Jove
Visualize
Contact Us

Related Concept Videos

Summation Notation01:25

Summation Notation

74
Sigma notation, also known as summation notation, provides a concise method for representing the sum of a sequence of terms that follow a regular pattern. It utilizes the uppercase Greek letter sigma (∑), A typical expression is:In this form, k the index of summation is 1, the starting value, and n the ending value. The term ak​ represents the general term of the sequence.For example, the increasing sequence 5, 7, 9, ..., 23 over 10 terms can be expressed as:This simplifies the...
74
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

2.8K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
2.8K
The Born-Haber Cycle02:44

The Born-Haber Cycle

24.6K
Lattice Energy 
24.6K
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

1.8K
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
1.8K
Geometric Sequences01:30

Geometric Sequences

130
In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...
130
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.1K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
26.1K

You might also read

Related Articles

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

Sort by
Same author

Accelerating molecular dynamics simulations using fast Ewald summation with prolates.

Nature communications·2026
Same author

Interpolative Separable Density Fitting on Adaptive Real Space Grids.

Journal of chemical theory and computation·2026
Same author

Author Correction: Forced and spontaneous symmetry breaking in cell polarization.

Nature computational science·2024
Same author

Robust ab initio solution of the cryo-EM reconstruction problem at low resolution with small data sets.

Journal of structural biology·2023
Same author

Forced and spontaneous symmetry breaking in cell polarization.

Nature computational science·2023
Same author

Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory Using Fourier Contour Deformation.

Journal of chemical theory and computation·2023
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 Experiment Video

Updated: Dec 4, 2025

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

6.9K

A Fast Summation Method for Oscillatory Lattice Sums.

Ryan Denlinger1, Zydrunas Gimbutas2, Leslie Greengard1

  • 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1110.

Journal of Mathematical Physics
|October 22, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a rapid summation method for lattice sums crucial in wave scattering. The new approach rigorously analyzes Wood's anomalies, offering a fast and accurate solution for periodic boundary conditions.

More Related Videos

Generation of Local CA1 γ Oscillations by Tetanic Stimulation
08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

9.4K
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.8K

Related Experiment Videos

Last Updated: Dec 4, 2025

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

6.9K
Generation of Local CA1 γ Oscillations by Tetanic Stimulation
08:02

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

9.4K
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.8K

Area of Science:

  • Physics
  • Computational Science

Background:

  • Wave scattering problems with periodic boundary conditions often involve complex lattice sums.
  • Existing algorithms for these calculations can be computationally intensive.
  • Wood's anomalies, singularities in spectral response, occur under specific grating illumination conditions.

Purpose of the Study:

  • To present a novel, fast summation method for lattice sums.
  • To provide a rigorous analysis of Wood's anomalies using this new method.
  • To develop an efficient algorithm for wave scattering calculations.

Main Methods:

  • Utilized the Euler-Maclaurin formula.
  • Employed a steepest descent argument.
  • Developed a new summation algorithm for lattice sums.

Main Results:

  • The new method achieves super-algebraic convergence.
  • The algorithm successfully analyzes Wood's anomalies.
  • The computational time required is on the order of milliseconds.

Conclusions:

  • The presented fast summation method is highly efficient for lattice sums in wave scattering.
  • This approach offers a rigorous framework for understanding Wood's anomalies.
  • The algorithm demonstrates significant improvements in speed and accuracy.