Thermosolutal-Convective Instability In Stern’s Type Configuration

The thermal-convective instability of a stellar atmosphere in the presence of stable solute gradient in Stern’s type configuration is studied in the presence of radiative transfer effect. A criterion for monotonic instability is obtained in terms of the source functions S. The criterion for monotonic instability is found to be unchanged in the presence of radiative transfer and rotation effects. The problem of thermosolutal-convective instability of a hydromagnetic composite medium is also studied to include the frictional effects with neutrals. The criterion derived for monotonic instability in terms of heat-loss function is found to be the same in the presence or absence of the collisional effects.

Electromagnetic properties of a composite medium comprising chains of tunnel-coupled carbon nanotubes

When creating a model of a composite medium based on carbon nanotubes in the gigahertz and subterahertz ranges, it is necessary to take into account the tunnel coupling between nanoparticles. To simplify the consideration, we present a model of a composite medium consisting of the same randomly oriented linear chains of parallel single walled metallic carbon nanotubes connected by tunnel contacts. The problem of scattering of electromagnetic radiation by the chains was solved through the application of the integral equation technique of classical electrodynamics and the Landauer – Buttiker formalism for quantum transport. It is shown that electron tunnelling between the nanotubes leads to the electromagnetic size effects in chains of finite length. In this case, in the gigahertz frequency range, there is a regime in which the comparable in magnitude real and imaginary parts of the effective permittivity of the composite medium decrease with increasing frequency that is often observed in experiments. It has been found that size effects can manifest themselves within small sections of the chain limited by contacts of low conductivity. The obtained results provide an understanding of the physical mechanisms responsible for the frequency dispersion of the permittivity of composite materials based on carbon nanotubes.

Two-scale, non-local diffusion in homogenised heterogeneous media

We study how and to what extent the existence of non-local diffusion affects the transport of chemical species in a composite medium. For our purposes, we prescribe the mass flux to obey a two-scale, non-local constitutive law featuring derivatives of fractional order, and we employ the asymptotic homogenisation technique to obtain an overall description of the species’ evolution. As a result, the non-local effects at the micro-scale are ciphered in the effective diffusivity, while at the macro-scale the homogenised problem features an integro-differential equation of fractional type. In particular, we prove that in the limit case in which the non-local interactions are neglected, classical results of asymptotic homogenisation theory are re-obtained. Finally, we perform numerical simulations to show the impact of the fractional approach on the overall diffusion of species in a composite medium. To this end, we consider two simplified benchmark problems, and report some details of the numerical schemes based on finite element methods.

Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system

The heat conduction process in composite medium can be modeled by a parabolic equation with discontinuous radiative coefficient. To detect the composite medium characterized by such a non-smooth coefficient from measurable information about the heat distribution, we consider a nonlinear inverse problem for parabolic equation, with the average measurement of temperature field in some time interval as the inversion input. We firstly establish the uniqueness for this nonlinear inverse problem, based on the property of the direct problem and the known uniqueness result for linear inverse source problem. To solve the inverse problem from a nonlinear operator equation, the differentiability and the tangential condition of this nonlinear map is analyzed. An iterative process called two-point gradient method is proposed by minimizing data-fit term and the penalty term alternatively, with rigorous convergence analysis in terms of the tangential condition. Numerical simulations are presented to illustrate the effectiveness of the proposed method.