New criteria for self-adjointness and its application to Dirac-Maxwell Hamiltonian

We present a new theorem concerning a sufficient condition for a symmetric operator acting in a complex Hilbert space to be essentially self-adjoint. By applying the theorem, we prove that the Dirac Maxwell Hamiltonian, which describes a quantum system of a Dirac particle and a radiation field minimally interacting with each other, is essentially self-adjoint. Our theorem covers the case where the Dirac particle is in the Coulomb type potential.Comment: 10 page

Finsler geometry modeling of phase separation in multi-component membranes

Finsler geometric surface model is studied as a coarse-grained model for membranes of three-component such as DOPC, DPPC and Cholesterol. To understand the phase separation of liquid ordered (DPPC rich) $L_o$ and the liquid disordered (DOPC rich) $L_d$, we introduce a variable $\sigma (\in \{1,-1\})$ in the triangulated surface model. We numerically find that there appear two circulars and stripe domains on the surface and that these two morphologies are separated by a phase transition. The morphological change from the one to the other with respect to the variation of the area fraction of $L_o$ is consistent with existing experimental results. This gives us a clear understanding of the origin of the line tension energy, which has been used to understand those morphological changes in the three-component membranes. In addition to these two circulars and stripe domains, raft-like domain and budding domain are also observed, and the corresponding several phase diagrams are obtained. Technical details of the Finsler geometry modeling are also shown.Comment: 18 pages, 11 figure

Numerical calculation of tensile test using a dumbbell-shaped in thickness direction specimen

This study is the product of a tensile test of a uniaxial tensile specimen having a thinner test section than parallel section, which is a tensile test piece with a dumbbell shape in the thickness direction, fabricated by means of cutting as a preliminary experiment and an evaluation of the mechanical properties of the tensile specimen. In the tensile test, we compared the tensile properties of the dumbbell-shaped in thickness direction tensile specimen with those of conventional tensile specimens. In addition, we analyzed the states of stress and strain in the tensile specimens during a tensile test by using the finite element method