The Photoemission from Quantum Wells, Wires and Carbon Nanotubes:Simplified Theory and Relative Comparison

We investigate the photoemission from quantum wells (QWs) in ultrathin films (UFs) and quantum well wires (QWWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined Ill-V compounds form the special cases of our generalized analysis. The photoemission has also been studied for quantum confined II-VI, n-GaP, n-Ge, PtSb2, stressed materials and Bismuth on the basis of respective dispersion relations. It has been found taking quantum confined CdGeAS(2), InAs, InSb, CdS, GaP, Ge, PtSb2, stressed n-InSb and B1 that the photoemission exhibits quantized variations with the incident photon energy, changing electron concentration and film thickness, respectively, for all types of quantum confinement. The photoemission from CNs exhibits oscillatory dependence with increasing normalized electron degeneracy and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of photoemission from non-degenerate semiconductors and parabolic energy bands, leading to the compatibility test.

Optical Studies of the Antarctic Glacio-Oceanic System

The Antarctic system comprises of the continent itself, Antarctica, and the ocean surrounding it, the Southern Ocean. The system has an important part in the global climate due to its size, its high latitude location and the negative radiation balance of its large ice sheets. Antarctica has also been in focus for several decades due to increased ultraviolet (UV) levels caused by stratospheric ozone depletion, and the disintegration of its ice shelves. In this study, measurements were made during three Austral summers to study the optical properties of the Antarctic system and to produce radiation information for additional modeling studies. These are related to specific phenomena found in the system. During the summer of 1997-1998, measurements of beam absorption and beam attenuation coefficients, and downwelling and upwelling irradiance were made in the Southern Ocean along a S-N transect at 6°E. The attenuation of photosynthetically active radiation (PAR) was calculated and used together with hydrographic measurements to judge whether the phytoplankton in the investigated areas of the Southern Ocean are light limited. By using the Kirk formula the diffuse attenuation coefficient was linked to the absorption and scattering coefficients. The diffuse attenuation coefficients (Kpar) for PAR were found to vary between 0.03 and 0.09 1/m. Using the values for KPAR and the definition of the Sverdrup critical depth, the studied Southern Ocean plankton systems were found not to be light limited. Variabilities in the spectral and total albedo of snow were studied in the Queen Maud Land region of Antarctica during the summers of 1999-2000 and 2000-2001. The measurement areas were the vicinity of the South African Antarctic research station SANAE 4, and a traverse near the Finnish Antarctic research station Aboa. The midday mean total albedos for snow were between 0.83, for clear skies, and 0.86, for overcast skies, at Aboa and between 0.81 and 0.83 for SANAE 4. The mean spectral albedo levels at Aboa and SANAE 4 were very close to each other. The variations in the spectral albedos were due more to differences in ambient conditions than variations in snow properties. A Monte-Carlo model was developed to study the spectral albedo and to develop a novel nondestructive method to measure the diffuse attenuation coefficient of snow. The method was based on the decay of upwelling radiation moving horizontally away from a source of downwelling light. This was assumed to have a relation to the diffuse attenuation coefficient. In the model, the attenuation coefficient obtained from the upwelling irradiance was higher than that obtained using vertical profiles of downwelling irradiance. The model results were compared to field measurements made on dry snow in Finnish Lapland and they correlated reasonably well. Low-elevation (below 1000 m) blue-ice areas may experience substantial melt-freeze cycles due to absorbed solar radiation and the small heat conductivity in the ice. A two-dimensional (x-z) model has been developed to simulate the formation and water circulation in the subsurface ponds. The model results show that for a physically reasonable parameter set the formation of liquid water within the ice can be reproduced. The results however are sensitive to the chosen parameter values, and their exact values are not well known. Vertical convection and a weak overturning circulation is generated stratifying the fluid and transporting warmer water downward, thereby causing additional melting at the base of the pond. In a 50-year integration, a global warming scenario mimicked by a decadal scale increase of 3 degrees per 100 years in air temperature, leads to a general increase in subsurface water volume. The ice did not disintegrate due to the air temperature increase after the 50 year integration.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.

Smoldering combustion of "incense" sticks - Experiments and modeling

This paper is concerned with the experimental and modeling studies on the smoldering rates of incense sticks as a function of ambient oxygen fraction in air, the flow velocity and size. The experimental results are obtained both for forward and reverse smolder conditions. The results are explained on the basis of surface combustion due to diffusion of oxygen to the surface by both free and forced convection supporting the heat transfer into the solid by conduction, into the stream by convection and the radiant heat transfer from the surface. The heat release at the surface is controlled by the convective transport of the oxidizer to the surface. To obtain the diffusion rates particularly for the reverse smolder, CFD calculations of fluid flow with along with a passive scalar are needed; these calculations have been made both for forward and reverse smolder. The interesting aspect of the CFD calculations is that while the Nusselt umber for forward smolder shows a clear root( Re-u) dependence ( Re-u = Flow Reynolds Number), the result for reverse smolder shows a peak in the variation with Reynolds number with the values lower than for forward smolder and unsteadiness in the flow beyond a certain flow rate. The results of flow behavior and Nusselt number are used in a simple model for the heat transfer at the smoldering surface to obtain the dependence of the smoldering rate on the diameter of the incense stick, the flow rate of air and the oxygen fraction. The results are presented in terms of a correlation for the non-dimensional smoldering rate with radiant flux from the surface and heat generation rate at the surface. The correlations appear reasonable for both forward and reverse smolder cases.

