Bozkaya, Uǧur; Sherrill, C. David
2013-08-01
Orbital-optimized coupled-electron pair theory [or simply "optimized CEPA(0)," OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N6) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm-1) is fortuitously even better than that of CCSD(T) (50 cm-1), while the MAEs of CEPA(0) (184 cm-1) and CCSD (84 cm-1) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol-1, which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol-1), and comparing to MP2 (7.7 kcal mol-1) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is only 0.1 kcal
Pandey, Krishna Kumar; Patidar, Pankaj; Patidar, Sunil Kumar; Vishwakarma, Ravi
2014-12-01
Quantum-chemical calculations have been performed to evaluate the geometries, bonding nature and harmonic frequencies of the compounds [Etbnd UX3] at DFT, DFT-D3, DFT-D3(BJ) and DFT-dDSc levels using different density functionals BP86, BLYP, PBE, revPBE, PW91, TPSS and M06-L. The stretching frequency of Utbnd N bond in [Ntbnd UF3] calculated with DFT/BLYP closely resembles with the experimental value. The performance of different density functionals for accurate Utbnd N vibrational frequencies follows the order BLYP > revPBE > BP86 > PW91 > TPSS > PBE > M06-L. The BLYP functional gives accurate value of the Utbnd E bond distances. The uranium atom in the studied compounds [Etbnd UX3] is positively charged. Upon going from [Etbnd UF3] to [Etbnd UCl3], the partial Hirshfeld charge on uranium atom decreases because of the lower electronegativity of chlorine compared to flourine. The Gopinathan-Jug bond order for Utbnd E bonds ranges from 2.90 to 3.29. The Utbnd E bond dissociation energies vary with different density functionals as M06-L < TPSS < BLYP < revPBE < BP86 < PBE ≈ PW91. The orbital interactions ΔEorb, in all studied compounds [Etbnd UX3] are larger than the electrostatic interaction ΔEelstat, which means the Utbnd N bonds in these compound have greater degree of covalent character (in the range 63.8-77.2%). The Usbnd E σ-bonding interaction is the dominant bonding interaction in the nitride and methylidyne complexes while it is weaker in [Ptbnd UX3]. The dispersion energy contributions to the total bond dissociation energies are rather small. Compared to the Grimme's D3(BJ) corrections, the Corminboeuf's dispersion corrections are larger with metaGGA functionals (TPSS, M06-L) while smaller with GGA functionals.
Harmonic generation with a dual frequency pulse.
Keravnou, Christina P; Averkiou, Michalakis A
2014-05-01
Nonlinear imaging was implemented in commercial ultrasound systems over the last 15 years offering major advantages in many clinical applications. In this work, pulsing schemes coupled with a dual frequency pulse are presented. The pulsing schemes considered were pulse inversion, power modulation, and power modulated pulse inversion. The pulse contains a fundamental frequency f and a specified amount of its second harmonic 2f. The advantages and limitations of this method were evaluated with both acoustic measurements of harmonic generation and theoretical simulations based on the KZK equation. The use of two frequencies in a pulse results in the generation of the sum and difference frequency components in addition to the other harmonic components. While with single frequency pulses, only power modulation and power modulated pulse inversion contained odd harmonic components, with the dual frequency pulse, pulse inversion now also contains odd harmonic components.
Energy Technology Data Exchange (ETDEWEB)
Miliordos, Evangelos; Aprà, Edoardo; Xantheas, Sotiris S.
2013-01-01
We report the first optimum geometries and harmonic vibrational frequencies for the ring pentamer and several water hexamer (prism, cage, cyclic and two book) at the CCSD(T)/aug-cc-pVDZ level of theory. All five hexamer isomer minima previously reported by MP2 are also minima on the CCSD(T) potential energy surface (PES). In addition, all CCSD(T) minimum energy structures for the n=2-6 cluster isomers are quite close to the ones previously obtained by MP2 on the respective PESs, as confirmed by a modified Procrustes analysis that quantifies the difference between any two cluster geometries. The CCSD(T) results confirm the cooperative effect of the homodromic ring networks (systematic contraction of the nearest-neighbor (nn) intermolecular separations with cluster size) previously reported by MP2, albeit with O-O distances shorter by ~0.02 Å, indicating that MP2 overcorrects this effect. The harmonic frequencies at the minimum geometries were obtained by the double differentiation of the CCSD(T) energy using an efficient scheme based on internal coordinates that reduces the number of required single point energy evaluations by ~15% when compared to the corresponding double differentiation using Cartesian coordinates. Negligible differences between MP2 and CCSD(T) are found for the librational modes, while uniform increases of ~15 and ~25 cm^{-1} are observed for the bending and “free” OH harmonic frequencies. The largest differences between MP2 and CCSD(T) are observed for the harmonic hydrogen bonded frequencies. The CCSD(T) red shifts from the monomer frequencies (Δω) are smaller than the MP2 ones, due to the fact that the former produces shorter elongations (ΔR) of the respective hydrogen bonded OH lengths from the monomer value with respect to the latter. Both the MP2 and CCSD(T) results for the hydrogen bonded frequencies were found to closely follow the relation - Δω = s · ΔR, with a rate of s = 20.3 cm^{-1} / 0.001 Å. The CCSD
Electroencephalography in ellipsoidal geometry with fourth-order harmonics.
Alcocer-Sosa, M; Gutierrez, D
2016-08-01
We present a solution to the electroencephalographs (EEG) forward problem of computing the scalp electric potentials for the case when the head's geometry is modeled using a four-shell ellipsoidal geometry and the brain sources with an equivalent current dipole (ECD). The proposed solution includes terms up to the fourth-order ellipsoidal harmonics and we compare this new approximation against those that only considered up to second- and third-order harmonics. Our comparisons use as reference a solution in which a tessellated volume approximates the head and the forward problem is solved through the boundary element method (BEM). We also assess the solution to the inverse problem of estimating the magnitude of an ECD through different harmonic approximations. Our results show that the fourth-order solution provides a better estimate of the ECD in comparison to lesser order ones.
Secondary magnetic field harmonics dependence on vacuum beam chamber geometry
Directory of Open Access Journals (Sweden)
S. Y. Shim
2013-08-01
Full Text Available The harmonic magnetic field properties due to eddy currents have been studied with respect to the geometry of the vacuum beam chamber. We derived a generalized formula enabling the precise prediction of any field harmonics generated by eddy currents in beam tubes with different cross-sectional geometries. Applying our model to study the properties of field harmonics in beam tubes with linear dipole magnetic field ramping clearly proved that the circular cross section tube generates only a dipole field from eddy currents. The elliptic tube showed noticeable magnitudes of sextupole and dipole fields. We demonstrate theoretically that it is feasible to suppress the generation of the sextupole field component by appropriately varying the tube wall thickness as a function of angle around the tube circumference. This result indicates that it is possible to design an elliptical-shaped beam tube that generates a dipole field component with zero magnitude of sextupole. In a rectangular-shaped beam tube, one of the selected harmonic fields can be prevented if an appropriate wall thickness ratio between the horizontal and vertical tube walls is properly chosen. Our generalized formalism can be used for optimization of arbitrarily complex-shaped beam tubes, with respect to suppression of detrimental field harmonics.
Second harmonic generation and sum frequency generation
International Nuclear Information System (INIS)
Pellin, M.J.; Biwer, B.M.; Schauer, M.W.; Frye, J.M.; Gruen, D.M.
1990-01-01
Second harmonic generation and sum frequency generation are increasingly being used as in situ surface probes. These techniques are coherent and inherently surface sensitive by the nature of the mediums response to intense laser light. Here we will review these two techniques using aqueous corrosion as an example problem. Aqueous corrosion of technologically important materials such as Fe, Ni and Cr proceeds from a reduced metal surface with layer by layer growth of oxide films mitigated by compositional changes in the chemical makeup of the growing film. Passivation of the metal surface is achieved after growth of only a few tens of atomic layers of metal oxide. Surface Second Harmonic Generation and a related nonlinear laser technique, Sum Frequency Generation have demonstrated an ability to probe the surface composition of growing films even in the presence of aqueous solutions. 96 refs., 4 figs
Frequency Adaptability of Harmonics Controllers for Grid-Interfaced Converters
DEFF Research Database (Denmark)
Yang, Yongheng; Zhou, Keliang; Blaabjerg, Frede
2017-01-01
sensitivity of the most popular harmonic controllers for grid-interfaced converters. The frequency adaptability of these harmonic controllers is evaluated in the presence of a variable grid frequency within a specified reasonable range, e.g., +-1% of the nominal grid frequency (50 Hz). Solutions...
High-frequency harmonic imaging of the eye
Silverman, Ronald H.; Coleman, D. Jackson; Ketterling, Jeffrey A.; Lizzi, Frederic L.
2005-04-01
Purpose: Harmonic imaging has become a well-established technique for ultrasonic imaging at fundamental frequencies of 10 MHz or less. Ophthalmology has benefited from the use of fundamentals of 20 MHz to 50 MHz. Our aim was to explore the ability to generate harmonics for this frequency range, and to generate harmonic images of the eye. Methods: The presence of harmonics was determined in both water and bovine vitreous propagation media by pulse/echo and hydrophone at a series of increasing excitation pulse intensities and frequencies. Hydrophone measurements were made at the focal point and in the near- and far-fields of 20 MHz and 40 MHz transducers. Harmonic images of the anterior segment of the rabbit eye were obtained by a combination of analog filtering and digital post-processing. Results: Harmonics were generated nearly identically in both water and vitreous. Hydrophone measurements showed the maximum second harmonic to be -5 dB relative to the 35 MHz fundamental at the focus, while in pulse/echo the maximum harmonic amplitude was -15dB relative to the fundamental. Harmonics were absent in the near-field, but present in the far-field. Harmonic images of the eye showed improved resolution. Conclusion: Harmonics can be readily generated at very high frequencies, and at power levels compliant with FDA guidelines for ophthalmology. This technique may yield further improvements to the already impressive resolutions obtainable in this frequency range. Improved imaging of the macular region, in particular, may provide significant improvements in diagnosis of retinal disease.
Frequency chirp of harmonic and attosecond pulses
International Nuclear Information System (INIS)
Varju, K.; Johansson, P; L'Huillier, A.L.; Mairesse, Y.; Salieres, P.
