International Journal of Mathematics and Physics

EXPERIMENTAL DATA AND THE NONLINEAR INVERSE PROBLEM OF HEAT TRANSFER

2022-06-23T19:25:21+00:00

In the paper the development a method for finding the nonlinear heat-conducting characteristics of the soil is being presented. Two-layer container complexes have been created, the side faces of which are thermally insulated so that the 1D heat equation can be used. In order not to solve the boundary value problem with a contact discontinuity and lose the accuracy of the method’s solution, a temperature sensor was placed at the junction of two media, and a mixed boundary value problem is solved in each area (container). To provide the initial data with an inverse coefficient problem, two temperature sensors are used: one sensor was placed at the open boundary of the container and recorded the soil temperature at this boundary, and the second sensor was placed at a short distance from the boundary, which recorded the air temperature. The measurements were carried out on the time interval First, the initial-boundary value problem of thermal conductivity with nonlinear coefficients of thermal conductivity, heat capacity, heat transfer, and material density are studied numerically. The nonlinear initial-boundary value problem is solved by the finite difference method. Based on the measured data of the complex, special functionals are constructed and the thermal conductivity coefficient , density , specific heat capacity , heat transfer coefficient are found, which depend on the temperature of the material.

Based on the experimentally measured data, the corresponding functional is minimized on each time interval using the gradient descent method. All thermophysical characteristics for a container with clay were found with a relative error of 5%.

ANALYSIS, RESEARCH AND DEVELOPMENT OF AN INNOVATIVE ENTERPRISE DIGITALIZATION SYSTEM FOR REMOTE WORK

2022-06-23T19:29:01+00:00

This article presents innovative development of the system for the remote activity implementation. It’s all about from remote customer service to the company and private conferences for employees, online conferences, meetings, training, etc. This system refers to devices for implementing the employees’ remote production activities of the enterprise, to devices for organizing and managing the business processes. The developed system may be used without restrictions. The most important particularity of this useful system is the opportunity to add various features depending on the demand for a separate enterprise, upon that having saved a range of using the already existing opportunities. By applying this system, it is possible to increase by several times the level of the information and communication technologies usage for enterprises. The developed data device essentially allows economizing various resources on data transmission and storage. Besides, the requirements to the infrastructure of the enterprise may be used either by browsers or mobile devices, upon that by increasing the efficiency of analysis and the agility of making production decisions. Research and analysis of fault tolerance, applicability of modern IT technologies to increase the efficiency of enterprise digitalization have been carried out

NUMERICAL SIMULATION OF PARTICLE DYNAMICS IN THE HYDROGEN-AIR MIXING LAYER

2022-06-23T19:32:16+00:00

In this paper, supersonic plane turbulent mixing layer of gases with injection of solid particles is studied numerically. The gas phase are determined by DNS solving the multi-species Navier-Stokes equations in the Eulerian approach , and the dynamic of solid particles are traced in the Lagrangian approach. The dynamics of hydrogen – air mixing and the formation of the vortex system in the mixing layer and its effect on the distribution of solid particles in the two free-flow speeds are investigated. The study focuses on detailed analysis an influence of the vortex system in the supersonic turbulent mixing layer on the dispersion solid particles with different size. The results show that heavy particles almost do not react to vortex structures. It is revealed that medium particles tend to accumulate along the circumference of the vortex and along the braid between the two vortices. A quasi-equilibrium state with a gas flow of light particles is established.

AN INITIAL-BOUNDARY VALUE PROBLEM FOR KELVIN-VOIGT EQUATIONS WITH (p(x), q(x),m(x))- STRUCTURE

2022-06-23T19:34:07+00:00

The proof of the global in time existence of solutions of initial-boundary value problems for nonlinear equations in many The proof of the global in time existence of solutions of initial-boundary value problems for nonlinear equations in many cases, is not easy, even in some cases it is impossible. However, by showing some qualitative properties of its solution, one can find answers to such questions. For example, by establishing the blow up in a finite time property of a solution, one can show that a solution does not exist globally in time. Such way, in last years, the investigating the quality properties of solutions as localization and/or blow up in a finite time, has been developing rapidly

In this paper, we study the initial-boundary value problem for the Kelvin-Voigt equations with both of diffusion and relaxation term, modified by (p(x),q(x))-Laplacian, respectively, and with the variable exponent damping term. The damping term in the equation realizes as nonlinear source term.

