Research

A study of pyramidal islands formation in epitaxy within the generalized phase-field model

We study epitaxial growth of pyramidal patterns in a framework of the phase-field model generalized by introduction of temperature field dynamics and an assumption of interacting adsorbate due to elastic effects. We have shown that in the system with different rates of the phase-field change oscillatory dynamics of surface pattern formation can be realized. Analytical results are verified by numerical simulations. We compare properties of surface structures within the framework of the standard phase-field model and proposed a generalized model of epitaxial growth using statistical approach. It is shown that in the generalized model pyramidal patterns can be sustained by thermodynamical force governing flux of interacting adsorbate.

Dmitrii O. Kharchenko, Vasyl O. Kharchenko, Tetyana Zhylenko, and Alina V. Dvornichenko A study of pyramidal islands formation in epitaxy within the generalized phase-field model Eur. Phys. J. B (2013) 86: 175

Phase-field modeling of epitaxial growth in stochastic systems with interacting adsorbate

We study epitaxial growth of pyramidal patterns in stochastic systems with interacting adsorbate within the framework of phase field approach based on the Burton-Cabrera-Frank model. Considering statistical criteria of the pattern formation it was shown that the system dynamics is governed by the interaction strength of adatoms and the noise intensity of the total flux fluctuations. We have shown that the noise action can crucially change processes of pyramidal pattern formation. Scaling behaviour of the height-height correlation function is discussed.

D.O.Kharchenko, V.O.Kharchenko, I.O.Lysenko. Phase-field modeling of epitaxial growth in stochastic systems with interacting adsorbate, Phys. Scr., 83, 045802 (2011).

Nano-islands formation in nonequilibrium reaction-diffusion systems

We study dynamics of pattern formation in systems belonging to class of reaction-Cattaneo models including persistent diffusion (memory effects of the diffusion flux). It was shown that due to the memory effects pattern selection process are realized. We have found that oscillatory behavior of the radius of the adsorbate islands is governed by finite propagation speed. It is shown that stabilization of nano-patterns in such models is possible only by nonequilibrium chemical reactions. Oscillatory dynamics of pattern formation is studied in details by numerical simulations.

V.O.Kharchenko, D.O.Kharchenko. Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate, Phys.Rev. E, 86, 041143 (2012).

V.O.Kharchenko, D.O.Kharchenko, S.V.Kokhan, I.V.Vernyhora, V.V.Yanovsky. Properties of nano-islands formation in nonequilibrium reaction-diffusion systems with memory effects, Phys. Scr., 86, 055401 (2012)

How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.

Igor Goychuk, Vasyl O. Kharchenko, Ralf Metzler. How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport, PLoS ONE 9(3): e91700 (2014)

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion

The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion, Phys.Chem.Chem.Phys., 16, 16524 (2014)

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