Сотсков А.И. «Математическая модель нелинейных процессов в больших артериях» Нелинейный мир, 12, № 8, с. 10-15 (2014)

Представлены аналитические решения системы уравнений типа Коши–Ковалевской, структура которых описывает основные типы нелинейных процессов гемодинамики больших артерий. Показано доминирующее влияние эластичной реакции стенки и конвективного слагаемого, влияние которых было выявлено в отдельных самостоятельных исследованиях.

Мкртчян А.Г., Мкртчян А.Р., Багдасарян А.С., Сарьян В.К., Котанджян Х.В., Асланян А.А., Мурадян О.Р., Миракян С.А. «Накопление акустических волн при распространении в слоистых средах» Нелинейный мир, 12, № 8, с. 16-21 (2014)

Сделана попытка теоретически обосновать возможность накопления акустических волн при их распространении в многослойной среде. Матричным методом решена задача трехмерного распространения акустических волн в слоистых средах. Показано, что при присутствии неоднородностей определенной формы с определенными граничными условиями в многослойной среде можно наблюдать явление накопления акустических волн. Paper is devoted to theoretical investigation of the propagation and definition of the possibility of the accumulation of the acoustic wave in the stratified medium. During the propagation through the medium the acoustic waves were affected by the medium properties, so in this aspect it is necessary to investigate the properties of medium. Particularly, if the medium is stratified and have certain inhomogeneities of specific forms then it is necessary to define the conditions, when the phenomenon of the accumulation and scattering of acoustic waves can be observed. Basically, generated acoustic vibrations from the excitation center propagate spherically. During the registration of acoustic vibrations at far from excitation centers locations mainly weak low frequency waves with large frontal line versus horizontal sizes of the stratified medium are registered. From the mathematical point of view this lead to approximation, while can be considered that the lower bound of the stratified structure performs identical motion along the whole line with certain time function and for description of the acoustic linearize equation, i.e. wave equation can be used. To solve the problem of three dimension propagation of the acoustic waves in the stratified medium the system from n homogeneous isotope elastic layer with plane parallel boundaries and with own Lame coefficients, density and thickness is examined. During the solution the matrix method is utilized, which allows to satisfy the boundary conditions with comparatively simple method. Deducing some assumption and mathematical conversion the problem of determination of acoustic field in plane-parallel stratified medium is reduced to calculation of matrix system from n⁶ algebraic equation with (n+1)⁶ unknowns and is solved for any 6 defined values from the set of amplitudes. The case when the upper layer is liquid and differs from the elastic medium, as the transverse wave can be propagated in it, is examined. For the case when the surface of the liquid layer has specific geometrical shape the matrix equations system is obtained. The analysis of calculation of the obtained matrix equation system for the cases of absence and presence of inhomogeneities of water reservoir form in upper layer of multilayer medium shows that the accumulation of the acoustic energy in the water reservoir can be obtained if the coefficients of absorption of layers is minimal and the layers are arranged in a way when the velocities of propagated acoustic wave in them decreases to the free boundary. At these conditions the wave propagation time in upper layer is greater than in forgoing layers, which is leading to acoustic energy accumulation. In other cases the amplitudes excited in the upper layer of acoustic vibration is significantly small. Cases were examined when accumulation of acoustic energy had been theoretically observed. Thereby, theoretically is predicted the ability of acoustic energy accumulation in multilayer medium with specific inhomogeneities.