Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
1.1K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.5K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.5K
Separable Differential Equations01:20

Separable Differential Equations

359
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
359
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

767
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
767
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

238
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
238
Introduction to Differential Equations01:20

Introduction to Differential Equations

540
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
540

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Probing Hydrogen Activation in a Dimetal Dihydride Complex by Symmetric Exchange with Parahydrogen.

Journal of the American Chemical Society·2026
Same author

Chemical hydrodynamics of nuclear spin states.

Science advances·2025
Same author

Simulation of pulsed dynamic nuclear polarization in the steady state.

The Journal of chemical physics·2025
Same author

Leveraging relaxation-optimized <sup>1</sup>H-<sup>13</sup>C<sub>F</sub> correlations in 4-<sup>19</sup>F-phenylalanine as atomic beacons for probing structure and dynamics of large proteins.

Nature chemistry·2025
Same author

Instrumental distortions in quantum optimal control.

The Journal of chemical physics·2025
Same author

Protein NMR assignment by isotope pattern recognition.

Science advances·2024

Related Experiment Video

Updated: Apr 25, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

42.6K

A partial differential equation for pseudocontact shift.

G T P Charnock1, Ilya Kuprov

  • 1Oxford e-Research Centre, University of Oxford, 7 Keble Road, Oxford OX1 3QG, UK.

Physical Chemistry Chemical Physics : PCCP
|August 21, 2014
PubMed
Summary

This study shows pseudocontact shift (PCS) data can predict and analyze unpaired electron behavior. The method also allows extraction of electron probability density from PCS measurements.

More Related Videos

Label-free Isolation and Enrichment of Cells Through Contactless Dielectrophoresis
10:38

Label-free Isolation and Enrichment of Cells Through Contactless Dielectrophoresis

Published on: September 3, 2013

17.0K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

5.0K

Related Experiment Videos

Last Updated: Apr 25, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

42.6K
Label-free Isolation and Enrichment of Cells Through Contactless Dielectrophoresis
10:38

Label-free Isolation and Enrichment of Cells Through Contactless Dielectrophoresis

Published on: September 3, 2013

17.0K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

5.0K

Area of Science:

  • Chemical Physics
  • Computational Chemistry
  • Quantum Chemistry

Background:

  • Pseudocontact shift (PCS) is a key NMR phenomenon providing insights into molecular structure and dynamics.
  • Understanding the behavior of unpaired electrons is crucial in various chemical and biological systems.
  • Accurate prediction and analysis of PCS are essential for interpreting experimental data.

Purpose of the Study:

  • To demonstrate that pseudocontact shift (PCS) obeys a specific elliptic partial differential equation.
  • To establish a method for straightforward PCS prediction and analysis in systems with delocalized unpaired electrons.
  • To show that unpaired electron probability density can be extracted from PCS data.

Main Methods:

  • Formulating PCS as a scalar or tensor field in three dimensions.
  • Deriving an elliptic partial differential equation governing PCS, incorporating the Hessian of electron probability density.
  • Employing a regularization procedure for extracting electron probability density from PCS data.

Main Results:

  • The derived partial differential equation accurately describes PCS behavior.
  • The method facilitates direct prediction and analysis of PCS, especially near delocalized unpaired electrons.
  • Successful extraction of unpaired electron probability density from PCS data was achieved.

Conclusions:

  • The established mathematical framework simplifies PCS analysis and prediction.
  • This approach offers a novel way to probe and quantify unpaired electron distributions.
  • The findings have implications for understanding paramagnetic systems and developing new analytical techniques.