International Journal of Mathematics and Physics

Convective Heat Transfer flow of MHD Hybrid Nanofluid over a Stretching sheet with velocity and thermal slip

suman sharma — 2024-12-20

In this study, we have investigated the convective heat transfer of a hybrid nanofluid with magnetohydrodynamic (MHD) properties over a permeable stretching sheet. The analysis takes into account the effects of velocity and thermal slip, and the hybrid nanofluid consists of two distinct nanoparticles—titanium dioxide (TiO2) and silver (Ag)—dispersed in water (H2O) as the base fluid. The use of Ag and TiO2 nano-composites is particularly significant in nano-biotechnology, especially in nano-medicine and cancer cell therapy, owing to their remarkable photocatalytic performances in handling pharmaceutical compounds and pollutants. The primary aim of this research is to explore how the behavior of the MHD hybrid nanofluid over a permeable stretching surface is influenced by velocity and thermal slip conditions. By employing appropriate similarity transformations, the governing partial differential equations (PDEs) are transformed into dimensionless nonlinear ordinary differential equations (ODEs), which are then analytically solved using the Keller-box finite difference method. The results indicate that the velocity profile decreases with an increase in velocity slip, while the temperature and concentration fields decrease with thermal slip. The study further analyzes the significant impact of various parameters, including velocity and thermal slip parameter, porosity parameter, magnetic parameter, Prandtl number, and Eckert number, on the velocity, temperature, and concentration profiles. These findings are presented in graphical and tabular form, showing excellent agreement with previous literature.

An eighth-order two-step with-memory adaptive method base on Hansen-Patrick’s method and its dynamic

Vali Torkashvand — 2024-12-20

A tri-parametric family of two-point iterative methods with 7.5 and 8-order convergence for solving nonlinear equations has been proposed. Each derivative-free method member of the family requires only three evaluations of the given function per iteration. It is optimal in the sense of the Kung and Traub conjecture.
The proposed family has an efficiency index of 1.96 and 2. Numerical comparisons have been made to reveal the high efficiency of the developed method. The dynamical study of iterative schemes reflects a good overview of their stability, convergence properties, and graphical aspects by drawing attraction basins in the complex plane. Also, we have examined the dynamic
behavior of new methods to select the best weight function has the largest attraction basins for different polynomials.

Numerical modeling of thrombus formation dynamics with the rheological properties of blood

Saule Maussumbekova — 2024-12-20

In this paper, the dynamics of blood clotting is numerically simulated when blood viscosity changes. Blood was considered as an incompressible fluid, the initial equations were the Navier-Stokes equations supplemented by equations for the dynamics of blood clotting. Two cases for modeling blood viscosity are considered: viscosity as a constant and as a function characterizing non-Newtonian effects. The effects of the Reynolds and Peclet numbers on the process of thrombus formation are studied. As the Reynolds number increases, an increase in shear stress is observed. Increasing of platelet activation tends to thrombus formation. For the lower Reynolds number the better the transport of oxygen and nutrients prevents thrombus formation. Comparing the results obtained using the Cross model (viscosity is considered as a function of the velocity shear) with the results in the case of constant viscosity, it was found how increased blood viscosity leads to an increase in flow resistance, which requires a larger pressure gradient to maintain normal blood flow. High viscosity promotes platelet aggregation, increasing the likelihood of thrombus formation. Changing the Peclet number significantly affects the balance between convection and diffusion, which in turn affects the distribution of thrombin in the blood. The study of the rheological properties of blood and the blood coagulation process provides important information for improving medical diagnostics and treatment methods. The results of the work contribute to a deeper understanding of the influence of rheological properties of blood on the blood coagulation process, improving diagnostic and therapeutic methods in medical practice.

Inverse problem for determining the coefficient in the heat conduction equation

Aiymzhan Baitureyeva — 2024-12-20

Abstract. This paper considers the inverse problem of determining the thermal conductivity coefficient in the heat equation. The objective of this study is to determine the unknown coefficient based on measured boundary temperature data over time. The governing equation is a parabolic partial differential equation that describes the heat transfer process, with the unknown thermal conductivity playing a decisive role in the solution. The inverse problem is formulated as an optimization problem, in which the discrepancy between the simulated temperature distribution and the experimental data is minimized. Numerical modeling methods were used to solve the problem, including the tridiagonal matrix algorithm (Thomas algorithm) for discretizing the heat equation. The optimization process was performed using gradient methods, where the adjoint problem was used to efficiently calculate the gradient of the objective function with respect to the thermal conductivity coefficient. The results demonstrated acceptable accuracy in reconstructing the coefficient. Different parameters for the reduction factor in the gradient method were also considered. These findings are important for applications in fields such as materials science, geophysics, and engineering, where accurate estimation of thermal properties is essential.

Keywords: inverse problem, heat transfer, adjoint problem, thermal conductivity coefficient, numerical modeling.

