PDE Seminar Pattern formation in membranes coupled to a vector field

2007-04-23 16:30 - 2007-04-23 17:30
Faculty of Science Building #8 Room 309
Nariya Uchida (Tohoku Univ.)
After a brief review of the phase transition dynamics governed bya 2D vector field, I will apply the concept to two types of membranes(deformable surfaces in E3) whose curvatures are coupled to a vectorfield in the energy functional:(i) liquid-crystal membranes(ii) buckling elastic membranesIn (i), a vector field coupled to the second fundamental form induceslocally saddle-shaped structures, while in (ii), isometric deformationcauses ridge-valley patterns like those in folded papers. In each case,the coupling alters the asymptotic power-law behavior in the dynamicsof energy minimization.