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Viscous flow of fluid film on outer surface of a sloped rotating cylinder in gravitational field is studied. Thickness of the fluid layer is assumed to be small compared to the cylinder radius, which allows asymptotic analysis. Governing equation for the thickness dynamics is derived. The equation accounts for viscous effects, gravity, centrifugal and capillary forces. A criterion for existence of steady flow on the sloped cylinder is obtained. Linear stability of stationary solution for the vertical cylinder is given. Film thickness response to oscillations of the cylinder axis around vertical line is studied. Numerical model is implemented for the case of arbitrary slope angle.

Mathematical and software model of oil-bearing layers was constructed in the form of an oriented graph. The problem is related to the flow in porous (particularly, micro-porous) medium. Systems of differential equations were recorded and solved, allowing to calculate the change in the unit concentration of bacteria, the density of the nutrient medium, as well as the change in the diameter of the "graph tubes" from time to time. Further, a comparative analysis of the results obtained with the known data is presented. This analysis allowed to draw conclusions about the reliability of the implemented model.

Charge transport in nanotube filled with an incompressible viscous electrolyte is considered. The flow is induced by elastic soliton wave in the nanotube wall. The soliton appears as an axisymmetric local deformation of the wall boundary propagating along the length of a nanotube. The Stokes approximation is used for the flow. As for the charge transport, different factors (identical charges repulsion, diffusion, convection) are taken into account. Picture of the streamlines and charge distribution are described. We estimate a value of charge transported by single solitary wave.

One-dimensional approaches of blood flow are widespread in studies of human circulatory system and provide sufficient accuracy for considerable part of practical applications. Here we present a model of agent propagation processes in one-dimensional approach. We believe that such progress of will additionally expands application area of one-dimensional blood flow simulations. The main feature of suggested model is account of uneven concentration in a cross section of vessel. The model includes system of two equations for average concertation and for parameter of concertation distribution in a cross section. Simple estimation shows that phenomenon related with uneven concentration distribution are presented in arterial blood flow for 10-5 m2/s or less order of magnitude of diffusion coefficient. We demonstrate agent propagation dynamics by examples of strain artery with constant velocity field and hi-detailed cerebral arterial system. Comparing of results of simulations with pattern of contrast agent propagation during X-ray angiography we notice qualitatively correct behavior of the model.

A theoretical study of phenanthrenequinone-doped polymethyl methacrylate (PQ/PMMA) samples parameter changes during irradiation is presented. The research has been carried out on the basis of the experimental study (Part 1, [Appl. Opt.56, 7351 (2017)APOPAI0003-693510.1364/AO.56.007351]) and a mathematical model that describes space–time reversible and irreversible light-induced changes of the PQ/PMMA sample parameters during exposition. Based on the numerical modeling results and the use of analytical dependencies, a number of practically important characteristics of the PQ/PMMA sample-exposure process are considered: conversion-induction period of phenanthrenequinone into a photoproduct, Δt ind ; bleaching time of a sample, t bl ; and thermal nonlocality of photoresponse, δl T . It is shown that the values Δt ind and t bl are on the order of tens and hundreds of seconds, respectively, and can be comparable to the exposure time. It is established that temperature increase leads to δl T value change by hundreds of nanometers and can cause considerable deformation of the interference structure under recording. The sample heating during exposition is considered in detail, and an algorithm for estimation of the maximum temperature increase to be used in experiments is proposed. Recommendations are made for the reduction of negative influence of sample heating on the parameters of recorded holograms.

A technique for complex investigation of the process of free liquid convection under the action of a heat source is presented, which is based on the use of digital holographic interferometry. The mode of studying an object, which is a flat liquid layer in a glass cell, has been developed. Experimental results have been obtained in the form of space–time temperature distributions for water, glycerol, and a mixture thereof. A dominant mechanism of heat transfer in different stages of heating the liquids under study has been revealed. A mathematical model of the process of free convection is constructed and the space–time temperature distribution is calculated for the case in which water is used as a test object. The results of mathematical simulation correctly describe the experimentally observed character of changes in the thermal field.

current on detectors after beam splitting. We derived equations allowing one to estimate the scheme parameters imperfection impact on measurement results. We also obtained mathematical expressions, demonstrating the equivalence of quantum description of Y-splitter and beam splitter with two inputs, which allows the use Y-splitter for the implementation of quantum random number generation systems based on vacuum quantum uctuations.

