Quasi-homogeneous Medium Research Articles

Ultrahigh-Performance Fiber-Supported Iron-Based Ionic Liquid for Synthesizing 3,4-Dihydropyrimidin-2-(1H)-ones in a Cleaner Manner.

Herein, a fiber-supported iron-based ionic liquid as a type of fibrous catalyst has been developed for the synthesis of bioactive 3,4-dihydropyrimidin-2-(1H)-ones (DHPMs) via three-component Biginelli reactions in a cleaner manner. The described fibrous catalyst was obtained from the commercially available polyetheretherketone (PEEK) fiber by postfunctionalization processes and was characterized and analyzed in detail by means of diversified technologies. Furthermore, the fiber-supported iron-based ionic liquids could mediate the classical three-component Biginelli reactions to proceed smoothly to gain a variety of substituted DHPMs with yields of up to 99%. The superior catalytic activities of the fibrous catalyst were ascribed to the quasi-homogeneous medium by ionic liquids generated in the surface layer of the PEEK fiber, which could afford an appropriate reaction zone and could further be available for the aggregation of substrates to facilitate the three-component reaction. Notably, the fibrous catalyst is available for recycling over 10 runs just by a pair of tweezers, and the operational procedure was capable of enlarging the catalytic system to the gram-scale without any performance degradation, which provided a cleaner manner to take advantage of the iron-based catalyst in organic synthesis with potential industrialization prospects.

Heat treatment of ground surface using an electric arc plasma generator

The article presents a generalization of the results of experimental and theoretical studies on the intensive thermal effect on the surface of foundations from cohesive soils (as opposed to deep heat treatment) using an electric arc generator of low-temperature plasma (plasmatron). A plasmatron with massive consumable electrodes made of borosilicated graphite and a wide "blurred" plasma torch was used for heat treatment. Physical and mathematical modeling of the thermal effect on the surface of clay soil by a moving high-temperature source has been performed. For the first time, a special installation was manufactured and experimental studies were carried out on the heat treatment of ground surfaces on the site with an electric arc plasma torch. It is established that the effective heat flux density reaches 2.5-.3.5 kW/cm2. The main part of the thermal energy for the used plasmatron enters the material due to radiant heat transfer. An analytical mathematical model of the temperature field of a three-dimensional semi-bounded body in the technological process under consideration is given by an essentially nonlinear boundary value problem for a nonlinear heat equation with nonlinear boundary conditions of the second kind. When solving thermophysical problems, the ground semi-bounded space was considered as a quasi-homogeneous medium having a constant initial temperature and initial thermophysical parameters that change in the process of temperature increase. The effective values of the thermophysical characteristics were determined on the basis of experimental data. Calculations and experiments have shown that the temperature boundary leading to significant changes in the structural properties of soils drops to a depth of 4-6 cm from the surface, despite the boiling of the ground melt with a temperature of 2500 ...2800 K on the ground surface. Therefore, a new technological principle of heat treatment is proposed, which consists in building up the ground melt in layers of 4-5 cm up from the initial surface. The impossibility of obtaining a positive effect even with the use of a powerful high-temperature source of exposure in the case of traditional surface heat treatment technology has been confirmed. The new plasma technology of surface heat treatment of ground surfaces to the stage of silicate melt allows to obtain a common layer of the required thickness. At the same time, the efficiency of surface heat treatment is significantly increased. The new technology of layer-by-layer surface deposition reduces cracking in the layer when the melt cools, but does not eliminate this negative process.

Модели искажений сигналов при распространении в лесных массивах

Models of signal propagation in forests are presented, based on the representation of forests as a continuous quasi-homogeneous medium and characterized by an effective complex permittivity. The values of the effective permittivity are a functional of the total volumetric concentration of the components of vegetation relative to the main medium - the atmosphere, of the frequency of signals, of the electrical and taxometric characteristics of forests. It is shown that when propagating along the lines under consideration, the spectral components of digital signals acquire partial phase and amplitude shifts, which causes distortions of the complex envelopes of signals and energy losses during reception with respect to propagation in free space. Modeling was carried out using models of signal propagation in forests with typical characteristics to estimate the probabilistic characteristics of receiving digital signals with 4-level phase shift keying with frequency band extension. It is shown that for these signals with a frequency band of 10...20 MHz with a center frequency of the P-band with horizontal polarization, the energy loss with respect to propagation in free space with equivalent attenuation exceeds 1.2 dB due to the distortion of the complex envelopes of the signals. A smaller effect on the probabilistic characteristics of receiving signals with vertical polarization is also shown - the energy loss in this case reaches 0.5 dB.

