- model A Phase transition dynamics of non-conserved systems, so called Ginzburg-Landau equation.
- model B Phase transition dynamics of conserved systems, so called Cahn-Hilliard equations.
- model H Phase transition dynamics with hydrodynamics.

- Phase
transition dynamics of binary alloys with elastic inhomogeneity.

(A. Onuki, A. Furukawa PRL 86, 452(2001)) Domain freezing occurs when elastic moduli depend on the composition. - Heat convection@

We apply constant heat flow from the bottom side of highly compressible fluid (He3) near critical point. Piston effect due to thermal plumes causes overall temperature fluctuations.

(A.Furukawa, A.Onuki, Phys. Rev. E66, 016302 (2002)) - Viscoelastic phase separation in shear flow.

In shear flow, phase separation occurs above coexisting lines of semi-dilute polymer solutions (shear induced phase separation). Under the coexisting lines, domain boundaries are formed. However, there is no theories of viscoelastic two-phase flow. In such system, viscoelastic stress is important differently from Newtonian flow studied in hydrodynamics.

(T.Imaeda, A.Furukawa, and A.Onuki, Phys. Rev. E70, 051503 (2004)) - Shear band formation in wormlike micellar
solution in shear flow.

Shear bands are formed in the presence of nonmonotonic stress-strain relation. Dynamic coupling betwen stress and composition is relevant. ( A.Furukawa, A.Onuki, Physica D 205 195-206 (2005)) - Plastic flow in one-phase and two-phase solids in 2D and 3D
in stretching (A. Onuki, A. Furukawa,
A. Minami, PRAMANA 64, 661 (2005),
A. Minami, A. Onuki, Acta. Materialia 55, 2375 (2007))
- 2D: Elongation strain in one-phase. Slips
- 2D: Elastic energy in one-phase. Dislocations
- 2D: Elongation strain in two-phase. Precipitates.
- 2D: Elastic energy in two-phase. Precipitates.
- 2D: Elongation strain in two-phase. Percolated.
- 2D: Elastic energy in two-phase. Percolated.
- 3D: Elastic energy outside a hard precipitate acting as a dislocation mill
- 3D: Elastic energy outside hard cuboids.

- Helium near the superfluid transition is very sensitive
to applied heat flow and gravity,
leading to a number of nonlinear effects
Helium
cooled from below in gravity.
Self-organized superfluid with defects expands from below into normal fluid.
Brightness represents the superfluid density.(movie by A. Minami (2006))

- Dynamic van der Waals theory describes nonequilibrium fluids with evaporation
and condensation. A number of effects can be newly explored such
as wetting dynamics, boiling, and heat pipe mechanism. (A. Onuki, Phys. Rev.E@75, 036304 (2007)).@
- Bubble in liquid in heat flow. Temperature gradient is zero inside bubble due to convective latent heat transport.
- Heat pipe in steady state. Evaporation at the bottom and wetting film flow
- Boiling in gravity where bubbles are formed at the bottom.
- Velocity and heat flux at the bottom in spreading. At the contact, heat absorption is maximum due to evaporation