The Construction of Optimized High-Order Surface Meshes by Energy-Minimization

Despite the increasing popularity of high-order methods in computational fluid dynamics, their application to practical problems still remains challenging. In order to exploit the advantages of high-order methods with geometrically complex computational domains, coarse curved meshes are necessary, i.e. high-order representations of the geometry. This dissertation presents a strategy for the generation of curved high-order surface meshes. The mesh generation method combines least-squares fitting with energy functionals, which approximate physical bending and stretching energies, in an incremental energy-minimizing fitting strategy. Since the energy weighting is reduced in each increment, the resulting surface representation features high accuracy. Nevertheless, the beneficial influence of the energy-minimization is retained. The presented method aims at enabling the utilization of the superior convergence properties of high-order methods by facilitating the construction of coarser meshes, while ensuring accuracy by allowing an arbitrary choice of geometric approximation order. Results show surface meshes of remarkable quality, even for very coarse meshes representing complex domains, e.g. blood vessels

Fermion Number Conservation Isn't Fermion Conservation

A nonperturbative regularization of the Standard Model may have a superficially undesirable exact global U(1) symmetry corresponding to exact fermion number conservation. We argue that such a formulation can still have the desired physics of fermion nonconservation, i.e. fermion particle creation and annihilation by sphaleron transitions. We illustrate our reasoning in massless axial QED in 1+1 dimensions.Comment: 3 pages to appear in the proceedings of Lattice '93, Dallas, Texas, 12-16 October 1993, comes as a single uuencoded postscript file (LaTeX source available from the authors), ITFA 93-3

Manifestly Gauge Invariant Models of Chiral Lattice Fermions

A manifestly gauge invariant lattice action for nonanomalous chiral models is proposed which leads in the continuum limit to the theory free of doublers.Comment: 9 pages, LaTeX. Revised version with an extended discussion of the role of higher derivative regulators. Submitted to Phys.Lett.B. Preprint SMI-9-9

Can baryogenesis occur on the lattice?

We examine the question of how baryogenesis can occur in lattice models of the Standard Model where there is a global $U(1)$ symmetry which is accompanied by an exactly conserved fermion number. We demonstrate that fermion creation and annihilation can occur in these models {\em despite} this exact fermion number conservation, by explicitly computing the spectral flow of the hamiltonian in the two dimensional U(1) axial model with Wilson fermions. For comparison we also study the closely related Schwinger model where a similar mechanism gives rise to anomalous particle creation and annihilation.Comment: 5 pp., contribution to the conference "Trends in Astroparticle Physics", Stockholm, 2 ps figs. (uuencoded

Lattice Chiral Gauge Theories

I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions which satisfy the Ginsparg-Wilson relation, and two gauge non-invariant methods, one using different cutoffs for the fermions and the gauge fields, and one using gauge fixing. Open problems within all three approaches are addressed.Comment: 15 pages, 2 figs, Lattice 2000 (Plenary

Non-gauge fixing approach to chiral gauge theories using staggered fermions

We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. Motivated by previous results in the non-gauge invariant massive Yang-Mills theory and certain gauge-fermion models we aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking is not too severe, this procedure could lead in the continuum limit to the desired gauge invariant chiral gauge theory. This scenario is very attractive since it does not rely on gauge fixing. We investigate a simple realization of this approach in a U(1) axial-vector model with dynamical fermions in four dimensions.Comment: 25 pages, 12 postscript figures (appended), ITFA 93-18, UCSD/PTH 93-1

Gauge-Fixing Approach to Lattice Chiral Gauge Theories, Part II

In this more technical part we give additional details on the gauge-fixing approach presented in hep-lat/9709113. We also explain how the gauge-fixing approach evades the Nielsen-Ninomiya no-go theorem.Comment: 6 pages, 5 figures, LaTeX, contribution to LATTICE'97, Edinburg

Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions

The fermion mass spectrum is studied in the quenched approximation in the strong coupling vortex phase (VXS) of a globally U(1)$_L \otimes$U(1)$_R$ symmetric scalar-fermion model in two dimensions. In this phase fermion doublers can be completely removed from the physical spectrum by means of a strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase consists most probably only of a massive Dirac fermion which has charge zero with respect to the $U(1)_L$ group. We give evidence that the fermion which is charged with respect to that subgroup is absent in the VXS phase. When the $U(1)_L$ gauge fields are turned on, the neutral fermion may couple chirally to the massive vector boson state in the confinement phase. The outcome is very similar to our findings in the strong coupling symmetric phase (PMS) of fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the exception that in four dimensions the neutral fermion does most probably decouple from the bosonic bound states.Comment: 21 pages, 6 postscript figures (appended), Amsterdam ITFA 92-21, HLRZ J\"ulich 92-5

Fermion production despite fermion number conservation

Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. A study of the vacuum energy shows that the perturbative counterterm needed for restoration of gauge invariance is insufficient in a nonperturbative setting. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the $\theta$-vacuum structure of both theories.Comment: 31 pages, LaTeX + uuencoded figs file (=5 PS figs). UvA-ITFA 94-17, UCSD/PTH 94-0