in conference Tomorrow's Mathematicians Today 2024

Geoemtric mechanics in soft matters
imperial college london
mingjia yan


Geometric mechanics has been a powerful tool in the study of many physical
systems, where symmetry in the systems plays an important role. While in soft
matter, the internal structure alternation or deformation due to thermal fluctuations
often associates with a symmetry breaking. In this talk, we will present a geometric
mechanics approach to study the nondissipative micromotion of liquid crystals
which are known as one class of soft matter.
We will first review the Euler-Poincaré reduction theorem for single scale physical
systems with Lie group symmetry, applying reduction by symmetry to Hamilton's
principle. For liquid crystals as hybrid systems whose motions may be expressed
as a composition of two or more Lie group actions with a broken symmetry, we will
discuss a geometric formulation to derive hybrid models of multiscale and
multiphysics motions, leading to modified Euler Poincaré equations. Then, by
Legendre transform to the Hamiltonian side, a Lie-Poisson Hamiltonian formulation
of the dynamics of liquid crystals can be found.
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修改:vinbo FROM 202.120.11.*
FROM 202.120.11.*