We have studied the mechanisms underlying the effect of pulsed broadband terahertz radiation on the growth of neurites of sensory ganglia using a comparative analysis of measured reflection spectra of ganglion neurites (in the frequency range 0.1 – 2.0 THz) and spectra obtained by numerical simulation with CST Microwave Studio. The observed changes are shown to be mainly due to pulse energy absorption in the ganglion neurites. Of particular interest are the observed single resonance frequencies related to resonance size effects, which can be used to irradiate ganglia in order to activate their growth. (laser biophotonics)

Ultrasonic near-field levitation allows for contactless support and transportation of an object over vibrating surface. We developed an accurate model predicting pressure distribution in the gap between the surface and levitating object. The formulation covers a wide range of the air flow regimes: from viscous squeezed flow dominating in small gap to acoustic wave propagation in larger gap. The paper explains derivation of the governing equations from the basic fluid dynamics. The nonreflective boundary conditions were developed to properly define air flow at the outlet. Comparing to direct computational fluid dynamics modeling our approach allows achieving good accuracy while keeping the computation cost low. Using the model we studied the levitation force as a function of gap distance. It was shown that there are three distinguished flow regimes: purely viscous, viscoacoustic, and acoustic. The regimes are defined by the balance of viscous and inertial forces. In the viscous regime the pressure in the gap is close to uniform while in the intermediate viscoacoustic and the acoustic regimes the pressure profile is wavy. The model was validated by a dedicated levitation experiment and compared to similar published results.

Quantum random number generators based on vacuum fluctuations produce truly random numbers that can be used for applications are requiring a high degree of randomness. A beam splitter with two inputs and two outputs is normally used in these systems. In this paper, mathematical descriptions were obtained for the use of such beam splitter and fiber Y-splitter in quantum random number generation systems with homodyne detection. We derived equations which allowed us to estimate the impact of the scheme parameters’ imperfection upon measurement results. We also obtained mathematical expressions, demonstrating the equivalence of quantum descriptions for a Y-splitter and a beam splitter with two inputs.

An explicitly solvable model of flow in a nanotube, which is caused by an elastic soliton propagating in the nanotube wall, is proposed. A mathematical basis for the model is provided by the theory of selfadjoint extensions of symmetrical operators.

An initial stage of nanoroll formation in a hydrothermal medium is investigated - the stage of rolling of a double layer under the action of internal stresses. A critical role in the rolling process is attributed to the viscous liquid surrounding the roll. A method is proposed to calculate the liquid flow around the forming nanoroll. A calculation of the rolling process is also performed. Finally, disturbance of the liquid by the rolling nanotube is studied.

Models of the formation of nanorolls in fluid media are constructed. The successive stages of the detachment of a stressed double nanolayer with the subsequent twisting into a nanoroll are calculated by the molecular dynamics method. The dynamics of twisting with the formation of a multiwalled nanoroll is described within a continuous model. The results of simulating the formation of different configurations of nanorolls during their diffusion growth are reported.

The present work is devoted to the theoretical study of the colloid nanoparticle interaction. A simple analytical model for the multi-particle interaction between the amphoteric oxide nanoparticles with low surface potential has been developed. The model utilizes the framework of the DLVO (Derjaguin, Landau, Verwey, Overbeak) theory and accounts for the surface charge regulation during the multi-particle interaction. The results of this study demonstrate a good qualitative agreement with the experimental data and reveal the presence of the orientation effects during nanoparticle aggregation, which may cause the formation of aggregates with different morphologies.

