Theory of rotating electrohydrodynamic flows in a liquid film

The mathematical model of rotating electrohydrodynamic flows in a thin suspended liquid film is proposed and studied. The flows are driven by the given difference of potentials in one direction and constant external electric field E(out) in another direction in the plane of a film. To derive the model, we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to |E(out)|3. This stress generates tangential velocity in the vicinity of the edges of a film that, in turn, causes the rotational motion of a liquid. The proposed model is used to explain the experimental observations of the liquid film motor.

Vibrational Fréedericksz transition in liquid crystals

Our aim is to show the possibility of a "vibrational Fréedericksz's transition" in nematic liquid crystals (LCs) consisting of asymmetric molecules (in the absence of the reflectional symmetry for the director field). For this purpose we study the effects of the external high-frequency vibrations imposed on LCs by employing the rigorous two-timing asymptotic averaging method to the governing LC equations in their most general form. We restrict our attention only to translational mechanical vibrations of an incompressible LC medium as a whole, so our vibrations are not related to acoustical waves. We show that the averaged "vibrogenic" torque acted on the director field is mathematically equivalent to the torque caused by an external magnetic field. This equivalence leads us to the key conclusion that the high-frequency mechanical vibrations can cause the vibrational Fréedericksz's transition. Our evaluation of the relevant physical parameters shows that this phenomenon can be observed in laboratory experiments.

Measurement of cell velocity distributions in populations of motile algae

The self-propulsion of unicellular algae in still ambient fluid is studied using a previously reported laser-based tracking method, supplemented by new tracking software. A few hundred swimming cells are observed simultaneously and the average parameters of the cells' motility are calculated. The time-dependent, two-dimensional distribution of swimming velocities is measured and the three-dimensional distribution is recovered by assuming horizontal isotropy. The mean and variance of the cell turning angle are quantified, to estimate the reorientation time and rotational diffusivity of the bottom-heavy cell. The cells' phototactic and photokinetic responses to the laser light are evaluated. The results are generally consistent both with earlier assumptions about the nature of cell swimming and quantitative measurements, appropriately adjusted. The laser-based tracking method, which makes it possible to average over a large number of motile objects, is shown to be a powerful tool for the study of microorganism motility.

[Screening for malignant neoplasms by using the new method of marker diagnosis, the Oncotest]

The proposed method for tumor screening ("Oncotest") is based on detecting substances (calcium-histone complexes) in the human blood which are markers of malignant neoplasia. Using "Oncotest" in a series of 5411 cases, we identified malignant tumors of various histogenesis (cancer, sarcoma) arising in different sites in 69 cases. "Oncotest" is especially important for early (pre-clinical) detection of malignant neoplasms during preventive population screenings.