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

Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

621
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
621
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

1.4K
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
1.4K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

420
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,...
420
Modes of Standing Waves - I01:03

Modes of Standing Waves - I

4.3K
A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
4.3K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

433
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....
433
Linearization and Approximation01:26

Linearization and Approximation

190
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
190

You might also read

Related Articles

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

Sort by
Same author

Harnessing the Reactivity of Sulfinate Salts With Cystine: An Umpolung Approach to Residue-Specific Peptide Modification.

Angewandte Chemie (International ed. in English)·2026
Same author

Experiences of a Pre-Treatment Sober Month in Individuals With Alcohol Use Disorder Pursuing Controlled Drinking Goals.

Drug and alcohol review·2026
Same author

Long-term health- and cost evaluation of two work-oriented rehabilitation models for women on long-term work disability due to common mental disorders or chronic pain - a randomized controlled trial.

BMC public health·2026
Same author

Bull's-Eye for Athletes (BEA): a measure of values-based behavior in sport and a psychometric evaluation using Rasch analysis.

Scientific reports·2026
Same author

Latent trait or sum score: addressing measurement challenges in the prediction of self-rated symptom outcomes in psychological treatment.

Frontiers in psychology·2026
Same author

Quantum Storage with Flat Bands.

Physical review letters·2026

Related Experiment Video

Updated: Mar 31, 2026

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
14:18

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

Published on: February 28, 2016

12.0K

Compactification tuning for nonlinear localized modes in sawtooth lattices.

Magnus Johansson1, Uta Naether2, Rodrigo A Vicencio3

  • 1Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
PubMed
Summary

Nonlinear localized modes in sawtooth lattices can become compact due to nonlinearity, extending linear compact modes. This phenomenon is tunable via lattice parameters and nonlinearities, with stable compact modes observed for focusing and defocusing cases.

More Related Videos

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
15:25

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

6.7K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Related Experiment Videos

Last Updated: Mar 31, 2026

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
14:18

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

Published on: February 28, 2016

12.0K
Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
15:25

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

6.7K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Area of Science:

  • Physics
  • Nonlinear Optics
  • Condensed Matter Physics

Background:

  • Localized modes in nonlinear lattices are crucial for wave phenomena.
  • Sawtooth lattices offer unique band structures, including flat bands.
  • Discrete nonlinear Schrödinger (DNLS) models describe many-body localization.

Purpose of the Study:

  • Investigate the existence and properties of nonlinear localized modes in sawtooth lattices.
  • Determine conditions for compact mode formation under various nonlinearities.
  • Analyze the stability and tunability of these compact modes.

Main Methods:

  • Analytical derivation of conditions for exact compact three-site solutions.
  • Numerical investigation of mode properties and stability for cubic and saturable nonlinearities.
  • Exploration of parameter space including coupling ratios, on-site energies, and anisotropy.

Main Results:

  • Exact compact three-site solutions exist for power-law and saturable nonlinearities.
  • Nonlinearity enables compactification of noncompact modes across a range of coupling ratios.
  • Compact nonlinear modes are stable for both focusing and defocusing nonlinearities.
  • Tunable compactness achieved through lattice parameters and nonlinear settings.

Conclusions:

  • Nonlinearity plays a key role in creating compact localized modes in sawtooth lattices.
  • These findings are relevant to experimental realizations in photonic systems.
  • The study provides a comprehensive understanding of nonlinear compact modes in engineered lattices.