Pulse transition to similaritons in normally dispersive fibre amplifiers

A detailed experimental characterization of the transition process of an initially Gaussian pulse to the asymptotic self-similar parabolic solution in optical fibre amplifiers operating in the normal dispersion regime is performed.

On-off and multistate intermittencies in cascaded random distributed feedback fibre laser

A range of physical and engineering systems exhibit an irregular complex dynamics featuring alternation of quiet and burst time intervals called the intermittency. The intermittent dynamics most popular in laser science is the on-off intermittency [1]. The on-off intermittency can be understood as a conversion of the noise in a system close to an instability threshold into effective time-dependent fluctuations which result in the alternation of stable and unstable periods. The on-off intermittency has been recently demonstrated in semiconductor, Erbium doped and Raman lasers [2-5]. Recently demonstrated random distributed feedback (random DFB) fiber laser has an irregular dynamics near the generation threshold [6,7]. Here we show the intermittency in the cascaded random DFB fiber laser. We study intensity fluctuations in a random DFB fiber laser based on nitrogen doped fiber. The laser generates first and second Stokes components 1120 nm and 1180 nm respectively under an appropriate pumping. We study the intermittency in the radiation of the second Stokes wave. The typical time trace near the generation threshold of the second Stokes wave (Pth) is shown at Fig. 1a. From the number of long enough time-traces we calculate statistical distribution between major spikes in time dynamics, Fig. 1b. To eliminate contribution of high frequency components of spikes we use a low pass filter along with the reference value of the output power. Experimental data is fitted by power law, ~(P-Pth)y, where is a mean time between pikes. There are two different intermittency regimes. Just above Pth, the mean time is approximated by the -3/2 power law. The -3/2 power law is typical to the on-off intermittency with hopping between two states (first and second Stokes waves in our case) [7]. At higher power, the mean time is approximated by -4 power law, that indicates a change in intermittency type to multistate. Multistable dynamics is observed in erbium-doped fiber lasers [8]. The origin of multiples states in our system could be probably connected with polarization hopping or other reasons and should be further investigated. We have presented a first experimental statistical characterisation of the on-off and multistate intermittencies that occur in the generation of the second Stokes wave in nitrogen doped random DFB fiber laser. References [1] H. Fujisaka and T. Yamada, “A New Intermittency in Coupled Dynamical Systems,” Prog. Theor. Phys. 74, 918 (1985). [2] S. Osborne, A. Amann, D. Bitauld, and S. O’Brien, “On-off intermittency in an optically injected semiconductor laser,” Phys. Rev. E 85, 056204 (2012). [3] S. Sergeyev, K. O'Mahoney, S. Popov, and A. T. Friberg, “Coherence and anticoherence resonance in high-concentration erbium-doped fiber laser,” Opt. Lett. 35, 3736 (2010). [4] A.E. El-Taher, S.V. Sergeyev, E.G. Turitsyna, P. Harper, and S. K. Turitsyn, “Intermittent Self-Pulsing in a Fiber Raman Laser”, In proc. Conf. Nonlin. Photon., paper ID 1367139, Colorado Springs, USA, 2012 [5] S.K. Turitsyn, S.A. Babin, A.E. El-Taher, P. Harper, D.V. Churkin, S.I. Kablukov, J.D. Ania-Castañón, V. Karalekas, and E.V. Podivilov, “Random distributed feedback fibre laser”, Nat. Photon..4, 231 (2010). [6] I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, "Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm," Opt. Express 19, 18486 (2011). [7] W. Feller, An introduction to probability theory and its applications, Vol. 1, 3rd ed. (Wiley, New-York, 1968). [8] G. Huerta-Cuellar, A.N. Pisarchik, and Y.O. Barmenkov, “Experimental characterization of hopping dynamics in a multistable fiber laser,” Phys. Rev. E 78, 035202(R) (2008).

