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A finite-difference scheme is presented for the solution of the problem on the interaction of a femtosecond laser pulse with glass in the approximation of nonlinear Maxwell equations supplemented by equations of the hydrodynamic type for conduction electrons. The model takes into account all the basic physical processes involved in this interaction. An axially symmetric problem is considered. The construction of the scheme allows for the specifics of the problem, which ensures the efficiency of the developed method. The use of the scheme is illustrated by the results of modeling the interaction between glass and femtosecond laser pulses of an ordinary Gaussian shape with linear polarization and doughnut pulses with radial and azimuthal polarization. Significant differences in the dynamics of the interaction between glass and these three types of pulses are revealed.

It is shown that the developed earlier model of joint grinding of dissimilar particulate solids based on the discrete models of the Boltzmann equation does not take into account the possible size and density classification of particles and the operating of technological equipment in a closed milling circuit. It is substantiated that the problem of improving the efficiency of separation of mixture components, based on the analysis of their treatment in a closed milling circuit is an actual problem in the field. Theoretical investigations were based on the discrete models of the Boltzmann equation and the methods of their solution related to the technology of treatment of dissimilar components mixture. A special program for measurements and experimental data treatment obtained at the laboratory fluidized bed jet mill and the impact mill was developed for the experimental investigations. In the course of computational and experimental study a mathematical model of classification of dissimilar components was proposed and tested as well as the algorithm of its implementation into the general model of a closed milling circuit. The computational investigations were carried out to estimate the model sensitivity to the input parameters disturbance. The directions of improving the efficiency of the objective component separation in the closed milling circuit with the fluidized bed jet mill are found. The developed model the closed milling circuit for grinding dissimilar particulate solids can be used in engineering practice with acceptable accuracy. It can be used to estimate the possible enrichment of particulate solids mixtures and to define the optimal technological conditions of their separation with taking into account the limitations on the objective product impurity. The paths are outlined and the order of selection of the parameters of the grinding processes and the classification for effective separation of the components of the mixture are shown.

Nonlinear photoionization of dielectrics and semiconductors is widely treated in the frames of the Keldysh theory whose validity is limited to small photon energies compared to the band gap and relatively low laser intensities. The time-dependent density functional theory (TDDFT) simulations, which are free of these limitations, enable to gain insight into non-equilibrium dynamics of the electronic structure. Here we apply the TDDFT to investigate photoionization of silicon crystal by ultrashort laser pulses in a wide range of laser wavelengths and intensities and compare the results with predictions of the Keldysh theory. Photoionization rates derived from the simulations considerably exceed the data obtained with the Keldysh theory within the validity range of the latter. Possible reasons of the discrepancy are discussed and we provide fundamental data on the photoionization rates beyond the limits of the Keldysh theory. By investigating the features of the Stark shift as a function of photon energy and laser field strength, a manifestation of the transient Wannier-Stark ladder states have been revealed which become blurred with increasing laser field strength. Finally, it is shown that the TDDFT simulations can potentially provide reliable data on the electron damping time that is of high importance for large-scale modeling., Main document: 8 pages, 4 figures. Suppl. Mat.: 10 pages, 5 figures, 1 table

Raw materials are used in many industrial technologies. The raw material frequently has to be prepared as an intermediate with an appropriate particle size distribution, which requires the use of grinding. In grinding processes, energy consumption is a very important profitability criterion for the applied particular size reduction technology. The paper describes the comminution process that takes place in the jet mill using a modified form of the thermodynamic theory of grinding. In this theory, new material characteristics have been added: the surface and volumetric density of grinding energy. The thermodynamic theory is a combination of the classical Kick’s theory and the modified form of Rittinger’s theory. The tested physical magnitudes are a measure of the energy consumption of the grinding process. They describe the energy that must be provided in the grinding process to overcome interactions between particles related to the volume and surface of the material. Knowledge of these magnitudes is necessary to model thermomechanical phenomena in the solid state. The paper presents the results of research on comminution in a jet mill, on the basis of which the values of the tested material magnitudes were determined. It is graphically shown how the values of the tested magnitudes depend on the grain size of the ground samples.