Open and closed boundaries in large-scale convective dynamos

Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. To test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation level of large-scale dynamos. Open (vertical field) and closed (perfect conductor) boundary conditions are used for the magnetic field. The contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate in this regime increases proportional to Rm^(1/2). In the nonlinear regime, the saturation level of the energy of the mean magnetic field is independent of Rm when open boundaries are used. In the case of perfect conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm^(-1) for Rm > 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

The buoyant plume above a heat source

The boundary-layer type conservation equations of mass, momentum and energy for the steady free turbulent flow in gravitational convection over heat sources are set up for both two-dimensional and axisymmetric cases. These are reduced to ordinary differential equations in a similarity parameter by suitable transformations. The three classical hypotheses of turbulent diffusion-the Constant Exchange Coefficient hypothesis, Prandtl's Momentum Transfer theory and Taylor's Vorticity Transfer theory-are then incorporated into these equations in succession. The resulting equations are solved numerically and the results compared with some experimental results on gravitational convection over heat sources reported by Rouse et al.

Quantum theoretic explanation of the Schwarz-Hora effect

Following the path-integral approach we show that the Schwarz-Hora effect is a one-electron quantum-mechanical phenomenon in that the de Broglie wave associated with a single electron is modulated by the oscillating electric field. The treatment brings out the crucial role played by the crystal in providing a discontinuity in the longitudinal component of the electric field. The expression derived for the resulting current density shows the appropriate oscillatory behaviour in time and distance. The possibility of there being a temporal counterpart of Aharonov-Bohm effect is briefly discussed in this context.

Phase change on transmission of microwaves through metal disc delay dielectrics

Expressions for the phase change Φ suffered by microwaves when transmitted through an artificial dielectric composed of metallic discs arranged in a three-dimensional array have been derived with different approaches as follows (i) molecular theory, (ii) electromagnetic theory and (iii) transmission line theory. The phase change depends on the distance t that the wave traverses inside the dielectric and also the spacing d between centre to centre of any two adjacent discs in the three principal directions. Molecular theory indicates Φ as an increasing function of t, whereas, the other two theories indicate Φ as an oscillatory function of t. The transmission line theory also exhibits Φ to be real or imaginary depending on t. Experimental values of Φ as a function of t have been obtained with the help of a microwave (3·2 cms wavelength) interferometer for two dielectrics having d as 1·91 cms and 2·22 cms respectively.

Large-scale structures in turbulent and reverse-transitional sink flow boundary layers

Aspects of large-scale organized structures in sink flow turbulent and reverse-transitional boundary layers are studied experimentally using hot-wire anemometry. Each of the present sink flow boundary layers is in a state of 'perfect equilibrium' or 'exact self-preservation' in the sense of Townsend (The Structure of Turbulent Shear Flow, 1st and 2nd edns, 1956, 1976, Cambridge University Press) and Rotta (Progr. Aeronaut. Sci., vol. 2, 1962, pp. 1-220) and conforms to the notion of 'pure wall-flow' (Coles, J. Aerosp. Sci., vol. 24, 1957, pp. 495-506), at least for the turbulent cases. It is found that the characteristic inclination angle of the structure undergoes a systematic decrease with the increase in strength of the streamwise favourable pressure gradient. Detectable wall-normal extent of the structure is found to be typically half of the boundary layer thickness. Streamwise extent of the structure shows marked increase as the favourable pressure gradient is made progressively severe. Proposals for the typical eddy forms in sink flow turbulent and reverse-transitional flows are presented, and the possibility of structural self-organization (i.e. individual hairpin vortices forming streamwise coherent hairpin packets) in these flows is also discussed. It is further indicated that these structural ideas may be used to explain, from a structural viewpoint, the phenomenon of soft relaminarization or reverse transition of turbulent boundary layers when subjected to strong streamwise favourable pressure gradients. Taylor's 'frozen turbulence' hypothesis is experimentally shown to be valid for flows in the present study even though large streamwise accelerations are involved, the flow being even reverse transitional in some cases. Possible conditions, which are required to be satisfied for the safe use of Taylor's hypothesis in pressure-gradient-driven flows, are also outlined. Measured convection velocities are found to be fairly close to the local mean velocities (typically 90% or more) suggesting that the structure gets convected downstream almost along with the mean flow.

