Entropy generation of MHD flow of sodium alginate (C6H9NAO7) fluid in thermal engineering

In this paper, impacts of magnetic field and porosity on the entropy generation of sodium-alginate (C6H9NaO7) fluid are studied. C6H9NaO7 is taken over a moving and heated vertical wall. Heat transfer is due to free convection. Initially, the problem is formulated in the form of PDEs along with physical conditions and then written in non-dimensional form. Problem is solved via Laplace transform and expression in analytical form is established for temperature and velocity field. The related relations for entropy generation and Bejan number and entropy generation are also examined. Nusselt number and Skin-friction are calculated and plotted in graphs. For numerical computations, a finite difference scheme is used using MATLAB software. The results in tables and graphs are discussed for embedded parameters. It is found that the magnetic field and porosity have strong influence on velocity, entropy generation and Bejan number. For greater Hartman number, entropy generation magnitude is greater compared to the Bejan number, conversely, this variation in Bejan number is more efficient. The porosity effect showed that if the medium is more porous, the entropy generation can decreases 50% when porosity increase from Ka = 1 to Ka = 2, however the Bejan number increases.

The Alternative Voltammetric Method for the Determination of Nicotine and Its Metabolite Nicotine N-Oxide

In the present paper, for the first time, the electrochemical behaviour of nicotine metabolite nicotine N-oxide (NNO) on static mercury dropping electrode (SMDE) and mercury meniscus modified silver solid amalgam electrode (m-AgSAE) has been reported. Nicotine N-oxide is reduced forming one peak at the potential -0.78 V on SDME and -0.86 V on m-AgSAE in Britton-Robinson buffer medium at pH 4.5 using cyclic voltammetry (CV). One electron and one proton take part in the reaction of NNO reduction. Calibration graphs for NNO determination using linear sweep voltammetry (LSV) on SDME and square-wave voltammetry (SWV) and differential pulse voltammetry (DPV) on m-AgSAE were obtained. Limit of detection (LOD) is 0.13 μM on SDME, and 0.16 μM (SWV) and 0.29 μM (DPV) on m-AgSAE. Since NNO can be used as an analytical form for nicotine voltammetric determination, so the developed methods were applied for the analysis of pharmaceutical preparations, and the recoveries from 97.3 to 104.6 % were achieved. Also, the elaborated methods were used in the analysis of biological fluids, and tobacco products. The obtained results were compared to those indicated in the certificates of drugs analysis, and to the results, obtained by reference methods (HPLC and GC).

Models of activated recrystallization on isolated grain boundaries in polycrystals

New phenomenological models of recrystallization of a polycrystalline material in two regimes are proposed taking into account the finite width of grain boundaries. The solutions are obtained in an analytical form for the initial-boundary value problems formulated. They describe the distributions of the concentration of impurities diffusing from the surface coating, both in the grain boundary and in the grain itself in the recrystallized region. The speed of the recrystallization front movement is indicated, which agrees with the types of the corresponding kinetic dependences observed in experiments.

The flow of the Berry curvature vector field

The concept of Berry phase and Berry curvature has become ubiquitous in solid state physics as it relates to variety of phenomena, such as topological insulators, polarization, and various Hall effects. It is well known that large Berry curvatures arise from close proximity of hybridizing bands, however, the vectorial nature of the Berry curvature is not utilized in current research. On bulk bcc Fe, we demonstrate the flow of the Berry curvature vector field which features not only monopoles but also higher dimensional structures with its own topological features. They can provide a novel unique view on the electronic structure in all three dimensions. This knowledge is also used to quantify particular contributions to the intrinsic anomalous Hall effect in a simple analytical form.

Locomotive Reliability Assessment Method

The authors describe the analysis of the current state of the problem under consideration. A definition of "averaged failure flow parameter" is given. The periods of traction rolling stock life cycle are considered. The assumption of event distribution laws exponentiality is introduced, which makes it possible to obtain expressions of the main reliability indices in the analytical form. The work of depot service locomotives to ensure the required reliability and readiness of the rolling stock during their normal operation has been assessed. The introduction of the term "readiness" into the modern practice of traction rolling stock reliability estimation is considered. The initial data for calculating the indexes of locomotive uptime and readiness are presented. Calculated values of readiness and no-failure indices of electric locomotives in operation are obtained. The calculated values of internal and technical availability coefficients are compared with similar indicators established by technical specifications. Control procedures were performed to determine the compliance of each set of locomotives (EP1, 2ES4K) with the uptime requirements. As a result of comparing the calculated values of internal and technical availability factors (for electric locomotives EP1 and 2ES4K with analogous values set by specifications (EP1 and 2ES4K) it was determined that the surveyed locomotives comply with the established availability requirements. As a result of control procedures to determine the compliance of each set of EP1 and 2ES4K locomotives with the uptime requirements, it was determined that the set of 2ES4K electric locomotives for the run in question does not fully comply with the uptime requirement. And the set of EP1 electric locomotives meets the reliability requirements, but the error value is higher than 20%. To clarify both events, it is necessary to increase the mileage interval of the locomotives and repeat the procedure for determining compliance with the uptime requirements. The method of assessing the uptime and readiness of locomotives during their normal operation makes it possible to identify existing shortcomings in the operation of rolling stock and to form measures to improve the quality of rolling stock operation.

