ZnO nanorods for efficient third harmonic UV generation.

ZnO nanorods grown by both high temperature vapour phase transport and low temperature chemical bath deposition are very promising sources for UV third harmonic generation. Material grown by both methods show comparable efficiencies, in both cases an order of magnitude higher than surface third harmonic generation at the quartz-air interface of a bare quartz substrate. This result is in stark contrast to the linear optical properties of ZnO nanorods grown by these two methods, which show vastly different PL efficiencies. The third harmonic generated signal is analysed using intensity dependent measurements and interferometric frequency resolved optical gating, allowing extraction of the laser pulse parameters. The comparable levels of efficiency of ZnO grown by these very different methods as sources for third harmonic UV generation provides a broad suite of possible growth methods to suit various substrates, coverage and scalability requirements. Potential application areas range from interferometric frequency resolved optical gating characterization of few cycle fs pulses to single cell UV irradiation for biophysical studies.

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.

Photic driving in the electroencephalogram of children and adolescents: harmonic structure and relation to the resting state

In order to identify latent bioelectrical oscillators, 15 normal subjects (aged 9-17 years, 8 males, 7 females) were subjected to intermittent photic stimulation. The EEG amplitude spectra corresponding to the 11 fixed frequencies of stimulation presented (3-24 Hz) were combined to form "profiles" of the driving reaction in the right occipital area. The driving response varied with frequency, and was demonstrable in 70-100% of cases (using as criterion peak amplitudes 20% larger than those of the neighbors). The strongest responses were observed at the frequency closest to the alpha peak of the resting EEG. A secondary profile maximum was in the theta band. In 10 subjects, this maximum exceeded half the alpha peak (with an average of 72.4% of the alpha peak), while in the resting spectra, theta amplitudes were much lower than the alpha maxima. This responsiveness in theta activity seems to be characteristic of prepubertal and pubertal subjects. The profiles and resting EEG spectra showed a highly significant Pearson's correlation, with the peak in the theta band of the profiles being the main difference observed between them. The correlation coefficient was significantly correlated with the ratio of the maxima in the theta and alpha bands (R = -0.77, P<0.001). The correlation coefficient between profile and resting spectrum may be a useful indicator in screening methods used to reveal latent cerebral oscillators. Profiles for the second and third harmonics were correlated with those of the first harmonic (fundamental frequency), when considering the corresponding EEG frequencies. Peak frequencies in all three profiles were close to those of the individual's background alpha rhythm, and peak amplitudes in higher harmonics were not much lower than those of the fundamental frequency (mean values of 84 and 63%, for second and third harmonics, respectively).

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

Studies on some nonlinear optical phenomena-optical phase conjugation and continuous wave second harmonic generation

Nonlinear optics has emerged as a new area of physics , following the development of various types of lasers. A number of advancements , both theoretical and experimental . have been made in the past two decades . by scientists al1 over the world. However , onl y few scientists have attempted to study the experimental aspects of nonlinear optical phenomena i n I ndian laboratories. This thesis is the report of an attempt made in this direction. The thesis contains the details of the several investigations which the author has carried out in the past few years, on optical phase conjugation (OPC) and continuous wave CCVD second harmonic generation CSHG). OPC is a new branch of nonlinear optics, developed only in the past decade. The author has done a few experiments on low power OPC in dye molecules held in solid matrices, by making use of a degenerate four wave mixing CDFWND scheme. These samples have been characterised by studies on their absorption-spectra. fluorescence spectra. triplet lifetimes and saturation intensities. Phase conjugation efficiencies with r espect to the various parameters have been i nvesti gated . DFWM scheme was also employed i n achievi ng phase conjugation of a br oadband laser C Nd: G1ass 3 using a dye solution as the nonlinear medium.

Compact CPW-Fed Slot Antenna with Harmonic Suppression

A compact coplanar waveguide (CPW)-fed uniplanar antenna with harmonic suppression characteristics is presented. The above characteristics are achieved by properly modifying the ground plane and adjusting the signal strip of an open-ended CPW-fed transmission line. The simulated and experimental characteristics of the antenna are presented, compared, and discussed.