Currently, due to the development of nanotechnology and metamaterials, it has become important to obtain regular nanoporous structures with different parameters, such as porous anodic alumina films that are used for synthesis of various nanocomposites. In this work we consider the motion of the interfaces between electrolyte and alumina layers, and between alumina and aluminum layers. We also took into account the dynamics of moving boundaries and the change of small perturbations of these boundaries. Each area under Laplace’s equation is solved for the potential of the electric field. The growth of porous alumina is described with the theory of small perturbations. Small perturbations of the interface are considered, which lead to small changes in potential and current in the boundaries. As a result of the developed model we obtained the minimum distance between centers of aluminum oxide pores in the beginning of anodizing process and the wavelength of porous structure irregularities.

Experimental research into changes of the optical thickness of phenanthrenequinone-doped polymethyl methacrylate samples in the process of irradiation by a 473 nm laser is presented. It was demonstrated that heating-induced reversible changes lead to a decrease in the optical thickness. The temperature coefficient of the relative changes of the optical thickness was measured to be -1.40×10-5 К-1, which matches the data published by other authors. It is also established that the irreversible changes induced by the photochemical transformation lead to an increase in the optical thickness outside of the absorption band of the samples (λ>530 nm), where the relative change of which at λ=532 nm is +3.7×10-5. It was demonstrated that the reversible and irreversible changes do not compensate for each other in the process of sample exposure.

Promising original materials for obtaining nanotubes are compounds with a layered structure [2], for example, hydrosilicates [3]. Irrespective of the structure of the original components, under hydrothermal conditions, nanotubes start to form only after intermediate compounds with a layered structure have been formed; it is precisely from these compounds that nanotubes are formed in the next stage of the synthesis [3, 4]. The investigation of the conditions and dynamics of layer twisting for compounds with a layered structure and their subsequent recrystallization with the formation of nanotubes with a certain morphology is of great importance for understanding the mechanism of nanotube formation.

The aim of this work is the theoretical investigation of instability development of the nanoparticle surface shape during diffuse growth. The unperturbed surface is considered as an ideal sphere. The mass diffusion flux promotes increase of the sphere volume and development of free surface perturbations. The relaxation of these perturbations due to action of capillary forces is also considered along with development of small perturbations of a free surface at the expense of perturbation of a mass diffusion flux. We use the effective coefficient of viscosity μ and surface tension coefficient σ of nanoparticle to describe a surface shape relaxation. As a result there were revealed various modes at which the surface of nanoparticle loses the stability and investigated dynamics of instability development of surface.

The paper is devoted to the problem of theoretical description and modeling of the nanoparticles size distribution functions evolution. Colloidal solutions of spherical zinc oxide nanoparticles with typical dimensions of 40 – 100 nm are considered. The modified DLVO theory is used to find an analytical solution for the interaction force between nanoparticles. The resulting expression is implemented into a numerical simulation program based on Langevin dynamics method for modeling the process of nanoparticle coagulation. The character of the dependences obtained in the limits of applicability of the model corresponds well to the experimentally determined curves for similar systems.

Artificially on the surface of aluminum there may be build a thick layer of Al2O3, which has a porous structure. In this paper we present a model of growth of porous alumina in the initial stage of anodizing, identifying dependencies anodizing parameters on the rate of growth of the film and the distance between the pores and as a result of the created model equations were found for changes in the disturbance of alumina for the initial stage of anodizing aluminum oxide porous border aluminum-alumina and alumina-electrolyte, with the influence of surface diffusion of aluminum oxide.

In this paper mathematical description of using of fiber Y-splitter and optical splitter with two input and two output ports in quantum random number generation systems were obtained.

Porous aluminum oxide is a regular self-assembled structure. During anodization it is possible to control nano-parameters of the structure using macroscopic parameters of anodization. Porous alumina films can be used as a template for the creation of hyperbolic media. In this work we consider the anodization process, our model takes into account the influence of layers of aluminum and electrolyte on the rate of growth of aluminum oxide, as well as the effect of surface diffusion. As a result of our model we obtain the minimum distance between centers of alumina pores in the beginning of anodizing process. We also present the results obtained by numerical modelling of hyperbolic media based on porous alumina film.