Investigation of drying the porous wood of a cylindrical shape

In the presented study, the mathematical model for drying the porous timber beam of a circular cross-section under the action of a convective-heat nonstationary flow of the drying agent is constructed. When solving the problem, a capillary-porous structure of the beam is described in terms of a quasi-homogeneous medium with effective coefficients, which are chosen so that the solution in a homogeneous medium coincides with the solution in the porous medium. The influence of the porous structure is taken into account by introducing into the Stefan–Maxwell equation the effective binary interaction coefficients. The problem of mutual phase distribution is solved using the principle of local phase equilibrium. The given properties of the material (heat capacity, density, thermal conductivity) are considered to be functions of the porosity of the material as well as densities and heat capacities of body components. The solution is obtained for determining the temperature in the beam at an arbitrary time of drying at any coordinate point of the radius, thermomechanical characteristics of the material, and the parameters of the drying agent.

Comprehensive kinetic model for acetylene pretreated mesoporous silica supported bimetallic Co-Ni catalyst during Fischer-Trospch synthesis

A new model by incorporating the porosity field during acetylene pretreatment (PT) into the Fischer-Trospch (FT) synthesis comprehensive kinetic is proposed for quantitatively describing the product distributions using a mesoporous silica supported Co-Ni bimetallic catalyst. Coupling the quasi-homogeneous medium model with the acetylene reaction kinetics via the Langmuir-Hinshelwood-Hougen-Watson (LHHW) approach, the model yields good predictions for breakthrough curves, pressure drops, and permeability during PT process. The active carbidic intermediates formed by the acetylene PT engaged with the subsequent CO dissociation and 1-olefin re-adsorption associated secondary reactions during FT synthesis. The constructed comprehensive kinetic model can predict the olefin to paraffin ratios (OPR) versus chain length when the catalyst was pretreated. A relatively good prediction from chain length dependent model (CLD) indicates the validity of assuming that Van Waals forces play a critical role during olefin re-adsorption in the secondary reactions for chain propagations once the mesoporous supported Co-Ni bimetallic catalyst was pretreated by acetylene. The proposed model successfully bridges the gaps between the PT and FT process at the investigated experimental conditions.

Micro-macro heat conduction model for the prediction of local, transient temperature in composite media

Heat flow in heterogeneous media with complex microstructure follows tortuous path and therefore the determination of local temperature distribution is a challenging task. The paper presents a micro-macro heat conduction model for the prediction of this distribution. The proposed solution is based on the prior determination of the macroscopic temperature in a quasi-homogeneous medium characterized by effective properties and then on using the relations between the macroscopic and microscopic temperatures. The Ensemble Averaging Method (EAM) was applied to derive the macroscopic transport equations while the combination of the EAM with the Green's Function Theory (GFT) was used to obtain relations between microscopic and macroscopic temperature fields. The expansion of these relations versus powers of the ratio of the micro to macro dimensions was then used to obtain a two-scale approximation of the mentioned relations. The model is applicable wherever the characteristic dimensions of the microstructure, i.e., distance between inclusions, are smaller than macro-dimension associated with time and spatial variation of macroscopic temperature distribution. The latter can be found from the respective expansion of the macroscopic temperature distribution into the Fourier series. The verification of the proposed model was carried out for 2D transient heat conduction in a periodic composite with the fixed microstructure by comparing direct numerical solution of the energy equation with the results of the approximate micro-macroscopic modelling. The model will be further extended to the prediction of temperature distribution in the case when the thermal contact resistance between constituents, species concentration in heterogeneous media, phase change phenomena and formation of a medium microstructure are present.

Condition for far-zone spectral isotropy of light transmitted from Young's pinholes scattering on a quasi-homogeneous medium.

The far-zone spectral isotropy of light transmitted from Young's pinholes on scattering from a quasi-homogeneous medium has been discussed. A sufficient condition for the far-zone spectral isotropy has been derived as a new scaling law. Our result not only is analogous with the scaling law for weak scattering in previous works but is also applicable for a more general situation where the incident light has an arbitrary spectral degree of coherence. More discussion about cross-spectral purity of the far field is presented.

