This paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations ...under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the multiple stochastic integrals of multiplicity 1–3 appearing in the Ito–Taylor expansion as an example, it is shown that their expansions obtained using multiple Fourier–Legendre series are significantly simpler and less computationally costly than their analogs obtained on the basis of multiple trigonometric Fourier series. The results obtained in this paper can be useful for constructing and implementing strong numerical methods for solving Ito stochastic differential equations with multidimensional nonlinear noise.
Abstract
The article is devoted to optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 4 based on multiple Fourier-Legendre series. ...The mentioned stochastic integrals are part of strong numerical methods with convergence orders 1.0, 1.5, and 2.0 for Ito stochastic differential equations with multidimensional non-commutative noise. We show that the lengths of sequences of independent standard Gaussian random variables required for the mean-square approximation of iterated Ito stochastic integrals can be significantly reduced without the loss of the mean-square accuracy of approximation for these stochastic integrals.
Numerical modeling methods with a strong convergence of order 2.5 are developed for the multidimensional dynamic systems under random perturbations described by Itô stochastic differential equations. ...Special attention is paid to the numerical modeling methods of the multiple Itô stochastic integrals of multiplicities 1–5 in terms of the mean-square convergence criterion, which are required to implement the former methods.
This paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of ...applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equations, which are proper mathematical models of various dynamic systems affected by random disturbances, has not been adequately studied. This paper partially fills this gap.
•Cryogenic quenching is enhanced by a structured capillary-porous coating of surface.•A new type of coating was produced by the directional plasma spraying technique.•Coating affects the process ...dynamics: reduces the total quench time by more than threefold.•Surface microstructure triggers the liquid-solid contacts at extremely high temperature.•The numerically obtained dynamic pattern of quenching correlates well with experimental data.
In the present study, the influence of structured capillary-porous coatings of surface on cryogenic quenching by the falling liquid nitrogen film is investigated. The coating was produced by the directional plasma spraying technique. The cryogenic quenching experiments were performed on high-temperature vertical copper slab with bare surface and on the surfaces with different orientation of coating protrusions. Thermocouples and a high-speed digital video camera were employed to obtain a synchronized data on the temperature-time history of the transient process and the pattern of quench front propagation. The peculiarities of quench front dynamics and heat transfer in the transient process are studied. The created numerical model determines the quench front velocity and the temperature fields in the heater, varying in space and time. The dynamic pattern of quench front propagation obtained numerically satisfactorily correlates with the observed in the experiments one. The heat transfer curves during quenching were determined for different surfaces based on the experimental cooling thermograms and visualization data. The results show that the cooling rate is influenced by the thermal properties of the coating as well as the geometry of the protrusions on the solid surface. The presence of capillary-porous coating significantly affects the dynamics of quenching, which results in the decrease more then threefold of the total quench time. In this way, the structured capillary-porous coating is a method for reducing the time and the total mass of cryogenic fluid required for a quenching process. The effect is due to the fact that the initialization of a quench front on a specimen with the coating occurs at a temperature significantly higher than the thermodynamic limit of a liquid superheat, when a stable solid-liquid contact is thermodynamically impossible. This phenomenon appears as a result of local contacts of the crests of wavy liquid flow at the liquid-vapor interface with the protrusions on the modified surface. The results indicated also the minimum film boiling temperature increase on heat transfer surface coated with capillary-porous layer. This increased temperature caused earlier transition to nucleate boiling, which results in the decrease in the quenching time. The results reliability is confirmed by direct comparison with experimental data on the quench front dynamics, velocity and geometry.
A strongly converging method of order 2.5 for Ito stochastic differential equations with multidimensional nonadditive noise based on the unified Taylor–Stratonovich expansion is proposed. The focus ...is on the approaches and methods of mean square approximation of iterated Stratonovich stochastic integrals of multiplicities 1–5 the numerical simulation of which is the main difficulty in the implementation of the proposed numerical method.
The paper was devoted to developing numerical methods with the orders 1.5 and 2.0 of strong convergence for the multidimensional dynamic systems under random perturbations obeying stochastic ...differential Ito equations. Under the assumption of a special mean-square convergence criterion, attention was paid to the methods of numerical modeling of the iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 4 that are required to realize the aforementioned numerical methods.
► MWNT-loaded polypropylene composites were prepared by twin-screw extrusion. ► Two different types of initial and oxidized nanotubes were loaded in composites. ► Low-defective thick nanotubes show ...higher dispersion state in composites. ► Higher thermal conductivity was obtained for composites with thick nanotubes.
Polypropylene-based composites filled with multiwall carbon nanotubes were prepared using twin-screw extrusion technique. Two types of nanotubes with different diameter, morphology and defectiveness were used as fillers. Influence of MWNT surface composition on properties of the composite was investigated for oxidized nanotubes. Thermal conductivity (TC) of MWNT/PP composites with different MWNT concentration was investigated, showing strong dependence of TC value on the MWNT type and structure, and MWNT content in composite. TC value of 0.55–0.6W/m×K was achieved for MWNT/PP samples filled with 16wt.% of low-defective MWNTs with mean diameter 22nm.
The aim of this study is to increase thermal conductivity of polypropylene (PP) composites filled with hexagonal boron nitride particles. Two types of BN with different types of surface treatment ...were used – pristine and covered with 3-amino-propyl-3-ethoxy-silane (APTES), which was bonded to hydroxyl groups, formed on the h-BN surface by annealing at 1100°C. The presence of covalently bonded silane functional groups on the surface of h-BN particles was proved by Fourier transform infrared spectroscopy (FTIR) method. Surface treatment of h-BN particles allowed to introduce 3-times increased amount of the filler in the composite produced by extrusion casting technique as compared with non-treated h-BN filler. The thermal conductivity of PP composites filled with surface-modified h-BN was effectively enhanced – up to 2 times as compared with the composite filled with pristine h-BN and more than 2.5–4 times as compared with pure PP.
Ni
Mn
In
(close to 2-1-1 system) Heusler alloy was studied by magnetization measurement dependence on the temperature in magnetic fields of up to 13.5 T. The magnetocaloric effect measured by the ...direct method in quasi-adiabatic conditions showed a maximum value of ∆T
= -4.2 K at a temperature T = 212 K in a magnetic field of 10 T in the region of martensitic transformation. The structure of the alloy was studied by transmission electron microscopy (TEM) as a function of the temperature and the thickness of the sample foil. In the temperature range from 353 to 215 K, at least two processes were established. The results of the study indicate that the concentration stratification occurs according to the mechanism of spinodal decomposition (conditionally spinodal decomposition) into nanoscale regions. At a temperature of 215 K and lower, martensitic phase with 14 M modulation is observed in the alloy at thicknesses greater than 50 nm. Some austenite is also observed. In foils with thickness of less than 50 nm in a temperature range from 353 to 100 Km only the initial austenite, which has not transformed, was found.
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