Half-space albedo problem for the Anlı-Güngör scattering function

One speed, time-independent and homogeneous medium neutron transport equation is solved for second order scattering using the Anlı-Güngör scattering function which is a recently investigated scattering function. The scattering function depends on Legendre polynomials and the t parameter which is defined on the interval [−1, 1]. A half-space albedo problem is examined with the FN method and the recently developed SVD method. Albedo values are calculated with two methods and tabulated. Thus, the albedo values for the Anlı-Güngör scattering are compared with these methods. The behaviour of the scattering function is similar to İnönü’s scattering function according to calculated results.

Reaction Monitoring by Ultrasounds in a Pseudohomogeneous Medium: Triglyceride Ethanolysis for Biodiesel Production

The sound propagation speed measurement us is used for monitoring triglyceride ethanolysis in a broad range of reaction conditions (mainly, temperature: 23–50 °C; ethanol/oil: from 6 to 24 mol/mol). Experimentally, us slightly increased with the reaction time in all cases as a result of the contribution of its dynamic mixture components. Nomoto’s expression for homogeneous mixtures offered suitable us estimation but with values notably higher than the experimental ones due to the resistance to sound propagation offered by the ethanol/oil interphase (non-homogeneous medium). Our strategy was based on both the comparison of the experimental us values and the theoretical ones correlated by means of triglyceride conversion and on the estimation of the sound speed of oil/ethanol that could emulate the resistance offered by the interphase. The evolution of the reactions was predicted quite well for all the experiments carried out with very different reaction rates. Nevertheless, at the beginning of the reaction, the estimated conversion (outside of industrial interests) showed important deviations. The presence of the intermediate reaction products, diglycerides, and monoglycerides could be responsible for those deviations.

Atomic force microscopy in the assessment of erythrocyte membrane mechanical properties with exposure to various physicochemical agents

Background: Mechanical properties of cell membranes and their structural organization are considered among the most important biological parameters affecting the functional state of the cell. Under the influence of various pathogenic factors, erythrocyte membranes lose their elasticity. The resulting changes in their biomechanical characteristics is an important, but poorly studied topic. It is of interest to study the deformation of native erythrocytes to a depth compatible with their deformation in the bloodstream.Aim: To investigate the patterns of deep deformation and the particulars of structural organization of native erythrocyte membranes before and after their exposure to physicochemical agents in vitro.Materials and methods: Cell morphology, nanostructure characteristics, and membrane deformation of native erythrocytes in a solution of hemoconservative CPD/SAGM were studied with atomic force microscope NTEGRA Prima. Hemin, zinc ions (Zn2+), and ultraviolet (UV) radiation were used as modifiers. To characterize the membrane stiffness, we measured the force curves F(h), hHz (the depth to which the probe immersion is described by interaction with a homogeneous medium), and the Young's modulus values of the erythrocyte membrane.Results: Exposure to hemin, Zn2+ and UV radiation led to transformation of the cell shape, appearance of topological defects and changes in mechanical characteristics of erythrocyte membranes. Under exposure to hemin, Young's modulus increased from 10±4 kPa to 27.2±8.6 kPa (p<0.001), exposure to Zn2+, to 21.4±8.7 kPa (p=0.002), and UV, to 18.8±5.6 kPa (p=0.001). The hHz value was 815±210 nm for the control image and decreased under exposure to hemin to 420±80 nm (p<0.001), Zn2+, to 370±90 nm (p<0.001), and UV, to 614±120 nm (p=0.001).Conclusion: The results obtained contribute to a deeper understanding of interaction between membrane surfaces of native erythrocytes and small vessel walls. They can be useful in clinical medicine as additional characteristics for assessment of the quality of packed red blood cells, as well as serve as a basis for biophysical studies into the mechanisms of action of oxidative processes of various origins.

Scattering of anti-plane waves by scalene trapezoidal boundary with embedded cavity in anisotropic material based on mapping space

Both surface motion and hole stress concentration have always been concerned in anisotropic medium. In this paper, a theoretical approach is used to study the scattering problem of circular holes under a scalene trapezoid on the surface. The mapping function that anisotropic medium to homogeneous medium is established, and the relationship between the free boundary of anisotropic medium and the mapping of homogeneous medium boundary is proved. In the space of homogeneous medium mapping, the wave displacement function is obtained by solving the equation of motion that meets the zero-stress boundary conditions by separating the variable method and the symmetric method. Based on the complex function, multi-polar coordinate method and region-matching technique, algebraic equations are established at auxiliary boundary and free boundary conditions in complex domain. Then according to sample statistics, least square method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary. Numerical results shows that the continuity of the auxiliary boundary and the accuracy of the zero-stress boundary are nice, and the displacement of the free surface and the stress of the circular hole are related to the parameters of material medium, the position of the circular hole, the direction of the incident wave and the frequency content of the excitation. Finally the process of the wave propagation and scattering around trapezoid and shallow circle are shown in time domain through the inverse fourier transform.

Simulation of wave propagation using graph-theoretical algorithm

We simulate the wave propagation through various mediums using a graph-theoretical path-finding algorithm. The mediums are discretized to the square lattices, where each node is connected up to its 4th nearest neighbours. The edge connecting any 2 nodes is weighted by the time of flight of the wave between the nodes, which is calculated from the Euclidean distance between the nodes divided by the average velocity at the positions of those nodes. According to Fermat’s principle of least time, wave propagation between 2 nodes will follow the path with minimal weight. We thus use the path-finding algorithm to find such a path. We apply our method to simulate wave propagation from a point source through a homogeneous medium. By defining a wavefront as a contour of nodes with the same time of flight, we obtain a spherical wave as expected. We next investigate the wave propagation through a boundary of 2 mediums with different wave velocities. The result shows wave refraction that exactly follows Snell’s law. Finally, we apply the algorithm to determine the velocity model in a wood sample, where the wave velocity is determined by the angle between the propagation direction and the radial direction from its pith. By comparing the time of flight from our simulation with the measurements, the parameters in the velocity model can be obtained. The advantage of our method is its simplicity and straightforwardness. In all the above simulations, the same simple path-finding code is used, regardless of the complexity of the wave velocity model of the mediums. We expect that our method can be useful in practice when an investigation of wave propagation in a complex medium is needed.