Long-term analysis of solutions with initial jumps in singularly perturbed equations

Zhanar Artykbayeva — 2024-12-20

This paper addresses a dilemma settled by contour stipulations involving a minor fluctuation related to a third-order linear IDE that features a negligible parameter modifying the two top slopes. The study specifically examines cases in which the intercepts of the corresponding attribute equation are detrimental. The objective of this report is to provide approaching assessments for the outcome of a problem settled by contour stipulations involving a minor fluctuation with preliminary discontinuities, as well as to analyze the approaching convergence of the outcome of a preliminary value issue subjected to prominent fluctuation toward the outcome of a steady preliminary value issue. This manuscript constructs the primary structure of outcomes and introductory operations for a distinct modified consistent differential statement, while also deriving their eventual assessments. The approaching response of the outcome to the distinctively modified a dilemma settled by contour stipulations at the points of preliminary shifts is demonstrated. A degenerate dilemma settled by contour stipulations is constructed. It is demonstrated that the outcome of the preliminary outstandingly ruffled problem settled by contour stipulations approaches the outcome of the corresponding degenerate dilemma.

The problem of translational-rotational motion of a non-stationary axisymmetric small body in the gravitational field of two spherical bodies with variable mass

Balnur Assan — 2024-12-20

Abstract. In the new formulation, the translational-rotational motion of a non-stationary axisymmetric body under the gravitational influence of two spherical bodies with time-varying masses is considered. The non-stationarity of the axisymmetric body is characterized by changes in its mass, dimensions, and compression along its axis of symmetry. Additionally, the axisymmetric body is assumed to possess an equatorial plane of symmetry. This case is examined within a specialized version of the non-stationary restricted three-body problem. The problem becomes significantly more complex due to the time-dependent changes in the masses and dimensions of the bodies, which may also generate reactive forces. Equations of motion for the problem under consideration have been derived in both absolute and relative coordinate systems. For the first time, the equations of motion for the barycenter of two spherical bodies with variable masses, accounting for reactive forces, have been obtained. Based on these equations, the equations of motion for the problem in the barycentric coordinate system have also been derived.

Keywords: restricted three-body problem, variable mass, non – stationary axisymmetric celestial bodies, translational-rotational motion.

Influence of weak molecular velocity autocorrelation on the diffusion NMR

Oleg Poznansky — 2024-12-20

Self-diffusion of spin-bearing molecules measured by magnetic resonance can noninvasively probe the microstructure of complex soft matter and serve as a powerful tool for different types of diagnostics. Theoretical methods are needed to determine the autocorrelation of molecular velocities and magnetic resonance signal characteristics related to the shape, size, and concentration of soft matter constituents, although their development represents a difficult inverse problem. In this paper, we propose a numerical renormalization method that provides understanding of the contrast diffusion mechanism closely related to both the component hierarchy and the dynamic of molecular motion with a weak correlation with underlying structure. We demonstrate simulations of our method on a heterogeneous material with a self-similar random organization and show that we derive efficient temporal diffusion properties for disordered geometry, size and concentration of its components at different Euclidean dimensions. The proposed approach provides a tool for interpretation of experimental data obtained for meta- and native materials.

Keywords: magnetic resonance, signal attenuation, temporal diffusion.

Numerical evaluation of parton distribution Mellin moments

Akbari Jahan — 2024-12-20

The detailed comprehension of momentum fraction and energy dependence of proton structure functions is one of the major difficulties in particle physics. Perturbative quantum chromodynamics (QCD) plays as an extensive framework for analysing deep inelastic scattering (DIS) and hadron-hadron collision experiments. In such a framework, where the hard collisions advance through the partonic components of hadrons, a pivotal contribution is imparted by parton distribution functions (PDFs). PDFs provide information about the nucleonic substructure in terms of its components. PDFs have become more and more convictive following the advent of the Large Hadron Collider (LHC). Moments of PDFs are important quantities for the analysis of hadronic internal structure. The Mellin moments of such parton distributions in QCD have been discussed and their analyses have been carried out numerically.

Keywords: Proton structure functions, Quantum Chromodynamics, Deep inelastic scattering, Parton distribution functions, Large Hadron Collider.

Study of phase formation mechanisms in composite xSi3N4 – (1-x)ZrO2 ceramics and their role in hardening of ceramics

Inesh Kenzhina — 2024-12-20

The paper presents the results of studies of the phase transformation dynamics in composite xSi₃N₄ – (1-x)ZrO₂ ceramics obtained using the mechanical activation method during thermal annealing of the obtained mixtures of components with different component ratios, leading to the initialization of phase formation processes. Using the X-ray phase analysis method, the dynamics of phase transformations in xSi₃N₄ – (1-x)ZrO₂ ceramics, the general form of which can be written as ZrO₂/ZrSiO₄ → ZrSiO₄/finely dispersed fraction of SiO₂, was established. It was found that addition of Si₃N₄ to ZrO₂ ceramics allows for the initiation of polymorphic transformations of the m-ZrO₂ → t-ZrSiO₄ type, the formation of which in combination with the finely dispersed fraction of SiO₂ leads to hardening of the ceramics and an enhabcement in their resistance to external influences. During the experimental work carried out, aimed at study of the influence of the phase polymorphic transformation processes in composite ceramics, caused by a change in the ratio of components, on resistance to mechanical loads, it was established that the formation of a finely dispersed fraction of SiO₂ in the structure of ceramics increases resistance to cracking by more than 1.5 times compared to single-component ceramics, the stability of which decreases in the case of the compression rate growth.

