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Related Concept Videos

Resonance and Hybrid Structures02:16

Resonance and Hybrid Structures

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According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
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Parallel Resonance01:23

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The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
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Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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Resonance in an AC Circuit01:26

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The property of an inductor makes it resist any change in the current passing through it, while the property of a capacitor is to build up the charge across its terminals. Hence, if an inductor and capacitor are connected in series, they have opposite effects on the relative phase between current and voltage. The current through the circuit undergoes forced oscillation at the frequency of the source. The resistance term in an R-L-C circuit acts as a damping term because power is dissipated...
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Sound Waves: Resonance01:14

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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
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Related Experiment Video

Updated: Jan 3, 2026

Shrinkage of Dental Composite in Simulated Cavity Measured with Digital Image Correlation
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Internal resonances and relaxation memory kernels in composites.

Elena Cherkaev1

  • 1Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, UT 84112-0090, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 26, 2019
PubMed
Summary

This study links composite material

Area of Science:

  • Solid mechanics
  • Materials science
  • Continuum mechanics

Background:

  • Composite materials' macroscopic behavior depends on their microscale properties.
  • Modeling these materials involves concepts of memory and time-domain convolutions.

Purpose of the Study:

  • To establish a connection between the viscoelastic relaxation kernel and the spectral measure in composite materials.
  • To link microstructural information to the macroscopic constitutive relations.

Main Methods:

  • Utilizing the Stieltjes integral representation for effective composite properties.
  • Analyzing the relationship between relaxation kernels and spectral measures.

Main Results:

  • The spectral measure encapsulates microstructural details.
Keywords:
Stieltjes analytic representationinternal variablesrelaxation function

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  • Internal microstructural resonances dictate relaxation times.
  • A method to introduce internal variables for microscale dissipation is presented.

    • Conclusions:

    • The spectral measure provides a direct link between composite microstructure and macroscopic viscoelastic behavior.
    • Internal variables can effectively model microscale dissipation phenomena.