In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on Sn+1, without performing an intervening surgery. In the restrictive context of rotational symmetry, this construction gives evidence in favor of Perelman’s hope for a “canonically defined Ricci flow through singularities”.

In the present study, the production of dextran from date extract and sucrose as carbon sources by the bacterium Leuconostoc mesenteroides NRRL B512 (f) was investigated. In comparison to blue dextran (Mw≈2000 Da), dextran molecular weight was reduced (Mw2000 KDa). Flow behavior indices of dextran solutions from date extracts were investigated and rheological parameters were evaluated at concen...

Shoulder geometry of tool plays an important role in friction-stir welding because it controls thermal interactions and heat generation. This work is proposed and developed a coupled rigid-viscoplastic numerical modeling based on computational fluid dynamics and finite element calculations aiming to understand these interactions. Model solves mass conservation, momentum, and energy equations in...