Frequency Shifts of Spectral Lines Generated by Young's Pinhole Wave Scattering Upon a Quasi-Homogeneous Medium

Frequency shifts of light scattered from either a deterministic or random medium have shown great importance in remote sensing imaging applications, however, such scattering system which combines random scatterer with obstacles has not been specifically discussed so far. To solve this problem, we derive analytical expressions for showing the phenomenon that the Young's pinhole wave scattered from a quasi-homogeneous (QH) medium exhibits the red shift of spectral lines, while the first-order Born approximation is applied to treat the weak scattering between the diffractive wave and the medium. The shifted amount of spectrum is strongly dependent of the scattering angle, correlation length of the medium, and Young's pinhole parameter. Furthermore, we also observe that the red shift of the scattered spectrum converts to the blue shift when the correlation length reaches a certain magnitude. Through numerical simulations, analyses are performed on revealing the effects of Young's pinhole parameter and medium's correlation on the spectral shift and spectral switch of the scattered spectrum.

Application of third-order correlation between intensity fluctuations to determination of scattering potential of quasi-homogeneous medium.

Within the first-order Born approximation, we introduce the third-order correlation between intensity fluctuation (CIF) of light scattered from a quasi-homogeneous (QH) medium. By utilizing the Gaussian moment theorem for describing the scattering potential statistics, analytic forms are derived for the third-order, normalized CIF and variance of intensity fluctuations (VIF) of the far-zone scattered field. It is found that the normalized CIF of the scattered field is proportional to the product of Fourier transforms of the strengths of the scattering potential, while the variance of intensity fluctuations (VIF) of the scattered field is the cube of the Fourier transform of the normalized correlation coefficient (NCC) of the scattering potential. Based on the derived formulas, we show that the correlation function of the scattering potential of the medium can be determined from the scattering equations where the third-order CIF properties of the scattered field must be known in advance.

Equivalence theorem of light waves on scattering from media with different types.

The equivalence theorem of light waves on scattering from two media with different types, i.e. the continuous medium and the particulate medium, is discussed. It is shown that the normalized spectral density or the spectral degree of coherence of the scattered field may demonstrate identical distribution when certain conditions between these two media are satisfied. As an example, the scattering of light waves from a Gaussian-centered quasi-homogeneous medium and from a collection of particles with Gaussian-centered quasi-homogeneous distribution is investigated, and the condition for identical normalized spectral density and the condition for identical spectral degree of coherence of the scattered field are obtained.

Condition for far-zone spectral isotropy of light radiated from a quasi-homogeneous source scattering on a quasi-homogeneous random medium.

The far-zone spectral isotropy of light radiated from a secondary planar quasi-homogeneous (QH) source scattering on a QH medium has been discussed. Without assuming the specified function of incident light, a sufficient condition for the far-zone spectral isotropy has been expressed as a new scaling law, which is analogous with the scaling law for weak scattering in previous works. Special examples are discussed to validate the obtained scaling law.

Far-zone behaviors of light waves on scattering from anisotropic quasi-homogeneous media with semisoft boundaries.

A model of anisotropic quasi-homogeneous media with adjustable boundaries is presented with the help of the three-dimensional multi-Gaussian function. After that, the behaviors of the far-zone field of light waves on scattering from an anisotropic semisoft-boundary quasi-homogeneous medium are illustrated. It is shown that the spectral density of the scattered field is flattened-Gaussian-centered, owing to the semisoft boundary of the scatterer, while the spectral degree of coherence is Gaussian-centered, which is independent of the boundary of scatterer. It is also shown that both the spectral density and the spectral degree of coherence are anisotropic because of the anisotropy of the scattering medium.

Reciprocal relations for light from Young’s pinholes scattering upon a quasi-homogeneous medium

Within the validity of the first-order Born approximation, a group of reciprocal relations are derived for light from Young’s pinholes scattering upon a spatially quasi-homogeneous (QH) medium. It is shown that the spectral degree of coherence (SDOC) of the scattered field is proportional to the Fourier transform of the strength of the scattering potential, and the spectral density of the scattered field is proportional to the Fourier transform of the normalized correlation coefficient of the scattering potential. By considering a particular case where the correlation function of the QH medium obeys the Gaussian distribution, we obtain the far-zone spectral density and SDOC of the scattered field which satisfy the derived reciprocal relations. Compared with previous reciprocal relations for scattering, our relations additionally introduce Young’s pinhole parameter that characterizes the geometry of Young’s pinholes.