2005-01-01
Full text: We have explored in detail the first- and second-order variations of the atomic phase as a function of the laser intensity and harmonic order. This unravels the similitudes and differences existing between the chirp of individual harmonic pulses and the chirp of the attosecond pulses. We show that the two techniques XFROG and RABITT used to characterize the two chirps (respectively) converge to give the same information, namely the values of the mixed partial derivatives of the atomic phase. This underlines the common physical origin of all these phenomena and provides a unified frame for their description and understanding. Ref. 1 (author)
Feaver, Ryan E; Gelfand, Bradley D; Blackman, Brett R
2013-01-01
Haemodynamic variations are inherent to blood vessel geometries (such as bifurcations) and correlate with regional development of inflammation and atherosclerosis. However, the complex frequency spectrum characteristics from these haemodynamics have never been exploited to test whether frequency variations are critical determinants of endothelial inflammatory phenotype. Here we utilize an experimental Fourier transform analysis to systematically manipulate individual frequency harmonics from human carotid shear stress waveforms applied in vitro to human endothelial cells. The frequency spectrum, specifically the 0 th and 1st harmonics, is a significant regulator of inflammation, including NF-κB activity and downstream inflammatory phenotype. Further, a harmonic-based regression-model predicts eccentric NF-κB activity observed in the human internal carotid artery. Finally, short interfering RNA-knockdown of the mechanosensor PECAM-1 reverses frequency-dependent regulation of NF-κB activity. Thus, PECAM-1 may have a critical role in the endothelium's exquisite sensitivity to complex shear stress frequency harmonics and provide a mechanism for the focal development of vascular inflammation.
International Nuclear Information System (INIS)
Kobayashi, K.
2009-01-01
In 2001, an international cooperation on the 3D radiation transport benchmarks for simple geometries with void region was performed under the leadership of E. Sartori of OECD/NEA. There were contributions from eight institutions, where 6 contributions were by the discrete ordinate method and only two were by the spherical harmonics method. The 3D spherical harmonics program FFT3 by the finite Fourier transformation method has been improved for this presentation, and benchmark solutions for the 2D and 3D simple geometries with void region by the FFT2 and FFT3 are given showing fairly good accuracy. (authors)
International Nuclear Information System (INIS)
Stoeger, W.R.; Whitman, A.P.; Knill, R.J.
1985-01-01
After showing that Rosen's bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the ''conserved quantities'' naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein's general relativity
Time-frequency analysis and harmonic Gaussian functions
International Nuclear Information System (INIS)
Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.
2013-01-01
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted Τ n , which associate to a function ψ, of the time variable t, a set of functions Ψ n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations Τ n and the functions Ψ n are given. It is proved in particular that the square of the modulus of each function Ψ n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ n .
Carette, Yannick; Vanhove, Hans; Duflou, Joost
2018-05-01
Single Point Incremental Forming is a flexible process that is well-suited for small batch production and rapid prototyping of complex sheet metal parts. The distributed nature of the deformation process and the unsupported sheet imply that controlling the final accuracy of the workpiece is challenging. To improve the process limits and the accuracy of SPIF, the use of multiple forming passes has been proposed and discussed by a number of authors. Most methods use multiple intermediate models, where the previous one is strictly smaller than the next one, while gradually increasing the workpieces' wall angles. Another method that can be used is the manufacture of a smoothed-out "base geometry" in the first pass, after which more detailed features can be added in subsequent passes. In both methods, the selection of these intermediate shapes is freely decided by the user. However, their practical implementation in the production of complex freeform parts is not straightforward. The original CAD model can be manually adjusted or completely new CAD models can be created. This paper discusses an automatic method that is able to extract the base geometry from a full STL-based CAD model in an analytical way. Harmonic decomposition is used to express the final geometry as the sum of individual surface harmonics. It is then possible to filter these harmonic contributions to obtain a new CAD model with a desired level of geometric detail. This paper explains the technique and its implementation, as well as its use in the automatic generation of multi-step geometries.
Holliday, Ezekiel S. (Inventor)
2014-01-01
Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.
Efficient broadband third harmonic frequency conversion via angular dispersion
International Nuclear Information System (INIS)
Pennington, D.M.; Henesian, M.A.; Milam, D.; Eimerl, D.
1995-01-01
In this paper we present experimental measurements and theoretical modeling of third harmonic (3ω) conversion efficiency with optical bandwidth. Third harmonic conversion efficiency drops precipitously as the input bandwidth significantly exceeds the phase matching limitations of the conversion crystals. For Type I/Type II frequency tripling, conversion efficiency be-gins to decrease for bandwidths greater than ∼60 GHz. However, conversion efficiency corresponding to monochromatic phase-matched beams can be recovered provided that the instantaneous Propagation vectors are phase matched at all times. This is achieved by imposing angular spectral dispersion (ASD) on the input beam via a diffraction grating, with a dispersion such that the phase mismatch for each frequency is zero. Experiments were performed on the Optical Sciences Laser (OSL), a 1--100 J class laser at LLNL. These experiments used a 200 GHz bandwidth source produced by a multipassed electro-optic phase modulator. The spectrum produced was composed of discrete frequency components spaced at 3 GHz intervals. Angular dispersion was incorporated by the addition of a 1200 gr/mm diffraction grating oriented at the Littrow angle, and capable of rotation about the beam direction. Experiments were performed with a pulse length of 1-ns and a 1ω input intensity of ∼ 4 GW/cm 2 for near optimal dispersion for phase matching, 5.2 μrad/GHz, with 0.1, 60, and 155 GHz bandwidth, as well as for partial dispersion compensation, 1.66 μrad/GHz, with 155 GHz and 0.1 GHz bandwidth. The direction of dispersion was varied incrementally 360 degrees about the beam diameter. The addition of the grating to the beamline reduced the narrowband conversion efficiency by approximately 10%
Frequency-chirp rates of harmonics driven by a few-cycle pulse
International Nuclear Information System (INIS)
Murakami, M.; Mauritsson, J.; Gaarde, M.B.
2005-01-01
We present numerical calculations of the time-frequency characteristics of cutoff harmonics generated by few-cycle laser pulses. We find that for driving pulses as short as three optical cycles, the adiabatic prediction for the harmonic chirp rate is very accurate. This negative chirp is so large that the resulting bandwidth causes substantial overlap between neighboring harmonics, and the harmonic phase therefore appears to not vary in time or frequency. By adding a compensating positive chirp to the driving pulse, which reduces the harmonic bandwidth and allows for the appearance of the negative chirp, we can measure the harmonic chirp rates. We also find that the positive chirp on the driving pulse causes the harmonics to shift down in frequency. We show that this counterintuitive result is caused by the change in the strong field continuum dynamics introduced by the variation of the driving frequency with time
DEFF Research Database (Denmark)
Bai, Haofeng; Wang, Xiongfei; Blaabjerg, Frede
2018-01-01
The output currents of high-power Voltage Source Inverters (VSIs) are distorted by the switching harmonics and the background harmonics in the grid voltage. This paper presents an active harmonic filtering scheme for high-power, low-frequency switching VSIs with an additional auxiliary VSI. In th...
Zhou, Hong; Melloni, Lucia; Poeppel, David; Ding, Nai
2016-01-01
Brain activity can follow the rhythms of dynamic sensory stimuli, such as speech and music, a phenomenon called neural entrainment. It has been hypothesized that low-frequency neural entrainment in the neural delta and theta bands provides a potential mechanism to represent and integrate temporal information. Low-frequency neural entrainment is often studied using periodically changing stimuli and is analyzed in the frequency domain using the Fourier analysis. The Fourier analysis decomposes a periodic signal into harmonically related sinusoids. However, it is not intuitive how these harmonically related components are related to the response waveform. Here, we explain the interpretation of response harmonics, with a special focus on very low-frequency neural entrainment near 1 Hz. It is illustrated why neural responses repeating at f Hz do not necessarily generate any neural response at f Hz in the Fourier spectrum. A strong neural response at f Hz indicates that the time scales of the neural response waveform within each cycle match the time scales of the stimulus rhythm. Therefore, neural entrainment at very low frequency implies not only that the neural response repeats at f Hz but also that each period of the neural response is a slow wave matching the time scale of a f Hz sinusoid.
Special frequencies and Lifshitz singularities in binary random harmonic chains
International Nuclear Information System (INIS)
Nieuwenhuizen, T.M.; Luck, J.M.; Canisius, J.; van Hemmen, J.L.; Ventevogel, W.J.
1986-01-01
The authors consider a one-dimensional chain of coupled harmonic oscillators; the mass of each atom is a random variable taking only two values (M or 1). They investigate the integrated density of states H(omega 2 ) near special frequencies: a given frequency omega/sub s/ with rational wavelength becomes special if the mass ratio M exceeds a certain critical value M/sub c/. They show that H has essential singularities of the types H/sub sg/∼ exp(-C 1 absolute value of omega 2 -omega/sub s/ 2 /sup 1/2/) or exp(-C 2 absolute value of omega 2 -omega/sub s/ 2 -1 ), according to the value of M and the sign of (omega 2 -omega/sub s/ 2 ). The Lifshitz singularity at the band edge is analyzed in the same way. In each case, the constant C 1 or C 2 is evaluated explicitly and compared with a vast amount of numerical work. All these exponential singularities are modulated by periodic amplitudes. The properties of the eigenfunctions with frequencies close to the special values are also discussed, and are illustrated by numerical data
General solution of the multigroup spherical harmonics equations in R-Z geometry
International Nuclear Information System (INIS)
Matausek, M.
1983-01-01
In the present paper the generalization is performed of the procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed foe one-dimensional systems in cylindrical or spherical geometry, and later extended for special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r and z directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. The analysis is performed of the possibilities to satisfy the boundary conditions in the case when the system considered represents an elementary reactor lattice cell and in the case when the system represents a reactor as a whole. The computational effort is estimated for system of a given configuration. (author)
Frequency Adaptive Selective Harmonic Control for Grid-Connected Inverters
DEFF Research Database (Denmark)
Yang, Yongheng; Zhou, Keliang; Wang, Huai
2015-01-01
SHC scheme consists of multiple parallel recursive (nk±m)-order (k = 0, 1, 2, . . ., and m ≤ n/2) harmonic control modules with independent control gains, which can be optimally weighted in accordance with the harmonic distribution. The hybrid SHC thus offers an optimal trade-off among cost...
Frequency dependence of quantum path interference in non-collinear high-order harmonic generation
International Nuclear Information System (INIS)
Zhong Shi-Yang; He Xin-Kui; Teng Hao; Ye Peng; Wang Li-Feng; He Peng; Wei Zhi-Yi
2016-01-01
High-order harmonic generation (HHG) driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders. This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe. (paper)
Wintucky, Edwin G.; Simons, Rainee N.
2014-01-01
This paper presents the design, fabrication and test results for a novel waveguide multimode directional coupler (MDC). The coupler fabricated from two dissimilar waveguides is capable of isolating the power at the second harmonic frequency from the fundamental power at the output port of a traveling-wave tube (TWT). In addition to accurate power measurements at harmonic frequencies, a potential application of the MDC is in the design of a beacon source for atmospheric propagation studies at millimeter-wave frequencies.
DEFF Research Database (Denmark)
Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede
2017-01-01
For the efficiency and simplicity of electric systems, the dc power electronic systems are widely used in a variety of applications such as electric vehicles, ships, aircraft and also in homes. In these systems, there could be a number of dynamic interactions and frequency coupling between network...... with different switching frequency or harmonics from ac-dc converters makes that harmonics and frequency coupling are both problems of ac system and challenges of dc system. This paper presents a modeling and simulation method for a large dc power electronic system by using Harmonic State Space (HSS) modeling...
