Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt. (25th December 2008) - Balint, Stefan; Balint, Agneta Maria
Abstract : The boundary value problemz ″ = ( ( ρ ⋅ g ⋅ z − p ) / γ ) [ 1 + ( z ′ ) 2 ] 3 / 2 − ( 1 / r ) ⋅ [ 1 + ( z ′ ) 2 ] ⋅ z ′,   r ∈ [ r 1, r 0 ], z ′ ( r 1 ) = − tan ⁡ ( π / 2 − α g ), z ′ ( r 0 ) = − tan ⁡ α c, z ( r 0 ) = 0, andz ( r ) is strictly decreasing on[ r 1, r 0 ], is considered. Here, 0 < r 1 < r 0,     ρ,     g,     γ,     p,     α c,     α g are constants having the following properties:ρ,     g,     γ are strictly positive and0 < π / 2 − α g < α c < π / 2 . Necessary or sufficient conditions are given in terms ofp for the existence of concave solutions of the above nonlinear boundary value problem (NLBVP). Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by edge-defined film-fed growth (EFG) method. With this aim, this study was undertaken.