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Phase Transitions02:31

Phase Transitions

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
23.9K
Phase Transitions01:21

Phase Transitions

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A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
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Phase Diagrams of Ternary Systems01:28

Phase Diagrams of Ternary Systems

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Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
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Phase Diagrams02:39

Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Phase Diagram01:24

Phase Diagram

131
A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
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Phase Diagram01:19

Phase Diagram

7.3K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Complex quantum network geometries: Evolution and phase transitions.

Ginestra Bianconi1, Christoph Rahmede2, Zhihao Wu3

  • 1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

This study introduces quantum geometric networks, complex structures with properties like small-world networks. These networks exhibit distinct behaviors based on quantum statistics and can undergo significant structural changes.

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Area of Science:

  • Quantum physics
  • Network science
  • Complex systems

Background:

  • Networks are fundamental structures modeling diverse systems, from the internet to the brain.
  • Understanding the quantum structure of space-time requires novel network descriptions.
  • Complex networks exhibit properties like scale-free distributions and high clustering.

Purpose of the Study:

  • To define and characterize complex quantum network geometries.
  • To explore the dynamics and statistical properties of these quantum networks.
  • To investigate potential structural phase transitions in quantum geometric networks.

Main Methods:

  • Defining growing simplicial 2-complexes as the basis for quantum networks.
  • Modeling network growth using nonequilibrium dynamics and link energies.
  • Mapping quantum network states to network elements via quantum occupation numbers.
  • Analyzing network properties such as degree distribution, clustering, and modularity.

Main Results:

  • Introduced quantum geometric networks with complex network properties (small-world, high clustering, modularity, scale-free).
  • Distinguished between Fermi-Dirac and Bose-Einstein quantum networks based on their statistics.
  • Demonstrated that these networks can undergo structural phase transitions.

Conclusions:

  • Quantum geometric networks provide a new framework for studying quantum structures.
  • The identified properties and behaviors offer insights into quantum complex systems.
  • Further research can explore connections to spin networks and triangulations.