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

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
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...
Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Properties of Laplace Transform-I01:15

Properties of Laplace Transform-I

The Laplace transform is a powerful mathematical tool used to convert functions from the time domain into the frequency domain, greatly simplifying the analysis and solution of linear time-invariant systems. This transformation is facilitated by several universal properties: Linearity, Time-Scaling, Time-Shifting, and Frequency Shifting.
The Linearity property is foundational to the Laplace transform. It states that the transform of a linear combination of functions is equivalent to the same...

You might also read

Related Articles

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

Sort by
Same author

Evidence for the Collective Nature of Radial Flow in Pb+Pb Collisions with the ATLAS Detector.

Physical review letters·2026
Same author

Evidence for the Dimuon Decay of the Higgs Boson in pp Collisions with the ATLAS Detector.

Physical review letters·2025
Same author

Evidence for Longitudinally Polarized W Bosons in the Electroweak Production of Same-Sign W Boson Pairs in Association with Two Jets in pp Collisions at sqrt[s]=13  TeV with the ATLAS Detector.

Physical review letters·2025
Same author

Observation of tt[over ¯] Production in Pb+Pb Collisions at sqrt[s_{NN}]=5.02  TeV with the ATLAS Detector.

Physical review letters·2025
Same author

Search for Dark Matter Produced in Association with a Dark Higgs Boson in the bb[over ¯] Final State Using pp Collisions at sqrt[s]=13  TeV with the ATLAS Detector.

Physical review letters·2025
Same author

Search for Magnetic Monopole Pair Production in Ultraperipheral Pb+Pb Collisions at sqrt[s_{NN}]=5.36  TeV with the ATLAS Detector at the LHC.

Physical review letters·2025

Related Experiment Video

Updated: May 8, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Linear-scaling time-dependent density-functional theory in the linear response formalism.

T J Zuehlsdorff1, N D M Hine, J S Spencer

  • 1Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom. tjz07@imperial.ac.uk

The Journal of Chemical Physics
|August 17, 2013
PubMed
Summary

We developed a new computational method for calculating optical absorption spectra of large molecules. This approach achieves linear-scaling computational cost, making it efficient for complex systems like carbon nanotubes.

More Related Videos

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Related Experiment Videos

Last Updated: May 8, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Calculating optical absorption spectra is crucial for understanding material properties.
  • Traditional methods face computational challenges with large molecules and nanostructures.
  • Linear response formalism in time-dependent density-functional theory (TDDFT) is a powerful tool.

Purpose of the Study:

  • To implement an efficient TDDFT method for low-energy optical absorption spectra.
  • To achieve linear-scaling computational effort with system size.
  • To overcome limitations of conventional localized orbital formulations.

Main Methods:

  • Utilized time-dependent density-functional theory (TDDFT) in the linear response formalism.
  • Developed a novel approach using two sets of in situ optimized localized orbitals for occupied and unoccupied states.
  • Avoided explicit reference to canonical Kohn-Sham states.

Main Results:

  • The method successfully calculates optical absorption spectra for large molecules and nanostructures.
  • Demonstrated linear-scaling computational cost with increasing system size.
  • Achieved good agreement with traditional TDDFT methods for organic molecules.

Conclusions:

  • The new TDDFT implementation offers an efficient and scalable approach for optical spectra calculations.
  • The double representation strategy effectively handles occupied and unoccupied electronic states.
  • This method is suitable for studying large molecular systems and carbon nanotubes.