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Elliptic particles (2D)Define for λ [0,1] the function :G( r , ) G ( r ) (1 ) G ( r )AFind the global minimum over all r for fixed λ by Gr r( , ) 0This minimum r m (λ) describes a path from the center of Bto the center of A parametrized by λ [0,1]: 11 1 1rm( ) ra (1 ) A (1 )A B rab 11 1 1 rb B (1 ) A B rab,rab rb raBElliptic particles (2D)Inserting the minimum r m (λ)) into G (r, λ) definesthe overlap function S(λ) (non-negativenegative for λ [0,1]): S( ) (1 ) r(1 ) A B r , r r r T11 1 ab ab ab b aMaximize S(λ) ) for λ [0,1] → λ m , defines contact index: F( AB , ) (1 ) e(1 ) A Ber,r reT11 1 2m m r m m r ab roverlap if F(A,B) ) < 1, tangent if F(A,B) ) = 1, no contact if F(A,B) ) > 1
Elliptic particles (2D)Set F(A,B) ) to unity to find distance r* * at whichthe particles would just touch:→ overlap vector: * rer rab 21 (1 ) T (1 )1/2m m r m m r* 1 1r e A B e Obtain contact point: *r r pcpcElliptic particles (2D)example:Influence of elongationon packing fractionfor elliptic particlesN. Berntsen, , 2001
Page 1: Elliptic particles (2D)Overlap algo
Page 5 and 6: F F mg Ti Tiji xit1 xitvi( t)t
Page 7 and 8: Polyhedra (3d)A.V. Potapov, , C. S.
Page 9 and 10: Particles in Fluids• Sedimentatio
Page 11 and 12: One particle in fluide.g. . pull sp
Page 13 and 14: Inhomogeneous flowIn velocity or pr
Page 15 and 16: Sedimentation• Sedimentation ist
Page 17 and 18: Flow through a porous mediumimporta

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