Estudo da variação da periodicidade e do acoplamento entre superfícies seletivas de frequência com elementos fractais e helicoidais em estruturas de multicamadas

This work aims to investigate the behavior of fractal and helical elements structures in planar microstrip. In particular, the frequency selective surfaces (FSSs) had changed its conventional elements to fractal and helical formats. The dielectric substrate used was fiberglass (FR-4) and has a thickness of 1.5 mm, a relative permittivity 4.4 and tangent loss equal to 0.02. For FSSs, was adopting the Dürer’s fractal geometry and helical geometry. To make the measurements, we used two antennas horns in direct line of sight, connected by coaxial cable to the vector network analyzer. Some prototypes were select for built and measured. From preliminary results, it was aimed to find practical applications for structures from the cascading between them. For FSSs with Dürer’s fractal elements was observed behavior provided by the multiband fractal geometry, while the bandwidth has become narrow as the level of iteration fractal increased, making it a more selective frequency with a higher quality factor. A parametric analysis allowed the analysis of the variation of the air layer between them. The cascading between fractal elements structure were considered, presented a tri-band behavior for certain values of the layer of air between them, and find applications in the licensed 2.5GHz band (2.3-2.7) and 3.5GHz band (3.3-3.8). For FSSs with helical elements, six structures were considered, namely H0, H1, H2, H3, H4 and H5. The electromagnetic behavior of them was analyzed separately and cascaded. From preliminary results obtained from the separate analysis of structures, including the cascade, the higher the bandwidth, in that the thickness of the air layer increases. In order to find practical applications for helical structures cascaded, the helical elements structure has been cascaded find applications in the X-band (8.0-12.0) and unlicensed band (5.25-5.85). For numerical and experimental characterization of the structures discussed was used, respectively, the commercial software Ansoft Designer and a vector network analyzer, Agilent N5230A model.

Characterizing the transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space near the transition to multi-pulse modelocking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single- and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N + 1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Caractérisation des propriétés mécaniques de la pâte de carbone à 150°C dans le but d’optimiser la mise en forme des anodes utilisées dans les cuves Hall-Héroult

Les anodes de carbone sont des éléments consommables servant d’électrode dans la réaction électrochimique d’une cuve Hall-Héroult. Ces dernières sont produites massivement via une chaine de production dont la mise en forme est une des étapes critiques puisqu’elle définit une partie de leur qualité. Le procédé de mise en forme actuel n’est pas pleinement optimisé. Des gradients de densité importants à l’intérieur des anodes diminuent leur performance dans les cuves d’électrolyse. Encore aujourd’hui, les anodes de carbone sont produites avec comme seuls critères de qualité leur densité globale et leurs propriétés mécaniques finales. La manufacture d’anodes est optimisée de façon empirique directement sur la chaine de production. Cependant, la qualité d’une anode se résume en une conductivité électrique uniforme afin de minimiser les concentrations de courant qui ont plusieurs effets néfastes sur leur performance et sur les coûts de production d’aluminium. Cette thèse est basée sur l’hypothèse que la conductivité électrique de l’anode n’est influencée que par sa densité considérant une composition chimique uniforme. L’objectif est de caractériser les paramètres d’un modèle afin de nourrir une loi constitutive qui permettra de modéliser la mise en forme des blocs anodiques. L’utilisation de la modélisation numérique permet d’analyser le comportement de la pâte lors de sa mise en forme. Ainsi, il devient possible de prédire les gradients de densité à l’intérieur des anodes et d’optimiser les paramètres de mise en forme pour en améliorer leur qualité. Le modèle sélectionné est basé sur les propriétés mécaniques et tribologiques réelles de la pâte. La thèse débute avec une étude comportementale qui a pour objectif d’améliorer la compréhension des comportements constitutifs de la pâte observés lors d’essais de pressage préliminaires. Cette étude est basée sur des essais de pressage de pâte de carbone chaude produite dans un moule rigide et sur des essais de pressage d’agrégats secs à l’intérieur du même moule instrumenté d’un piézoélectrique permettant d’enregistrer les émissions acoustiques. Cette analyse a précédé la caractérisation des propriétés de la pâte afin de mieux interpréter son comportement mécanique étant donné la nature complexe de ce matériau carboné dont les propriétés mécaniques sont évolutives en fonction de la masse volumique. Un premier montage expérimental a été spécifiquement développé afin de caractériser le module de Young et le coefficient de Poisson de la pâte. Ce même montage a également servi dans la caractérisation de la viscosité (comportement temporel) de la pâte. Il n’existe aucun essai adapté pour caractériser ces propriétés pour ce type de matériau chauffé à 150°C. Un moule à paroi déformable instrumenté de jauges de déformation a été utilisé pour réaliser les essais. Un second montage a été développé pour caractériser les coefficients de friction statique et cinétique de la pâte aussi chauffée à 150°C. Le modèle a été exploité afin de caractériser les propriétés mécaniques de la pâte par identification inverse et pour simuler la mise en forme d’anodes de laboratoire. Les propriétés mécaniques de la pâte obtenues par la caractérisation expérimentale ont été comparées à celles obtenues par la méthode d’identification inverse. Les cartographies tirées des simulations ont également été comparées aux cartographies des anodes pressées en laboratoire. La tomodensitométrie a été utilisée pour produire ces dernières cartographies de densité. Les résultats des simulations confirment qu’il y a un potentiel majeur à l’utilisation de la modélisation numérique comme outil d’optimisation du procédé de mise en forme de la pâte de carbone. La modélisation numérique permet d’évaluer l’influence de chacun des paramètres de mise en forme sans interrompre la production et/ou d’implanter des changements coûteux dans la ligne de production. Cet outil permet donc d’explorer des avenues telles la modulation des paramètres fréquentiels, la modification de la distribution initiale de la pâte dans le moule, la possibilité de mouler l’anode inversée (upside down), etc. afin d’optimiser le processus de mise en forme et d’augmenter la qualité des anodes.

