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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

49.9K
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 Diagram01:19

Phase Diagram

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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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Phase I Reactions: Oxidation of Aliphatic and Aromatic Carbon-Containing Systems01:19

Phase I Reactions: Oxidation of Aliphatic and Aromatic Carbon-Containing Systems

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Phase I biotransformation reactions are integral to drug metabolism, predominantly involving oxidative, reductive, and hydrolytic transformations. Chief among these are oxidative reactions, which enhance the hydrophilicity of xenobiotics and introduce polar functional groups to facilitate their elimination from the body.
Oxidation reactions are fundamental in aromatic carbon-containing systems. An example is the hydroxylation of phenobarbital, a process that transforms it into...
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Phase I Reactions: Oxidation of Carbon-Heteroatom and Miscellaneous Systems01:15

Phase I Reactions: Oxidation of Carbon-Heteroatom and Miscellaneous Systems

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Oxidative reactions are pivotal in metabolizing numerous compounds, including pharmaceutical drugs. These reactions often occur in carbon-heteroatom systems, such as carbon-nitrogen, carbon-sulfur, and carbon-oxygen.
In carbon-nitrogen systems, aliphatic and aromatic amines can undergo oxidative reactions. Secondary and tertiary amines, like those found in tricyclic antidepressants, can undergo N-dealkylation, a process that involves the oxidation of the alkyl group. In addition, oxidative...
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Energy Diagrams - II01:10

Energy Diagrams - II

11.8K
Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...
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pV-Diagrams01:18

pV-Diagrams

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The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
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Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
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Phase Diagram for Logistic Systems under Bounded Stochasticity.

Yitzhak Yahalom1, Nadav M Shnerb1

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan IL52900, Israel.

Physical Review Letters
|April 2, 2019
PubMed
Summary
This summary is machine-generated.

Understanding population extinction is crucial. This study reveals three distinct phases influencing extinction time in stochastic birth-death processes, with bounded noise critical for exponential survival phases.

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Area of Science:

  • Ecology
  • Population Dynamics
  • Mathematical Biology

Background:

  • Extinction is a critical endpoint for populations.
  • Stochastic birth-death processes model population dynamics.
  • Understanding factors influencing time to extinction is vital for conservation.

Purpose of the Study:

  • To investigate the time to extinction in logistic and logistic-like systems.
  • To analyze the impact of demographic and bounded environmental stochasticity.
  • To identify and characterize different phases of population decline.

Main Methods:

  • Analysis of logistic and logistic-like population models.
  • Inclusion of demographic and bounded environmental stochasticity.
  • Development of a new WKB scheme for analyzing power-law phases.

Main Results:

  • Identified three phases: inactive (logarithmic T vs. initial size), active (exponential T vs. carrying capacity N), and Griffiths (power-law T vs. N).
  • The exponential phase requires bounded noise, where diffusion approximation fails in the Griffiths phase.
  • A novel WKB scheme effectively analyzes both diffusive and non-diffusive regimes.

Conclusions:

  • Bounded noise is essential for supporting exponential population survival phases.
  • The breakdown of diffusion approximation signifies a crossover in survival and decline dynamics.
  • The new WKB scheme provides a robust tool for studying extinction dynamics across different regimes.