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Related Concept Videos

Entropy02:39

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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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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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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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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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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Chaotic Map with No Fixed Points: Entropy, Implementation and Control.

Van Van Huynh1, Adel Ouannas2, Xiong Wang3

  • 1Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary
This summary is machine-generated.

This study introduces a novel chaotic map lacking equilibrium and fixed points. The research details its dynamics, experimental implementation, and control strategies for stabilization and synchronization.

Keywords:
approximate entropychaoschaotic mapfixed pointimplementation

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Applied Mathematics

Background:

  • Equilibrium and fixed points are common in dynamical systems.
  • Understanding chaotic systems is crucial for various scientific and engineering fields.

Purpose of the Study:

  • To propose and analyze a novel dynamical map without equilibrium.
  • To investigate the chaotic behavior of this new map.
  • To implement and experimentally validate the map and its control schemes.

Main Methods:

  • Analysis of dynamical systems, including return maps, bifurcation diagrams, and Lyapunov exponents.
  • Entropy calculation for the proposed map.
  • Implementation on an open microcontroller platform for experimental observation.
  • Development of control schemes for stabilization and synchronization.

Main Results:

  • Demonstration of chaotic behavior in the proposed map.
  • Successful experimental implementation and observation.
  • Validation of the map's unique properties (no equilibrium, no fixed point).

Conclusions:

  • The proposed map is a novel system exhibiting chaos without equilibrium.
  • The study provides a comprehensive analysis and experimental validation.
  • Effective control strategies were developed for practical applications.