The present paper is devoted to the theoretical study of the morphology of nanocrystals formed through self-assembly of amphoteric oxide colloidal nanoparticles in weak electrolytes. A mathematical model of multi-particle colloidal interaction was developed within the framework of the Derjaguin, Landau, Verwey, Overbeak (DLVO) theory. This model accounts for the surface charge regulation during the multi-particle interaction and reveals the presence of orientation effects during nanoparticle aggregation. These effects are presumed to affect the morphology of the self-assembled nanocrystals and may present the means of controlling the structure of synthesised nanomaterials.

The influence of non-spherical nanopartides' shape on sedimentation process was studied. Six different shape of particles were considered. From proposed mathematical model it was shown that for non-spherical nanoparticles the perturbation of Z-component of velocity is slightly lower comparing to spherical particles.

In this paper we consider the dependence of the supported modes and the type of its polarization on the profile of the waveguide. Investigated possibility of production of beam splitters designed on the conventional waveguide.

This work proposes an explicit analytical model for the surface potential of a colloidal nano-agglomerate. The model predicts that when an agglomerate reaches a certain critical size, its surface potential becomes independent of the agglomerate radius. The model also provides a method for identifying and quantifying the solute-indifferent charge in nanocolloids, that allows to assess the stability of toxicologically significant parameters of the system.

In this paper described the operability of some quantum optical circuits which depends on their constructions, such as reflectivity of beam splitters in the linear optical controlled-NOT gate in the coincidence basis.

Nanoparticle surface charge plays an important role in many biological applications. In this study, an analytical surface charging model for the amphoteric oxide nanoparticles has been presented. The model accounts for the particle's electric double layer self-action on the charging process and the charge regulation during multi-particle interactions in aqueous solutions. The employment of the model allows to explicitly describe the nanoparticle agglomeration process and the accompanying agglomerate surface charge variation.

In this paper the sedimentation process of nanoparticles which have distribution in sizes was studied. The mathematical model under consideration gives a rise of velocity which resembles Rayleigh-Taylor instability. The numerical solution is consistent with results predicted by the model. The maximum value of concentration, where instability does not occur, was found.

Currently it has become important for the development of metamaterials and nanotechnology to obtain regular self-assembled structures. One such structure is porous anodic alumina film that consists of hexagonally packed cylindrical pores. In this work we consider the anodization process, our model takes into account the influence of layers of aluminum and electrolyte on the rate of growth of aluminum oxide, as well as the effect of surface diffusion. In present work we consider those effects. And as a result of our model we obtain the minimum distance between centers of alumina pores in the beginning of anodizing process.

The quasi-stationary Stokes approximation (Frenkel, 1945; Happel & Brenner, 1965) is used to describe viscous flows with small Reynolds numbers. Two-dimensional Stokes flow with free boundary attracted the attention of many researches. In particular, an analogy is drawn (Ionesku, 1965) between the equations of the theory of elasticity (Muskeleshvili, 1966) and the equations of hydrodynamics in the Stokes approximation. This idea allowed (Antanovskii, 1988) to study the relaxation of a simply connected cylinder under the effect of capillary forces. Hopper (1984) proposed to describe the dynamics of the free boundary through a family of conformal mappings. This approach was later used in (Jeong & Moffatt, 1992; Tanveer & Vasconcelos, 1994) for analysis of free-surface cusps and bubble breakup. We have developed a method of flow calculation, which is based on the expansion of pressure in a complete system of harmonic functions. The structure of this system depends on the topology of the region. Using the pressure distribution, we calculate the velocity on the boundary and investigate the motion of the boundary. In case of capillary forces the pressure is the projection of a generalized function with the carrier on the boundary on the subspace of harmonic functions (Chivilikhin, 1992). We show that in the 2D case there exists a non-trivial variation of pressure and velocity which keeps the Reynolds stress tensor unchanged. The correspondent variations of pressure give us the basis for pressure presentation in form of a series. Using this fact and the variation formulation of the Stokes problem we obtain a system of equations for the coefficients of this series. The variations of velocity give us the basis for the vortical part of velocity presentation in the form of a serial expansion with the same coefficients as for the pressure series. We obtain the potential part of velocity on the boundary directly from the boundary conditions known external stress applied to the boundary. After calculating velocity on the boundary with given shape we calculate the boundary deformation during a small time step. Based on this theory we have developed a method for calculation of the planar Stokes flows driven by arbitrary surface forces and potential volume forces. We can apply this method for investigating boundary deformation due to capillary forces, external pressure, centrifugal forces, etc.

