# Center for Mathematics and Physics in Engineering Education

## Faculty and Staff

## Curriculum

## Research Activities

This department offers the educational programs in physics and mathematics for the students of seven departments. The emphasis is on fundamental principles, as well as the recognition of the importance of applied phisics and mathematics to engineering fields. The department is divided into two research groups: applied physics and applied mathematics.

### APPLIED PHYSICS

The research field of this group is solid state phisics; the subjects concern the physical investigations of materials such as ceramics, ionic conductors, superconductors, in which nuclear magnetic resonance (NMR) method is mainly used. Current topics of each staff are as follows.

- Studies on superionic conductors by NMR and ultrasonic techniques; Chemical bonding and ionic conduction in noble metal halides; Fast ion transport in lithium transition metal oxides; Ionic behavior in lithium sodium sulphate; Elastic constants analysis of lithium ion conductors. (T.Kanashiro)
- NMR and Nuclear Quadrupole Resonance (NQR) studies on metals and alloys; Physical properties of High-Tc superconductors; Low temperature physics in strongly correlated electron systems and heavy Femion systems; NQR and hole transfer in rareearth copper oxides. (T.Ohno)
- Chemical bonding nature of ionic crystals; Polarizabilities and the quadrupoleshielding factor of the closed shell ions in solids; Theoretical treatment of superionic behavior based on the density functional theory; Effective charges of rock-salt and zincblende crystals. (Y.Michihiro)
- NMR studies on superconducting and relating materials; NMR analysis of the charge density wave transition in copper-based compounds; Nuclear relaxation in superconductors with A15 or C15 structure; NMR and amorphous dense Kondo cerium copper compounds. (Y.Kishimoto)
- NMR and electrical impedance studies on superionic conductors; NMR investigation in electrode materials in lithium ion batteries; Impedance analysis of lithium transition metal oxides; Ionic conduction and nuclear relaxation in copper halides. (K.Nakamura)
- Magnetism and superconductivity in strongly correlated electron systems; Unconventional superconductivity; Kondo insulator; Non-Fermi liquid effect in heavy-fermion compound. (Y.Kawasaki)

### APPLIED MATHEMATICS

The research subjects of this group are related to the fields such as numerical analysis of chaotic phenomena, mathematical treatments of quantum field theory, analysis of nonlinear differential equations, and algebraic topology. Current studies are as follows.

- Mathematical treatments of quantum field theory; Edge of the Wedge theorem for Fourier hyperfunctions; Time development of quantum lattice systems; Linear canonical supertransformation; Hilbert superspace and unitary representation of Lie supergroup. (S.Nagamachi)
- Development of numerical methods; Infinite-Precision Numerical Simulation; Numerical analysis for various problems,e.g. free boundary problems, inverse problems, etc.; PC cluster and parallel computing. (H.Imai)
- Numerical analysis and the algorithms for solving a large system of linear equations; Application to numerical computation of the Navier-Stokes equation with the free boundary conditions; Numerical simulation of partial differential equations in infinite precision. (T.Takeuchi)
- Numerical linear algebra with appplications; Iterative methods for large-scale systems of linear equations. (C.Jin)
- Theory and application of modern mathematics; Algebraic Topology; Algebraic homotopy; Set of homotopy classes of self-homotopy equivalences of a space; Homology and cohomology. (N.Sawashita)
- Mathematical theories and analysis of ordinary and partial differential equations; Study on the conditions under which quasiperiodic solution exists; Nonlinearity and the structure of solutions of elliptic equations; Blow-up pattern for a parabolic equation. (A.Kohda)
- Partial differential equations of elliptic type; Variational methods for second-order, elliptic equations; Boundary value problems for second-order, elliptics equations; Elliptic partial differential equations of degenerate type; Qualitative properties of solutions. (N.Fukagai)
- Functional analytic treatment of nonlinear evolution equations in mathematical physics; Hyperbolic systems of coservation laws; Nonlinear evolution operators associated with nonlinear degenerate parabolic equations. (K.Okamoto)
- Pattern formations in nonlinear phenomena and numerical simulation for solving these model equations; Formation of colony patterns by a bacterial cell population. (H.Sakaguchi)