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Related Concept Videos

Mechanical Systems01:22

Mechanical Systems

Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically described...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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Fabrication and Testing of Microfluidic Optomechanical Oscillators
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Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

Nonlinear mode-coupling in nanomechanical systems.

M H Matheny1, L G Villanueva, R B Karabalin

  • 1Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, United States.

Nano Letters
|March 19, 2013
PubMed
Summary
This summary is machine-generated.

Accurately characterizing nonlinearities in nanomechanical systems (NEMS) is challenging. This study introduces a linear transduction scheme for precise NEMS nonlinearity measurement, showing excellent agreement with Euler-Bernoulli theory.

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A Novel Method for In Situ Electromechanical Characterization of Nanoscale Specimens
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A Novel Method for In Situ Electromechanical Characterization of Nanoscale Specimens

Published on: June 2, 2017

Area of Science:

  • Nanotechnology
  • Mechanical Engineering
  • Materials Science

Background:

  • Nonlinear coupling in nanomechanical devices is crucial for applications like sensing.
  • Existing methods for characterizing NEMS nonlinearities are often inaccurate due to inherent nonlinearities in detection/actuation.
  • Accurate measurement of nonlinearities is essential for advancing NEMS technology.

Purpose of the Study:

  • To develop a reliable experimental protocol for characterizing nonlinearities in NEMS.
  • To introduce a highly linear transduction scheme to overcome limitations of current methods.
  • To enable accurate in situ measurement of device nonlinearities.

Main Methods:

  • Developed a novel, highly linear transduction scheme tailored for NEMS.
  • Implemented an experimental protocol for in situ characterization of nonlinearities.
  • Compared experimental results with predictions from Euler-Bernoulli theory.

Main Results:

  • Achieved accurate, in situ characterization of NEMS nonlinearities.
  • Demonstrated the effectiveness of the linear transduction scheme.
  • Found excellent agreement between experimental data and theoretical predictions for intra- and intermodal nonlinearities.

Conclusions:

  • The developed protocol and linear transduction scheme provide a robust method for NEMS nonlinearity characterization.
  • This advancement is critical for the design and application of next-generation nanomechanical devices.
  • The findings validate the use of Euler-Bernoulli theory in analyzing NEMS nonlinear behavior.