Related Experiment Video
Updated: Feb 13, 2026
09:51
Atom Probe Tomography Studies on the CuIn,GaSe2 Grain Boundaries
Published on: April 22, 2013
13.3K
The phase structure of grain boundaries.
Nicholas M Ercolani1, Nikola Kamburov2, Joceline Lega3
1Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.
Summary
This study examines grain boundary defects in pattern-forming systems like the Swift-Hohenberg equation. It reveals how decreasing roll angles leads to dislocations, offering insights into defect formation mechanisms.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Mathematical physics
Background:
- Grain boundaries are line defects separating differently oriented patterns in physical systems.
- Dislocations form at grain boundaries as the angle between patterns decreases.
- Variational pattern-forming systems provide a framework for studying defect dynamics.
Purpose of the Study:
- To investigate the transition to dislocations at grain boundaries in variational pattern-forming systems.
- To analyze the phase structure of grain boundaries using numerical and analytical methods.
- To connect findings from the Swift-Hohenberg equation to its phase diffusion equation.
Main Methods:
- Numerical simulations of the Swift-Hohenberg (SH) equation.
- Analytical investigation of the regularized Cross-Newell equation.
- Harmonic analysis to understand phase structure.
Main Results:
- Numerical results illuminate the phase structure of grain boundaries.
- Observations are linked to the behavior of the phase diffusion equation.
- The role of phase derivatives in defect creation is explored.
Conclusions:
- The study provides insights into defect formation in variational pattern-forming systems.
- Harmonic analysis is a valuable tool for understanding pattern system phase structures.
- Future research directions in nonlinear wave stability are suggested.
More Related Videos
07:58Improving the Combustion Performance of a Hybrid Rocket Engine using a Novel Fuel Grain with a Nested Helical Structure
Published on: January 18, 2021
6.6K
09:13Characterization of Ultra-fine Grained and Nanocrystalline Materials Using Transmission Kikuchi Diffraction
Published on: April 1, 2017
14.2K
Related Concept Videos
02:39Phase Diagrams
50.5K
A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
50.5K
01:26Areas Within Irregular Boundaries
388
Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...
388
02:40Pollination and Flower Structure
75.9K
Flowers are the reproductive, seed-producing structures of angiosperms. Typically, flowers consist of sepals, petals, stamens, and carpels. Sepals and petals are the vegetative flower organs. Stamens and carpels are the reproductive organs.
75.9K
01:16Electrostatic Boundary Conditions
982
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
982
01:28Magnetostatic Boundary Conditions
1.7K
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
1.7K
01:18Boundary Layer Characteristics
664
When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
664