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Related Concept Videos

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Steady, Laminar Flow in Circular Tubes01:23

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Bernoulli's Equation for Flow Normal to a Streamline

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Updated: May 17, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

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Published on: May 1, 2018

Gradient Flow for Parton Distribution Functions: First Application to the Pion.

Anthony Francis1, Patrick Fritzsch2, Robert V Harlander3

  • 1National Yang Ming Chiao Tung University, Institute of Physics, 30010 Hsinchu, Taiwan.

Physical Review Letters
|May 15, 2026
PubMed
Summary
This summary is machine-generated.

Lattice QCD calculations of Parton Distribution Functions (PDFs) are improved using a novel gradient flow method. This technique allows for higher moment computations, enhancing precision QCD phenomenology and agreeing with experimental data.

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Related Experiment Videos

Last Updated: May 17, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
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Published on: May 1, 2018

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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Published on: February 27, 2016

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Area of Science:

  • High Energy Physics
  • Quantum Chromodynamics (QCD)
  • Lattice Field Theory

Background:

  • Parton Distribution Functions (PDFs) are crucial for understanding particle interactions in QCD.
  • Calculating Mellin moments of PDFs on the lattice is computationally challenging, especially for higher moments.
  • Existing methods face limitations due to reduced hypercubic symmetry.

Purpose of the Study:

  • To demonstrate the efficacy of a new gradient flow method for computing PDF Mellin moments.
  • To overcome limitations of traditional lattice methods for higher moment calculations.
  • To provide precise lattice calculations of flavor nonsinglet pion PDF moments.

Main Methods:

  • Utilizing a recently proposed gradient flow technique.
  • Computing ratios of flavor nonsinglet pion PDF moments.
  • Performing calculations on four lattice spacings with pion masses around 411 MeV.

Main Results:

  • Successfully computed PDF Mellin moments up to ⟨x⁵⟩.
  • The gradient flow method effectively resolves challenges associated with reduced hypercubic symmetry.
  • Reconstructed PDF from calculated moments shows quantitative agreement with phenomenological extractions.

Conclusions:

  • The gradient flow method is a powerful tool for lattice QCD calculations of PDFs.
  • This advancement enables more precise determinations of PDF moments, improving QCD phenomenology.
  • Results validate the accuracy and potential of this novel computational approach.