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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 Fluctuation theory of the liquid-glass transition(Trans Tech Publications Ltd, 2004) Dimitrov, Ventzislav IvanovThe glassy state and the character of the liquid-glass transition from undercooled liquid to amorphous solid is one of the biggest challenges of our time. In spite of significant progress we still cannot explain accurately the sudden solidification of undercooled liquids on the atomic scale. In the present paper we present an analytical theory of the dependence of the glass transition temperature on the rate of cooling: the glass transition temperature increases with increasing cooling rate but does not exceed some upper limit. At almost zero cooling rates (hypothetical reversible transformation of the liquid into glass) the glass transition temperature reduces to a critical temperature, similar to a phase transition temperature.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.
