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

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

12.6K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
12.6K
Band Theory02:35

Band Theory

17.3K
When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...
17.3K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.8K
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:
26.8K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.5K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
1.5K
Energy Bands in Solids01:01

Energy Bands in Solids

2.0K
Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
 Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states...
2.0K
Flat Belts: Problem Solving01:28

Flat Belts: Problem Solving

848
Flat belts are crucial in many industrial applications as they help transmit power from one pulley to another. The concept of forces and moments is used to determine the maximum moment on a pulley. For instance, consider a flat belt that wraps around two pulleys, A and B, with radii of 30 cm and 10 cm, respectively. The angle between the belt and the horizontal is 20 degrees at the pulleys. As pulley B rotates clockwise and drives pulley A, tension T2 is caused at one end of the belt, while...
848

You might also read

Related Articles

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

Sort by
Same author

Modal and wave synchronization in coupled self-excited oscillators.

Chaos (Woodbury, N.Y.)·2025
Same author

Kapitza resistance at a domain boundary in linear and nonlinear chains.

Physical review. E·2021
Same author

Kapitza thermal resistance in linear and nonlinear chain models: Isotopic defect.

Physical review. E·2021
Same author

Kinks in chains with on-site bistable nondegenerate potential: Beyond traveling waves.

Physical review. E·2018
Same author

Introduction to a topical issue 'nonlinear energy transfer in dynamical and acoustical Systems'.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2018
Same author

Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2018

Related Experiment Video

Updated: Feb 15, 2026

Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
08:32

Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting

Published on: May 14, 2016

13.0K

Flat bands and compactons in mechanical lattices.

Nathan Perchikov1, O V Gendelman1

  • 1Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel.

Physical Review. E
|January 20, 2018
PubMed
Summary

Local configurational symmetry in lattice structures generates compactons, which are stationary solutions. Nonlinearity can destabilize these, but new discrete mechanical and nonlinear lattice models allow for stability analysis and reveal two localization types and instability mechanisms.

More Related Videos

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

8.4K
Trapping of Micro Particles in Nanoplasmonic Optical Lattice
07:20

Trapping of Micro Particles in Nanoplasmonic Optical Lattice

Published on: September 5, 2017

7.0K

Related Experiment Videos

Last Updated: Feb 15, 2026

Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
08:32

Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting

Published on: May 14, 2016

13.0K
Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

8.4K
Trapping of Micro Particles in Nanoplasmonic Optical Lattice
07:20

Trapping of Micro Particles in Nanoplasmonic Optical Lattice

Published on: September 5, 2017

7.0K

Area of Science:

  • Condensed Matter Physics
  • Nonlinear Dynamics
  • Lattice Dynamics

Background:

  • Local configurational symmetry in lattice structures can create stationary, compact solutions, termed compactons, even without disorder or nonlinearity.
  • These compact solutions are linked to flat dispersion bands, a key feature in various physical systems.
  • Nonlinearity, while sometimes destabilizing compactons, is crucial for understanding their behavior in realistic scenarios.

Purpose of the Study:

  • To investigate compacton formation and stability in discrete mechanical and nonlinear lattice systems.
  • To analyze the role of different types of nonlinearity (impact constraints vs. smooth anharmonic oscillators) on compacton behavior.
  • To identify and characterize the mechanisms leading to the loss of stability in these compacton-supporting systems.

Main Methods:

  • Analysis of a discrete mechanical system with impact constraints, utilizing the saltation matrix for stability analysis.
  • Study of a smooth nonlinear lattice model with anharmonic oscillators, amenable to stability analysis in the anticontinuum limit.
  • Examination of two localization types: complete and exponential (associated with discrete breathers).

Main Results:

  • Demonstration of compacton emergence in both impact-constrained and smooth nonlinear lattice models.
  • Identification of two primary instability mechanisms: internal cell instability (compacton-discrete breather resonance) and global instability (resonance with propagation frequencies).
  • Observation of distinct bifurcations at the stability threshold corresponding to different instability pathways.

Conclusions:

  • Discrete mechanical and nonlinear lattice systems provide robust platforms for studying compactons and their stability.
  • The nature of nonlinearity significantly influences compacton behavior and stability analysis.
  • Understanding these instability mechanisms is crucial for predicting the behavior of localized solutions in complex lattice structures.