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2004•Journal of Beijing Technology and Business UniversityRequires access

EXACT SOLUTIONS OF GOVERNING EQUATIONS FOR TWO-DIMENSION STEADY STATE CRYSTAL GROWTH

Fucheng Liao

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Abstract

A class of partial differential equations (PDE) which describe two-dimension steady state crystal growth for concentration were studied. By using Fourier series expansion method, we can change the PDE into a set of ordinary differential equations (ODEs). Making use of properties of ODEs, the exact solution of the PDE was obtained. The result shows that the concentration in the solid-liquid interface is exponentially damped oscillation.

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What this paper is about

A class of partial differential equations (PDE) which describe two-dimension steady state crystal growth for concentration were studied. By using Fourier series expansion method, we can change the PDE into a set of ordinary differential equations (ODEs). Making use of properties of ODEs, the exact solution of the PDE was obtained. The result shows that the concentration in the solid-liquid interface is exponentially damped oscillation.

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Available abstract

A class of partial differential equations (PDE) which describe two-dimension steady state crystal growth for concentration were studied. By using Fourier series expansion method, we can change the PDE into a set of ordinary differential equations (ODEs). Making use of properties of ODEs, the exact solution of the PDE was obtained. The result shows that the concentration in the solid-liquid interface is exponentially damped oscillation.

Key concepts: Ordinary differential equation, Mathematical analysis, Mathematics, Partial differential equation, Ode, Dimension (graph theory), Steady state (chemistry), Fourier series

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