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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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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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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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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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To calculate the inductance of a solid cylindrical conductor, consider a 1-meter section of a non-magnetic, current-carrying conductor with radius r. Disregarding end effects and assuming uniform current density, Ampere's law helps determine the magnetic field inside the conductor. This law states that the magnetic field intensity H is concentric and constant within the conductor.
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Patterning via Optical Saturable Transitions - Fabrication and Characterization
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Pattern Transitions in a Soft Cylindrical Shell.

Yifan Yang1, Hui-Hui Dai2, Fan Xu1

  • 1Institute of Mechanics and Computational Engineering, Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, People's Republic of China.

Physical Review Letters
|June 9, 2018
PubMed
Summary
This summary is machine-generated.

Soft shells on curved surfaces exhibit complex pattern transitions, moving from wrinkles to ridges and then sagging folds. This study reveals multiple successive bifurcations in soft shell instability.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Soft Matter Physics

Background:

  • Uniaxially compressed soft films on stiff substrates exhibit intricate instability patterns.
  • Curvature effects significantly influence pattern transitions in soft materials.
  • Previous studies primarily focused on flat substrates, limiting understanding of curved systems.

Purpose of the Study:

  • To investigate pattern transitions and postbuckling phenomena in a soft shell sliding on a rigid cylinder.
  • To reveal novel bifurcation scenarios on curved surfaces.
  • To understand the role of curvature in soft shell instabilities.

Main Methods:

  • Experimental investigation of soft shell behavior on a rigid cylinder.
  • Computational modeling to simulate pattern transitions.
  • Theoretical analysis to explain observed bifurcation phenomena.

Main Results:

  • A novel postbuckling phenomenon with multiple successive bifurcations was identified: smooth-wrinkle-ridge-sagging transitions.
  • The shell initially buckles into periodic axisymmetric wrinkles, transitioning to ridges and then sagging folds upon increased compression.
  • Hysteresis loops and Maxwell equal-energy conditions were associated with the coexistence of different patterns.

Conclusions:

  • The observed bifurcation scenario is general and independent of specific material constitutive models.
  • Curvature plays a critical role in dictating the complex instability patterns of soft shells.
  • This research provides fundamental insights into the mechanics of soft materials on curved surfaces.