Self-Assembled InAs/GaAs Quantum Dot Solar Cells

Our work focuses on experimental and theoretical studies aimed at establishing a fundamental understanding of the principal electrical and optical processes governing the operation of quantum dot solar cells (QDSC) and their feasibility for the realization of intermediate band solar cell (IBSC). Uniform performance QD solar cells with high conversion efficiency have been fabricated using carefully calibrated process recipes as the basis of all reliable experimental characterization. The origin for the enhancement of the short circuit current density (Jsc) in QD solar cells was carefully investigated. External quantum efficiency (EQE) measurements were performed as a measure of the below bandgap distribution of transition states. In this work, we found that the incorporation of self-assembled quantum dots (QDs) interrupts the lattice periodicity and introduce a greatly broadened tailing density of states extending from the bandedge towards mid-gap. A below-bandgap density of states (DOS) model with an extended Urbach tail has been developed. In particular, the below-bandgap photocurrent generation has been attributed to transitions via confined energy states and background continuum tailing states. Photoluminescence measurement is used to measure the energy level of the lowest available state and the coupling effect between QD states and background tailing states because it results from a non-equilibrium process. A basic I-V measurement reveals a degradation of the open circuit voltage (Voc) of QD solar cells, which is related to a one sub-bandgap photon absorption process followed by a direct collection of the generated carriers by the external circuit. We have proposed a modified Shockley-Queisser (SQ) model that predicts the degradation of Voc compared with a reference bulk device. Whenever an energy state within the forbidden gap can facilitate additional absorption, it can facilitate recombination as well. If the recombination is non-radiative, it is detrimental to solar cell performance. We have also investigated the QD trapping effects as deep level energy states. Without an efficient carrier extraction pathway, the QDs can indeed function as mobile carriers traps. Since hole energy levels are mostly connected with hole collection under room temperature, the trapping effect is more severe for electrons. We have tried to electron-dope the QDs to exert a repulsive Coulomb force to help improve the carrier collection efficiency. We have experimentally observed a 30% improvement of Jsc for 4e/dot devices compared with 0e/dot devices. Electron-doping helps with better carrier collection efficiency, however, we have also measured a smaller transition probability from valance band to QD states as a direct manifestation of the Pauli Exclusion Principle. The non-linear performance is of particular interest. With the availability of laser with on-resonance and off-resonance excitation energy, we have explored the photocurrent enhancement by a sequential two-photon absorption (2PA) process via the intermediate states. For the first time, we are able to distinguish the nonlinearity effect by 1PA and 2PA process. The observed 2PA current under off-resonant and on-resonant excitation comes from a two-step transition via the tailing states instead of the QD states. However, given the existence of an extended Urbach tail and the small number of photons available for the intermediate states to conduction band transition, the experimental results suggest that with the current material system, the intensity requirement for an observable enhancement of photocurrent via a 2PA process is much higher than what is available from concentrated sun light. In order to realize the IBSC model, a matching transition strength needs to be achieved between valance band to QD states and QD states to conduction band. However, we have experimentally shown that only a negligible amount of signal can be observed at cryogenic temperature via the transition from QD states to conduction band under a broadband IR source excitation. Based on the understanding we have achieved, we found that the existence of the extended tailing density of states together with the large mismatch of the transition strength from VB to QD and from QD to CB, has systematically put into question the feasibility of the IBSC model with QDs.

