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Yayın Theoretical calculation of the kinetic coefficient of normal crystal growth(Trans Tech Publications Ltd, 2004) Dimitrov, Ventzislav IvanovAn expression for the velocity u of migration of a diffuse simple crystal-melt interface has been derived on the basis of the theory of atomic mobility in supercooled liquids: u = K-0 (T / T-m) DeltaT, where DeltaT = T-m - T the undercooling below the melting point T-m; K-0 is the kinetic coefficient of atomic attachment, which is used in models of crystal growth. It has been calculated for a number of metals. u(max) = K0Tm / 4 is the theoretical limit of the velocity of crystal growth. For a number of FCC metals the theoretical limit of crystal growth has been found to be of order of 200 m/s. The crystal growth kinetics has been shown to be limited by the atomic self-diffusion in the interface, for which the strong dependence on the orientation of the crystal/melt interface has been explained.Yayın Breakdown of the Stokes-Einstein relation in supercooled liquids(Trans Tech Publications Ltd, 2004) Dimitrov, Ventzislav IvanovBreakdown of the Einstein-Stokes relation in undercooled liquids is one of the unsolved problems in the theory of liquids. The self-diffusion coefficient follows the temperature dependence of the Einstein-Stokes equation D = kT / 6pietar at high temperatures but only down to approximately 1.2T(g) (T-g - glass-temperature). Below 1.2T(g) the temperature behavior of the diffusion coefficient is weaker than 1/eta. In the present study we show that this is a consequence of increasing correlations in the Brownian motion of the constituting particles of the liquid. We derive a relation, which includes the Einstein-Stokes equation as a limiting case for high temperatures.Yayın Some boundary Harnack principles with uniform constants(Springer Science and Business Media B.V., 2022-10) Barlow, Martin T.; Karlı, DenizWe prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.Yayın Some remarks on uniform boundary Harnack principles(Cornell Univ, 2021-03-18) Barlow, Martin T.; Karlı, DenizWe prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.
