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Phase Transitions02:31

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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...
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The concept of the looking-glass self describes how an individual's self-concept is shaped by their perception of how others see them. This psychological theory, first introduced by sociologist Charles Horton Cooley in 1902, posits that self-identity emerges in a social context and is influenced by the judgments—real or imagined—of others.Research suggests that individuals frequently overestimate how positively others perceive them. This is particularly evident in physical...
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Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.
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Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
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Related Experiment Video

Updated: Feb 12, 2026

Patterning via Optical Saturable Transitions - Fabrication and Characterization
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Transition between crack patterns in quenched glass plates.

A Yuse, M Sano

    Nature
    |April 11, 2018
    PubMed
    Summary

    Researchers observed crack propagation in glass plates. As crack tip speed increased, cracks transitioned from straight to wavy, indicating a Hopf bifurcation, and then branched at higher speeds.

    Area of Science:

    • Materials Science
    • Physics
    • Fracture Mechanics

    Background:

    • Fracture mechanics studies crack formation and propagation.
    • Crack morphology can be fractal and complex, especially in brittle materials under stress.
    • Previous research linked dynamic crack instability to complex structures near the speed of sound.

    Purpose of the Study:

    • To investigate crack propagation and morphology in glass plates under controlled cooling conditions.
    • To analyze the transition in crack patterns as a function of crack tip speed.
    • To identify the underlying physical mechanisms driving these morphological changes.

    Main Methods:

    • Controlled cooling of glass plates to induce fracture.
    • Observation and analysis of crack morphology and propagation speed.

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  • Mathematical analysis of relaxation time to identify bifurcation behavior.

    • Main Results:

    • A transition from straight to regular, wavy crack patterns was observed as crack tip speed increased.
    • The observed transition is consistent with a Hopf bifurcation, a common phenomenon in nonlinear systems.
    • At higher speeds, oscillatory cracks further evolved, splitting into multiple branches.

    Conclusions:

    • Crack morphology in quasistatic fracture is sensitive to tip speed and can exhibit significant changes.
    • The transition to wavy cracks suggests a dynamic instability, specifically a Hopf bifurcation, even at speeds far below the speed of sound.
    • The study provides new insights into the complex dynamics of fracture and pattern formation in materials.