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Design Example: Aggregate Gradation01:24

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The right type and quality of aggregates are crucial for concrete as they significantly influence its properties, mix proportions, and cost-effectiveness. If different sources are available for sand, the commonly used fine aggregate in concrete, the selection of sand is primarily based on its gradation.
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Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
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Published on: August 5, 2016

Pattern formation in fast-growing sandpiles.

Tridib Sadhu1, Deepak Dhar

  • 1Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 3, 2012
PubMed
Summary
This summary is machine-generated.

Researchers explored patterns in Abelian sandpile models, discovering intermediate growth behaviors. Finite avalanches occur, with pattern diameter scaling as N(α), where 1/2 < α ≤ 1, offering new insights into complex system dynamics.

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Area of Science:

  • Complex Systems
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Abelian sandpile models exhibit diverse behaviors based on initial configurations.
  • Proportionate growth (diameter ~ N(1/d)) observed for low initial heights.
  • Infinite clusters at maximum stable height lead to non-terminating avalanches.

Purpose of the Study:

  • Investigate novel patterns in Abelian sandpile models with specific periodic backgrounds.
  • Characterize intermediate growth behaviors between standard proportionate growth and non-terminating avalanches.
  • Analyze the relationship between pattern growth exponent (α) and background configurations.

Main Methods:

  • Simulations of adding N sand grains to a single site on periodic backgrounds.
  • Relaxation of configurations to stable states.
  • Analysis of pattern diameter growth and avalanche finiteness.
  • Exact asymptotic characterization for illustrative examples (α=1).

Main Results:

  • Discovery of an intermediate behavior class in 2D Abelian sandpiles.
  • Finite avalanches observed for any N, with pattern diameter growing as N(α) for large N.
  • Growth exponent α satisfies 1/2 < α ≤ 1, tunable by background choice.
  • Noncompact growth simplifies analysis; exact pattern characterized for α=1.

Conclusions:

  • Intermediate growth regimes exist in Abelian sandpiles, distinct from known behaviors.
  • The growth exponent α provides a quantitative measure of pattern expansion.
  • Periodic backgrounds offer a method to control and analyze these complex growth dynamics.