Энергетический спектр и спектр оптического поглощения эндоэдральных фуллеренов Lu-=SUB=-3-=/SUB=-N@C-=SUB=-80-=/SUB=- и Y-=SUB=-3-=/SUB=-N@C-=SUB=-80-=/SUB=- в модели Хаббарда

Anticommutator Green’s functions and energy spectra of fullerene C80, endohedral fullerenes Lu3N@С80 and Y3N@С80 with the Ih symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecules C80, Lu3N@С80 and Y3N@С80have been determined. On the basis of these spectra, an interpretation of experimentally observed optical absorption bands endohedral fullerenes Lu3N@С80 and Y3N@С80.

Constant stress arches and their design space

It is generally accepted that an optimal arch has a funicular (moment-less) form and least weight. However, the feature of least weight restricts the design options and raises the question of durability of such structures. This study, building on the analytical form-finding approach presented in Lewis (2016. Proc. R. Soc. A 472 , 20160019. ( doi:10.1098/rspa.2016.0019 )), proposes constant axial stress as a design criterion for smooth, two-pin arches that are moment-less under permanent (statistically prevalent) load. This approach ensures that no part of the structure becomes over-stressed under variable load (wind, snow and/or moving objects), relative to its other parts—a phenomenon observed in natural structures, such as trees, bones, shells. The theory considers a general case of an asymmetric arch, deriving the equation of its centre-line profile, horizontal reactions and varying cross-section area. The analysis of symmetric arches follows, and includes a solution for structures of least weight by supplying an equation for a volume-minimizing, span/rise ratio. The paper proposes a new concept, that of a design space controlled by two non-dimensional input parameters; their theoretical and practical limits define the existence of constant axial stress arches. It is shown that, for stand-alone arches, the design space reduces to a constraint relationship between constant stress and span/rise ratio.

Inertial Waves in a Rotating Spherical Shell with Homogeneous Boundary Conditions

We find the analytical form of inertial waves in an incompressible, rotating fluid constrained by concentric inner and outer spherical surfaces with homogeneous boundary conditions on the normal components of velocity and vorticity. These fields are represented by Galerkin expansions whose basis consists of toroidal and poloidal vector functions, i.e., products and curls of products of spherical Bessel functions and vector spherical harmonics. These vector basis functions also satisfy the Helmholtz equation and this has the benefit of providing each basis function with a well-defined wavenumber. Eigenmodes and associated eigenfrequencies are determined for both the ideal and dissipative cases. These eigenmodes are formed from linear combinations of the Galerkin expansion basis functions. The system is truncated to numerically study inertial wave structure, varying the number of eigenmodes. The largest system considered in detail is a 25 eigenmode system and a graphical depiction is presented of the five lowest dissipation eigenmodes, all of which are non-oscillatory. These results may be useful in understanding data produced by numerical simulations of fluid and magnetofluid turbulence in a spherical shell that use a Galerkin, toroidal–poloidal basis as well as qualitative features of liquids confined by a spherical shell.

USING OF MULTILAYER NEURAL NETWORKS FOR THE SOLVING SYSTEMS OF DIFFERENTIAL EQUATIONS

The article considers the study of methods for numerical solution of systems of differential equations using neural networks. To achieve this goal, thefollowing interdependent tasks were solved: an overview of industries that need to solve systems of differential equations, as well as implemented amethod of solving systems of differential equations using neural networks. It is shown that different types of systems of differential equations can besolved by a single method, which requires only the problem of loss function for optimization, which is directly created from differential equations anddoes not require solving equations for the highest derivative. The solution of differential equations’ system using a multilayer neural networks is thefunctions given in analytical form, which can be differentiated or integrated analytically. In the course of this work, an improved form of constructionof a test solution of systems of differential equations was found, which satisfies the initial conditions for construction, but has less impact on thesolution error at a distance from the initial conditions compared to the form of such solution. The way has also been found to modify the calculation ofthe loss function for cases when the solution process stops at the local minimum, which will be caused by the high dependence of the subsequentvalues of the functions on the accuracy of finding the previous values. Among the results, it can be noted that the solution of differential equations’system using artificial neural networks may be more accurate than classical numerical methods for solving differential equations, but usually takesmuch longer to achieve similar results on small problems. The main advantage of using neural networks to solve differential equations` system is thatthe solution is in analytical form and can be found not only for individual values of parameters of equations, but also for all values of parameters in alimited range of values.

The classical solution of one problem of an absolutely inelastic impact on a long elastic semi-infinite bar

In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom boundary, the Cauchy conditions are specified, meanwhile, the second of them has a discontinuity of the first kind at one point. The smooth boundary condition, which has the first and the second order derivatives, is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved and the conditions are established under which a piecewise-smooth solution exists. The problem with matcing conditions is considered.