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The surface phenomena, such as the growth, roughening and penetration into the surrounding medium, as well as their modeling and efficient control, represent long standing research topic in many branches of science and technology. The special case is the close-tocircular growth observed very often in biological systems, like bacterial colonies and tumors.… (More)

A number of random processes in various fields of science is described by phenomenological equations of motion containing stochastic forces, the best known example being the Langevin equation (LE) for the Brownian motion (BM) of particles. Long ago Vladimirsky (1942) in a little known paper proposed a simple method for solving such equations. The method,… (More)

A generalization of the Rouse model of the dynamics of polymers in solution is proposed. The motion of long polymer chains is considered to be due to exponentially correlated random forces driving the polymer segments, which is a more realistic model than the approximation of white thermal noise in the standard theory. Due to the fluctuationdissipation… (More)

- Vladimír Lisý, Jana Tóthová
- Physical review letters
- 2016

- Vladimír Lisý, Jana Tóthová
- Journal of magnetic resonance
- 2017

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins,… (More)

Traditional bead-spring models of the polymer dynamics are based on the Einstein theory of the Brownian motion (BM), valid only at the times much larger than the particle ́s relaxation time. The reason is in neglecting the inertial and memory effects in the dynamics. In the present work we use a generalized theory of the BM to build models of the dynamics… (More)

A multi-pulsed free-induction NMR experiment is described theoretically for spins diffusing within a cylindrical capillary. The characteristic time for the particles to move on a distance of the capillary diameter is smaller or comparable to the time interval between the applied 90° rf pulses and the relaxation times entering the Bloch equations. In this… (More)

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