International Nuclear Information System (INIS)
Lu Yujie; Zhu Banghe; Rasmussen, John C; Sevick-Muraca, Eva M; Shen Haiou; Wang Ge
2010-01-01
Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N ) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.
A controlled filtering method for estimating harmonics of off-nominal frequencies
Marques, C.A.G.; Ribeiro, M.V.; Duque, C.A.; Ribeiro, P.F.; Da Silva, E.A.B.
2012-01-01
The increasing use of power electronics in power systems causes a high injection of harmonic components which can in turn interfere with utility equipment and customer loads. Therefore, the correct estimation and measurement of harmonics have become an important issue. If the power frequency of the
Harmonic Frequency Lowering: Effects on the Perception of Music Detail and Sound Quality.
Kirchberger, Martin; Russo, Frank A
2016-02-01
A novel algorithm for frequency lowering in music was developed and experimentally tested in hearing-impaired listeners. Harmonic frequency lowering (HFL) combines frequency transposition and frequency compression to preserve the harmonic content of music stimuli. Listeners were asked to make judgments regarding detail and sound quality in music stimuli. Stimuli were presented under different signal processing conditions: original, low-pass filtered, HFL, and nonlinear frequency compressed. Results showed that participants reported perceiving the most detail in the HFL condition. In addition, there was no difference in sound quality across conditions. © The Author(s) 2016.
Zhu, Yu; Liu, Zhigang; Deng, Wen; Deng, Zhongwen
2018-05-01
Frequency-scanning interferometry (FSI) using an external cavity diode laser (ECDL) is essential for many applications of the absolute distance measurement. However, owing to the hysteresis and creep of the piezoelectric actuator inherent in the ECDL, the optical frequency scanning exhibits a nonlinearity that seriously affects the phase extraction accuracy of the interference signal and results in the reduction of the measurement accuracy. To suppress the optical frequency nonlinearity, a harmonic frequency synthesis method for shaping the desired input signal instead of the original triangular wave is presented. The effectiveness of the presented shaping method is demonstrated through the comparison of the experimental results. Compared with an incremental Renishaw interferometer, the standard deviation of the displacement measurement of the FSI system is less than 2.4 μm when driven by the shaped signal.
International Nuclear Information System (INIS)
Sahni, D.C.; Sharma, A.
2000-01-01
The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1986-01-01
In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)
Oh, Soo Hee; Donaldson, Gail S; Kong, Ying-Yee
2016-04-01
Low-frequency acoustic cues have been shown to enhance speech perception by cochlear-implant users, particularly when target speech occurs in a competing background. The present study examined the extent to which a continuous representation of low-frequency harmonicity cues contributes to bimodal benefit in simulated bimodal listeners. Experiment 1 examined the benefit of restoring a continuous temporal envelope to the low-frequency ear while the vocoder ear received a temporally interrupted stimulus. Experiment 2 examined the effect of providing continuous harmonicity cues in the low-frequency ear as compared to restoring a continuous temporal envelope in the vocoder ear. Findings indicate that bimodal benefit for temporally interrupted speech increases when continuity is restored to either or both ears. The primary benefit appears to stem from the continuous temporal envelope in the low-frequency region providing additional phonetic cues related to manner and F1 frequency; a secondary contribution is provided by low-frequency harmonicity cues when a continuous representation of the temporal envelope is present in the low-frequency, or both ears. The continuous temporal envelope and harmonicity cues of low-frequency speech are thought to support bimodal benefit by facilitating identification of word and syllable boundaries, and by restoring partial phonetic cues that occur during gaps in the temporally interrupted stimulus.
Yang, Yi; Ng, Ching-Tai; Kotousov, Andrei; Sohn, Hoon; Lim, Hyung Jin
2018-01-01
This paper presents experimental and theoretical analyses of the second harmonic generation due to non-linear interaction of Lamb waves with a fatigue crack. Three-dimensional (3D) finite element (FE) simulations and experimental studies are carried out to provide physical insight into the mechanism of second harmonic generation. The results demonstrate that the 3D FE simulations can provide a reasonable prediction on the second harmonic generated due to the contact nonlinearity at the fatigue crack. The effect of the wave modes on the second harmonic generation is also investigated in detail. It is found that the magnitude of the second harmonic induced by the interaction of the fundamental symmetric mode (S0) of Lamb wave with the fatigue crack is much higher than that by the fundamental anti-symmetric mode (A0) of Lamb wave. In addition, a series of parametric studies using 3D FE simulations are conducted to investigate the effect of the fatigue crack length to incident wave wavelength ratio, and the influence of the excitation frequency on the second harmonic generation. The outcomes show that the magnitude and directivity pattern of the generated second harmonic depend on the fatigue crack length to incident wave wavelength ratio as well as the ratio of S0 to A0 incident Lamb wave amplitude. In summary, the findings of this study can further advance the use of second harmonic generation in damage detection.
International Nuclear Information System (INIS)
Pachtman, A.
1986-09-01
Measurements of Extraordinary mode absorption at the electron cyclotron harmonic frequencies are of unique value in high temperature, high density Tokamak plasma diagnostic applications. An experimental study of Extraordinary mode absorption at the semi-opaque second and third harmonics has been performed on the ALCATOR C Tokamak. A narrow beam of submillimeter laser radiation was used to illuminate the plasma in a horizontal plane, providing a continuous measurement of the one-pass, quasi-perpendicular transmission
International Nuclear Information System (INIS)
Zhao Yiguang
1991-01-01
The method of obtaining self-consistent solutions of the field equation and the rate equations of photon density and carrier concentration has been used to study frequecny locking, quasiperiodicity, subharmonic bifurcations and chaos in high frequency modulated stripe geometry DH semiconductor lasers. The results show that the chaotic behavior arises in self-pulsing stripe geometry semiconductor lasers. The route to chaos is not period-double, but quasiperiodicity to chaos. All of the results agree with the experiments. Some obscure points in previous theory about chaos have been cleared up
Energy Technology Data Exchange (ETDEWEB)
Hanson-Heine, Magnus W. D., E-mail: magnus.hansonheine@nottingham.ac.uk [School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2015-10-28
Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.
Cheng, Zhongtao; Liu, Dong; Zhou, Yudi; Yang, Yongying; Luo, Jing; Zhang, Yupeng; Shen, Yibing; Liu, Chong; Bai, Jian; Wang, Kaiwei; Su, Lin; Yang, Liming
2016-09-01
A general resonant frequency locking scheme for a field-widened Michelson interferometer (FWMI), which is intended as a spectral discriminator in a high-spectral-resolution lidar, is proposed based on optimal multi-harmonics heterodyning. By transferring the energy of a reference laser to multi-harmonics of different orders generated by optimal electro-optic phase modulation, the heterodyne signal of these multi-harmonics through the FWMI can reveal the resonant frequency drift of the interferometer very sensitively within a large frequency range. This approach can overcome the locking difficulty induced by the low finesse of the FWMI, thus contributing to excellent locking accuracy and lock acquisition range without any constraint on the interferometer itself. The theoretical and experimental results are presented to verify the performance of this scheme.
Directory of Open Access Journals (Sweden)
S. A. Hamzah
2013-01-01
Full Text Available Harmonic suppressed fractal antenna with switches named TMFDB25 is developed to select desired frequency band from 400 MHz to 3.5 GHz. The radiating element length is changed to tune the operating frequency while the stub is used to eliminate the undesired harmonic frequency. The balun circuit is reduced by 75% from the original size. The antenna is built on a low loss material. It has the ability to select a single frequency out of fifteen different bands and maintain the omnidirectional radiation pattern properties. Furthermore, the antenna is designed, built, and tested. Simulation and measurement results show that the antenna operates well at the specific frequency range. Therefore, the antenna is suitable to be used for switching frequencies in the band of TV, GSM900/1800, 3G, ISM 2.4 GHz, and above.
Can temporal fine structure represent the fundamental frequency of unresolved harmonics?
Oxenham, Andrew J; Micheyl, Christophe; Keebler, Michael V
2009-04-01
At least two modes of pitch perception exist: in one, the fundamental frequency (F0) of harmonic complex tones is estimated using the temporal fine structure (TFS) of individual low-order resolved harmonics; in the other, F0 is derived from the temporal envelope of high-order unresolved harmonics that interact in the auditory periphery. Pitch is typically more accurate in the former than in the latter mode. Another possibility is that pitch can sometimes be coded via the TFS from unresolved harmonics. A recent study supporting this third possibility [Moore et al. (2006a). J. Acoust. Soc. Am. 119, 480-490] based its conclusion on a condition where phase interaction effects (implying unresolved harmonics) accompanied accurate F0 discrimination (implying TFS processing). The present study tests whether these results were influenced by audible distortion products. Experiment 1 replicated the original results, obtained using a low-level background noise. However, experiments 2-4 found no evidence for the use of TFS cues with unresolved harmonics when the background noise level was raised, or the stimulus level was lowered, to render distortion inaudible. Experiment 5 measured the presence and phase dependence of audible distortion products. The results provide no evidence that TFS cues are used to code the F0 of unresolved harmonics.
Localized, Non-Harmonic Active Flap Motions for Low Frequency In-Plane Rotor Noise Reduction
Sim, Ben W.; Potsdam, Mark; Kitaplioglu, Cahit; LeMasurier, Philip; Lorber, Peter; Andrews, Joseph
2012-01-01
A first-of-its-kind demonstration of the use of localized, non-harmonic active flap motions, for suppressing low frequency, in-plane rotor noise, is reported in this paper. Operational feasibility is verified via testing of the full-scale AATD/Sikorsky/UTRC active flap demonstration rotor in the NFAC's 40- by 80-Foot anechoic wind tunnel. Effectiveness of using localized, non-harmonic active flap motions are compared to conventional four-per-rev harmonic flap motions, and also active flap motions derived from closed-loop acoustics implementations. All three approaches resulted in approximately the same noise reductions over an in-plane three-by-three microphone array installed forward and near in-plane of the rotor in the nearfield. It is also reported that using an active flap in this localized, non-harmonic manner, resulted in no more that 2% rotor performance penalty, but had the tendency to incur higher hub vibration levels.
International Nuclear Information System (INIS)
Saidi, E.H.; Zakkari, M.
1990-05-01
N=4SU(2) conformal invariance is studied in harmonic superspace. It is shown that the N=4SU(2) conformal structure is equivalent to the harmonic analyticity. The solutions of the superconformal constraints are worked out in detail and the conformal properties of all objects of interests are given. A realization of the N=4 current in terms of the free (F.S.) hypermultiplet is obtained. (author). 10 refs
Harmonic Phase Responses of Radio Frequency Electronics: Wireline Test
2015-12-01
low- or intermediate -frequency port is terminated in a matched load. The radios were powered and left in standby mode (i.e., turned on and tuned, but...M HIGGINS D LIAO A MARTONE D MCNAMARA G MAZZARO K RANNEY M RESSLER K SHERBONDY G SMITH A SULLIVAN
International Nuclear Information System (INIS)
Klimas, A.J.