Представлена конечно-разностная схема для решения задач о взаимодействии фемтосекундного лазерного импульса со стеклами в приближении нелинейных уравнений Максвелла, дополненных уравнениями гидродинамического типа для электронов проводимости. В модели учтены все основные физические процессы, имеющие место в этом взаимодействии. Рассматривается аксиально-симметричная задача. При построении схемы учитываются особенности задачи, что обеспечивает высокую эффективность разработанного метода. В качестве примера использования схемы приведены результаты моделирования взаимодействия со стеклом фемтосекундных лазерных импульсов обычной гауссовой формы с линейной поляризацией и импульсов тороидальной формы с радиальной и азимутальной поляризациями. Выявлены существенные различия в динамике взаимодействии со стеклом этих трех видов импульсов.

At joint grinding, classification and mixing of dissimilar particulate solids, not only the total content of each in a mixture is the point of researcher’s interest but also the particle size distribution in each component. It is particularly important for enrichment and purification of components at their joint grinding and classification. Tracers of different type (radioactive, colored, etc.) are commonly used for this purpose. However, such methods are available not for any materials due to technological, financial and sanitary limitations. An alternative simple and easy available approach to investigate the particle size distributions in a mixture is proposed. It is based on application of soluble tracers and can be used in the case of selective solution of one of the components in a chosen solvent. Such method to define the particle size distribution can be interesting for the chemical and other industries. A laboratory impact mill was used for experimentation and identification of the model of joint grinding of a components mixture. This part of the research allowed obtaining and testing the method to define the particle size distributions in the binary mixture of components one of which was solvable in water, and another one was not. The developed method was used for grinding kinetics of joint grinding of two dissimilar components. The conducted research allowed developing a conception of modeling of the selective grinding of dissimilar components mixture. The computational analysis showed that the proposed model with calibrating parameters obtained from the experiments allows describing the process of selective grinding of a dissimilar components mixture with the accuracy that is acceptable for engineering practice. It allows using the model for practical estimation of the objective components enrichment and defining the optimal conditions for dissimilar components separation.

Theoretical and experimental studies have demonstrated that bi-chromatic laser action on bandgap materials can result in highly enhanced efficiency of local energy coupling at properly chosen combinations of wavelengths and energies.

A visco-elastic model is suggested to recover the P−T−t paths of spherically symmetrical host-inclusion systems from residual pressure patterns. For a coesite–garnet, aragonite–garnet and diamond–garnet system with partial transition of high pressure polymorphs to low pressure ones, the model predicts that the exhumation history of ultra-high pressure metamorphic rocks from depths below 90 km began with pressure decrease to ∼1 GPa (∼40 km depth), while the temperature remained high (>800 C); then the system cooled and decompressed to ambient conditions. Non-spherical inclusion shapes in the 3-D model lead to heterogeneities in residual pressure and shear stress distributions as well as to significant gradients of shear stress, which may affect the kinetics and thermodynamics of phase transformation in the inclusions.

The paper presents an application of the Boltzmann kinetic equation to the simultaneous modeling of multi-dimensional processes. This equation defines the evolution of the distribution of the probability density in a given phase space. In the case of a grinding process, the considered phase space is defined by the Cartesian coordinates of particle position, the components of particle velocity and the particle size. The theory of Markov processes is used in the paper to solve the Boltzmann equation for the multi-dimensional space of system states. In order to verify the presented model, research into the simultaneous comminution and movement of material in a drum ball mill was performed. The methodology developed to solve the Boltzmann equation significantly reduces the computational time, which is particularly important in the solution of multi-dimensional problems.

The interaction of short and ultrashort pulse laser radiation with glass materials is addressed. Particular attention is paid to regimes which are important in industrial applications such as laser cutting, drilling, functionalization of material surfaces, etc. Different factors influencing the ablation efficiency and quality are summarized and their importance is illustrated experimentally. The effects of ambient gas ionization in front of the irradiated target are also analyzed. A possibility to enhance laser coupling with transparent solids by bi-wavelength irradiation is discussed.

