Download PDF by Vijay P. Singh: Introduction to Tsallis entropy theory in water engineering

By Vijay P. Singh

ISBN-10: 1498736610

ISBN-13: 9781498736619

Focuses On an rising box in Water Engineering

A large therapy of the Tsallis entropy conception awarded from a water assets engineering standpoint, Introduction to Tsallis Entropy idea in Water Engineering fills a becoming want for fabric in this thought and its suitable functions within the zone of water engineering. This self-contained textual content comprises numerous solved examples, and calls for just a uncomplicated wisdom of arithmetic and chance conception. Divided into 4 components, the publication starts off with an in depth dialogue of Tsallis entropy, strikes directly to hydraulics, expounds near to hydrology, and ends with huge insurance on a large choice of components in water engineering.

The writer addresses:

  • The Tsallis entropy concept for either discrete and non-stop variables
  • The technique for deriving likelihood distributions
  • One-dimensional pace distributions
  • Two-dimensional speed distributions
  • Methods for selecting sediment concentration
  • Sediment discharge
  • Stage–discharge score curve
  • Precipitation variability
  • Infiltration and the derivation of infiltration equations
  • An advent to soil moisture, soil moisture profiles, and their estimation
  • Flow length curves
  • The eco-index and signs of hydrologic alteration (IHA)
  • Measures of redundancy for water distribution networks, and more

Introduction to Tsallis Entropy thought in Water Engineering

examines the elemental thoughts of the Tsallis entropy idea, and considers its present functions and strength for destiny use. This booklet advances additional study on water engineering, hydrologic sciences, environmental sciences, and water assets engineering as they relate to the Tsallis entropy theory.

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Extra resources for Introduction to Tsallis entropy theory in water engineering

Example text

39 describe the additivity property. This property can be extended to any number of systems. In all cases, H ≥ 0 (nonnegativity property). 41) úû for all (i, j). 38. For correlated X and Y, T(pij) < 0 for m = 1, and T(pij) = 0 for m = 0. For arbitrary values of m, it will be sensitive to pij; it can take on negative or positive values for both m < 1 and m > 1 with no particular regularity and can exhibit more than one extremum. 6. 7. Both systems are independent. Compute the joint Tsallis entropy of the two systems.

75 shows that the maximum Tsallis entropy depends on the entropy index m and is independent of state, but its position can vary. In the case of the Shannon partial entropy, the position is fixed. Further, it implies that it does not accommodate the local effect of constraints. It may be noted that Hi(m = 0) = 1 − pi, which is a linear relation; Hi(m → ∞) = 0 in the limit m → 1, Hi reduces to the Shannon entropy. 11 shows that the Tsallis partial entropy does not have a realvalued extremum and tends to infinity as pi → 0 for −1 < m < 0 and/or over some finite range of pi for −∞ < m < 1 The Tsallis partial entropy is nonnegative but the constrained partial Shannon entropy may not be.

Internal Report, Department of Water Resources, National Technical University of Athens, Athens, Greece. Koutsoyiannis, D. (2005b). Uncertainty, entropy, scaling and hydrological stochastics: 1. Marginal distributional properties of hydrological processes and state scaling. Hydrological Sciences Journal, 50(3), 381–404. Koutsoyiannis, D. (2005c). Uncertainty, entropy, scaling and hydrological stochastics: 2. Time dependence of hydrological processes and state scaling. Hydrological Sciences Journal, 50(3), 405–426.

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