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Related Concept Videos

Bewley Lattice Diagram01:12

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...

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Related Experiment Video

Updated: Jun 5, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Adaptive multigrid algorithm for the lattice Wilson-Dirac operator.

R Babich1, J Brannick, R C Brower

  • 1Center for Computational Science, Boston University, 3 Cummington Street, Boston, Massachusetts 02215, USA.

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

We developed a new adaptive multigrid solver for Quantum Chromodynamics (QCD) calculations. This method overcomes critical slowing down, making QCD simulations more efficient, especially in the chiral limit.

Related Experiment Videos

Last Updated: Jun 5, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

  • Computational Physics
  • Quantum Chromodynamics (QCD)
  • Numerical Analysis

Background:

  • The non-Hermitian Wilson-Dirac operator is crucial in lattice QCD simulations.
  • Solving large linear systems in QCD is computationally intensive.
  • Critical slowing down hinders efficiency in the chiral limit.

Purpose of the Study:

  • To present an adaptive multigrid solver for the non-Hermitian Wilson-Dirac system.
  • To overcome limitations of existing solvers, particularly critical slowing down.
  • To improve the efficiency of lattice QCD calculations.

Main Methods:

  • Developed an adaptive multigrid solver.
  • Utilized adaptive projection onto coarse grids to preserve the system matrix's near null space.
  • Employed a simplified correction form based on the Dirac operator's γ5-Hermitian symmetry.

Main Results:

  • The proposed algorithm nearly eliminates critical slowing down in the chiral limit.
  • Demonstrated weak dependence of the algorithm on lattice volume.
  • Achieved efficient solutions for the non-Hermitian Wilson-Dirac system.

Conclusions:

  • The adaptive multigrid solver offers a significant improvement for lattice QCD simulations.
  • The method shows excellent scaling properties and robustness.
  • This approach enhances computational efficiency in exploring the QCD phase diagram.