Computer simulations and theoretical analysis of laser-materials interactions are playing an increasingly important role in the advancement of modern laser technologies and broadening the range of laser applications. In this chapter, we first provide an overview of the current understanding of the laser coupling and transient variation of optical properties in metals, semiconductors and dielectrics, with the focus on the practical implications on the energy deposition and distribution in the irradiated targets. The continuum-level modeling of the dynamic evolution of laser-induced stresses, nonequilibrium phase transformations, and material redistribution within the laser spot are then discussed, and the need for the physical insights into the mechanisms and kinetics of highly nonequilibrium processes triggered by the laser excitation is highlighted. The physical insights can be provided by atomistic modeling, and several examples are discussed where large-scale molecular dynamics simulations are used for investigation of the mechanisms of the generation of crystal defects (vacancies, interstitials, dislocations, and twin boundaries) and the material redistribution responsible for the formation of laser-induced periodic surface structures in the single-pulse ablative regime. The need for the integrated computational approach fully accounting for the strong coupling between processes occurring at different time- and length-scales is highlighted.

Sophisticated modeling of propagation of ultrashort laser pulses with spatio-temporal coupling through transparent medium has enabled reproducing the effect of directional asymmetry in direct laser writing and gaining a deep insight into the underlying physics.

Ultrashort laser pulses are usually described in terms of temporal and spatial dependences of their electric field, assuming that the spatial dependence is separable from time dependence. However, in most situations this assumption is incorrect as generation of ultrashort pulses and their manipulation lead to couplings between spatial and temporal coordinates resulting in various effects such as pulse front tilt and spatial chirp. One of the most intriguing spatiotemporal coupling effects is the so-called “lighthouse effect”, the phase front rotation with the beam propagation distance [Akturk et al., Opt. Express 13, 8642 (2005)]. The interaction of spatiotemporally coupled laser pulses with transparent materials have interesting peculiarities, such as the effect of nonreciprocal writing, which can be used to facilitate microfabrication of photonic structures inside optical glasses. In this work, we make an attempt to numerically investigate the influence of the pulse front tilt and the lighthouse effect on the absorption of laser energy inside fused silica glass. The model, which is based on nonlinear Maxwell’s equations supplemented by the hydrodynamic equations for free electron plasma, is applied. As three-dimensional solution of such a problem would require huge computational resources, a simplified two-dimensional model has been proposed. It has enabled to gain a qualitative insight into the features of propagation of ultrashort laser pulses with the tilted front in the regimes of volumetric laser modification of transparent materials, including directional asymmetry upon direct laser writing in glass materials.

Interaction of femtosecond laser pulses with a bulk glass (fused silica as an example) has been studied numerically based on non-linear Maxwell’s equations supplemented by the hydrodynamics-type equations for free electron plasma for the cases of Gaussian linearly-polarized and doughnut-shaped radially-polarized laser beams. For Gaussian pulses focused inside glass (800 nm wavelength, 45 fs duration, numerical aperture of 0.25), the free electron density in the laser-excited region remains subcritical while the locally absorbed energy density does not exceed ~2000 J/cm3 in the range of pulse energies of 200 nJ – 2 μJ. For doughnut-shaped pulses, the initial high-intensity ring of light is shrinking upon focusing. Upon reaching a certain ionization level on its way, the light ring splits into two branches, one of which shrinks swiftly toward the beam axis well before the geometrical focus, leading to generation of supercritical free electron density. The second branch represents the laser light scattered by the electron plasma away from the beam axis. The final laserexcited volume represents a tube of 0.5–1 μm in radius and 10-15 μm long. The local maximum of absorbed energy can be more than 10 times higher compared to the case of Gaussian beams of the same energy. The corresponding pressure levels have been evaluated. It is anticipated that, in the case of doughnut-shaped pulses, the tube-like shape of the deposited energy should lead to implosion of material that can be used for improving the direct writing of high-refractive index optical structures inside glass or for achieving extreme thermodynamic states of matter.

Many needs have to be met in human life. One of the key needs is to provide living comfort, which is clearly associated with heat. Analyzing the amount of produced heat, it should be emphasized that the higher the development of a country, the greater the demand for heat. In the era of the debate on the impact of human activities on the climate, it is impossible not to emphasize the importance of conserving energy and heat, and thus the rational management of these goods. The paper proposes a mathematical description of the complex systems of heat exchangers in the form of linear differential equations. Their analytical solution is presented in the form of temperature change of the heat carrier along the heating surface of a four-thread heat exchanger. Analysis of the possible heat exchange cases for eight possible flow systems is presented. In addition, the most effective minimization of heat losses was found.