In this work, we study the nonlinear initial-boundary value problem for generalized Kelvin-Voigt equations describing the motion of incompressible viscoelastic non-Newtonian fluids. The equations generalized by replacing the diffusion and relaxation terms in equation with p(x)-Laplacian and q(x)-Laplacian, respectively, and adding a nonlinear absorption term with variable exponents and coefficients. The definition of a weak solution is given. Under suitable conditions for variable exponents and coefficients, and data of the problem, the blow up of weak solutions are established.

SIMULATION OF TERNARY FLUID MIXTURES SEPARATION BY PHASE-FIELD FREE ENERGY LBM

2022-06-23T19:38:27+00:00

This article reviews the mathematical and computer modeling of the process of ternary fluid mixture separation by free energy based phase flied Lattice Boltzmann method. The process under study is considered in a limited area having the shape of a rectangle. Three different sets of fluid components with different structures are specified. The mathematical model constructed to describe this process is based on the Navier-Stokes equation for an incompressible fluid and the Cahn-Hilliard equation. The numerical model is built on the basis of LBM using the D2Q9 model. Numerical experiments were performed for two scenarios: (1) – investigate the model without gravity, in order to determine the patterns of the surface tension effect and (2) - investigate the model with gravity force. The results obtained determine the adequacy of the constructed model for a three-component fluid.

SCATTERING PHASE SHIFTS OF LITHIUM ISOTOPES

2022-06-27T16:12:45+00:00

Scattering phase shifts on negative and positive parity states of ⁵Li, ⁶Li and ⁷Li nuclei are calculated applying two-body a+p, a+d and a+t systems and the complex scaling method. ⁶Li and ⁷Li are stable nuclei and their ground and low-lying excited states are considered in this work.

In this study, we calculated scattering phase shifts of the negative parity J^pi=3/2-, and 1/2+ states for p-wave ⁵Li, J^pi=7/2-, 5/2-, 3/-2 and 1/2⁻states for p- and f-waves of ⁷Li and the positive parity J^pi=1+, 2+, 3+ states for s- and d-waves of ⁶Li.

ARBITRARY AMPLITUDE NONLINEAR WAVES IN A FOUR COMPONENT QUANTUM PLASMA

2022-06-27T16:13:26+00:00

Based on the approach of Sagdeev pseudo-potential, the fully nonlinear structures of a four-component quantum plasma have been extensively investigated. The plasma under consideration consists of negative and positive dust particulates and quantum distributed electrons and ions. For typical plasma parameters, the bifurcation analysis enables us to distinguish three types of nonlinear waves, namely compressive soliton, rarefactive soliton and double-layer depending on the magnitude of the configurational plasma parameters. The formations and the existence ranges of both solitons and double-layers are found to be highly sensitive to the values of the chosen plasma parameters and the quantum indices as well. The implications of the obtained results have a wide relevance in the study of space and laboratory quantum dusty plasmas where the positive and negative dust particulates are presented and quantum effects are taken into account.

GAMMA-RADIATION-INDUCED ATTENUATION OF LIGHT IN PURE-SILICA CORE OPTICAL FIBER IN LONG-WAVELENGTH REGION

2022-06-27T16:14:23+00:00

The dependences of the spectra of radiation-induced attenuation (RIA) of light in a pure-silica core (PSC) optical fiber (OF) during and after gamma-irradiation up to 590 kGy at a dose rate of 7.6 Gy/s in the near infrared range have been investigated. It was shown that starting with an absorbed dose of ~100 kGy, the RIA at 1550 nm becomes larger than at 1310 nm due to an increase in long-wavelength (LWL) RIA. The absorption band, with a maximum at a wavelength near 1800 nm, responsible for the LWL RIA is fully defined for the first time. At an absorbed dose of 590 kGy at wavelengths of 1310 and 1550 nm, the RIA is 14.1 and 23.3 dB/km, respectively. During 3.5 years of annealing of the OF at room temperature the RIA in the entire spectral range of 1100-1700 nm decreases by 40-50%.

