This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumour. The classical mixture theory is adopted for mass and momentum balance equations for a two-phase system. A main contribution of this study is we treat the physiological transport parameter (i.e., hydraulic resistivity) as anisotropic and heterogeneous, thus the governing system is strongly coupled and non-linear. We derived a weak formulation and then formulated the equivalent fixed-point problem. This enabled us to use the Galerkin method, and the classical results on monotone operators combined with the well-known Schauder and Banach fixed-point theorems to prove the existence and uniqueness of results.

Extensive studies have focused on the self-propulsion of a droplet in a viscous environment driven by the Marangoni effect in the absence of inertial effects. In order to capture the influence of inertia on the self-propulsion of a droplet, we use the singular perturbation solution for small but finite Reynolds number ($Re$) flow past a spherical droplet with inhomogeneous surface tension. We calculate the swimming speed and the corresponding flow fields generated by the droplet in an axisymmetric unbounded medium at $O(Re^2)$. The present results reveal how the choice of the stress parameter $\sigma$, which is the ratio of the first two modes of the induced stress field, distinguishes between the different swimming styles, and determines the role of inertia on the swimming speed, energy expenditure and swimming efficiency of the droplet. Inertia enhances the swimming speed and the associated swimming efficiency of the droplet by abating the energy expenditure. It is striking to observe how a droplet swimmer with $\sigma <0$ has a competitive advantage over a rigid squirmer with an equivalent surface activity due to the existence of an internal flow. We independently treat the potential influence of the viscosity ratio on the swimming properties of the droplet at finite $Re$. Additionally, using linear stability analysis, we provide insights into the stability of the estimated migration velocity at $O(Re)$. We argue that the droplet achieves a distinct stable equilibrium velocity, which occurs due to the inertial effect of the surrounding medium.

Beam-Foil spectroscopy(BFS) has proved to be a valuable technique for the determination of radiative lifetimes of excited atomic levels leading to the evaluation of the transition probabilities. The time- resolved nature of the decay process in a collisionless environment is a unique characterstic of the beam-foil light source. The relevance of BFS to astrophysics comes from the importance of radiative transition probabilities in the quantitative analysis of optical spectra. Stellar abundances are obtained from the intensity of a spectral line which essentially is a product of the abundance of the element in the source and the probability of the transition. Thus the evaluation of accurate values of transition probabilities contribute significantly to stellar abundance analysis.

Emission spectroscopic methods are very useful in determining the plasma parameters such as electron density, electron temperature, chemical abundances and energy levels of atoms and ions. A knowledge of the above mentioned parameters and collision cross sections provides an insight into various plasma processes on the Sun. As one passes from photosphere to chromosphere and corona the temperature as well as the electron density changes drastically (Te ~4500 − 2×1060K; n e ~ 108 − 1013 cm−3) (1). Hence the solar spectrum.excited by different mechanisms and different equilibrium conditions, extends from vacuum ultraviolet to visible and infrared regions. For example the spectrum in the region between 3000−1300Å is produced by the upper photosphere and lower chromosphere. In this region the temperature is in the range of 6000-10000 K. This region is characterised by several emission and absorption Lines superimposed over continuum. Below 1600Å consists of emissions from highly ionised atomic species originating from chromosphere and corona (2).A correct interpretation of the spectral features is possible only after understanding the influence of various factors on spectral line shapes and intensities. They are 1) damping by collisions with neutral atoms; 2) collisions by charged particles leading to linear and quadratic Stark effects on atomic lines of hydrogen and helium; 3)thermal Doppler broadening 4) Doppler broadening or shift due to microturbulent velocity field.