Numerous experimental studies in recent years have revealed intriguing symmetry breakings during non-linear interaction of ultrashort laser pulses with materials. Dependence of the formed structures on the direction of laser scanning and polarization, an effect known as non-reciprocal writing, is one of the most commonly observed asymmetries. These observations are generally attributed to spatio-temporal couplings (primarily pulse-front tilt) in the laser pulses. Even though such couplings indeed break the spatial symmetry of the light–matter interactions, a detailed understanding of ongoing phenomena in the microscopic level is still lacking. In this work, we present our theoretical results, which, to the best of our knowledge, constitute the first demonstration of the physical mechanisms behind non-reciprocal writing and related effects in transparent media. Our model is based on non-linear Maxwell’s equations supplemented by the hydrodynamic equations for free electron plasma, and rate equations for the evolution of defects inside the material. It has enabled us to gain a qualitative insight into the features of propagation of ultrashort laser pulses with tilted pulse fronts, in the regimes of volumetric laser modification of transparent materials.

Results of experimental study of the effect of initial maldistribution of structured packing irrigation on efficiency of binary mixture separation are presented in this article. The studies were carried out in the experimental distillation column with the diameter of 0.9 m using the R114 and R21 freon mixture. Experiments were performed on the structured Mellapak 350.Y packing of stainless steel 316L, containing 19 layers with the total height of 4.016 m at the ratio of mole liquid and vapor flow rates L/V = 1 and 1.7, respectively, and the pressure in the upper part of the column ptop = 3 bars. Nonuniformity at the packing inlet was generated via the blocking of some holes in the liquid distributor. Here, we present some results on efficiency of mixture separation, pressure drop on the packing, distribution of local liquid flow rate under the packing over the cross-section and on the column wall within the range of vapor loading factor (0.69

The problem of the applicability of the six-band kp -model to heterostructures with sharp boundaries is studied by calculating the energy spectrum of holes in the Ge/Si system with quantum dots. The boundary conditions which satisfy the conditions of particle flux conservation and the wave function continuity on the heterojunction are formulated at the level of differential equations and are characterized by a single parameter µ, which depends on the heterojunction properties. It is shown that a certain choice of µ leads to nonphysical interface states that fill the entire band gap. Conditions (range of µ) for the absence of such nonphysical states are determined by considering the simplest cases —a single heterojunction and a quantum well..

Results of experimental studies of heat-and-mass transfer and hydrodynamic processes at distillation on a regular packing are presented. The mixture of freons R114–R21 at the pressure of 0.3 MPa was used as a working mixture. The mixture was separated on the Mellapak 350Y structured packing with the diameter of 0.9 m under the conditions of complete reflux ( L/V = 1) at different packing heights. A specially designed liquid distributor with a possibility to change the density and pattern of drip points was used to irrigate the packing. The experimental data on the efficiency of mixture separation (height of transfer unit HTU ) and distribution of the local flow rate density over the column cross-section were compared. It is shown that an increase in the height of the structured packing from 2.1 m to 4.0 m leads to a significant decrease in the efficiency of mixture separation in the distillation column.

Interaction of ultrashort laser pulses with transparent materials is a powerful technique of modification of material properties for various technological applications. The physics behind laser-induced modification phenomenon is rich and still far from complete understanding. We present an overview of our models developed to describe processes induced by ultrashort laser pulses inside and on the surface of bulk glass. The most sophisticated model consists of two parts. The first part solves Maxwell’s equations supplemented by the rate and hydrodynamics equations for free electrons. The model resolves spatiotemporal dynamics of free-electron population and yields the absorbed energy map. The latter serves as an initial condition for thermoelastoplastic simulations of material redistribution. The simulations performed for a wide range of irradiation conditions have allowed to clarify timescales at which modification occurs after single laser pulses. Simulations of spectrum of laser light scattered by laser-generated plasma revealed considerable blueshifting which increases with pulse energy. To gain insight into temperature evolution of a glass material under the surface irradiation conditions, we employ a model based on the rate equation describing free electron generation coupled with the energy equations for electrons and lattice. Swift heating of electron and lattice subsystems to extremely high temperatures at fs timescale has been found at laser fluences exceeding the threshold fluence by 2-3 times that can result in efficient bremsstrahlung emission from the irradiation spot. The mechanisms of glass ablation with ultrashort laser pulses are discussed by comparing with the experimental data. Finally, a model is outlined, developed for multi-pulse irradiation regimes, which enables gaining insight into the roles of defects and heat accumulation.