Keywords: composite ceramics, phase transformations, dispersion hardening, nanosized grains, finely dispersed fraction.

Structural and electrical characteristics of the ZnO/porous-Si/Si heterostructure: from synthesis to analysis of photocell efficiency

A. Dyadenchuk — 2024-12-20

The article deals with the step-by-step production of the ZnO/porous-Si/Si heterostructure: electrochemical etching of monocrystalline Si plates (100); deposition of ZnO films by the sol-gel method followed by centrifugation.

A comprehensive study of the morphology of the obtained structure using a scanning electron microscope and an atomic force microscope confirms the high degree of structural order of the obtained film and the presence of the main chemical elements of the ZnO:Al film on its surface. It was established that the thickness of the ZnO:Al film is 395 nm, and the thickness of the porous-Si layer is 90 nm. An atomic force microscope showed that the surface of the material has a complex and heterogeneous structure with pronounced roughness. The maximum height of the profile is ⁓188 nm, indicating significant explosions and protrusions on the surface. The obtained values of the thickness and roughness of the manufactured structure were used to model the ZnO:Al/porous-Si/Si heterostructure in the PC1D program in order to find the optimal parameters of the solar cell. The values of no-load voltage, short-circuit current and maximum power were obtained from the simulation results, the filling factor and efficiency were calculated theoretically. Simulation results show that the fill factor of the fabricated structure is ~70.4%, and the efficiency of the ZnO/porous-Si/Si photoconverter is 22.4%. Increasing the level of doping to 1019 cm-3 leads to an increase in the efficiency of the photocell to a maximum value of 23%.

Keywords: electrochemical etching, sol-gel method, heterostructure photoconverter, simulation

Effects of gamma radiation on lung and colon cancer cell viability

Odsuren Myagmarjav — 2024-12-20

In Mongolia, cancer treatment is carried out through radiation, chemotherapy and surgery, and there is only one state hospital that specializes in this field, the National Cancer Center of Mongolia.

As our country's population has grown in recent years, data for 2023 from the Central Statistical Office show that the incidence of cancer, on the one hand, and the number of cases of the disease, on the other, are increasing as patients get younger. This study concerns an important part of the triad of cancer treatment, namely the evaluation of the efficacy of radiotherapy in an "in vitro" situation. Ionizing radiation has been shown to have a number of biological effects, including damage to DNA. This damage can manifest as double-strand breaks (DSB), base damage and single-strand breaks (SSB).

The ⁶⁰Co radiation source "Bhabhatron", which is installed at the National Cancer Center of Mongolia, is used as a gamma source for the cell viability experiment. In this experiment, we use two different cancer cell samples (A549, HCT116) and all used samples prepared in the Gene Engineering Laboratory of the National University of Mongolia in a quantity of 1 ml, and the cell samples were irradiated with doses of 2 Gy, 4 Gy, 6 Gy and 8 Gy. The cell viability of A549 and HCT116 cancer cells after gamma irradiation was determined using the WST assay and calculated using an analytical formula. The calculated and measured results are comparable for two different cancer cells.

Keywords: cancer cells, cell viability, WST assay, cancer treatment, radiation doses.

Study of the influence of structural modification of ZrO2 ceramics on resistance to hydrogen absorption and gas swelling processes

Artem Kozlovskiy — 2024-12-20

The main purpose of this work is to study the influence of structural modifications in ZrO₂ ceramics on the resistance to hydrogenation processes arising as a result of testing the performance of ceramics as materials for solid oxide fuel cells. During the studies conducted it was established that the use of stabilizing MgO and CaCO₃ additives to initiate the polymorphic transformation processes in ZrO₂ ceramics makes it possible to enhance the resistance of ceramics to hydrogen swelling due to the stabilization of the crystal structure, the change of which is associated with polymorphic transformations. Suppression of volumetric swelling processes due to polymorphic transformations caused by the addition of stabilizing additives made it possible to elevate resistance to hydrogen absorption and destabilization of the near-surface layer by preventing hydrogen agglomeration processes in the near-surface layer. It has been determined that the modification of ZrO₂ ceramics by initializing the polymorphic transformation processes of the m-ZrO₂ → t – ZrO₂ and m-ZrO₂ → c-ZrO₂ type leads not only to an elevation in strength parameters, but also to an increase in resistance to embrittlement processes during hydrogenation and high-temperature degradation.

Keywords: ZrO2 ceramics, gas swelling processes, modification, mechanochemical solid-phase synthesis, polymorphic transformations.