Coarse Graining to Invesitigate Peptide-Lipid Interactions

Experimental characterization of molecular details is challenging, and although single molecule experiments have gained prominence, oligomer characterization remains largely unexplored. The ability to monitor the time evolution of individual molecules while they self assemble is essential in providing mechanistic insights about biological events. Molecular dynamics (MD) simulations can fill the gap in knowledge between single molecule experiments and ensemble studies like NMR, and are increasingly used to gain a better understanding of microscopic properties. Coarse-grained (CG) models aid in both exploring longer length and time scale molecular phenomena, and narrowing down the key interactions responsible for significant system characteristics. Over the past decade, CG techniques have made a significant impact in understanding physicochemical processes. However, the realm of peptide-lipid interfacial interactions, primarily binding, partitioning and folding of amphipathic peptides, remains largely unexplored compared to peptide folding in solution. The main drawback of existing CG models is the inability to capture environmentally sensitive changes in dipolar interactions, which are indigenous to protein folding, and lipid dynamics. We have used the Drude oscillator approach to incorporate structural polarization and dipolar interactions in CG beads to develop a minimalistic peptide model, WEPPROM (Water Explicit Polarizable PROtein Model), and a lipid model WEPMEM (Water Explicit Polarizable MEmbrane Model). The addition of backbone dipolar interactions in a CG model for peptides enabled us to achieve alpha-beta secondary structure content de novo, without any added bias. As a prelude to studying amphipathic peptide-lipid membrane interactions, the balance between hydrophobicity and backbone dipolar interactions in driving ordered peptide aggregation in water and at a hydrophobic-hydrophilic interface, was explored. We found that backbone dipole interactions play a crucial role in driving ordered peptide aggregation, both in water and at hydrophobic-hydrophilic interfaces; while hydrophobicity is more relevant for aggregation in water. A zwitterionic (POPC: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and an anionic lipid (POPS: 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine) are used as model lipids for WEPMEM. The addition of head group dipolar interactions in lipids significantly improved structural, dynamic and dielectric properties of the model bilayer. Using WEPMEM and WEPPROM, we studied membrane-induced peptide folding of a cationic antimicrobial peptide with anticancer activity, SVS-1. We found that membrane-induced peptide folding is driven by both (a) cooperativity in peptide self interaction and (b) cooperativity in membrane-peptide interactions. The dipolar interactions between the peptide and the lipid head-groups contribute to stabilizing folded conformations. The role of monovalent ion size and peptide concentration in driving lipid domain formation in anionic/zwitterionic lipid mixtures was also investigated. Our study suggest monovalent ion size to be a crucial determinant of interaction with lipid head groups, and hence domain formation in lipid mixtures. This study reinforces the role of dipole interactions in protein folding, lipid membrane properties, membrane induced peptide folding and lipid domain formation. Therefore, the models developed in this thesis can be used to explore a multitude of biomolecular processes, both at longer time-scales and larger system sizes.

Avaliação do comportamento reológico de pastas de cimento para poços de petróleo com adição de plastificantes