1983-01-01
A bump-on-tail unstable reduced velocity distribution has been constructed from data obtained at the upstream boundary of the electron foreshock by the GSFC electron spectrometer experiment on the ISEE 1 satellite. This distribution is used as the initial plasma state for a numerical integration of the one-dimensional Vlasov-Maxwell system of equations. The integration is carried through the growth of the instability, beyond its saturation, and well into the stabilized plasma regime. A power spectrum for the electric field of the stabilized plasma is computed. The spectrum is dominated by a narrow peak at the Bohm-Gross frequency of the unstable field mode but it also contain significant power at the harmonics of the Bohm-Gross frequency. The harmonic power is in sharp peaks which are split into closely spaced doublets. The fundamental peak at the Bohm-Gross frequency is also split, in this case into a closely space triplet. The fundamental peak at the Bohm-Gross frequency is also split, in this case into a closely space triplet. The splitting is due to slow modulations of the stabilized electric field oscillations which, it is thought, are caused by wave-particle trapping. The wavelength of mth harmonic of the Bohm-Gross frequency is given by lambda/sub u//m, where lambda/sub u/ is the wavelength of the unstable mode. The mechanism for excitation of the second harmonic is shwn to be second-order wave-wave coupling which takes place during that period in the evolution of the instability which would otherwise be called the linear growth phase. It is conjectured that the higher harmonics are excited by the same mechanism. It is further argued that harmonic excitation at the boundary of the electron foreshock should be a common occurrence
Multicascade X-Ray Free-Electron Laser with Harmonic Multiplier and Two-Frequency Undulator
Zhukovsky, K. V.
2018-06-01
The feasibility of generation of powerful x-ray radiation by a cascade free-electron laser (FEL) with amplification of higher harmonics using a two-frequency undulator is studied. To analyze the FEL operation, a complex phenomenological single-pass FEL model is developed and used. It describes linear and nonlinear generation of harmonics in the FEL with seed laser that takes into account initial electron beam noise and describes all main losses of each harmonic in each FEL cascade. The model is also calibrated against and approved by the experimental FEL data and available results of three-dimensional numerical simulation. The electron beam in the undulator is assumed to be matched and focused, and the dynamics of power in the singlepass FEL with cascade harmonic multipliers is investigated to obtain x-ray laser radiation in the FEL having the shortest length, beam energy, and frequency of the seed laser as low as possible. In this context, the advantages of the two-frequency undulator used for generation of harmonics are demonstrated. The evolution of harmonics in a multicascade FEL with multiplication of harmonics is investigated. The operation of the cascade FEL at the wavelength λ = 1.14 nm, generating 30 MW already on 38 m with the seed laser operating at a wavelength of 11.43 nm corresponding to the maximal reflectivity of the multilayered mirror MoRu/Be coating is investigated. In addition, the operation of the multicascade FEL with accessible seed UVlaser operating at a wavelength of 157 nm (F2 excimer UV-laser) and electron beam with energy of 0.5 GeV is investigated. X-ray radiation simulated in it at the wavelength λ 3.9 nm reaches power of 50 MW already at 27 m, which is by two orders of magnitude shorter than 3.4 km of the x-ray FEL recently put into operation in Europe.
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken
1993-01-01
A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)
Harmonic-suppressed quadrature-input frequency divider for OFDM systems
International Nuclear Information System (INIS)
Fu Haipeng; Ren Junyan; Li Wei; Li Ning
2011-01-01
A fully balanced harmonic-suppressed quadrature-input frequency divider is proposed. The frequency divider improves the quadrature phase accuracy at the output by using both input I/Q signals. Compared with conventional dividers, the circuit achieves an output I/Q phase sequence that is independent of the input I/Q phase sequence. Moreover, the third harmonic is effectively suppressed by employing a double degeneration technique. The design is fabricated in TSMC 0.13-μm CMOS and operated at 1.2 V. While locked at 8.5 GHz, the proposed divider measures a maximum third harmonic rejection of 45 dB and a phase noise of −124 dBc/Hz at a 10 MHz offset. The circuit achieves a locking range of 15% while consuming a total current of 4.5 mA. (semiconductor integrated circuits)
Accuracy of finite-difference harmonic frequencies in density functional theory.
Liu, Kuan-Yu; Liu, Jie; Herbert, John M
2017-07-15
Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors numbers. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
RF-heating of plasma in the frequency domain of the ion cyclotron harmonics
International Nuclear Information System (INIS)
Hahnekamp, H.G.; Stampa, A.; Tuczek, H.; Laeuter, R.; Wulf, H.O.
1976-01-01
Experiments on rf-heating of plasmas in the frequency domain of the ion cyclotron harmonics are reported. The rf-power is coupled to the magneto-acoustic wave for frequencies between ωsub(ci) and 5ωsub(ci). The measurements indicate that the damping of the pump wave is mainly due to the excitation of turbulence, whereas direct resonance at 2ωsub(ci) seems to be of minor importance
Equatorial insolation: from precession harmonics to eccentricity frequencies
Directory of Open Access Journals (Sweden)
A. Berger
2006-01-01
Full Text Available Since the paper by Hays et al. (1976, spectral analyses of climate proxy records provide substantial evidence that a fraction of the climatic variance is driven by insolation changes in the frequency ranges of obliquity and precession variations. However, it is the variance components centered near 100 kyr which dominate most Upper Pleistocene climatic records, although the amount of insolation perturbation at the eccentricity driven periods close to 100-kyr (mainly the 95 kyr- and 123 kyr-periods is much too small to cause directly a climate change of ice-age amplitude. Many attempts to find an explanation to this 100-kyr cycle in climatic records have been made over the last decades. Here we show that the double maximum which characterizes the daily irradiation received in tropical latitudes over the course of the year is at the origin in equatorial insolation of not only strong 95 kyr and 123 kyr periods related to eccentricity, but also of a 11-kyr and a 5.5-kyr periods related to precession.
Liu, Chang; Azimi, Behnam; Bhandary, Moulesh; Hu, Yi
2014-01-01
The goal of this study was to investigate Mandarin Chinese tone identification in quiet and multi-talker babble conditions for normal-hearing listeners. Tone identification was measured with speech stimuli and stimuli with low and/or high harmonics that were embedded in three Mandarin vowels with two fundamental frequencies. There were six types of stimuli: all harmonics (All), low harmonics (Low), high harmonics (High), and the first (H1), second (H2), and third (H3) harmonic. Results showed that, for quiet conditions, individual harmonics carried frequency contour information well enough for tone identification with high accuracy; however, in noisy conditions, tone identification with individual low harmonics (e.g., H1, H2, and H3) was significantly lower than that with the Low, High, and All harmonics. Moreover, tone identification with individual harmonics in noise was lower for a low F0 than for a high F0, and was also dependent on vowel category. Tone identification with individual low-frequency harmonics was accounted for by local signal-to-noise ratios, indicating that audibility of harmonics in noise may play a primary role in tone identification.
DEFF Research Database (Denmark)
Jacobsen, Niels-Jørgen; Andersen, Palle; Brincker, Rune
2006-01-01
The presence of harmonic components in the measured responses is unavoidable in many applications of Operational Modal Analysis. This is especially true when measuring on mechanical structures containing rotating or reciprocating parts. This paper describes a new method based on the popular...... agreement is found and the method is proven to be an easy-to-use and robust tool for handling responses with deterministic and stochastic content....... Enhanced Frequency Domain Decomposition technique for eliminating the influence of these harmonic components in the modal parameter extraction process. For various experiments, the quality of the method is assessed and compared to the results obtained using broadband stochastic excitation forces. Good...
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2012-01-01
Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.
Li, Guicun; Zheng, Yinghui; Ge, Xiaochun; Zeng, Zhinan; Li, Ruxin
2016-08-08
We have experimentally investigated the frequency modulation of high-order harmonics in an orthogonally polarized two-color laser field consisting of a mid-infrared 1800nm fundamental pulse and its second harmonic pulse. It is demonstrated that the high harmonic spectra can be fine-tuned as we slightly change the relative delay of the two-color laser pulses. By analyzing the relative frequency shift of each harmonic at different two-color delays, the nonadiabatic spectral shift induced by the rapid variation of the intensity-dependent intrinsic dipole phase can be distinguished from the blueshift induced by the change of the refractive index during self-phase modulation (SPM). Our comprehensive analysis shows that the frequency modulation pattern is a reflection of the average emission time of high-order harmonic generation (HHG), thus offering a simple method to fine-tune the spectra of the harmonics on a sub-cycle time scale.
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
In-phased second harmonic wave array generation with intra-Talbot-cavity frequency-doubling.
Hirosawa, Kenichi; Shohda, Fumio; Yanagisawa, Takayuki; Kannari, Fumihiko
2015-03-23
The Talbot cavity is one promising method to synchronize the phase of a laser array. However, it does not achieve the lowest array mode with the same phase but the highest array mode with the anti-phase between every two adjacent lasers, which is called out-phase locking. Consequently, their far-field images exhibit 2-peak profiles. We propose intra-Talbot-cavity frequency-doubling. By placing a nonlinear crystal in a Talbot cavity, the Talbot cavity generates an out-phased fundamental wave array, which is converted into an in-phase-locked second harmonic wave array at the nonlinear crystal. We demonstrate numerical calculations and experiments on intra-Talbot-cavity frequency-doubling and obtain an in-phase-locked second harmonic wave array for a Nd:YVO₄ array laser.
Three-Dimensional Geometry of Collagenous Tissues by Second Harmonic Polarimetry.
Reiser, Karen; Stoller, Patrick; Knoesen, André
2017-06-01
Collagen is a biological macromolecule capable of second harmonic generation, allowing label-free detection in tissues; in addition, molecular orientation can be determined from the polarization dependence of the second harmonic signal. Previously we reported that in-plane orientation of collagen fibrils could be determined by modulating the polarization angle of the laser during scanning. We have now extended this method so that out-of-plane orientation angles can be determined at the same time, allowing visualization of the 3-dimensional structure of collagenous tissues. This approach offers advantages compared with other methods for determining out-of-plane orientation. First, the orientation angles are directly calculated from the polarimetry data obtained in a single scan, while other reported methods require data from multiple scans, use of iterative optimization methods, application of fitting algorithms, or extensive post-optical processing. Second, our method does not require highly specialized instrumentation, and thus can be adapted for use in almost any nonlinear optical microscopy setup. It is suitable for both basic and clinical applications. We present three-dimensional images of structurally complex collagenous tissues that illustrate the power of such 3-dimensional analyses to reveal the architecture of biological structures.
