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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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 occupy...
Phase Transitions01:21

Phase Transitions

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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...

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Updated: Jun 21, 2026

Sealable Femtoliter Chamber Arrays for Cell-free Biology
13:44

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Published on: March 11, 2015

Multiplicative noise and second order phase transitions.

Alon Manor1, Nadav M Shnerb

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review Letters
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

Phase transitions exhibit scale-free cluster sizes governed by proportional effects. Numerical simulations reveal multiplicative birth-death processes and power-law distributions at critical points.

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Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • Continuous phase transitions exhibit scale-free phenomena.
  • The law of proportional effect governs these distributions.

Purpose of the Study:

  • Investigate cluster size distributions in phase transitions.
  • Compare multiplicative birth-death processes with percolation dynamics.

Main Methods:

  • Numerical simulation of a two-dimensional Ising model.
  • Analysis of cluster size distributions and birth-death rates.
  • Characterization of percolation dynamics.

Main Results:

  • Cluster sizes follow a multiplicative birth-death process at critical points.
  • Steady states display power-law behavior.
  • Percolation transitions show Lévi flights instead of birth-death jumps.

Conclusions:

  • The study links scale-free cluster sizes to proportional effects and birth-death processes.
  • Percolation dynamics offer an alternative model for geometric phase transitions without ergodicity breaking.