Experimental study of radiative transfer in semi-transparent composite materials at different temperatures

This study deals with the analysis of the propagation of radiation within a diffusing semi-transparent composite medium with rough boundaries. The two-phase medium (resin matrix and glass fibers reinforcement) is treated as an equivalent homogeneous medium characterized by volumetric radiative properties (extinction coefficient, albedo and phase function) and boundary scattering properties. The aim is to identify the radiative properties at different temperatures ranging from room temperature to 200°C. The identification method (Gauss-Newton) uses bidirectional reflectance and transmittance values. The experimental results are obtained using a spectrophotometer equipped with a goniometer and a heated sample holder. The Monte Carlo method is used to solve the Radiative Transfer Equation (RTE) in order to obtain the theoretical values.

Ultrasonic Total Focusing Imaging Method of Multilayer Composite Structures Using the Root-Mean-Square (RMS) Velocity

Multilayer composite structures have been widely used in industrial manufacturing, and nondestructive testing of these multilayer structures is to ensure their reliable quality and performance. Currently, ultrasonic total focusing method (TFM) imaging using full-matrix capture (FMC) technology has been proven to sense small defects in a single homogeneous medium and improve the imaging signal-to-noise ratio. However, these algorithms cannot be accurately applied to imaging of multilayer composite structures, due to the acoustic impedance variation and because reflection and refraction occur at the interface between the layers, which makes it very difficult to calculate the ultrasonic propagation path and time. To solve this problem, a root-mean-square (RMS) velocity algorithm for total focusing imaging of multilayer structures is proposed in the article. Based on the theory of RMS velocity for processing of seismic data, the approximated delays can be easily and quickly calculated by a hyperbolic time-distance relationship under circumstances of short lateral distance and horizontal layers. The performance of the proposed algorithm is evaluated by total focusing imaging of a two-layer medium with drilled holes and conducted by the finite element simulation. To further improve imaging efficiency, the partial data in the full-matrix data were used for imaging which is the simplified matrix focusing method (SFM). The results verify that the proposed methods are capable of total focusing imaging of two-layered structures. However, the imaging performance and efficiency of these algorithms are different.

ρ-Libration point in the three body problem

Herein, the restricted circular three-body problem in homogeneous and inhomogeneous media is considered. Particular attention is paid to libration points. The conditions of their existence or non-existence in the Newtonian and post-Newtonian approximations of the general theory of relativity are derived. Several regularities, new Newtonian and relativistic effects arising due to the impact of the additional relativistic forces on bodies of gravitational fields of mediums in the differential equations of the motion of bodies are indicated. Using the previously derived equations of the motion of two bodies A1, A2 in the medium, the authors substantiated the following statements. In a homogeneous medium (density of the medium ρ = const) in the Newtonian approximation of the general theory of relativity there are ρ-libration points , 1,...,5, moving along the same circles as the Euler and Lagrangian libration points Li but with an angular velocity 0 , greater than the angular velocity ω0 of libration points Li in a vacuum. Bodies A1, A2 also move along their circles with an angular velocity 0 > w When passing from the Newtonian approximation of the general theory of relativity to the post-Newtonian approximation of the general theory of relativity, the centre of mass of two bodies, resting in a homogeneous medium in the Newtonian approximation of the general theory of relativity, must move along a cycloid. The trajectories of the bodies can not be circles, the libration points Li disappear. In the case of an inhomogeneous medium distributed, for example, spherically symmetrically, the centre of mass of two bodies, already in the Newtonian approximation of the general theory of relativity, must move along the cycloid, despite it was at rest in the void. Therefore, bodies A1, A2 must describe loops that form, figuratively speaking, a «lace», as in the case of a homogeneous medium in the post-Newtonian approximation of the general theory of relativity. The figure illustrating the situation is provided. Due to the existence of the «lace» effect, the libration point Li movements are destroyed. In the special case, when the masses of bodies A1, A2 are equal (m1 = m2), the cycloids disappear and all the ρ-libration points exist in homogeneous and inhomogeneous media in the Newtonian and post-Newtonian approximations of the general theory of relativity. Numerical estimates of the predicted patterns and effects in the Solar and other planetary systems, interstellar and intergalactic mediums are carried out. For example, displacements associated with these effects, such as the displacement of the centre of mass, can reach many billions of kilometres per revolution of the two-body system. The possible role of these regularities and effects in the theories of the evolution of planetary systems, galaxies, and their ensembles is discussed. A brief review of the studies carried out by the Belarusian scientific school on the problem of the motion of bodies in media in the general theory of relativity is given.

THERMAL STRESSES FOR FUNCTIONALLY GRADED MATERIALS (FGMS) SUBJECT TO HEAT FLUX

In this paper, the thermal stress due to heat flux at the far field is derived for an infinitely extended elastic medium which contains a spherical inclusion made of functionally graded materials (FGMs). The 3-D heat conduction equation subject to uniform heat flux at the far field is solved analytically to derive the temperature distribution. Based on the temperature solution, the thermal stress field due to heat flux is obtained by solving a set of two ordinary differential equations using the method of weighted residuals. Unlike the two-phase homogeneous medium, the von Mises stress distribution is continuous at the interface of the FGM-matrix medium.