FEM based Virtual Prototyping and Design of Third Harmonic Excitation System for Low Voltage Brushless Alternators

Salient pole brushless alternators coupled to IC engines are extensively used as stand-by power supply units for meeting in- dustrial power demands. Design of such generators demands high power to weight ratio, high e ciency and low cost per KVA out- put. Moreover, the performance characteristics of such machines like voltage regulation and short circuit ratio (SCR) are critical when these machines are put into parallel operation and alterna- tors for critical applications like defence and aerospace demand very low harmonic content in the output voltage. While designing such alternators, accurate prediction of machine characteristics, including total harmonic distortion (THD) is essential to mini- mize development cost and time. Total harmonic distortion in the output voltage of alternators should be as low as possible especially when powering very sophis- ticated and critical applications. The output voltage waveform of a practical AC generator is replica of the space distribution of the ux density in the air gap and several factors such as shape of the rotor pole face, core saturation, slotting and style of coil disposition make the realization of a sinusoidal air gap ux wave impossible. These ux harmonics introduce undesirable e ects on the alternator performance like high neutral current due to triplen harmonics, voltage distortion, noise, vibration, excessive heating and also extra losses resulting in poor e ciency, which in turn necessitate de-rating of the machine especially when connected to non-linear loads. As an important control unit of brushless alternator, the excitation system and its dynamic performance has a direct impact on alternator's stability and reliability. The thesis explores design and implementation of an excitation i system utilizing third harmonic ux in the air gap of brushless al- ternators, using an additional auxiliary winding, wound for 1=3rd pole pitch, embedded into the stator slots and electrically iso- lated from the main winding. In the third harmonic excitation system, the combined e ect of two auxiliary windings, one with 2=3rd pitch and another third harmonic winding with 1=3rd pitch, are used to ensure good voltage regulation without an electronic automatic voltage regulator (AVR) and also reduces the total harmonic content in the output voltage, cost e ectively. The design of the third harmonic winding by analytic methods demands accurate calculation of third harmonic ux density in the air gap of the machine. However, precise estimation of the amplitude of third harmonic ux in the air gap of a machine by conventional design procedures is di cult due to complex geome- try of the machine and non-linear characteristics of the magnetic materials. As such, prediction of the eld parameters by conven- tional design methods is unreliable and hence virtual prototyping of the machine is done to enable accurate design of the third har- monic excitation system. In the design and development cycle of electrical machines, it is recognized that the use of analytical and experimental methods followed by expensive and in exible prototyping is time consum- ing and no longer cost e ective. Due to advancements in com- putational capabilities over recent years, nite element method (FEM) based virtual prototyping has become an attractive al- ternative to well established semi-analytical and empirical design methods as well as to the still popular trial and error approach followed by the costly and time consuming prototyping. Hence, by virtually prototyping the alternator using FEM, the important performance characteristics of the machine are predicted. Design of third harmonic excitation system is done with the help of results obtained from virtual prototype of the machine. Third harmonic excitation (THE) system is implemented in a 45 KVA ii experimental machine and experiments are conducted to validate the simulation results. Simulation and experimental results show that by utilizing third harmonic ux in the air gap of the ma- chine for excitation purposes during loaded conditions, triplen harmonic content in the output phase voltage is signi cantly re- duced. The prototype machine with third harmonic excitation system designed and developed based on FEM analysis proved to be economical due to its simplicity and has the added advan- tage of reduced harmonics in the output phase voltage.

Effect of dressing on high-order harmonic generation in vibrating H2 molecules

Wir entwickeln die Starkfeldnäherung für die Erzeugung hoher Harmonischer in Wasserstoffmolekülen, wobei die Vibrationsbewegung berücksichtigt wird, sowie die laserinduzierte Kopplung zwischen den beiden untersten Born-Oppenheimer-Zuständen im Molekülion, das durch die anfängliche Ionisation des Moleküls erzeugt wird. Wir zeigen, dass die Kopplung bei längeren Laserwellenlängen (≈ 2 μm) wichtig wird und zu einer Reduzierung der Erzeugung von Harmonischen führt, sowie zu einer Änderung des Verhältnisses von Harmonischen in verschiedenen Isotopen. ----------------------------------------------------------------------- We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths (≈ 2 μm), leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.

The PHD: A Planar, Harmonic Drive Robot for Joint Torque Control

This thesis details the development of a model of a seven degree of freedom manipulator for position control. Then, it goes on to discuss the design and construction of a the PHD, a robot built to serve two purposes: first, to perform research on joint torque control schemes, and second, to determine the important dynamic characteristics of the Harmonic Drive. The PHD, is a planar, three degree of freedom arm with torque sensors integral to each joint. Preliminary testing has shown that a simple linear spring model of the Harmonic Drive's flexibility is suitable in many situations.

If factor shares are not constant then we have a measurment problem. can we solve it?

Recent evidence show that factor shares, if properly measured, are far from constant. Moreover, the shares of natural resources and raw labor seem to be negatively correlated with income per capita while the share of human and physical capital is positively correlated with income per capita. Now, if factor shares are not constant then (i) growth accounting exercises rely on a false assumption and (ii) there is a measurement problem. The effect that change s in factor shares ha ve on output depend on the relative abundance of factors and, fo r this reason, it is necessary to have correct measures. We propose an empiri cal methodology to solve the measurement issue and estimate TFP growth.

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy