On rational Abel – Poisson means on a segment and approximations of Markov functions

Approximations on the segment [−1, 1] of Markov functions by Abel – Poisson sums of a rational integral operator of Fourier type associated with the Chebyshev – Markov system of algebraic fractions in the case of a fixed number of geometrically different poles are investigated. An integral representation of approximations and an estimate of uniform approximations are found. Approximations of Markov functions in the case when the measure µ satisfies the conditions suppµ = [1, a], a > 1, dµ(t) = φ(t)dt and φ(t) ≍ (t − 1)α on [1, a], a are studied and estimates of pointwise and uniform approximations and the asymptotic expression of the majorant of uniform approximations are obtained. The optimal values of the parameters at which the majorant has the highest rate of decrease are found. As a corollary, asymptotic estimates of approximations on the segment [−1, 1] are given by the method of rational approximation of some elementary Markov functions under study.

Augmentation of heat transfer via nanofluids in duct flows using Fourier-type conditions: Theoretical and numerical study

Motivated by developments in thermal duct processing, an investigation is presented to study the behavior of viscous nanoparticle suspensions flowing in a vertical duct subject to Fourier-type conditions. The left wall temperature is kept lower than that of the right wall. Brownian motion and thermophoresis which are invoked via the presence of nanoparticles are incorporated in the study. Numerical solutions with an efficient Runge–Kutta shooting method are also presented at all values of the control parameters. The impact of thermal Grashof number [Formula: see text], Eckert number [Formula: see text], thermophoresis [Formula: see text], and Brownian motion parameters [Formula: see text] on the velocity, temperature, and nanoparticle concentration distributions for identical [Formula: see text] and differing Biot numbers [Formula: see text] (at the duct walls) are computed and visualized graphically. With vanishing thermophoresis and Brownian motion parameters, the solutions match exactly with the earlier Newtonian viscous flow computations. Symmetric and asymmetric wall heat conditions are also acknowledged. Intensifying the thermal Grashof number, Eckert number, thermophoresis parameter, and Brownian parameter serve to amplify magnitudes of the velocity and temperature, whereas the nanoparticle concentration field is suppressed. The skin friction and Sherwood number are also computed with various combinations of the flow control parameters. Nusselt number values at the hot duct wall are enhanced with an increase in thermal buoyancy parameter, Eckert number, Brownian motion parameter, and thermophoresis parameter for equal Biot numbers. The opposite trend is computed for different Biot numbers. For any given values of Biot numbers, the mean velocity and bulk temperature are boosted with increase in thermal buoyancy parameter, Eckert number, Brownian motion parameter, and thermophoresis parameter. Hence, it may be inferred that the transport characteristics computed using Fourier-type boundary conditions are substantially different from those based on isothermal boundary conditions in nanofluid duct flows.

Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach

A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

Occlusion Culling for Wide-Angle Computer-Generated Holograms Using Phase Added Stereogram Technique

A computer-generated hologram (CGH) allows synthetizing view of 3D scene of real or virtual objects. Additionally, CGH with wide-angle view offers the possibility of having a 3D experience for large objects. An important feature to consider in the calculation of CGHs is occlusion between surfaces because it provides correct perception of encoded 3D scenes. Although there is a vast family of occlusion culling algorithms, none of these, at the best of our knowledge, consider occlusion when calculating CGHs with wide-angle view. For that reason, in this work we propose an occlusion culling algorithm for wide-angle CGHs that uses the Fourier-type phase added stereogram (PAS). It is shown that segmentation properties of the PAS can be used for setting efficient conditions for occlusion culling of hidden areas. The method is efficient because it enables processing of dense cloud of points. The investigated case has 24 million of point sources. Moreover, quality of the occluded wide-angle CGHs is tested by two propagation methods. The first propagation technique quantifies quality of point reproduction of calculated CGH, while the second method enables the quality assessment of the occlusion culling operation over an object of complex shape. Finally, the applicability of proposed occlusion PAS algorithm is tested by synthetizing wide-angle CGHs that are numerically and optically reconstructed.

Theoretical studies of the electron paramagnetic resonance parameters and local structures for Cu2+ in (100-2x)TeO2-xAg2O-xWO3 glasses

The electron paramagnetic resonance (EPR) parameters and local structures for Cu2+ in (100-2x)TeO2-xAg2O-xWO3 (TAW) (7.5 ≤ x ≤ 30 mol %) glasses are quantitatively studied for distinct modifier concentrations x. The octahedral Cu2+ centers are subject to the medium tetragonal elongations of about 2% along the C4 axis due to the Jahn-Teller effect. By utilizing only three adjusted coefficients a, b and ω, the quantities (Dq, k, t and κ) can be suitably characterized by the Fourier type functions, which reasonably account for the experimental concentration dependences of the d-d transition bands and EPR parameters. The calculation results are discussed, and the mechanisms of the above concentration dependences of these quantities are illustrated by the modifications of the local structures and the electron cloud distribution around the Cu2+ dopant with the variations of the concentration x.

Simulation of thermomechanical processes in disc brakes of wheeled vehicles

Purpose: Ensuring the required operational reliability of disc brakes by forecasting their technical condition taking into account thermomechanical processes. Design/methodology/approach: Differential equations of rotation of a rigid body around a fixed axis are solved, it is established that the equations of motion and the equations of thermal conductivity are indirectly related. The use of these analytical dependences provides a better understanding of thermomechanical transients. Findings: The solution is obtained on the basis of the differential equation of thermal conductivity of the hyperbolic type, which does not allow an infinite velocity of propagation of temperature perturbations in contrast to the differential equation of thermal conductivity of the parabolic Fourier type. The obtained analytical dependences provide a better understanding of thermomechanical transients and develop a theoretical basis for determining stresses and heat fluxes in solving problems of reliability and durability of disc brakes. Research limitations/implications: The work uses generally accepted assumptions and limitations for thermomechanical calculations. Practical implications: It is shown, that transients in a mechanical system - a brake disk at impulse loadings cause emergence of thermal effects which arise under the influence of external loadings. Originality/value: The application of these analytical dependences provides a better understanding of thermomechanical transients and develops a theoretical basis for solving problems of reliability and durability of disc brakes.

Controllability to rest of the Gurtin-Pipkin model

<p style='text-indent:20px;'>This paper is devoted to analyzing the controllability to rest of the Gurtin-Pipkin model, which is a class of differential equations with memory terms. The goal is not only to derive the state to vanish at some time but also to require the memory term to vanish at the same time, ensuring that the controlled system is controllable to rest. In order to get rid of the influence of memory, the controllability result is obtained by means of the Fourier type approach and the moment theory.</p>