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Related Concept Videos

Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy01:18

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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Entropy and the Second Law of Thermodynamics01:20

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications.

Robert K Niven1, Markus Abel2,3, Michael Schlegel4

  • 1School of Engineering and Information Technology, The University of New South Wales, Northcott Drive, Canberra, ACT 2600, Australia.

Entropy (Basel, Switzerland)
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A new maximum entropy framework infers flow network states probabilistically. This method handles uncertainty and incomplete data for diverse network types, from pipe flow to social networks.

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flow networkmaximum entropy analysisprobabilistic inference

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Area of Science:

  • Multidisciplinary science
  • Network science
  • Statistical mechanics

Background:

  • Flow networks, comprising nodes and links carrying flows, are fundamental across diverse fields like engineering, ecology, and economics.
  • Inferring the precise state of these networks, including flow rates and properties, is challenging due to inherent uncertainties and incomplete data.
  • Existing methods often struggle with probabilistic inference and incorporating complex constraints.

Purpose of the Study:

  • To present a generalized maximum entropy framework for inferring the probabilistic state of flow networks.
  • To develop a method capable of handling uncertainty in network structure and parameters.
  • To enable prediction of network properties even with insufficient information for deterministic solutions.

Main Methods:

  • A generalized maximum entropy framework is employed to represent network uncertainty via a joint probability function.
  • Relative entropy is maximized subject to known constraints, including observable, physical (e.g., conservation laws), and graphical uncertainties.
  • The framework accommodates nonlinear constraints and interdependencies, potentially requiring numerical solutions.

Main Results:

  • The developed framework provides a probabilistic inference of flow network states, including flow rates and other properties.
  • It effectively quantifies and manages uncertainty in network parameters and structure.
  • The method demonstrates applicability to various flow network types, offering predictive capabilities beyond deterministic approaches.

Conclusions:

  • The maximum entropy framework offers a robust and versatile approach for analyzing complex flow networks.
  • It enhances understanding and prediction capabilities in systems with incomplete information.
  • This probabilistic method has broad implications for diverse scientific and engineering disciplines involving flow networks.