Search results for " lattice"

On the lattice of J-subnormal subgroups

1992

Hyperidentities of some generalizations of lattices

1998

In the paper we present bases and hyperbases of hyperidentities of some generalizations of the variety L of all lattices and the variety D of distributive lattices. We describe the form of hyperidentities of some varieties with two binary operations.

Markov Chains and Electrical Networks

2020

There is a natural connection between electrical networks and so called reversible Markov chains. An example for such a chain is the symmetric graph random walk which, in each step, jumps to a randomly chosen graph neighbor at equal probability. This connection is studied here in some detail. As an application, we prove the statement that if such a graph random walk is recurrent, then it is recurrent also on each subgraph. (Although this statement is rather plausible, it is hard to show by different means.) In particular, the graph random walk on a percolation cluster of the planar integer lattice is recurrent.

Estimation of the photon production rate using imaginary momentum correlators

2023

The thermal photon emission rate is determined by the spatially transverse, in-medium spectral function of the electromagnetic current. Accessing the spectral function using Euclidean data is, however, a challenging problem due to the ill-posed nature of inverting the Laplace transform. In this contribution, we present the first results on implementing the proposal of directly computing the analytic continuation of the retarded correlator at fixed, vanishing virtuality of the photon via the calculation of the appropriate Euclidean correlator at imaginary spatial momentum. We employ two dynamical O(a)-improved Wilson fermions at a temperature of 250 MeV.

Noise correlations of the ultracold Fermi gas in an optical lattice

2008

In this paper we study the density noise correlations of the two component Fermi gas in optical lattices. Three different type of phases, the BCS-state (Bardeen, Cooper, and Schieffer), the FFLO-state (Fulde, Ferrel, Larkin, and Ovchinnikov), and BP (breach pair) state, are considered. We show how these states differ in their noise correlations. The noise correlations are calculated not only at zero temperature, but also at non-zero temperatures paying particular attention to how much the finite temperature effects might complicate the detection of different phases. Since one-dimensional systems have been shown to be very promising candidates to observe FFLO states, we apply our results als…

(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver

2015

We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD computations. Since the $\gamma_5$-preserving aggregation based interpolation used in our multigrid method is valid for both, the Hermitian and the non-Hermitian case, inversions of very ill-conditioned shifted systems with the Hermitian operator become feasible. This enables the use of multigrid within shift-and-invert type eigensolvers. We show numerical results from our MPI-C implementation of a Rayleigh quotient iteration with multigrid. For state-of-the-art lat…

Reduction of the number of spectral bands in Landsat images: a comparison of linear and nonlinear methods

2006

We describe some applications of linear and nonlinear pro- jection methods in order to reduce the number of spectral bands in Land- sat multispectral images. The nonlinear method is curvilinear component analysis CCA, and we propose an adapted optimization of it for image processing, based on the use of principal-component analysis PCA, a linear method. The principle of CCA consists in reproducing the topol- ogy of the original space projection points in a reduced subspace, keep- ing the maximum of information. Our conclusions are: CCA is an im- provement for dimension reduction of multispectral images; CCA is really a nonlinear extension of PCA; CCA optimization through PCA called CCAinitP…

An efficient swap algorithm for the lattice Boltzmann method

2007

During the last decade, the lattice-Boltzmann method (LBM) as a valuable tool in computational fluid dynamics has been increasingly acknowledged. The widespread application of LBM is partly due to the simplicity of its coding. The most well-known algorithms for the implementation of the standard lattice-Boltzmann equation (LBE) are the two-lattice and two-step algorithms. However, implementations of the two-lattice or the two-step algorithm suffer from high memory consumption or poor computational performance, respectively. Ultimately, the computing resources available decide which of the two disadvantages is more critical. Here we introduce a new algorithm, called the swap algorithm, for t…

Parallelization of Cellular Automata for Surface Reactions

2002

We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T is the computer time used for one single processor and P the number of processors. Two examples are presented to test the algorithm, the simple A+B->0 model and a realistic model for CO oxidation on Pt(110). By using large parallel simulations, it is possible to derive scaling laws which allow us to extrapolate to even larger system sizes and faster diffusion coefficients allowing us to make direct comparisons with experiments.

LCAO calculation of neutral defects in GaN

2005

Four well known HF, LDA, GGA and B3LYP Hamiltonians in LCAO approximation have been used in band structure calculations to obtain the main properties of the perfect GaN crystal with hexagonal lattice (C space group). Calculated lattice parameters, elastic constants and the band gap have been compared with the experimental data and the results of other calculations. As a consequence, the GGA Hamiltonian has been chosen, giving the lattice parameters a = 3.20 A, c = 5.20 A, u = 0.377, the bulk modulus B = 206 GPa and the energy gap Eg = 2.7 eV. These results reasonably reproduce the experimental data. For the point defects calculation (VGa, VN, MgGa, ZnGa, CN, and SiN) the supercell model was…