Directory of Open Access Journals (Sweden)
M. J. Kosch
2005-07-01
Full Text Available High-power high-frequency radio waves beamed into the ionosphere cause plasma turbulence, which can accelerate electrons. These electrons collide with the F-layer neutral oxygen causing artificial optical emissions identical to natural aurora. Pumping at electron gyro-harmonic frequencies has special significance as many phenomena change their character. In particular, artificial optical emissions become strongly reduced for the third and higher gyro-harmonics. The High frequency Active Auroral Research Program (HAARP facility is unique in that it can select a frequency near the second gyro-harmonic. On 25 February 2004, HAARP was operated near the third and passed through the second gyro-harmonic for the first time in a weakening ionosphere. Two novel observations are: firstly, a strong enhancement of the artificial optical emission intensity near the second gyro-harmonic, which is opposite to higher gyro-harmonics; secondly, the optical enhancement maximum occurs for frequencies just above the second gyro-harmonic. We provide the first experimental evidence for these effects, which have been predicted theoretically. In addition, irregular optical structures were created when the pump frequency was above the ionospheric critical frequency.
Keywords. Active experiments – Auroral ionosphere – Wave-particle interactions
Directory of Open Access Journals (Sweden)
M. J. Kosch
2005-07-01
Full Text Available High-power high-frequency radio waves beamed into the ionosphere cause plasma turbulence, which can accelerate electrons. These electrons collide with the F-layer neutral oxygen causing artificial optical emissions identical to natural aurora. Pumping at electron gyro-harmonic frequencies has special significance as many phenomena change their character. In particular, artificial optical emissions become strongly reduced for the third and higher gyro-harmonics. The High frequency Active Auroral Research Program (HAARP facility is unique in that it can select a frequency near the second gyro-harmonic. On 25 February 2004, HAARP was operated near the third and passed through the second gyro-harmonic for the first time in a weakening ionosphere. Two novel observations are: firstly, a strong enhancement of the artificial optical emission intensity near the second gyro-harmonic, which is opposite to higher gyro-harmonics; secondly, the optical enhancement maximum occurs for frequencies just above the second gyro-harmonic. We provide the first experimental evidence for these effects, which have been predicted theoretically. In addition, irregular optical structures were created when the pump frequency was above the ionospheric critical frequency.Keywords. Active experiments – Auroral ionosphere – Wave-particle interactions
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
DEFF Research Database (Denmark)
Mathe, Laszlo; Iov, Florin; Sera, Dezso
2014-01-01
The accurate tracking of phase, frequency, and amplitude of different frequency components from a measured signal is an essential requirement for many digitally controlled equipment. The accurate and robust tracking of a frequency component from a complex signal was successfully applied for example...... in: grid connected inverters, sensorless motor control for rotor position estimation, grid voltage monitoring for ac-dc converters etc. Usually, the design of such trackers is done in continuous time domain. The discretization introduces errors which change the performance, especially when the input...... signal is rich in harmonics and the sampling frequency is close to the tracked frequency component. In this paper different discretization methods and implementation issues, such as Tustin, Backward-Forward Euler, are discussed and compared. A special case is analyzed, when the input signal is reach...
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Murasawa, Kengo; Sato, Koki; Hidaka, Takehiko
2011-05-01
A new method for measuring optical-beat frequencies in the terahertz (THz) region using microwave higher harmonics is presented. A microwave signal was applied to the antenna gap of a photoconductive (PC) device emitting a continuous electromagnetic wave at about 1 THz by the photomixing technique. The microwave higher harmonics with THz frequencies are generated in the PC device owing to the nonlinearity of the biased photoconductance, which is briefly described in this article. Thirteen nearly periodic peaks in the photocurrent were observed when the microwave was swept from 16 to 20 GHz at a power of -48 dBm. The nearly periodic peaks are generated by the homodyne detection of the optical beat with the microwave higher harmonics when the frequency of the harmonics coincides with the optical-beat frequency. Each peak frequency and its peak width were determined by fitting a Gaussian function, and the order of microwave harmonics was determined using a coarse (i.e., lower resolution) measurement of the optical-beat frequency. By applying the Kalman algorithm to the peak frequencies of the higher harmonics and their standard deviations, the optical-beat frequency near 1 THz was estimated to be 1029.81 GHz with the standard deviation of 0.82 GHz. The proposed method is applicable to a conventional THz-wave generator with a photomixer.
Suhaimi, Nurul Sheeda; Ohae, Chiaki; Gavara, Trivikramarao; Nakagawa, Ken'ichi; Hong, Feng-Lei; Katsuragawa, Masayuki
2015-12-15
We report the generation of five phase-locked harmonics, f₁:2403 nm, f₂:1201 nm, f₃:801 nm, f₄:600 nm, and f₅:480 nm with an exact frequency ratio of 1:2:3:4:5 by implementing a divide-by-three optical frequency divider in the high harmonic generation process. All five harmonics are generated coaxially with high phase coherence in time and space, which are applicable for various practical uses.
Bandrauk, André D.; Mauger, François; Yuan, Kai-Jun
2016-12-01
Numerical solutions of time-dependent Schrödinger equations for one and two electron cyclic molecules {{{H}}}nq+ exposed to intense bichromatic circularly polarized laser pulses of frequencies {ω }1 and {ω }2, such that {ω }1/{ω }2={n}1/{n}2 (integer) produce circularly polarized high order harmonics with a cut-off recollision maximum energy at and greater than the linear polarization law (in atomic units) {N}m{ω }1={I}p+3.17{U}p, where I p is the ionization potential and {U}p={(2{E}0)}2/4{ω }2 is the ponderomotive energy defined by the field E 0 (intensity I={{cE}}02/8π ) from each pulse and mean frequency ω =({ω }1+{ω }2)/2 . An electron recollision model in a rotating frame at rotating frequency {{Δ }}ω =({ω }1-{ω }2)/2 predicts this simple result as a result of recollision dynamics in a combination of bichromatic circularly polarized pulses. The harmonic helicities and their intensities are shown to depend on compatible symmetries of the net pulse electric fields with that of the molecules.
Terahertz repetition frequencies from harmonic mode-locked monolithic compound-cavity laser diodes
International Nuclear Information System (INIS)
Yanson, D. A.; Street, M. W.; McDougall, S. D.; Thayne, I. G.; Marsh, J. H.; Avrutin, E. A.
2001-01-01
Compound-cavity laser diodes are mode locked at a harmonic of the fundamental round-trip frequency to achieve repetition rates of up to 2.1 THz. The devices are fabricated from GaAs/AlGaAs material at a wavelength of 860 nm and incorporate two gain sections with an etched slot reflector between them, and a saturable absorber section. Autocorrelation studies are used to investigate device behavior for different reflector types and reflectivity. These lasers may find applications in terahertz imaging, medicine, ultrafast optical links, and atmospheric sensing. [copyright] 2001 American Institute of Physics
Gibson, Andrew R.; Gans, Timo
2017-11-01
The charged particle dynamics in low-pressure oxygen plasmas excited by odd harmonic dual frequency waveforms (low frequency of 13.56 MHz and high frequency of 40.68 MHz) are investigated using a one-dimensional numerical simulation in regimes of both low and high electronegativity. In the low electronegativity regime, the time and space averaged electron and negative ion densities are approximately equal and plasma sustainment is dominated by ionisation at the sheath expansion for all combinations of low and high frequency and the phase shift between them. In the high electronegativity regime, the negative ion density is a factor of 15-20 greater than the low electronegativity cases. In these cases, plasma sustainment is dominated by ionisation inside the bulk plasma and at the collapsing sheath edge when the contribution of the high frequency to the overall voltage waveform is low. As the high frequency component contribution to the waveform increases, sheath expansion ionisation begins to dominate. It is found that the control of the average voltage drop across the plasma sheath and the average ion flux to the powered electrode are similar in both regimes of electronegativity, despite the differing electron dynamics using the considered dual frequency approach. This offers potential for similar control of ion dynamics under a range of process conditions, independent of the electronegativity. This is in contrast to ion control offered by electrically asymmetric waveforms where the relationship between the ion flux and ion bombardment energy is dependent upon the electronegativity.
International Nuclear Information System (INIS)
Superfine, R.; Huang, J.Y.; Shen, Y.R.
1988-12-01
We have used sum frequency generation (SFG) to study the order in a silane monolayer before and after the deposition of a coadsorbed liquid crystal monolayer. We observe an increase in the order of the chain of the silane molecule induced by the interpenetration of the liquid crystal molecules. By using second harmonic generation (SHG) and SFG, we have studied the orientation and conformation of the liquid crystal molecule on clean and silane coated glass surfaces. On both surfaces, the biphenyl group is tilted by 70 degree with the alkyl chain end pointing away from the surface. The shift in the C-H stretch frequencies in the coadsorbed system indicates a significant interaction between molecules. 9 refs., 3 figs
International Nuclear Information System (INIS)
Nieuwenhuizen, T.M.; Luck, J.M.
1987-01-01
The authors give a complete description of the scaling behavior of the integrated density of states of random harmonic chains with random masses near the band edge omega/sub max/ and near special frequencies omega/sub s/. There are four different situations: omega upward arrow omega/sub max/, omega upward arrow omega/sub s/, omega upward arrow omega/sub s/ (critical case), omega upward arrow omega/sub s/ (general case). Their analytic results have the form of infinite sums involving Fourier coefficients of the scaling behavior of the Dyson-Schmidt function at the special frequency or the band edge. Binary mass distributions are considered in detail in the limit of a small fraction rho of light masses. Their predictions are compared with extensive numerical data
Directory of Open Access Journals (Sweden)
Hristo D. Hristov
2011-01-01
Full Text Available This paper examines the binary Fresnel zone plate (FZP lens frequency-harmonic and space-resolution focusing, and its application as a FZP lens antenna. A microwave FZP lens antenna (FZPA radiates both at design (90 GHz and terahertz (THz odd harmonic frequencies. Frequency and space domain antenna operation are studied analytically by use of the vector diffraction integral applied to a realistic printed FZPA. It is found that all harmonic gain peaks are roughly identical in form, bandwidth, and top values. At each harmonic frequency, the FZPA has a beamwidth that closely follows the Rayleigh resolution criterion. If the lens/antenna resolution is of prime importance and the small aperture efficiency is a secondary problem the microwave-design FZP lens antenna can be of great use at much higher terahertz frequencies. Important feature of the microwave FZP lens is its broader-zone construction compared to the equal in resolution terahertz-design FZP lens. Thus, unique and expensive microtechnology for the microwave FZP lens fabrication is not required. High-order harmonic operation of the FZP lens or lens antenna could find space resolution and frequency filtering applications in the terahertz and optical metrology, imaging tomography, short-range communications, spectral analysis, synchrotron facilities, and so on.
