Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Diffusion of Be, Co and Mn impurities in compound semiconductors and glassy carbon studied by the modified radiotracer technique

The main method of modifying properties of semiconductors is to introduce small amount of impurities inside the material. This is used to control magnetic and optical properties of materials and to realize p- and n-type semiconductors out of intrinsic material in order to manufacture fundamental components such as diodes. As diffusion can be described as random mixing of material due to thermal movement of atoms, it is essential to know the diffusion behavior of the impurities in order to manufacture working components. In modified radiotracer technique diffusion is studied using radioactive isotopes of elements as tracers. The technique is called modified as atoms are deployed inside the material by ion beam implantation. With ion implantation, a distinct distribution of impurities can be deployed inside the sample surface with good con- trol over the amount of implanted atoms. As electromagnetic radiation and other nuclear decay products emitted by radioactive materials can be easily detected, only very low amount of impurities can be used. This makes it possible to study diffusion in pure materials without essentially modifying the initial properties by doping. In this thesis a modified radiotracer technique is used to study the diffusion of beryllium in GaN, ZnO, SiGe and glassy carbon. GaN, ZnO and SiGe are of great interest to the semiconductor industry and beryllium as a small and possibly rapid dopant hasn t been studied previously using the technique. Glassy carbon has been added to demonstrate the feasibility of the technique. In addition, the diffusion of magnetic impurities, Mn and Co, has been studied in GaAs and ZnO (respectively) with spintronic applications in mind.

Heat transfer in plane Couette flow of a rarefied gas using Bhatnagar-Gross-Krook model

Using the linearized BGK model and the method of moments of half-range distribution functions the temperature jumps at two plates are determined, and it is found that the results are in fair agreement with those of Gross and Ziering, and Ziering.

Electron temperature distribution across a shock wave in a partially ionized gas

The electron temperature structure in a weakly ionized plasma is studied allowing the degree of ionization to vary across the shock wave. The values of the electron temperature and the downstream equilibrium temperature obtained with variable ionization are less than those for frozen ionization. The electron temperature rises sharply behind the shock for variable ionization while a gradual increase is predicted by frozen ionization.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Localised modes due to impurities in III–V semiconductors

Local mode frequencies due to substitutional impurities in some III–V semiconductors are calculated using Green functions on the mass defect approximation and compared with experimental results.

Lattice vibrations in alkali azides

The longwavelength lattice vibrations in potassium, rubidium and caesium azides have been calculated using Born's lattice dynamics.

Reverse bias capacitance measurements on copper-doped germanium p-n junctions in the breakdown region

Results of measurements at a high frequency on reverse bias capacitance of copper-doped germanium junctions are reported. Phenomenal increase in capacitance is found in the breakdown region, particularly at low temperatures.

Moment methods and "restricted variation" in kinetic theory

It is shown that there is a strict one-to-one correspondence between results obtained by the use of "restricted" variational principles and those obtained by a moment method of the Mott-Smith type for shock structure.

Temperature dependence of g values in tetragonal ionic Cu++ salts

A temperature dependence has been observed in the spin-Hamiltonian parameters of the Cu++ ion in a tetragonal crystal field and the variation has been interpreted in terms of vibronic effects.

Molecular model for localised modes in zincblende structures

A molecular model for substitutional defects in a zincblende lattice has been worked out. The infrared absorption due to A1 in InSb and Li in GaAs are interpreted on the basis of this model.

Strong shock with radiation near the surface of a star

The propagation of a shock wave, originating in a stellar interior, is considered when it approaches the surface of the star and assumes a self-similar character, "forgetting" its initial conditions. The flow behind the shock is assumed to be spatially isothermal rather than adiabatic to simulate the conditions of large radiative transfer near the stellar surface. The adiabatic and isothermal flows behind such a shock are compared. The exact shock-propagation laws, obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ0 ∝ xδ, and γ, the ratio of specific heats, are compared with the approximate values calculated by Whitham's characteristic rule and the two show a generally good agreement.

Negative differential conductance and effective electron mass in highly asymmetric ballistic bilayer graphene nanoribbon

We present a simplified theory of the effective momentum mass (EMM) and ballistic current–voltage relationship in a degenerate two-folded highly asymmetric bilayer graphene nanoribbon. With an increase in the gap, the density-of-states in the lower set of subbands increases more than that of the upper set. This results in a phenomenological population inversion of carriers, which is reflected through a net negative differential conductance (NDC). It is found that with the increase of the ribbon width, the NDC also increases. The population inversion also signatures negative values of EMM above a certain ribbon-width for the lower set of subbands, which increases in a step-like manner with the applied longitudinal static bias. The well-known result for symmetric conditions has been obtained as a special case.

Undamped Cooper pairs in a non-degenerate electron system

Following the reaction matrix technique and the Kanamori approximation. a condition is obtained for the occurence of undamped Cooper pairs in a non-degenerate electron system. Its relevance to induced superconductivity in systems with artificially populated (optically pumped) bands is pointed out.