An Integrated Design Procedure for High Frequency AC Inductors for Inverters

Inductors are important energy storage elements that are used as filters in switching power converters. The operating efficiency of power inductors depend on the initial design choices and they remain as one of the most inefficient elements in a power converter. The focus of this paper is to explore the inductor design procedure from the point of efficiency and operating temperature. A modified form of the area product approach is used as starting point for the inductor design. The equations which estimate the power loss in core and copper winding are described. The surface temperature of the inductor is modelled using heat transfer equations for radiation and natural convection. All design assumptions are verified by actual experimental data and results show a good match with the analysis.

Robust/optimal temperature profile control using neural networks

An approximate dynamic programming (ADP) based neurocontroller is developed for a heat transfer application. Heat transfer problem for a fin in a car's electronic module is modeled as a nonlinear distributed parameter (infinite-dimensional) system by taking into account heat loss and generation due to conduction, convection and radiation. A low-order, finite-dimensional lumped parameter model for this problem is obtained by using Galerkin projection and basis functions designed through the 'Proper Orthogonal Decomposition' technique (POD) and the 'snap-shot' solutions. A suboptimal neurocontroller is obtained with a single-network-adaptive-critic (SNAC). Further contribution of this paper is to develop an online robust controller to account for unmodeled dynamics and parametric uncertainties. A weight update rule is presented that guarantees boundedness of the weights and eliminates the need for persistence of excitation (PE) condition to be satisfied. Since, the ADP and neural network based controllers are of fairly general structure, they appear to have the potential to be controller synthesis tools for nonlinear distributed parameter systems especially where it is difficult to obtain an accurate model.

Magnetotransport of Dirac fermions on the surface of a topological insulator

We study the properties of Dirac fermions on the surface of a topological insulator in the presence of crossed electric and magnetic fields. We provide an exact solution to this problem and demonstrate that, in contrast to their counterparts in graphene, these Dirac fermions allow relative tuning of the orbital and Zeeman effects of an applied magnetic field by a crossed electric field along the surface. We also elaborate and extend our earlier results on normal-metal-magnetic film-normal metal (NMN) and normal-metal-barrier-magnetic film (NBM) junctions of topological insulators [S. Mondal, D. Sen, K. Sengupta, and R. Shankar, Phys. Rev. Lett. 104, 046403 (2010)]. For NMN junctions, we show that for Dirac fermions with Fermi velocity vF, the transport can be controlled using the exchange field J of a ferromagnetic film over a region of width d. The conductance of such a junction changes from oscillatory to a monotonically decreasing function of d beyond a critical J which leads to the possible realization of magnetic switches using these junctions. For NBM junctions with a potential barrier of width d and potential V-0, we find that beyond a critical J, the criteria of conductance maxima changes from chi=eV(0)d/h upsilon(F)=n pi to chi=(n+1/2)pi for integer n. Finally, we compute the subgap tunneling conductance of a normal-metal-magnetic film-superconductor junctions on the surface of a topological insulator and show that the position of the peaks of the zero-bias tunneling conductance can be tuned using the magnetization of the ferromagnetic film. We point out that these phenomena have no analogs in either conventional two-dimensional materials or Dirac electrons in graphene and suggest experiments to test our theory.

Exact solution for the unsteady flow and heat transfer between eccentrically rotating disks

The unsteady heat transfer associated with flow due to eccentrically rotating disks considered by Ramachandra Rao and Kasiviswanathan (1987) is studied via reformulation in terms of cylindrical polar coordinates. The corresponding exact solution of the energy equation is presented when the upper and lower disks are subjected to steady and unsteady temperatures. For an unsteady flow with nonzero mean, the energy equation can be solved by prescribing the temperature on the disk as a sum of steady and oscillatory parts

Influence of crossed electric and quantizing magnetic fields on the Einstein relation in nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) under crossed fields' configuration in nonlinear optical materials on the basis of a newly formulated electron dispersion law by incorporating the crystal field in the Hamiltonian and including the anisotropies of the effective electron mass and the spin-orbit splitting constants within the framework of kp formalisms. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for II-VI and stressed materials on the basis of various appropriate dispersion relations. We have considered n-CdGeAs2, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, p-CdS and stressed n-InSb materials as examples. The DMR also increases with increasing electric field and the natures of oscillations are totally band structure dependent with different numerical values. It has been observed that the DMR exhibits oscillatory dependences with inverse quantizing magnetic field and carrier degeneracy due to the Subhnikov-de Haas effect. An experimental method of determining the DMR for degenerate materials in the present case has been suggested. (C) 2010 Elsevier B.V. All rights reserved.

Generalized Burgers equations and Euler–Painlevé transcendents. III

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1oscillatory behavior either at η=+∞ or at η=−∞, or at η=+∞ and η=−∞. For β=βn, there exists a single parameter family of exact single hump solutions, similar to those found for the nonplanar Burgers equations in Paper II. Thus the parametric value β=βn seems to bifurcate the families of solutions, which remain bounded at η=±∞. Other GBE’s considered here are also found to be reducible to Euler–Painlevé equations.