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Directory of Open Access Journals (Sweden)
N. F. Blagoveshchenskaya
2009-01-01
Full Text Available Multi-instrument observational data from an experiment on 13 October 2006 at the EISCAT/HEATING facility at Tromsø, Norway are analysed. The experiment was carried out in the evening hours when the electron density in the F-region dropped, and the HF pump frequency f_{H} was near and then above the critical frequency of the F2 layer. The distinctive feature of this experiment is that the pump frequency was just below the third electron gyro harmonic frequency, while both the HF pump beam and UHF radar beam were directed towards the magnetic zenith (MZ. The HF pump-induced phenomena were diagnosed with several instruments: the bi-static HF radio scatter on the London-Tromsø-St. Petersburg path, the CUTLASS radar in Hankasalmi (Finland, the European Incoherent Scatter (EISCAT UHF radar at Tromsø and the Tromsø ionosonde (dynasonde. The results show thermal electron excitation of the HF-induced striations seen simultaneously from HF bi-static scatter and CUTLASS radar observations, accompanied by increases of electron temperature when the heater frequency was near and then above the critical frequency of the F2 layer by up to 0.4 MHz. An increase of the electron density up to 25% accompanied by strong HF-induced electron heating was observed, only when the heater frequency was near the critical frequency and just below the third electron gyro harmonic frequency. It is concluded that the combined effect of upper hybrid resonance and gyro resonance at the same altitude gives rise to strong electron heating, the excitation of striations, HF ray trapping and extension of HF waves to altitudes where they can excite Langmuir turbulence and fluxes of electrons accelerated to energies that produce ionization.
Directory of Open Access Journals (Sweden)
N. F. Blagoveshchenskaya
2009-01-01
Full Text Available Multi-instrument observational data from an experiment on 13 October 2006 at the EISCAT/HEATING facility at Tromsø, Norway are analysed. The experiment was carried out in the evening hours when the electron density in the F-region dropped, and the HF pump frequency fH was near and then above the critical frequency of the F2 layer. The distinctive feature of this experiment is that the pump frequency was just below the third electron gyro harmonic frequency, while both the HF pump beam and UHF radar beam were directed towards the magnetic zenith (MZ. The HF pump-induced phenomena were diagnosed with several instruments: the bi-static HF radio scatter on the London-Tromsø-St. Petersburg path, the CUTLASS radar in Hankasalmi (Finland, the European Incoherent Scatter (EISCAT UHF radar at Tromsø and the Tromsø ionosonde (dynasonde. The results show thermal electron excitation of the HF-induced striations seen simultaneously from HF bi-static scatter and CUTLASS radar observations, accompanied by increases of electron temperature when the heater frequency was near and then above the critical frequency of the F2 layer by up to 0.4 MHz. An increase of the electron density up to 25% accompanied by strong HF-induced electron heating was observed, only when the heater frequency was near the critical frequency and just below the third electron gyro harmonic frequency. It is concluded that the combined effect of upper hybrid resonance and gyro resonance at the same altitude gives rise to strong electron heating, the excitation of striations, HF ray trapping and extension of HF waves to altitudes where they can excite Langmuir turbulence and fluxes of electrons accelerated to energies that produce ionization.
DEFF Research Database (Denmark)
Ashouri, Mani; Khazraj, Hesam; Silva, Filipe Miguel Faria da
This paper investigates the response of first carrier frequency harmonic (FCFH) current for designing a protection algorithm for multi-terminal Voltage source converter-based HVDC (VSC-MTDC) transmission grids. This transient harmonic current has been used before, to discriminate external AC faults...... various kinds of faults with different locations and resistances. This paper will also consider half-bridge MMC instead of two-level VSCs to test the sensitivity of the FCFH based algorithm for lower harmonic values. A modified meshed version of CIGRE DC model has been used in PSCAD and the signal...
Directory of Open Access Journals (Sweden)
Gonzalo Abad
2018-05-01
Full Text Available This paper presents an analytical model, oriented to study harmonic mitigation aspects in AC grids. As it is well known, the presence of non-desired harmonics in AC grids can be palliated in several manners. However, in this paper, a power electronic-based active impedance at selective frequencies (ACISEF is used, due to its already proven flexibility and adaptability to the changing characteristics of AC grids. Hence, the proposed analytical model approach is specially conceived to globally consider both the model of the AC grid itself with its electric equivalent impedances, together with the power electronic-based ACISEF, including its control loops. In addition, the proposed analytical model presents practical and useful properties, as it is simple to understand and simple to use, it has low computational cost and simple adaptability to different scenarios of AC grids, and it provides an accurate enough representation of the reality. The benefits of using the proposed analytical model are shown in this paper through some examples of its usefulness, including an analysis of stability and the identification of sources of instability for a robust design, an analysis of effectiveness in harmonic mitigation, an analysis to assist in the choice of the most suitable active impedance under a given state of the AC grid, an analysis of the interaction between different compensators, and so on. To conclude, experimental validation of a 2.15 kA ACISEF in a real 33 kV AC grid is provided, in which real users (household and industry loads and crucial elements such as wind parks and HVDC systems are near inter-connected.
Hirth, Michael; Kuhn, Jochen; Müller, Andreas
2015-02-01
Recent articles about smartphone experiments have described their applications as experimental tools in different physical contexts.1-4 They have established that smartphones facilitate experimental setups, thanks to the small size and diverse functions of mobile devices, in comparison to setups with computer-based measurements. In the experiment described in this article, the experimental setup is reduced to a minimum. The objective of the experiment is to determine the speed of sound with a high degree of accuracy using everyday tools. An article published recently proposes a time-of-flight method where sound or acoustic pulses are reflected at the ends of an open tube.5 In contrast, the following experiment idea is based on the harmonic resonant frequencies of such a tube, simultaneously triggered by a noise signal.
Effect of Frequency and Spatial-Harmonics on Rotary and Linear Induction Motor Characteristics
1972-03-01
A computer analysis is made of the effect of current and MMF airgap harmonics on the output characteristics of rotary and linear induction motors. The current harmonics accompanying thyristor-control operation are evaluated by Fourier analyzing the p...
de Souza, Russell J; Zulyniak, Michael A; Desai, Dipika; Shaikh, Mateen R; Campbell, Natalie C; Lefebvre, Diana L; Gupta, Milan; Wilson, Julie; Wahi, Gita; Atkinson, Stephanie A; Teo, Koon K; Subbarao, Padmaja; Becker, Allan B; Mandhane, Piushkumar J; Turvey, Stuart E; Sears, Malcolm R; Anand, Sonia S
2016-11-01
Canada is an ethnically diverse nation, which introduces challenges for health care providers tasked with providing evidence-based dietary advice. We aimed to harmonize food-frequency questionnaires (FFQs) across 4 birth cohorts of ethnically diverse pregnant women to derive robust dietary patterns to investigate maternal and newborn outcomes. The NutriGen Alliance comprises 4 prospective birth cohorts and includes 4880 Canadian mother-infant pairs of predominantly white European [CHILD (Canadian Healthy Infant Longitudinal Development) and FAMILY (Family Atherosclerosis Monitoring In earLY life)], South Asian [START (SouTh Asian birth cohoRT)-Canada], or Aboriginal [ABC (Aboriginal Birth Cohort)] origins. CHILD used a multiethnic FFQ based on a previously validated instrument designed by the Fred Hutchinson Cancer Research Center, whereas FAMILY, START, and ABC used questionnaires specifically designed for use in white European, South Asian, and Aboriginal people, respectively. The serving sizes and consumption frequencies of individual food items within the 4 FFQs were harmonized and aggregated into 36 common food groups. Principal components analysis was used to identify dietary patterns that were internally validated against self-reported vegetarian status and externally validated against a modified Alternative Healthy Eating Index (mAHEI). Three maternal dietary patterns were identified-"plant-based," "Western," and "health-conscious"-which collectively explained 29% of the total variability in eating habits observed in the NutriGen Alliance. These patterns were strongly associated with self-reported vegetarian status (OR: 3.85; 95% CI: 3.47, 4.29; r 2 = 0.30, P < 0.001; for a plant-based diet), and average adherence to the plant-based diet was higher in participants in the fourth quartile of the mAHEI than in the first quartile (mean difference: 46.1%; r 2 = 0.81, P < 0.001). Dietary data collected by using FFQs from ethnically diverse pregnant women can be
Matte, Guillaume M; Van Neer, Paul L M J; Danilouchkine, Mike G; Huijssen, Jacob; Verweij, Martin D; de Jong, Nico
2011-03-01
Second-harmonic imaging is currently one of the standards in commercial echographic systems for diagnosis, because of its high spatial resolution and low sensitivity to clutter and near-field artifacts. The use of nonlinear phenomena mirrors is a great set of solutions to improve echographic image resolution. To further enhance the resolution and image quality, the combination of the 3rd to 5th harmonics--dubbed the superharmonics--could be used. However, this requires a bandwidth exceeding that of conventional transducers. A promising solution features a phased-array design with interleaved low- and high-frequency elements for transmission and reception, respectively. Because the amplitude of the backscattered higher harmonics at the transducer surface is relatively low, it is highly desirable to increase the sensitivity in reception. Therefore, we investigated the optimization of the number of elements in the receiving aperture as well as their arrangement (topology). A variety of configurations was considered, including one transmit element for each receive element (1/2) up to one transmit for 7 receive elements (1/8). The topologies are assessed based on the ratio of the harmonic peak pressures in the main and grating lobes. Further, the higher harmonic level is maximized by optimization of the center frequency of the transmitted pulse. The achievable SNR for a specific application is a compromise between the frequency-dependent attenuation and nonlinearity at a required penetration depth. To calculate the SNR of the complete imaging chain, we use an approach analogous to the sonar equation used in underwater acoustics. The generated harmonic pressure fields caused by nonlinear wave propagation were modeled with the iterative nonlinear contrast source (INCS) method, the KZK, or the Burger's equation. The optimal topology for superharmonic imaging was an interleaved design with 1 transmit element per 6 receive elements. It improves the SNR by ~5 dB compared with
International Nuclear Information System (INIS)
Laeuter, R.
1976-05-01
Experiments on the HF heating of a plasma in a cylindrical arrangement with pump frequencies ω 0 in the ion cyclotron harmonics nωsub(ci) are described. A magnetized plasma of relativily high density (approximately 10 14 cm -3 ) is generated in a pinch-like source with pulsated gas inlet, and said plasma then expands along diverging magnetic-field lines in a quasi-static homogeneous guide field B 0 = 330 G. This results in a practically fully ionized, low-impurity and more or less homogeneous plasma column of a diameter of approximately 20 cm at a variable density between 5 x 10 11 and 5 x 10 12 cm -3 and at electron temperatures of 5 to 8 eV. A standing magneto-hydrodynamic wave is excited in this plasma by means of a 1.8 m Stix coil which is part of the anode resonant circuit of a pulsated 1 MHz 500-kW transmitter. The axial wavelength is lambdasub(z) = 45 cm, the pulse duration amounts to tau = 200 μs. The degree of modulation B tilde/B 0 of the quasi-static magnetic field by the HF field is adjustable and ranges between 0.015 and 0.06. The heating at 2ωsub(ci) and 4ωsub(ci) is investigated within this study. Efficiency measurements show that a very effective energy transfer to the plasma occurs with both frequencies. Ion temperatures between 70 and 100 eV are ascertained by means of a retarding-potential spectrometer. For plasma heating, similar turbulent mechanisms seem to be responsible in both cases whereas the linear wave-particle resonance at 2ωsub(ci) seems to be of subordinated importance. The theoretically assumed parametric decay into ion-Bernstein waves, which should be possible at 4 ωsub(ci), is not observed. Measurements with compensated magnetic loops and electrostatic probes make a disturbance of the radial plasma confinement obvious, by which an anormally high pulse frequency might be explained. (orig.) [de
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2011-01-01
Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.
Directory of Open Access Journals (Sweden)
William E Wood
Full Text Available Complex motor skills are more difficult to perform at certain points in the day (for example, shortly after waking, but the daily trajectory of motor-skill error is more difficult to predict. By undertaking a quantitative analysis of the fundamental frequency (FF and amplitude of hundreds of zebra finch syllables per animal per day, we find that zebra finch song follows a previously undescribed daily oscillation. The FF and amplitude of harmonic syllables rises across the morning, reaching a peak near mid-day, and then falls again in the late afternoon until sleep. This oscillation, although somewhat variable, is consistent across days and across animals and does not require serotonin, as animals with serotonergic lesions maintained daily oscillations. We hypothesize that this oscillation is driven by underlying physiological factors which could be shared with other taxa. Song production in zebra finches is a model system for studying complex learned behavior because of the ease of gathering comprehensive behavioral data and the tractability of the underlying neural circuitry. The daily oscillation that we describe promises to reveal new insights into how time of day affects the ability to accomplish a variety of complex learned motor skills.
Sum frequency and second harmonic generation from the surface of a liquid microjet
Energy Technology Data Exchange (ETDEWEB)
Smolentsev, Nikolay; Chen, Yixing; Roke, Sylvie, E-mail: sylvie.roke@epfl.ch [Laboratory for Fundamental Biophotonics (LBP), Institute of Bioengineering (IBI), School of Engineering STI, École Polytechnique Fédérale de Lausanne EPFL, 1015 Lausanne (Switzerland); Jena, Kailash C. [Laboratory for Fundamental Biophotonics (LBP), Institute of Bioengineering (IBI), School of Engineering STI, École Polytechnique Fédérale de Lausanne EPFL, 1015 Lausanne (Switzerland); Department of Physics, Indian Institute of Technology Ropar, Rupnagar, 140001 (India); Brown, Matthew A. [Laboratory for Surface Science and Technology, Department of Materials, ETH Zürich, CH-8093 Zurich (Switzerland)
2014-11-14
The use of a liquid microjet as a possible source of interest for Second Harmonic Generation (SHG) and Sum Frequency Generation (SFG) spectroscopy is examined. We measured non-resonant SHG scattering patterns from the air/water interface of a microjet of pure water and observe a strong enhancement of the SHG signal for certain scattering angles. These enhancements can be explained by the optical properties and the shape of the liquid microjet. SFG experiments at the surface of a liquid microjet of ethanol in air show that it is also possible to measure the coherent vibrational SFG spectrum of the ethanol/air interface in this way. Our findings are useful for future far-UV or X-ray based nonlinear optical surface experiments on liquid jets. In addition, combined X-ray photoelectron spectroscopy and SHG/SFG measurements are feasible, which will be very useful in improving our understanding of the molecular foundations of electrostatic and chemical surface properties and phenomena.
Sum frequency and second harmonic generation from the surface of a liquid microjet
Smolentsev, Nikolay; Chen, Yixing; Jena, Kailash C.; Brown, Matthew A.; Roke, Sylvie
2014-11-01
The use of a liquid microjet as a possible source of interest for Second Harmonic Generation (SHG) and Sum Frequency Generation (SFG) spectroscopy is examined. We measured non-resonant SHG scattering patterns from the air/water interface of a microjet of pure water and observe a strong enhancement of the SHG signal for certain scattering angles. These enhancements can be explained by the optical properties and the shape of the liquid microjet. SFG experiments at the surface of a liquid microjet of ethanol in air show that it is also possible to measure the coherent vibrational SFG spectrum of the ethanol/air interface in this way. Our findings are useful for future far-UV or X-ray based nonlinear optical surface experiments on liquid jets. In addition, combined X-ray photoelectron spectroscopy and SHG/SFG measurements are feasible, which will be very useful in improving our understanding of the molecular foundations of electrostatic and chemical surface properties and phenomena.
Sum frequency and second harmonic generation from the surface of a liquid microjet
International Nuclear Information System (INIS)
Smolentsev, Nikolay; Chen, Yixing; Roke, Sylvie; Jena, Kailash C.; Brown, Matthew A.
2014-01-01
The use of a liquid microjet as a possible source of interest for Second Harmonic Generation (SHG) and Sum Frequency Generation (SFG) spectroscopy is examined. We measured non-resonant SHG scattering patterns from the air/water interface of a microjet of pure water and observe a strong enhancement of the SHG signal for certain scattering angles. These enhancements can be explained by the optical properties and the shape of the liquid microjet. SFG experiments at the surface of a liquid microjet of ethanol in air show that it is also possible to measure the coherent vibrational SFG spectrum of the ethanol/air interface in this way. Our findings are useful for future far-UV or X-ray based nonlinear optical surface experiments on liquid jets. In addition, combined X-ray photoelectron spectroscopy and SHG/SFG measurements are feasible, which will be very useful in improving our understanding of the molecular foundations of electrostatic and chemical surface properties and phenomena
Harmonic content in the variable-frequency ac power line of TFTR
International Nuclear Information System (INIS)
Zabar, Z.; Bronner, G.; McMurray, S.; Karady, G.
1979-12-01
Studies were made of the harmonic content of the current and voltage at the generator bus of the Tokamak Fusion Test Reactor. Out of numerous load scenarios, one case was considered in detail. The harmonics were found acceptable for the generator; however, control problems and substantial telecommunications interference may result, requiring appropriate control measures and shielded telecommunication lines
DEFF Research Database (Denmark)
Bruun, Erik
1999-01-01
One of the origins of harmonic distortion in current mirrors is the inevitable mismatch between the mirror transistors. In this brief we examine both single current mirrors and complementary class AB current mirrors and develop analytical expressions for the mismatch induced harmonic distortion. ...
Olsen, M. K.
2018-03-01
The development of quantum technologies which use quantum states of the light field interacting with other systems creates a demand for such states over wide frequency ranges. In this work we compare the bipartite entanglement and Einstein-Podolsky-Rosen (EPR) -steering properties of the two different parametric schemes which produce third-harmonic optical fields from an input field at the fundamental frequency. The first scheme uses second harmonic cascaded with sum-frequency generation, while the second uses triply degenerate four- wave mixing, also known as direct third-harmonic generation. We find that both schemes produce continuous-variable bipartite entanglement and EPR steering over a frequency range which has previously been unobtainable. The direct scheme produces a greater degree of EPR steering, while the cascaded scheme allows for greater flexibility in having three available bipartitions, thus allowing for greater flexibility in the tailoring of light matter interfaces. There are also parameter regimes in both for which classical mean-field analyses fail to predict the mean-field solutions. Both schemes may be very useful for applications in quantum communication and computation networks, as well as providing for quantum interfaces between a wider range of light and atomic ensembles than is presently practicable.
Measurement and control of the frequency chirp rate of high-order harmonic pulses
International Nuclear Information System (INIS)
Mauritsson, J.; Johnsson, P.; Lopez-Martens, R.; Varju, K.; L'Huillier, A.; Kornelis, W.; Biegert, J.; Keller, U.; Gaarde, M.B.; Schafer, K.J.
2004-01-01
We measure the chirp rate of harmonics 13 to 23 in argon by cross correlation with a 12 femtosecond probe pulse. Under low ionization conditions, we directly measure the negative chirp due to the atomic dipole phase, and show that an additional chirp on the pump pulse is transferred to the qth harmonic as q times the fundamental chirp. Our results are in accord with simulations using the experimentally measured 815 nm pump and probe pulses. The ability to measure and manipulate the harmonic chirp rate is essential for the characterization and optimization of attosecond pulse trains
Sum frequency generation image reconstruction: Aliphatic membrane under spherical cap geometry
Energy Technology Data Exchange (ETDEWEB)
Volkov, Victor [Bereozovaya 2A, Konstantinovo, Moscow Region 140207 (Russian Federation)
2014-10-07
The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal – a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance.
International Nuclear Information System (INIS)
Fueloep, L.
1987-10-01
The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)
Modeling of large aperture third harmonic frequency conversion of high power Nd:glass laser systems
International Nuclear Information System (INIS)
Henesian, M.A.; Wegner, P.J.; Speck, D.R.; Bibeau, C.; Ehrlich, R.B.; Laumann, C.W.; Lawson, J.K.; Weiland, T.L.
1991-01-01
To provide high-energy, high-power beams at short wavelengths for inertial-confinement-fusion experiments, we routinely convert the 1.053-μm output of the Nova, Nd:phosphate-glass, laser system to its third-harmonic wavelength. We describe performance and conversion efficiency modeling of the 3 x 3 arrays potassium-dihydrogen-phosphate crystal plates used for type II/type II phase-matched harmonic conversion of Nova 0.74-m diameter beams, and an alternate type I/type II phase-matching configuration that improves the third-harmonic conversion efficiency. These arrays provide energy conversion of up to 65% and intensity conversion to 70%. 19 refs., 11 figs
International Nuclear Information System (INIS)
Lim, Gwon; Jeong, Do Young; Ko, Kwang Hoon; Kim, Jae Woo; Kim, Taek Soo; Rho, Sipyo; Kim, Cheol Jung
2003-01-01
We have constructed the frequency-locked pulsed dye laser system. It is composed with a GIM-type oscillator and 3 stage longitudinally pumped amplifiers. The pump laser is the second harmonic of pulse Nd:YAG laser at the repetition rate of 6 kHz. Frequency-locking of dye laser oscillator is actively controlled by the feedback loop between a photoionization signal of T1-203 isotope and a wavelength tuning control. The tuning mirror rotates the order of micro degree per a step of step motor. Feedback system for frequency locking is operated with a PC-based control interface, including the data analysis of photoionization signals and the wavelength control using step pumping method for a medical application. Therefor, the dye laser has to be locked at 583.66 nm for SHG or BBO crystal. With the frequency-locking system, the photoionization experiment has been done for more than 10 hours.
Zhang, Yu-Ru; Hu, Yan-Ting; Gao, Fei; Song, Yuan-Hong; Wang, You-Nian
2018-05-01
A novel method, the so-called electrical asymmetry effect (EAE), is gaining increasing interest for realizing the separate control of the ion flux and ion energy. In this paper, a two-dimensional fluid model combined with the full set of Maxwell equations is used to investigate the plasma properties in an electrically asymmetric capacitive discharge sustained by multiple consecutive harmonics operating in the very high frequency regime. The results indicate that by increasing the total number of consecutive harmonics k, the modulation of the dc self-bias induced by changing {θ }1 (the relative phase of the fundamental frequency) becomes different, especially for k ≤slant 6. In a discharge driven by eight consecutive harmonics, the dc self-bias varies with a period 2π, and the most positive value appears at {θ }1 = 3π/2. In addition, with the electromagnetic effects taken into account, the plasma density shifts from edge-high to uniform when {θ }1 increases from 0 to π, and the maximum moves again towards the radial wall at {θ }1 = 3π/2. Moreover, the transient behavior of electrodynamics is also important for a better understanding of the EAE. Within a period, three positive peaks of {P}z are observed, which cause substantial ionization at similar places. {P}r is characterized by a pronounced peak at the end of the period, and the lowest peak value appears at {θ }1 = π. The results obtained in this work are important for improving the plasma processes by utilizing the EAE, especially when the higher order harmonics are included.
