Pattern formation during diffusion limited transformations in solids

We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase equilibrium conditions. We formulate equations for the interface kinetics similar to dendritic growth and study the growth of a stable phase from a metastable solid in both a channel geometry and in free space. We perform sharp interface calculations based on Green's function methods and phase field simulations, supplemented by analytical investigations. For pure dilatational transformations we find a single growing finger with symmetry breaking at higher driving forces, whereas for shear transformations the emergence of twin structures can be favorable. We predict the steady state shapes and propagation velocities, which can be higher than in conventional dendritic growth.Comment: submitted to Philosophical Magazin

Theory of dendritic growth in the presence of lattice strain

Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques and a closed nonlinear integro-differential equation for the evolution of the interface is derived. In the case of pure dilatation, the elastic effects lead only to a trivial shift of the transition temperature while in the case of shear transitions, dendritic patterns are found even for isotropic surface energy

Nonlinear Two-Dimensional Green's Function in Smectics

The problem of the strain of smectics subjected to a force distributed over a line in the basal plane has been solved

Crack growth by surface diffusion in viscoelastic media

We discuss steady state crack growth in the spirit of a free boundary problem. It turns out that mode I and mode III situations are very different from each other: In particular, mode III exhibits a pronounced transition towards unstable crack growth at higher driving forces, and the behavior close to the Griffith point is determined entirely through crack surface dissipation, whereas in mode I the fracture energy is renormalized due to a remaining finite viscous dissipation. Intermediate mixed-mode scenarios allow steady state crack growth with higher velocities, leading to the conjecture that mode I cracks can be unstable with respect to a rotation of the crack front line

Effect of small scale density perturbations on the formation of dark matter halo profiles

With help of a set of toy N-body models of dark halo formation we study the impact of small scale initial perturbations on the inner density profiles of haloes. We find a significant flattening of the inner slope $\alpha={d \log \rho \over d \log r}$ to $\alpha=-0.5$ in some range of scales and amplitudes of the perturbations (while in the case of absence of these perturbations the NFW profile with $\alpha=-1$ is reproduced). This effect may be responsible for the formation of cuspless galactic haloes.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter

Organization and management of clusters in Russia in the context of import substitution

The article covers the trends of the agribusiness development in Russia. It is shown that it is desirable to develop organizational-economic forms of entrepreneurship based on the cluster approach in the modern realities. The most famous agribusiness clusters in the world are explored. Regions of Russia that have achieved the most significant results in agribusiness clustering are mentioned. It is found that the establishment of agribusiness in Russia is defined by the political decision of regional authorities rather than based on research and development. An algorithm for establishing the agribusiness cluster is proposed, which includes four stages: methodological, analytical, organizational-economic and control. The key areas of state support for the development of agribusiness clusters in Russia are defined.peer-reviewe