Mean-field theory for coarsening faceted surfaces

Scott A Norris1, Stephen J Watson

  • 1Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA. snorris@smu.edu

Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Surface Tension01:24

Surface Tension

Surface tension is defined as the force per unit length (γ) acting along the surface of a liquid. It arises due to strong intermolecular forces of attraction. A molecule located inside the bulk of the liquid is surrounded by other molecules and experiences equal forces in all directions. However, a molecule at the surface experiences unbalanced forces because there are more neighboring molecules below than above. This creates a net inward force that pulls surface molecules toward the interior,...
Surface Tension and Surface Energy01:16

Surface Tension and Surface Energy

When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension.
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
Surface Tension of Fluid01:22

Surface Tension of Fluid

Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
Surface tension varies with...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model01:09

Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model

Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...