Generalization of deep convection equations for gas for an arbitrary medium is suggested. Some details of solvability and applicability conditions for these equations and selection of equilibrium pressure are considered.

The paper summarizes recent advances in physics of multiple-mirror confinement. GOL-3 in Novosibirsk is the only existing large-scale device of this type. Achieved plasma parameters are: n ~ 1021 m...

Transmission measurements for femtosecond laser pulses focused in air with spectral analysis of emission from the focal region have been carried out for various pulse energies and air pressures. The air breakdown threshold and pulse attenuation due to plasma absorption are evaluated and compared with calculations based on the multiphoton ionization model. The plasma absorption is found to depend on the pulse repetition rate and is considerably stronger at 1 kHz than at 1-10 Hz. This suggests that accumulation of metastable states of air molecules plays an important role in initiation of air breakdown, enhancing the ionization efficiency at high repetition rates. Possible channels of metastable-state-assisted air ionization and the role of the observed accumulation effect in laser material processing are discussed.

We report a model of nanosecond laser ablation of compound semiconductors taking into account stoichiometry loss as a result of different volatilities of the material components. The model is based on the heat-flow equation for the bulk material and the diffusion equation for its atomic constituents and takes into account variations of material properties as functions of temperature and composition. Changing the optical response which results from stoichiometry violation is described within the concept of an effective medium and a multi-layer reflection model is applied. For cadmium telluride, as an example, the processes of ablation, melting, and resolidification under the action of a KrF laser have been studied in dynamics for particular experimental conditions in a wide range of laser fluences from the ablation threshold to the plasma shielding regimes described by the effective plasma plume representation. Multi-shot irradiation regimes have been investigated and the mechanism of the irradiation-controlled stoichiometry reversal has been elucidated.

The presence of aragonite in polycrystalline carbonate inclusions in garnet in diamond-grade metamorphic rocks from the Kokchetav Massif, N. Kazakhstan was identified for the first time by means of Raman analyses and mapping, cathodoluminescence images and optical and scanning electron microscopy. Aragonite appears within the inclusions as dirty, chaotically oriented materials surrounded by a clean monocrystalline calcite shell; the grain boundary between the host-garnet and the aragonite-bearing inclusions is often characterized by a wavy or amoeboid shape; no cracks occur around the aragonite-bearing inclusior s; no significant shift in the main aragonite Raman band was measured. These observations indicate that residual pressure within the inclusion is minor. These features are inconsistent with an origin of aragonite at peak metamorphic conditions (6 GPa) by decomposition of dolomite.

Laser Raman microspectroscopy was applied to quartz inclusions in coesite- and diamond-grade metapelites from the Kokchetav ultrahigh-pressure metamorphic (UHPM) complex, Northern Kazakhstan, and diamond-grade eclogite xenoliths from the Mir kimberlite pipe, Yakutiya, Russia to assess the quantitative correlation between the Raman frequency shift and metamorphic pressure. Quartz crystals sealed in garnets have a higher frequency shift than those in the matrix. Residual pressures retained by quartz inclusions depend on the metamorphic history of the garnet host. The Raman frequency saift of quartz inclusions in garnet from coesite-grade and diamond-grade metamorphic rocks shows no systematic change with increasing peak metamorphic pressures. The highest shifts of the main Raman bands of quartz were documented for monocrystalline quartz inclusions in garnets from a diamond-grade eclogite xenolith. Calibrations based on experimental work suggest that the measured Raman frequency shifts signify residual pressures of 0.1-0.6 GPa for quartz. inclusions from coesite-grade metapelites from Kokchetav, 0.1-0.3 GPa for quartz inclusions from diamond-grade metapelites from Kokchetav, and 1.0-1.2 GPa for quartz inclusions from the diamond-grade eclogite xenoliths from the Mir kimberlite pipe. Normal stresses and internal (residual) pressures of quartz inclusions in garnet were numerically simulated with a 3-shell elastic model. Estimated values of residual pressures are inconsistent with the residual pressures estimated from the frequency shifts. Residual pressure slightly depends on P-T conditions at peak metamorphic stage. Laser Raman microspectroscopic analysis of quartz is a potentially powerful method for recovering an ultrahigh pressure metamorphic event. Monocrystalline quartz inclusions yielding a residual pressure greater than 2.5 GPa might indicate the presence of a former coesite.

