Kinetic Models Versus Hodograph Equation

Classic kinetic theories for crystal growth and meltingMelting are stated through diffusion- or collision-limited models of fluxes of particle attachment/detachment to/from the interface. These kinetic theories have recently experienced a common crisis in the description of the molecular dynamicsMolecular dynamics data (MD-data) on the interface movements within the range of driving forces on phase transformationPhasetransformation accessible in atomistic simulations. The classic kinetic theories exhibit difficulty in describing the interface velocityInterfacevelocity at large values of the driving force. One possible exit from such a crisis might be seen in taking both fluxes (particle velocity) and their temporal relaxation (particle acceleration) into account using the unified equation, which is given by the hodograph equationEquationhodograph.