In this paper we present a formulation of spectral vanishing viscosity (SVV) for the stabilisation of spectral/hp element methods applied to the solution of the incompressible Navier–Stokes equations. We construct the SVV around a filter with respect to an orthogonal expansions, and prove that this methodology provides a symmetric semi-positive definite SVV operator. After providing a few simpl...

In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capabl...

Large eddy simulation techniques offer a wealth of valuable information for engineering design purposes, but in many cases the required mesh resolution is prohibitive. Combining the dynamic LES procedure with unstructured mesh adaptivity offers a robust and efficient way of capturing the inhomogeneity and anisotropy of complex turbulent flows. However, this may result in a non-vanishing commuta...

We develop a fully scalable parallel implementation of an iterative solver for the time-harmonic Maxwell equations with vanishing wave numbers. We use a mixed finite element discretization on tetrahedral meshes, based on the lowest order Nédélec finite element pair of the first kind. We apply the block diagonal preconditioning approach of Greif and Schötzau (Numer. Linear Algebra Appl. 2007; 14...

The two-state model of stochastic resonance is extended to a chain of coupled two-state elements governed by the dynamics of Glauber’s stochastic Ising model. Appropriate assumptions on the model parameters turn the chain into a prototype system of coupled stochastic resonators. In a weak-signal limit analytical expressions are derived for the spectral power amplification and the signal-to-nois...

Simple transformation formulas between fermion matrices and observables, and numerical values of quark matrices, are obtained on a particular weak basis with one quark matrix diagonal and the other with vanishing elements 1-1, 1-3 and 3-1, and with only the element 2-2 complex. When we chooseMu diagonal, thenMd shows intriguing numerical properties which suggest a four parameter description of ...

In this paper, which follows closely the talk given at the conference, I will sketch an example of a non-trivial element of K2 of a certain threefold, whose existence is related to the vanishing of an incomplete L-function of a modular form at s = 1. To explain how this fits into a general picture, we begin with a simple account, for the non-specialist, of some of the conjectures (mostly due to...

We calculate the logarithmic corrections to the matrix elements for K → π and K → vacuum (which are used on the lattice to determine K → ππ amplitudes), in one-loop quenched and unquenched Chiral Perturbation Theory. We find that these corrections can be large. We also discuss, and present some results for, the direct determination of K → ππ amplitudes. In particular, we address effects from ch...

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with γ5. For a twisted Ginsparg-Wilson operator the spectrum is located on two arcs in the complex plane. Modes due to non-trivial topological charge of the underlyin...