In this work we consider an experimentally observed effect of significant increasing of the residual heat in metal targets at their irradiation with femtosecond laser pulses in an ambient gas in respect to the vacuum conditions. Numerical modelling of heating of a platinum target by femtosecond laser pulses in argon under normal conditions has been performed taking into account gas breakdown in the focussing region of the laser beam in front of the target. The applied model is based on a combination of a thermal model describing heating and phase transitions in irradiated samples and a hydrodynamic model to describe motion of the ambient gas perturbed by laser irradiation as a result of multiphoton ionization. The hot ambient gas is shown to heat efficiently the irradiated sample. The hydrodynamic processes in the ambient gas play an important role in heating.

New instability conditions for some classes of nonlinear dynamical systems of an arbitrary order are considered. These conditions reduce the investigation of instability of the initial nonlinear system to the investigation of instability of the linearized system. In this connection, the considered conditions are similar to the hypothesis of the instability theorem of the first Lyapunov method (the stability investigation by the first approximation), but they are applicable to more complicated nonlinear systems, because it takes into account the non-autonomy of the linearized system and the fact that the nonlinear terms in the right-hand sides of the equations of the initial system belong not only to the class of analytical functions. For different classes of the nonlinear systems, sufficient instability conditions are presented.

To describe the effect of significant enhancement in thermal energy retained in metal targets following femtosecond laser ablation in a gas environment, we develop a combined model based on both 2D thermal modeling of laser-induced target heating and dynamics of the ambient gas perturbed by multiphoton absorption of laser energy in close proximity to the target. Using our model, we find that thermal energy coupling to the sample is significantly enhanced due to laser-induced gas-dynamic motion in plasma. Another finding is that total thermal energy coupled to the sample due to gas-dynamic energy transfer and thermal energy conduction is close to that measured in our experiment.

Dynamics of the plasma in open magnetic traps with an electron beam, in particular, in a GOL-3 trap, is studied. The possibility of the formation of a resonant surface of the magnetic field and the development of helical instability caused by the presence of this surface is studied numerically.

A method for studying the stability of the equilibrium points of linearized, nonlinear dynamic systems of arbitrary order is considered. The method is based on the fact that, due to the nature of the mutual arrangement of the trajectories of the corresponding linearized system, and the boundaries of some simply-connected, bounded neighborhood of its equilibrium point, one can judge the asymptotic stability and instability of both this point and the equilibrium point of the nonlinear system. Necessary and sufficient conditions of asymptotic stability and sufficient conditions of instability of equilibrium points of linear systems are given. Together with the theorems of the first Lyapunov method, these conditions determine the sufficient conditions of asymptotic stability and instability of equilibrium points of nonlinear systems. In some cases, the proposed conditions may turn out to be preferable to the known ones.

The penetration of the rotating magnetic field of the dynamic ergodic divertor (DED) into the TEXTOR tokamak plasma has been investigated, using a two-dimensional reduced magnetohydrodynamics model and taking into account the effects of plasma-neutral interaction and neoclassical viscosity. The real three-dimensional structure of the DED coils design results in a mixture of several spatial Fourier modes which rotate at different phase velocities. It is shown that the field penetration is accompanied by poloidal acceleration of the plasma, which plays a crucial role in the process. For the DED TEXTOR parameters, the plasma-neutral interaction and the neoclassical viscosity allow for a distribution of the perturbed magnetic field close to vacuum one. If the mixture of harmonics is taken into account, the acceleration of the plasma in poloidal direction does not provide a complete penetration of the perturbation.

The relaxation of a magnetic field perturbation periodic in two directions is studied in the electron magnetohydrodynamic approximation. It is shown that the relaxation is accompanied by the coalescence of magnetic cells. When transport coefficients are sufficiently low, the nonlinear stage of the coalescence process is independent of their values. This effect may help to explain why the duration of the crash phase of sawtooth oscillations in tokamaks is anomalously short.