ADIABATIC THEORY OF MOTION OF BODIES IN THE HARTLE-THORNE SPACETIME

2022-06-27T16:15:05+00:00

We study the motion of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. For this purpose, the Hartle-Thorne metric written in harmonic coordinates is employed in the post-Newtonian approximation where the adiabatic theory is valid. As a result, we obtain the perihelion shift formula for test particles orbiting on the equatorial plane of a rotating and deformed object. Based on the perihelion shift expression, we show that the principle of superposition is valid for the individual effects of the gravitational source mass, angular momentum and quadrupole moment. The resulting formula was applied to the inner planets of the Solar system. The outcomes are in a good agreement with observational data. It was also shown that the corrections related to the Sun's angular moment and quadrupole moment have little impact on the perihelion shift. On the whole, it was demonstrated that the adiabatic theory, along with its simplicity, leads to correct results, which in the limiting cases correspond to the ones reported in the literature.

EFFECT OF THERMAL ANNEALING ON PHASE TRANSFORMATIONS AND ORDERING OF THE MAGNETIC TEXTURE OF Fe3O4/Nd2O3 NANOCOMPOSITES

2022-06-27T16:15:45+00:00

The paper presents the results of a study of the effect of thermal annealing on the phase transformations and subsequent ordering of the magnetic texture and superfine magnetic parameters in Fe₃O₄/Nd₂O₃ nanocomposites obtained by chemical deposition and subsequent mechanochemical synthesis. X-ray phase analysis and Mössbauer spectroscopy were used to characterize the properties of the obtained Fe₃O₄/Nd₂O₃ nanocomposites. Thermal annealing was carried out in an oxygen-containing medium in the temperature range of 400°C - 1000°C for 5 hours followed by cooling for 24 hours until reaching room temperature. The phase transformation dynamics of Fe₂O₃/NdFeO₃ → NdFeO₃ >>Fe₂O₃→ NdFeO₃ type was established using X-ray phase analysis. According to the data of Mössbauer spectroscopy it was established that the domination of the NdFeO₃ phase in the nanocomposite structure at annealing temperatures above 800°С leads to an ordering of the magnetic texture and an increase in the value of the superfine magnetic field to 502.8 kOe, approaching the values characteristic of the Fe₂O₃ structure (513 kOe).

STAROBINSKY MODEL WITH A VISCOUS FLUID

2022-06-27T16:16:23+00:00

The article considers some cosmological solutions of the Starobinsky model for a flat inhomogeneous viscous Universe. The first section contains a brief of the F(R) theory of gravity. One of the most common examples of F(R) gravity with a high degree of curvature is the Starobinsky model. For the Starobinsky F(R)=aR+bR²model, the cosmological model of a flat and homogeneous Universe is considered. For the Friedmann-Robertson-Walker metric, the Lagrange function is defined, and the corresponding equations are determined by the Euler-Lagrange equations and the Hamilton energy condition. Using the equation of state for inhomogeneous viscous fluid, we considered two cases of the viscosity parameter when the state parameter is constant. Next, using the results obtained, we determined the dynamics of the Hubble parameter H. At constant viscosity, has a negative value of the Hubble parameter and decreases with time along a hyperbola, while the viscosity parameter with proportional dependence on H has a positive value that decreases along a hyperbola.

If we compare it with the well-known de Sitter solution describing the accelerated expansion of the Universe and take into account that time in physics should only be positive, then the change in the Hubble parameter for the viscosity with proportional dependence on H occurs later. An analysis of this solution shows that at a certain point in time the acceleration of the Universe turns into a process of instantaneous compression. However, in the end, the result is similar to the de Sitter solution tends to zero, i.e. the Universe stops accelerating. Based on the results obtained, a graph was constructed with respect to the de Sitter solution. The analysis was carried out according to the graph. These results are useful for describing the accelerated expansion of the modern Universe and do not contradict modern astronomical observations.