The isolation of adjacent zones encountered during oilwell drilling is carried out by Portland-based cement slurries. The slurries are pumped into the annular positions between the well and the casing. Their rheological behavior is a very important component for the cementing process. Nowadays, several alternative materials are used in oilwell cementing, with goal the modification and the improvement of their properties, mainly the increase of the fluidity. And this can be reached by using plasticizers additives able to account for different oilwell conditions, yielding compatible cement slurries and allowing enough time for the complete cementing operation. If the rheological properties of the slurry are properly characterized, the load loss and flow regime can be correctly predicted. However, this experimental characterization is difficult. Rheological models capable of describing the cement slurry behavior must be capable of predicting the slurry cement deformation within reasonable accuracy. The aim of this study was to characterize rheologically the slurries prepared with a especial class of Portland cement, water and plasticizers based on lignosulfonate, melamine and polycarboxylate at temperatures varying from 27°C to 72°C. The tests were carried out according to the practical recommendations of the API RP 10B guidelines. The results revealed a great efficiency and the dispersive power of the polycarboxylate, for all temperatures tested. This additive promoted high fluidity of the slurries, with no sedimentation. High lignosulfonate and melamine concentrations did not reduce the rheological parameters (plastic viscosity and yield stress) of the slurries. It was verified that these additives were not compatible with the type of cement used. The evaluated rheological models were capable of describing the behavior of the slurries only within concentration and temperature ranges specific for each type of additive

Avaliação do petróleo por termogravimetria para simulação de curva PEV, fator de caracterização e resíduo de carbono

Petroleum evaluation is analyze it using different methodologies, following international standards to know their chemical and physicochemical properties, contaminant levels, composition and especially their ability to generate derivatives. Many of these analyzes consuming a lot of time, large amount of samples , supplies and need an organized transportation logistics, schedule and professionals involved. Looking for alternatives that optimize the evaluation and enable the use of new technologies, seven samples of different centrifuged Brazilian oils previously characterized by Petrobras were analyzed by thermogravimetry in 25-900° C range using heating rates of 05, 10 and 20ºC per minute. With experimental data obtained, characterizations correlations were performed and provided: generation of true boiling point curves (TBP) simulated; comparing fractions generated with appropriate cut standard in temperature ranges; an approach to obtain Watson characterization factor; and compare micro carbon residue formed. The results showed a good chance of reproducing simulated TBP curve from thermogravimetry taking into account the composition, density and other oil properties. Proposed correlations for experimental characterization factor and carbon residue followed Petrobras characterizations, showing that thermogravimetry can be used as a tool on oil evaluation, because your quick analysis, accuracy, and requires a minimum number of samples and consumables

Molecular mechanism of stabilization of thin films for improved water evaporation protection

All-atom molecular dynamics simulations and experimental characterization have been used to examine the structure and dynamics of novel evaporation-suppressing films where the addition of a water-soluble polymer to an ethylene glycol monooctadecyl ether monolayer leads to improved water evaporation resistance. Simulations and Langmuir trough experiments demonstrate the surface activity of poly(vinyl pyrrolidone) (PVP). Subsequent MD simulations performed on the thin films supported by the PVP sublayer show that, at low surface pressures, the polymer tends to concentrate at the film/water interface. The simulated atomic concentration profiles, hydrogen bonding patterns, and mobility analyses of the water-polymer-monolayer interfaces reveal that the presence of PVP increases the atomic density near the monolayer film, improves the film stability, and reduces the mobility of interfacial waters. These observations explain the molecular basis of the improved efficacy of these monolayer/polymer systems for evaporation protection of water and can be used to guide future development of organic thin films for other applications.

Experimental and theoretical characterization of 5,10- diminoporphodimethenes: Dearomatized porphyrinoids from palladium-catalyzed hydrazinations of 5,10-diarylporphyrins

A new dearomatized porphyrinoid, 5,10-diiminoporphodimethene (5,10-DIPD), has been prepared by palladium-catalyzed hydrazination of 5,10-dibromo-15,20-bis(3,5-di-tert-butylphenyl)porphyrin and its nickel(II) complex, by using ethyl and 4-methoxybenzyl carbazates. The oxidative dearomatization of the porphyrin ring occurs in high yield. Further oxidation with 2,3-dichloro-5,6-dicyanobenzoquinone forms the corresponding 5,10-bis(azocarboxylates), thereby restoring the porphyrin aromaticity. The UV/visible spectra of the NiII DIPDs exhibit remarkable redshifts of the lowest-energy bands to 780 nm, and differential pulse voltammetry reveals a contracted electrochemical HOMO–LUMO gap of 1.44 V. Density functional theory (DFT) was used to calculate the optimized geometries and frontier molecular orbitals of model 5,10-DIPD Ni7c and 5,10-bis(azocarboxylate) Ni8c. The conformations of the carbamate groups and the configurations of the CNZ unit were considered in conjunction with the NOESY spectra, to generate the global minimum geometry and two other structures with slightly higher energies. In the absence of solution data regarding conformations, ten possible local minimum conformations were considered for Ni8c. Partition of the porphyrin macrocycle into tri- and monopyrrole fragments in Ni7c and the inclusion of terminal conjugating functional groups generate unique frontier molecular orbital distributions and a HOMO–LUMO transition with a strong element of charge transfer from the monopyrrole ring. Time-dependent DFT calculations were performed for the three lowest-energy structures of Ni7c and Ni8c, and weighting according to their energies allowed the prediction of the electronic spectra. The calculations reproduce the lower-energy regions of the spectra and the overall forms of the spectra with high accuracy, but agreement is not as good in the Soret region below 450 nm.

