Essentially nonlinear theory of microdeformations in medium with periodic structure

Essentially nonlinear theory of micro and macro deformations of a medium with cardinally rearranging periodic structure is presented using a new model of double continuum with variable local topology. In a frame of proposed model there are two deformation modes (macroscopic and microscopic) when some threshold is reached. Some problems such as twin transitions, catastrophic deformation waves, shock and tilting bifurcation waves are considered. An exact solution describing elasto plastic fragmentation of medium is constructed also when double periodic domain superstructure are formed. There are solid rotons of opposite signs with singular defects between them. They appear in a critical field of macroscopic deformations of pure shear. When this bifurcation point is overcome then dimensions of domains are stabilized. The letter depend on value of macroscopic deformations. Some criterion of global stability is established.

Kinetic theory of microphase separation in block copolymers

A semiphenomenological theory that has the advantage of taking into account nonlinear and nonlocal contributions in the free energy for microphase separation of block copolymers is proposed. A kinetic nonlinear equation defining the process of structure formation from a melt is obtained, and its analytical solution at the melt-structure transition temperature is examined. In this region, the structure formation proceeds in two stages. The first one is characterized by damping of all but stable Fourier-components of density distribution and the second, by stabilization of the amplitude of the distribution. Characteristic times of these processes are estimated. The applied approach allows a comparatively simple definition of lamellar, hexagonal and body-centered cubic structures near Ts. Equilibrium structures at T <<; Ts are described as well