Global symmetry-breaking bifurcation in a model for 2-phase lipid-bilayer vesicles - analysis and computation

2017. 04. 25. 14:00
BME K épület 354/A
Tim Healey (Dept. Mathematics, Cornell University)

Megszokottól eltérő időpont és hely!!!

We study a model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field together with membrane fluidity and bending elasticity. We prove the existence of a plethora of equilibria in the large, corresponding to symmetry-breaking solutions of the Euler-Lagrange equations. We also numerically compute a special class of such solutions, namely those possessing icosahedral symmetry. We overcome several difficulties along the way. Due to inherent surface fluidity combined with finite curvature elasticity, neither the Eulerian (spatial) nor the Lagrangian (material) description of the model lends itself well to analysis. This is resolved via a singularity-free radial-map description, which effectively eliminates the grossly under-determined mid-plane deformation. We then use well known group-theoretic selection techniques combined with global bifurcation methods to obtain our results.

Operator method in the theory of differential equations

2017. 04. 06. 10:15
H. épület 306-os terem
Liepa Bikulciene (Kaunasi Műszaki Egyetem, Litvánia)

The Operator method for differential equations solving can be applied in nonlinear dynamics for exact solutions finding. Starting from basics of this method and Hankel matrices ranks possibilities of evaluation of DE and special PDE solutions using MAPLE mathematical software will be introduced. Examples of solved ODE and PDE: Huxley, Liouville, KdV equations and their soliton solutions will be presented. It will be shown that special solitary solutions exist only on a line in the parameter plane of initial and boundary conditions. This result may lead to important findings in a variety of practical applications as nonlinear evolution equations in mathematical physics.

Joint work with Research Group for Mathematical and Numerical Analysis of Dynamical Systems (The talk will be in English)