Experimental and Computational Characterization of Alloy--Spinel--Corundum Equilibrium in the System Fe--Co--Al--O at 1873K

The three-phase equilibrium between alloy, spinel solid solution and alpha -Al sub 2 O sub 3 in the Fe--Co--Al--O system at 1873k was fully characterized as a function of alloy composition using both experimental and computational methods. The equilibrium oxygen content of the liquid alloy was measured by suction sampling and inert gas fusion analysis. The O potential corresponding to the three-phase equilibrium was determined by emf measurements on a solid state galvanic cell incorporating (Y sub 2 O sub 3 )ThO sub 2 as the solid electrolyte and Cr + Cr sub 2 O sub 3 as the reference electrode. The equilibrium composition of the spinel phase formed at the interface between the alloy and alumina crucible was measured by electron probe microanalysis (EPMA). The experimental results were compared with the values computed using a thermodynamic model. The model used values for standard Gibbs energies of formation of pure end-member spinels and Gibbs energies of solution of gaseous O in liquid Fe and cobalt available in the literature. The activity--composition relationship in the spinel solid solution was computed using a cation distribution model. The variation of the activity coefficient of O with alloy composition in the Fe--Co--O system was estimated using both the quasichemical model of Jacob and Alcock and Wagner's model along with the correlations of Chiang and Chang and Kuo and Chang. The computed results of spinel composition and O potential are in excellent agreement with the experimental data. Graphs. 29 ref.--AA

Characterization of Interactions Involving Bromine in 2,2-Dibromo2,3-dihydroinden-1-one via Experimental Charge Density Analysis

Experimental and theoretical charge density analyses on 2,2-dibromo-2,3-dihydroinden-1-one have been carried out to quantify the topological features of a short CBr....O halogen bond with nearly linear geometry (2.922 angstrom, angle CBr....O = 172.7 degrees) and to assess the strength of the interactions using the topological features of the electron density. The electrostatic potential map indicates the presence of the s-hole on bromine, while the interaction energy is comparable to that of a moderate OH....O hydrogen bond. In addition, the energetic contribution of CH.....Br interaction is demonstrated to be on par with that of the CBr....O halogen bond in stabilizing the crystal structure.

Acoustic Noise Characterization of Space-Vector Modulated Induction Motor Drives-An Experimental Approach

This paper presents an experimental procedure to determine the acoustic and vibration behavior of an inverter-fed induction motor based on measurements of the current spectrum, acoustic noise spectrum, overall noise in dB, and overall A-weighted noise in dBA. Measurements are carried out on space-vector modulated 8-hp and 3-hp induction motor drives over a range of carrier frequencies at different modulation frequencies. The experimental data help to distinguish between regions of high and low acoustic noise levels. The measurements also bring out the impact of carrier frequency on the acoustic noise. The sensitivity of the overall noise to carrier frequency is indicative of the relative dominance of the high-frequency electromagnetic noise over mechanical and aerodynamic components of noise. Based on the measured current and acoustic noise spectra, the ratio of dynamic deflection on the stator surface to the product of fundamental and harmonic current amplitudes is obtained at each operating point. The variation of this ratio of deflection to current product with carrier frequency indicates the resonant frequency clearly and also gives a measure of the amplification of vibration at frequencies close to the resonant frequency. This ratio is useful to predict the magnitude of acoustic noise corresponding to significant time-harmonic currents flowing in the stator winding.