Abstract: We offer a new technique for research of stability of current sheaths in space plasma taking into account the effect of polarization. At the beginning, the found perturbation of the distribution function is used for calculation of the dielectric permeability tensor, which simulates inhomogeneous medium of a current sheath. Further, we in the usual manner solve the system of Maxwell's equations closed with the material equation. The amplitudes of Fourier perturbations are considered to be exponentially decaying through the current sheath thickness. The dispersion equation follows from the nontrivial solution requirement for perturbations of the electromagnetic field. The resulting dispersion equation allows one to study the temporal and spatial characteristics of instability modes of the current sheath (within the limits of the proposed model) over a wide frequency range, including low frequencies.
Abstract: Homogeneous graft copolymerization of methyl methacrylate (MMA) onto cellulose was carried out in N, N – dimethyl acetamide/LiCl (DMAc/LiCl) and dimethyl sulfoxide/ paraformaldehyde (DMSO/PF) solvent system taking ceric ammonium nitrate (CAN), benzoyl peroxide (BPO) and tin (II)-2-ethyl hexanoate [Sn(Oct)2] as initiators. Different grafting parameters like graft yield (GY), grafting efficiency (GE) and total conversion of monomer to polymer (TC) were evaluated at different reaction conditions of temperature, time, and variation of the amount of monomer and initiator. The viscosity average molecular weight of grafted PMMA and number of grafts per cellulose chain were also calculated. The products were characterized by FT-IR and 1H-NMR analyses and possible reaction mechanisms were deduced. Thermal degradation of the grafted products was also studied by thermo-gravimetric analysis (TG) and differential thermo-gravimetry (DTG).
Abstract: A filtering problem of almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain is studied. In this work general approaches to the solution of twodimensional filtering problems in ananisotropic, inhomogeneous and multilayered medium are developed, and on the basis of the obtained results mathematical models are constructed (according to Ollendorff method) for studying the certain engineering and technical problem of filtering the almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain. For some of the formulated mathematical problems with additional requirements for the structure of the porous inhomogeneous medium, namely, its isotropy, spatial periodicity of its permeability coefficient, solution algorithms are proposed. Continuation of the current work titled ”On one mathematical model for filtration of weakly compressible chemical compound in the porous heterogeneous 3D medium. Part II: Determination of the reference directions of anisotropy and permeabilities on these directions” will be prepared in the shortest terms by the authors.
Abstract: Radiofrequency (RF) lesioning of nerves have been commonly used to alleviate chronic pain, where RF current preventing transmission of pain signals through the nerve by heating the nerve causing the pain. There are some factors that affect the temperature distribution and the nerve lesion size, one of these factors is the inhomogeneities in the tissue medium. Our objective is to calculate the temperature distribution and the nerve lesion size in an inhomogeneous medium surrounding the RF electrode. A two 3-D finite element models are used to compare the temperature distribution in the homogeneous and inhomogeneous medium. Also the effect of temperature-dependent electric conductivity on maximum temperature and lesion size is observed. Results show that the presence of an inhomogeneous medium around the RF electrode has a valuable effect on the temperature distribution and lesion size. The dependency of electric conductivity on tissue temperature increased lesion size.