| Summary: | 碩士 === 國立中正大學 === 物理系 === 90 === The shape energy of a biological membrane was formulated previously in terms of the Helfrich Hamiltonian. Due to the softness of the biomembrane its surface usually undergoes large deformations even at room temperature.
Here we extend the work by Ou-Yang and Helfrich, to expand the bending energy up to 4-th order in the deformation function with the help of the differential geometry tools.
After obtaining 4-th order correction for the bending energy, we
investigate its role in the bending deformation by illustrating two special cases --- the spherical and cylindrical surfaces. In the case of a sphere, we restricted ourselves to its two possible shapes, a prolate and an oblate ones. The analysis indicates that, upon taking account of 4-th order corrections, the critical value determining the oblate-to-prolate transition will behave in a more complicated way than the case being considered only up to 3-rd order corrections. We also compare the present results with the previous ones. In the case of a circular cylinder, two special surface deformations were considered and stable conditions for the surface under such deformations are found.
The formation of possible surface shapes slightly deviated from a cylinder are also predicted.
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