Physics

This course offers a study of the fundamental and applied knowledge of the laws that determine fluid motion with an emphasis on high-Reynolds-numbers flows and gases and their application to the description of problems of interest in aerospace engineering.

This course provides a conceptual-level introduction to the field of machine learning and its most important techniques. Students examine how machine learning (ML) is the dominant component of modern research in artificial intelligence and that although ML is largely associated with computer science and software engineering, many of its foundational techniques have historical roots in the natural and social sciences and are commonly used in those fields.

The course covers the following topics. Newtonian dynamics of a particle in various coordinate systems. Harmonic, damped, and forced oscillations of a pendulum. Nonlinear oscillations and chaos. Gravitation and tidal forces. Calculus of variations. Lagrangian and Hamiltonian dynamics, generalized coordinates and constraints. Central force motion and planetary orbits. Dynamics of a system of particles, collisions in a center-of-mass coordinate system and in a lab system. Motion in a non-inertial reference frame, Coriolis and centrifugal forces. Motion relative to the Earth. Mechanics of rigid bodies, inertia tensors and principal axes of inertia. Eulerian angles, and Euler's equations for a rigid body. Precession, motion of a symmetric top and stability of rigid body rotations. Coupled oscillations, eigenfrequencies and normal modes.

Topics in this Engineering Physics course include: bonding in solids; lattice vibrations, phonons, and heat capacity; theory of free electrons in metals; band theory of solids; semiconductors; dielectric materials; magnetic materials; optical properties of materials; superconductivity.

This course, comprised of a lecture and discussion section, includes the following topics: 1) Introduction (historical notes, coordinate dependence of Newton‘s equations, systems with constraints); 2) Lagrange equations (systems w/o constraints, non-inertial reference frames, constraints and generalized coordinates, virtual displacements, D’Alembert’s principle, systems w/ constraints); 3) Hamilton‘s principle (variational calculus, derivation of Lagrange equations from Hamilton’s principle, Lagrange multipliers and constraints); 4) Symmetries and conservation laws (cyclic coordinates and canonical momenta, translational and rotational invariance, Noether theorem, translational invariance in time and energy conservation, energy conservation in 1D systems, Galilei invariance and Lagrangian of free particles, relativistic mechanics of free particles, gauge invariance, mechanical similarity); 5) Oscillations (coupled oscillators, driven oscillators, Green function of damped oscillator, parametric resonance, motion in rapidly oscillating fields); 6) Rigid bodies (degrees of freedom, tensor of inertia and kinetic energy, angular momentum, principal axes of tensor of inertia, equations of motion, Euler angles, free symmetric top, heavy symmetric top, fast top).

This six-week summer course provides individual research training through the experience of belonging to a specific laboratory at Tohoku University. Students are assigned to a laboratory research group with Japanese and international students under the supervision of Tohoku University faculty. They participate in various group activities, including seminars, for the purpose of training in research methods and developing teamwork skills. The specific topic studied depends on the instructor in charge of the laboratory to which each student is assigned. The methods of assessment vary with the student's project and laboratory instructor. Students submit an abstract concerning the results of their individual research each semester and present the results near the end of this program.