Molecular Dimerisation in a Multilayer Adsorption Phase on Homogeneous Surfaces of a Solid Adsorbent

Continuing the discussion on the description of adsorbate-adsorbate association on homogeneous surfaces of solids, an attempt was made to formulate an analytical form of adsorption equation for a multilayer adsorption phase. The validity of Berezin’s and Kiselev’s assumptions concerning the independence of adsorption in further layers from the model of the phenomenon in the first of them was discussed. The fundamental validity of this assumption has been demonstrated, simultaneously ridding it of its arbitrary character. The main aim of the study was to demonstrate the possibility of formulating a description assuming molecule association in the entire adsorption phase (and not only in the first layer). Theoretical considerations are confined to the case of dimerisation in the concentration range thus warranting the approximation characteristic of the Berezin and Kiselev model. The obtained final adsorption equation exhibits physically acceptable boundary properties; with adequate assumptions it amounts to the Brunauer, Emmett and Teller equation, the equation formulated earlier by one of the authors of this paper or the Langmuir equation.

Adaptive Fuzzy Super-Twisting Sliding Mode Control for Microgyroscope

This paper proposes a novel adaptive fuzzy super-twisting sliding mode control scheme for microgyroscopes with unknown model uncertainties and external disturbances. Firstly, an adaptive algorithm is used to estimate the unknown parameters and angular velocity of microgyroscopes. Secondly, in order to improve the performance of the system and the superiority of the super-twisting algorithm, this paper utilizes the universal approximation characteristic of the fuzzy system to approach the gain of the super-twisting sliding mode controller and identify the gain of the controller online, realizing the adaptive adjustment of the controller parameters. Simulation results verify the superiority and the effectiveness of the proposed approach, compared with adaptive super-twisting sliding mode control without fuzzy approximation; the proposed method is more effective.

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface. In the conventional two-beam approximation, each branch or wing of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities that specify the degree of departure from the exact Bragg condition and the reflection strength. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters with no approximation. Characteristic features of the dispersion surface are also revealed by geometrical considerations with respect to the Riemann surface.

Active control of flow and heat transfer in boundary layer on the porous body of arbitrary shape

The paper discusses the possibility of active control of flow and heat transfer using a magnetic field and suction in a generalized form. The unsteady temperature two-dimensional laminar magnetohydrodynamic boundary layer of incompressible fluid on a porous body of arbitrary shape is analyzed. Outer electric filed is neglected, magnetic Reynolds number is significantly lower than one i. e. the considered problem is in inductionless approximation. Characteristic properties of fluid are constant and it is assumed that a uniform suction or injection of a fluid, same as the fluid in primary flow, can take place through the body surface. The boundary-layer equations are generalized such that the equations and the boundary conditions are independent of the particular conditions of the problem, and this form is considered as universal. Obtained universal equations are numerically solved using the ?progonka? method. Numerical results for the dimensionless velocity, temperature, shear stress and heat transfer as functions of introduced sets of parameters are obtained, displayed graphically and used to carry out general conclusions about the development of temperature magnetohydrodynamic boundary layer.

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.

Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD) boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50?C ). Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.