenched simulations with beta=5.7 and 6.0 and domain wall separations varying between 12 and 48 on 8^3x32 and 16^3x32 lattices. Using the resulting values for the residual mass we perform two complete and independent calculations of the pion decay constant. Good agreement is found between these two methods and with experiment.Comment: 4 pages, 6 figures, Lattice 2000 (Chiral Fermions), RBC Collaboratio

Gap Domain Wall Fermions

I demonstrate that the chiral properties of Domain Wall Fermions (DWF) in the large to intermediate lattice spacing regime of QCD, 1 to 2 GeV, are significantly improved by adding to the action two standard Wilson fermions with supercritical mass equal to the negative DWF five dimensional mass. Using quenched DWF simulations I show that the eigenvalue spectrum of the transfer matrix Hamiltonian develops a substantial gap and that the residual mass decreases appreciatively. Furthermore, I confirm that topology changing remains active and that the hadron spectrum of the added Wilson fermions is above the lattice cutoff and therefore is irrelevant. I argue that this result should also hold for dynamical DWF and furthermore that it should improve the chiral properties of related fermion methods.Comment: 12 pages of text, 14 figures, added sect.6 on topology and reference

Domain-Wall Fermions at Strong Coupling

The DWF formulation becomes increasingly problematic at gauge couplings for which $a^{-1}<2$ GeV, where the roughness of the gauge field leads to increased explicit chiral symmetry breaking (\mres). This problem becomes especially severe for sufficiently strong coupling where the underlying 4-dimensional Wilson theory is in the Aoki phase. We review our attempts to find a suitable modification of the gauge and/or the fermion action which would allow the DWF method to work reliably at stronger coupling.Comment: 4 pages, 4 figures, Lattice2004(chiral

How well do domain wall fermions realize chiral symmetry?

In the domain wall fermion formulation, chiral symmetry breaking in full QCD is expected to fall exponentially with the length of the extra dimension. We measure the chiral symmetry breaking due to a finite extra dimension in two ways, which can be affected differently by finite volume and explicit fermion mass. For quenched QCD the two methods generally agree, except for the largest extent of the extra dimension, which makes the limit uncertain. We have less data for full QCD, but see exponential suppression for the method where we have data.Comment: 3 pages, 2 figures, LATTICE99(hightemp

K→ππK \to \pi \pi Decays with Domain Wall Fermions: Towards Physical Results

We are using domain wall fermions to study $K \to \pi \pi$ matrix elements by measuring $K \to \pi$ and $K \to 0$ matrix elements on the lattice and employing chiral perturbation theory to relate these to the desired physical result. The residual chiral symmetry breaking of domain wall fermions with a finite extent in the fifth dimension impacts these measurements. Using the Ward-Takahashi identities, we investigate residual chiral symmetry breaking effects for divergent quantities and study pathologies of the quenched approximation for small quark mass. We then discuss the $\Delta S = 1$ operator $O_2$, where chiral symmetry is vital for the subtraction of unphysical effects.Comment: 4 pages, 3 figures, Lattice 2000 (Hadronic Matrix Elements), RBC Collaboration, corrected equations 2 and