At joint grinding of components with different strength the particles of more strong material are of larger size than the particles of less strong material. The size classification of such mixture allows enriching the objective component in the end product. The scientifically grounded choice of technological conditions for effective separation of a mixture of materials of different strength is an actual problem for chemical and other industries. The computational research was done using the conception of chemical processes modeling based on the discrete analogues of the Boltzmann equation. A special program for experimentations and experimental data treatment obtained at a lab-scale fluidized bed jet mill was developed. A model to describe the grinding kinetics for each component of a mixture was developed. It allows estimating the efficiency of enrichment of the end product by the objective component. A method to solve the equations of the selective model of grinding and the computer algorithm for its realization was developed as well. The experimental data on grinding of binary mixture of components at their different content in the fluidized bed jet mill hold-up were obtained. These data were used to identify the model with respect to the parameters that characterized the grindability of each component. The model adequacy was checked using the data on joint grinding of mixtures with different content of components. These data were not used for the model identification. Comparison of calculated and experimental data showed the model adequacy and possibility of its usage to estimate the efficiency of components separation. The investigation allowed generalizing the conceptions of chemical processes modeling based on the discrete analogues of the Boltzmann equation to the case of selective grinding of a mixture of components with different strength. The computational analysis showed that the model allowed describing the process with acceptable for engineering practice accuracy, practical estimating the possibility of components enrichment and defining the optimal technological conditions for their separation.Forcitation:Zhukov V.P., Osipov D.А., Otwinowski H., Urbaniak D. Numerical and experimental study of mixture grinding of materials with different strengths. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2017. V. 60. N 6. P. 109-115.

This paper compares models based on nonlinear Maxwell’s and Schrodinger equations developed for modeling typical experiments involving the three-dimensional modification of glasses (using fused quartz as an example) under the action of femtosecond laser pulses. It is shown that the results can be appreciably different when the Maxwell’s and Schrodinger equations are used. A substantial role in this case is played not only by the equations themselves, but also by the form of the boundary condition that describes the focused laser pulse at the input to the region of calculation.

We discuss methods for coherently controlling mesoscopic atomic ensembles where the number of atoms varies randomly from one experimental run to the next. The proposed schemes are based on adiabatic passage and Rydberg blockade and can be used for implementation of a scalable quantum register formed by an array of randomly loaded optical dipole traps., 14 pages, 7 figures, to be published in Proceedings of the 6th International Symposium on Modern Problems of Laser Physics (MPLP-2013)

A study is made of the propagation of an Alfven pulse and the superposition of an Alfven and a magnetosonic pulse in the vicinity of the magnetic null line (the X point). It is shown that, on long time scales, the poloidal components of the velocity and magnetic field relax to steady-state distributions similar to those in the case of a magnetosonic pulse. In the essentially nonlinear problem under investigation, the steady-state distributions of the toroidal components of the velocity and magnetic field are found to be close to those in the corresponding linear problem. It is established that two-dimensional effects play an important role in the evolution of the forming current sheets.

The so-called reduced magnetohydrodynamics, which deals with the motion of incompressible fluids and is usually applied to describe plasma flows in a strong toroidal magnetic field, has a number of drawbacks and, in some cases, fails to produce correct results. The equations proposed here are simpler than the original MHD equations and are free of these drawbacks. These equations, like reduced MHD equations, make it possible to remove from consideration fast magnetosonic waves and to introduce the vector potential for the poloidal magnetic field. However, our equations differ from the reduced MHD equations in that they completely incorporate slow magnetosonic waves, the specific features of the toroidal geometry, and the effects of the toroidal velocity.

The specific features of the density and total pressure (the sum of magnetic and gas-kinetic pressures) behavior in the process of forced (by the example of propagation of a magnetic acoustic wave in the vicinity of the X-point) and spontaneous (by the example of development of a helical Thirring mode) reconnection are considered. It is shown that the total pressure distribution depends weakly on the initial value of the gas-kinetic pressure, the strength of the z-component of the magnetic field, and the thermal conductivity in a wide range of parameters. The character of density distribution is determined only by the thermal conductivity. It is also shown that the behavior of the total pressure and density in the case of spontaneous reconnection weakly depends on the thermal conductivity, in contrast to the forced case.

With reference to the problem of the development of tiring instability in a helical geometry it is shown that, as distinct from traditional gas dynamics, in plasma dynamics the incompressibility approximation cannot generally be used for describing slow flows. This is associated with the fact that several types of disturbances whose interaction results in possible density variations of the order of unity can propagate in plasma.

The development of the tearing instability is studied in the presence of a high toroidal magnetic field and a high plasma conductivity. The variation of the plasma density is shown to be significant in this case.