Search results for: Arsenij D. Shishkin

Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

Abstract:

In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: Radik D. Aglyamov, Alexander K. Naumov, Alexey A. Shavelev, Oleg A. Morozov, Arsenij D. Shishkin, Yury P.Brodnikovsky, Alexander A.Karabutov, Alexander A. Oraevsky, Vadim V. Semashko

Abstract:

The development of medical optoacoustic tomography with the using human blood as endogenic contrast agent is constrained by the lack of reliable, easy-to-use and inexpensive sources of high-power pulsed laser radiation in the spectral region of 750-900 nm [1-2]. Currently used titanium-sapphire, alexandrite lasers or optical parametric light oscillators do not provide the required and stable output characteristics, they are structurally complex, and their cost is up to half the price of diagnostic optoacoustic systems. Here we are developing the lasers based on Cr:LiCaAlF6 crystals which are free of abovementioned disadvantages and provides intensive ten’s ns-range tunable laser radiation at specific absorption bands of oxy- (~840 nm) and -deoxyhemoglobin (~757 nm) in the blood. Cr:LiCAF (с=3 at.%) crystals were grown in Kazan Federal University by the vertical directional crystallization (Bridgman technique) in graphite crucibles in a fluorinating atmosphere at argon overpressure (P=1500 hPa) [3]. The laser elements have cylinder shape with the diameter of 8 mm and 90 mm in length. The direction of the optical axis of the crystal was normal to the cylinder generatrix, which provides the π-polarized laser action correspondent to maximal stimulated emission cross-section. The flat working surfaces of the active elements were polished and parallel to each other with an error less than 10”. No any antireflection coating was applied. The Q-switched master oscillator-power amplifiers laser system (MOPA) with the dual-Xenon flashlamp pumping scheme in diffuse-reflectivity close-coupled head were realized. A specially designed laser cavity, consisting of dielectric highly reflective reflectors with a 2 m-curvature radius, a flat output mirror, a polarizer and Q-switch sell, makes it possible to operate sequentially in a circle (50 ns - laser one pulse after another) at wavelengths of 757 and 840 nm. The programmable pumping system from Tomowave Laser LLC (Russia) provided independent to each pulses (up to 250 J at 180 μs) pumping to equalize the laser radiation intensity at these wavelengths. The MOPA laser operates at 10 Hz pulse repetition rate with the output energy up to 210 mJ. Taking into account the limitations associated with physiological movements and other characteristics of patient tissues, the duration of laser pulses and their energy allows molecular and functional high-contrast imaging to depths of 5-6 cm with a spatial resolution of at least 1 mm. Highly likely the further comprehensive design of laser allows improving the output properties and realizing better spatial resolution of medical multispectral optoacoustic tomography systems.

Keywords: medical optoacoustic, endogenic contrast agent, multiwavelength tunable pulse lasers, MOPA laser system

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Authors: Andrei Shishkin, Aleksandrs Korjakins, Viktors Mironovs

Abstract:

Present paper describes method of obtaining clay ceramic foam (CCF) and foam concrete (FC), by direct foaming with high speed mixer-disperser (HSMD). Three foaming agents (FA) are compared for the FC and CCF production: SCHÄUMUNGSMITTEL W 53 FLÜSSIG (Zschimmer & Schwarz Gmbh, Germany), SCF-1245 (Sika, test sample, Latvia) and FAB-12 (Elade, Latvija). CCF were obtained at 950, 1000°C, 1150°C and 1150°C firing temperature and have mechanical compressive strength 1.2, 2.55, and 4.3 MPa and porosity 79.4, 75.1, 71.6%, respectively. Obtained FC has 6-14 MPa compressive strength and porosity 44-55%. The goal of this work was the development of a sustainable and durable ceramic cellular structures using HSMD.

Keywords: ceramic foam, foam concrete, clay foam, open cell, close cell, direct foaming

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Authors: A. Shishkin, V. Mironovs, D. Goljandin, A. Korjakins

Abstract:

The goal of this work is to develop sustainable and durable ceramic cellular structures using widely available natural resources- clay and milled waste glass. Present paper describes method of obtaining clay ceramic foam (CCF) with addition of milled waste glass in 5, 7 and 10 wt% by direct foaming with high speed mixer-disperser (HSMD). For more efficient clay and waste glass milling and mixing, the high velocity disintegrator was used. The CCF with 5, 7, and 10 wt% were obtained at 900, 950, 1000 and 1050 °C firing temperature and they have demonstrated mechanical compressive strength for all 12 samples ranging from 3.8 to 14.3 MPa and porosity 76-65%. Obtained CCF has compressive strength 14.3 MPa and porosity 65.3%.

Keywords: ceramic foam, waste glass, clay foam, glass foam, open cell, direct foaming

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Authors: Anna D. Kotrova, Alexandr N. Shishkin, Elena I. Ermolenko

Abstract:

The aim. To study the quantitative and qualitative colon bacteria ratio from patients with metabolic syndrome. Materials and methods. Fecal samples from patients of 2 groups were identified and analyzed: the first group was formed by patients with metabolic syndrome, the second one - by healthy individuals. The metagenomics method was used with the analysis of 16S rRNA gene sequences. The libraries of the variable sites (V3 and V4) gene 16S RNA were analyzed using the MiSeq device (Illumina). To prepare the libraries was used the standard recommended by Illumina, a method based on two rounds of PCR. Results. At the phylum level in the microbiota of patients with metabolic syndrome compared to healthy individuals, the proportion of Tenericutes was reduced, the proportion of Actinobacteria was increased. At the genus level, in the group with metabolic syndrome, relative to the second group was increased the proportion of Lachnospira. Conclusion. Changes in the colon bacteria ratio in the gut microbiota of patients with metabolic syndrome were found both at the type and the genus level. In the metabolic syndrome group, there is a decrease in the proportion of bacteria that do not have a cell wall. To confirm the revealed microbiota features in patients with metabolic syndrome, further study with a larger number of samples is required.

Keywords: gut microbiota, metabolic syndrome, metagenomics, tenericutes

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