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Underflow gates are vital for controlling water flow in irrigation canals. The three main types of underflow gates — vertical, radial, and drum gates — serve different purposes while ensuring effective flow management. Vertical gates move up and down, generating a free-flowing water jet; radial gates pivot to regulate the flow; and drum gates rotate for precise adjustments. The flow through these gates is influenced by downstream conditions, resulting in free or drowned outflow.Free and...
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The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
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Directed negative-weight percolation.

C Norrenbrock1, M M Mkrtchian1, A K Hartmann1

  • 1Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany.

Physical Review. E
|October 3, 2019
PubMed
Summary

This study explores negative-weight percolation on directed graphs, finding a unique phase transition and critical exponents distinct from standard models. The research offers insights into complex systems and random media.

Area of Science:

  • Statistical physics
  • Graph theory
  • Complex systems

Background:

  • Percolation models are crucial for understanding connectivity in random systems.
  • Negative-weight variations introduce unique behaviors not seen in standard models.
  • Directed graphs add complexity to connectivity analysis.

Purpose of the Study:

  • To investigate the negative-weight percolation model on a 2D directed lattice.
  • To identify and characterize phase transitions and critical exponents.
  • To compare universality classes with existing percolation models.

Main Methods:

  • Utilizing a transformation to a minimum-weight perfect matching problem.
  • Employing fast polynomial-time algorithms for accurate analysis of large systems.

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  • Conducting finite-size scaling analysis to estimate critical exponents.

    • Main Results:

    • A continuous phase transition was identified based on the fraction of negative and positive bond weights.
    • Critical exponents were estimated, revealing a different universality class.
    • The model's behavior differs significantly from standard directed percolation and undirected negative-weight percolation.

    Conclusions:

    • The negative-weight percolation model on directed lattices exhibits distinct critical phenomena.
    • This research highlights a novel universality class in disordered systems.
    • The findings have implications for understanding directed polymers in random media.