Reciprocal Relations for Third-Order Correlation Between Intensity Fluctuations of Light Scattered From a Quasi-Homogeneous Medium

Within the validity of the first-order Born approximation, we introduce the third-order correlation between intensity fluctuation (CIF) of light scattered from a quasi-homogeneous medium. The third-order CIF is defined as the degree of intensity correlations specified at three position vectors in scattered field. Expressions are derived for the normalized CIF and variance in intensity fluctuations (VIF) of the scattered field. Two reciprocal relations are generalized for the third-order CIF of the scattered field: 1) The normalized CIF is proportional to the real portion of the Fourier transform products of the strength of the scattering potential; 2) the third-order VIF of the scattered field is proportional to the cube of the Fourier transform of the normalized correlation coefficient of the scattering potential.

Intensity and coherence modulation of scattering of multi-Gaussian Schell-model beams from a quasi-homogeneous medium with adjustable boundary

We investigate the intensity and coherence modulation of the far-zone scattered field generated by scattering of multi-Gaussian Schell-model beams from a quasi-homogeneous medium with adjustable boundary. The influences of the scatterer parameters and the beam parameters on the scattered field have been illustrated in detail by numerical simulations. The results indicate that the correlation length of the medium is the key to determine whether the beam or the scatterer plays a leading role in the modulation of the scattered field. When the value of the correlation length of the medium is on the order of the wavelength, the modulation is dominated by the scatterer, while in the case of the value being much larger than the wavelength, the scatterer-led modulation is transformed into the beam-led modulation. Besides, during the transformation process there is a critical value of the correlation length of the medium for the beam to dominate the modulation, and the correlation width of the beam has an impact on the critical value.

部分空间相干光经准均匀介质的散射

部分空间相干光经准均匀介质的散射

Tunable scattering intensity with prescribed weak media.

Far-zone scattered intensity of a quasi-homogeneous medium illuminated with a plane scalar field is re-derived under the first Born approximation. Markov-like approximation is introduced to obtain a concise expression for the scattered intensity. Our work is an extension of the one in [Opt. Lett.40, 1709, (2015)] to a more general mathematical model. Our result provides a convenient way for one to steer the scattered intensity with the prescribed weak scattering media. Two examples of novel media are introduced to illustrate the result.

Correlation between intensity fluctuations induced by scattering of a partially coherent, electromagnetic wave from a quasi-homogeneous medium

Based on the first-order Born approximation, the correlation between intensity fluctuations is derived for a partially coherent, electromagnetic plane wave scattering from a spatially quasi-homogeneous medium. Young׳s pinholes are utilized to control the degree of coherence of the incident field. For the electromagnetic scattering case, it is shown that the CIF of the scattered field strongly depends on the degree of polarization of the incident wave, Young׳s pinhole parameter, effective radius and correlation length of the medium. The influences of these parameters on the CIF distributions are revealed by numerical calculations.

Scattering of an electromagnetic light wave from a quasi-homogeneous medium with semisoft boundary

Based on the first-order Born approximation, the scattering of an electromagnetic plane wave from a relatively more realistic random medium, a quasi-homogeneous medium with semisoft boundary, has been investigated. The analytic expressions for the spectral density, the spectral degree of coherence and the spectral degree of polarization have been derived, and the effects of the characteristics of the medium and the polarization of the incident light wave on the far-zone scattered field are determined. The numerical simulations indicate that, with the increasing of the edge softness M of the medium, the spectral density presents a pattern with interference fringes, and the number, position and width of interference fringes can be modified by the parameter. It is also found that there is an obvious value saltation in the coherence profile. Besides, unlike the intensity and the coherence are significantly affected by the properties of the medium, the polarization of the scattered field is irrelevant to them due to the quasi-homogeneity and isotropy of the medium, and it is only connected with the polarization of the incident light.

Determination of correlation function of scattering potential of quasi-homogeneous medium by Young׳s pinhole configuration

An approach is presented to determine the correlation function of the scattering potential of a quasi-homogeneous (QH) medium, whereby Young׳s pinholes are employed to block a monochromatic plane wave before scattering upon the medium. Given the following quantities: (i) the spectral density of the incident field; (ii) the on-axis spectral density of the scattered field if one pinhole is blocked; and (iii) the on-axis spectral density if no pinhole is blocked, the approach can be applied to obtain both the strength and the normalized correlation coefficient (NCC) of the scattering potential. Numerical results are displayed to verify the validity of the introduced approach.