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Hydraulic Jumps09:15

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Source: Alexander S Rattner and Mahdi Nabil; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA
When liquid flows along an open channel at high velocity, the flow can become unstable, and slight disturbances can cause the liquid upper surface to transition abruptly to a higher level (Fig. 1a). This sharp increase in the liquid level is called a hydraulic jump. The increase in the liquid level causes a reduction in the average flow velocity....
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To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:Calculate Effective Upstream Velocity:When the downstream gate closes, a hydraulic jump forms, traveling upstream at 2 meters per second. This wave speed combines with the initial channel flow velocity, creating an effective upstream velocity.Identify Flow Velocities Before and After the Hydraulic Jump:Upstream of the hydraulic jump, the effective flow velocity includes both the...
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Hydraulic Jumps in Radial Outflow of Water
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Single-big-jump principle in physical modeling.

Alessandro Vezzani1,2, Eli Barkai3, Raffaella Burioni2,4

  • 1IMEM, CNR Parco Area delle Scienze 37/A 43124 Parma.

Physical Review. E
|September 11, 2019
PubMed
Summary
This summary is machine-generated.

The big-jump principle explains rare events in fat-tailed distributions, where one large jump, not many small ones, dominates. This extended principle now handles complex factors like correlations and memory for better risk prediction.

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Area of Science:

  • Probability Theory
  • Stochastic Processes
  • Statistical Physics

Background:

  • The big-jump principle, a key result for sums of independent and identically distributed random variables from fat-tailed distributions, posits that the sum's tail distribution mirrors the largest summand's distribution.
  • In practical terms, this means rare, large fluctuations in stochastic processes are often driven by a single dominant jump rather than numerous small deviations.

Purpose of the Study:

  • To generalize the big-jump principle, extending its applicability beyond its original formulation.
  • To incorporate complex phenomena such as correlations, finite cutoffs, continuous paths, memory effects, and quenched disorder into the principle.

Main Methods:

  • Reformulation of the big-jump principle to accommodate advanced statistical concepts.
  • Application of the extended principle to diverse systems including Lévy walks, laser cooling models, scattering processes, and Lévy walks with memory.

Main Results:

  • Demonstrated the predictive power of the extended big-jump principle in various complex scenarios.
  • Showcased the principle's ability to accurately model rare events influenced by factors like correlations and memory.

Conclusions:

  • The generalized big-jump principle offers a robust framework for understanding and predicting rare events in systems with heavy-tailed distributions.
  • This principle provides a valuable tool for reliable risk assessment in diverse fields, from environmental science to cellular biology.