A modification of the linear superposition approximation for the linearized Poisson- Boltzmann equation, describing the interaction of colloidal nanoparticles, is proposed based on the implementation of a phenomenological charge regulation model to allow for the more accurate description of the interaction at small particle separations and multi-particle interactions.

Currently, the development of nanotechnology and metamaterials requires the ability to obtain regular self-assembled structures with different parameters. One such structure is porous alumina in which the pores grow perpendicular to the substrate and are hexagonally packed. Pore size and the distance between them can be varied depending on the anodization voltage, the electrolyte and the anodization time (pore diameter – from 2 to 350 nm, the distance between the pores – from 5 to 50 nm). At the moment, there are different models describing the process of anodizing aluminum, in this paper we propose a model that takes into account the effect of layers of aluminum, aluminum oxide, and the electrolyte, as well as the influence of the effect of surface diffusion.

This work is devoted to theoretical investigation of instability development of surface shape of high-viscosity liquid under the influence of diffusion mass flux. If there is a local eminence on the surface it can lead to growth of perturbation of surface shape. Stability and instability of perturbation depends on factors which will prevail. Diffusion causes distortion of surface shape and dominance of capillary forces achieves the opposite effect.

Quantum random number generation allows acquiring true random numbers which can be used in applications that require a high degree of randomness. This paper assesses the influence of non-ideal scheme parameters on measurement results in two quantum random number generation schemes: based on laser radiation splitting, and using vacuum fluctuations.

We consider the possibility of multiplexing the classical and quantum signals in a quantum cryptography system with optical fiber used as a transmission medium. If the quantum signal is located at a frequency close to the frequency of classical signals, a set of nonlinear effects such as FWM (four-wave mixing) and Raman scattering is observed. The impact of four-wave mixing (FWM) effect on error level is described and analyzed in this work in case of large frequency diversity between classical and quantum signals. It is shown that the influence of FWM is negligible for convenient quantum key distribution.

The hydrodynamic two-scale model of hydrothermal synthesis inorganic nanotubes is proposed. The model, which proposed at this paper is consist from two scale of parameters: micro and macro. The macro parameters are: distribution of temperature, velocity and concentrations. The distribution of concentration is binds two scales. Boundary conditions for micro-scale is concentration, which calculated from macro-scale parameters.

Quantum generation of random numbers makes it possible to obtain truly random numbers that can be used in applications where a high degree of randomness is needed. This paper presents an estimate of how the nonideal nature of the setup parameters affects the results of measurements carried out for two quantum random-number generators: one based on separation of laser radiation, and one based on the use of vacuum fluctuations.

The fluid flow in carbon nanotubes caused by a soliton in its wall is considered. The profile of the wall deformation is derived. The picture of the flow for different parameters of the perturbation is obtained. Due to the smallness of the Reynolds number the Stokes approximation is used.

In this paper, we propose an original method for determining the size of nanoscale inhomogeneities in scattering and absorbing medium by comparing the theoretical and experimental dependences of the transmission medium on the wavelength of light. The method was tested on a sample of nanoporous glasses and gave satisfactory results. Were also carried out numerical evaluation of this phenomenon by using the software package CST Microwave Studio.