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Related Concept Videos

Partial Fractions01:28

Partial Fractions

291
A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
291
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

391
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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The Buckingham Pi Theorem01:09

The Buckingham Pi Theorem

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The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
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State Function, Exact and Inexact Differentials01:27

State Function, Exact and Inexact Differentials

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A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
61
Integration of Rational Functions Using Partial Fractions01:29

Integration of Rational Functions Using Partial Fractions

212
Rational functions are expressions written as the ratio of two polynomials, and their integrals are evaluated by simplifying the integrand into manageable parts. These functions are classified as proper or improper based on the degrees of the numerator and denominator.A rational function is proper when the degree of the numerator is less than the degree of the denominator. In this case, partial fraction decomposition is used to rewrite the function as a sum of simpler rational terms. The...
212
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

584
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
584

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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Preface: Recent Advances in Fractional Dynamics.

H M Srivastava1, Dumitru Baleanu2, Changpin Li3

  • 1Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.

Chaos (Woodbury, N.Y.)
|September 3, 2016
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Summary

This issue highlights recent advancements in Fractional Dynamics, exploring its diverse applications across mathematics, physics, and engineering. Discover cutting-edge developments in this dynamic scientific field.

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Area of Science:

  • Mathematics
  • Physics
  • Engineering Sciences

Background:

  • Fractional Dynamics is an emerging field with significant theoretical and practical implications.
  • The study of fractional calculus extends classical dynamics to non-integer orders.

Purpose of the Study:

  • To present recent developments and advances in Fractional Dynamics.
  • To showcase the widespread applications of Fractional Dynamics in various scientific disciplines.

Main Methods:

  • This Special Focus Issue compiles recent research findings.
  • The methodologies employed span theoretical advancements and applied studies within Fractional Dynamics.

Main Results:

  • Several new developments and advances in Fractional Dynamics are presented.
  • The applications discussed span across mathematical, physical, and engineering sciences.

Conclusions:

  • Fractional Dynamics is a rapidly evolving field with broad applicability.
  • Continued research in this area promises further innovative applications across science and engineering.