National Research Council Canada - National Science Library
Gelmont, Boris
2002-01-01
... polar optical vibration frequency When a high frequency input signal is applied to a frequency multiplier device polar-optical phonons can enhance the non-linearities inherent in this device, enabling...
Fischer, P.; Jardani, A.; Cardiff, M.; Lecoq, N.; Jourde, H.
2018-04-01
In a karstic field, the flow paths are very complex as they globally follow the conduit network. The responses generated from an investigation in this type of aquifer can be spatially highly variable. Therefore, the aim of the investigation in this case is to define a degree of connectivity between points of the field, in order to understand these flow paths. Harmonic pumping tests represent a possible investigation method for characterizing the subsurface flow of groundwater. They have several advantages compared to a constant-rate pumping (more signal possibilities, ease of extracting the signal in the responses and possibility of closed loop investigation). We show in this work that interpreting the responses from a harmonic pumping test is very useful for delineating a degree of connectivity between measurement points. We have firstly studied the amplitude and phase offset of responses from a harmonic pumping test in a theoretical synthetic modeling case in order to define a qualitative interpretation method in the time and frequency domains. Three different type of responses have been separated: a conduit connectivity response, a matrix connectivity, and a dual connectivity (response of a point in the matrix, but close to a conduit). We have then applied this method to measured responses at a field research site. Our interpretation method permits a quick and easy reconstruction of the main flow paths, and the whole set of field responses appear to give a similar range of responses to those seen in the theoretical synthetic case.
Directory of Open Access Journals (Sweden)
I. V. Bandurkin
2005-01-01
Full Text Available A method of organizing electron-wave interaction at the multiplied frequency of the signal wave is proposed. This type of electron-wave interaction provides multiplied-frequency electron bunching, which leads to formation of an intense harmonic of the electron current at a selected multiplied frequency of the signal wave. This effect is attractive for the use in klystron-type cyclotron masers with frequency multiplication as a way to increase the output frequency and improve the selectivity.
Danylov, A A; Light, A R; Waldman, J; Erickson, N
2015-12-10
Measurements of the frequency stability of a far-infrared molecular laser have been made by mixing the harmonic of an ultrastable microwave source with a portion of the laser output signal in a terahertz (THz) Schottky diode balanced mixer. A 3 GHz difference-frequency signal was used in a frequency discriminator circuit to lock the laser to the microwave source. Comparisons of the short- and long-term laser frequency stability under free-running and locked conditions show a significant improvement with locking. Short-term frequency jitter was reduced by an order of magnitude, from approximately 40 to 4 kHz, and long-term drift was reduced by more than three orders of magnitude, from approximately 250 kHz to 80 Hz. The results, enabled by the efficient Schottky diode balanced mixer downconverter, demonstrate that ultrastable microwave-based frequency stabilization of THz optically pumped lasers (OPLs) will now be possible at frequencies extending well above 4.0 THz.
The origin of high frequency radiation in earthquakes and the geometry of faulting
Madariaga, R.
2004-12-01
In a seminal paper of 1967 Kei Aki discovered the scaling law of earthquake spectra and showed that, among other things, the high frequency decay was of type omega-squared. This implies that high frequency displacement amplitudes are proportional to a characteristic length of the fault, and radiated energy scales with the cube of the fault dimension, just like seismic moment. Later in the seventies, it was found out that a simple explanation for this frequency dependence of spectra was that high frequencies were generated by stopping phases, waves emitted by changes in speed of the rupture front as it propagates along the fault, but this did not explain the scaling of high frequency waves with fault length. Earthquake energy balance is such that, ignoring attenuation, radiated energy is the change in strain energy minus energy released for overcoming friction. Until recently the latter was considered to be a material property that did not scale with fault size. Yet, in another classical paper Aki and Das estimated in the late 70s that energy release rate also scaled with earthquake size, because earthquakes were often stopped by barriers or changed rupture speed at them. This observation was independently confirmed in the late 90s by Ide and Takeo and Olsen et al who found that energy release rates for Kobe and Landers were in the order of a MJ/m2, implying that Gc necessarily scales with earthquake size, because if this was a material property, small earthquakes would never occur. Using both simple analytical and numerical models developed by Addia-Bedia and Aochi and Madariaga, we examine the consequence of these observations for the scaling of high frequency waves with fault size. We demonstrate using some classical results by Kostrov, Husseiny and Freund that high frequency energy flow measures energy release rate and is generated when ruptures change velocity (both direction and speed) at fault kinks or jogs. Our results explain why super shear ruptures are
International Nuclear Information System (INIS)
Fenstermacher, T.E.
1981-01-01
The solution of the neutron transport equation has long been a subject of intense interest to nuclear engineers. Present computer codes for the solution of this equation, however, are expensive to run for large, multidimensional problems, and also suffer from computational problems such as the ray effect. A method has been developed which eliminates many of these problems. It consists of transforming the transport equation into a set of linear partial differential equations by the use of spherical harmonics. The problem volume is divided into mesh boxes, and the flux components are approximated within each mesh box by spatially orthogonal quadratic polynomials, which need not be continuous at mesh box interfaces. A variational principle is developed, and used to solve for the unknown coefficients of these polynomials. Both one dimensional and two dimensional computer codes using this method have been written. The codes have each been tested on several test cases, and the solutions checked against solutions obtained by other methods. While the codes have some difficulty in modeling sharp transients, they produce excellent results on problems where the characteristic lengths are many mean free paths. On one test case, the two dimensional code, SHOP/2D, required only one-fourth the computer time required by the finite difference, discrete ordinates code TWOTRAN to produce a solution. In addition, SHOP/2D converged much better than TWOTRAN and produced more physical-appearing results
Mahajan, Dhruv; Ramamoorthi, Ravi; Curless, Brian
2008-02-01
This paper develops a theory of frequency domain invariants in computer vision. We derive novel identities using spherical harmonics, which are the angular frequency domain analog to common spatial domain invariants such as reflectance ratios. These invariants are derived from the spherical harmonic convolution framework for reflection from a curved surface. Our identities apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting conditions. One important case we consider is two different glossy objects in two different lighting environments. For this case, we derive a novel identity, independent of the specific lighting configurations or BRDFs, that allows us to directly estimate the fourth image if the other three are available. The identity can also be used as an invariant to detecttampering in the images. While this paper is primarily theoretical, it has the potential to lay the mathematical foundations for two important practical applications. First, we can develop more general algorithms for inverse rendering problems, which can directly relight and change material properties by transferring the BRDF or lighting from another object or illumination. Second, we can check the consistency of an image, to detect tampering or image splicing.
Laas, Katrin; Mankin, Romi; Rekker, Astrid
2009-05-01
The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.
Torrezan, Antonio C.; Han, Seong-Tae; Mastovsky, Ivan; Shapiro, Michael A.; Sirigiri, Jagadishwar R.; Temkin, Richard J.; Griffin, Robert G.; Barnes, Alexander B.
2012-01-01
The design, operation, and characterization of a continuous-wave (CW) tunable second-harmonic 460-GHz gyrotron are reported. The gyrotron is intended to be used as a submillimeter-wave source for 700-MHz nuclear magnetic resonance experiments with sensitivity enhanced by dynamic nuclear polarization. The gyrotron operates in the whispering-gallery mode TE11,2 and has generated 16 W of output power with a 13-kV 100-mA electron beam. The start oscillation current measured over a range of magnetic field values is in good agreement with theoretical start currents obtained from linear theory for successive high-order axial modes TE11,2,q. The minimum start current is 27 mA. Power and frequency tuning measurements as a function of the electron cyclotron frequency have also been carried out. A smooth frequency tuning range of 1 GHz was obtained for the operating second-harmonic mode either by magnetic field tuning or beam voltage tuning. Long-term CW operation was evaluated during an uninterrupted period of 48 h, where the gyrotron output power and frequency were kept stable to within ±0.7% and ±6 ppm, respectively, by a computerized control system. Proper operation of an internal quasi-optical mode converter implemented to transform the operating whispering-gallery mode to a Gaussian-like beam was also verified. Based on the images of the gyrotron output beam taken with a pyroelectric camera, the Gaussian-like mode content of the output beam was computed to be 92% with an ellipticity of 12%. PMID:23761938
Second-harmonic and sum-frequency generation for surface studies
International Nuclear Information System (INIS)
Hunt, J.H.; Guyot-Sionnest, P.; Shen, Y.R.
1987-07-01
Second harmonic generation (SHG) has now been well established as a versatile surface-sensitive probe. It has been used to study electrochemical processes at electrode surfaces, molecular adsorption and desorption at metal and semiconductor surfaces, orientational phase transition of molecular monolayers on water, surface reconstruction and epitaxial growth, and so on. More recently, it has been employed as a tool to monitor monolayer polymerization and other surface reactions, to probe polar order of molecules at interfaces, and to measure molecular nonlinearity. While most surface techniques are restricted to the solid/vacuum environment, SHG is applicable to nearly all interfaces as long as the interfaces are accessible by light. In addition, SHG has the advantages of being capable of in-situ measurements with high temporal, spatial, and spectral resolutions
International Nuclear Information System (INIS)
Cairns, I.H.
1988-01-01
A theory is presented for the radiation at the third to fifth harmonics of the plasma frequency observed upstream from the Earth's bow shock: the radiation is produced by the process L+T'→T in the foreshock, with the initial T' radiation being the frequently observed second harmonic radiation (generated by another process) and the L waves being products of the decay L'→L+S of L' waves generated by a streaming instability. (Here L, S, and T denote Langmuir, ion acoustic, and 'transverse electromagnetic waves, respectively.) The theory can account for the observed radiation when unusually large levels (electric fields in excess of 10 mV/m) of suitable L waves are present. Such levels of L waves are possible, in principle, but have not been reported before; the radiation is observed quite infrequently, thereby implying a requirement for unusual foreshock conditions. Predictions for the characteristics of the source regions (one to each wing of the foreshock) and the bandwidth of the radiation are given. Potential problems for the theory, relating to the large levels of L waves required to account for the radiation, are discussed. copyright American Geophysical Union 1988
Khripunov, Sergey; Kobtsev, Sergey; Radnatarov, Daba
2016-01-20
This work presents for the first time to the best of our knowledge a comparative efficiency analysis among various techniques of extra-cavity second harmonic generation (SHG) of continuous-wave single-frequency radiation in nonperiodically poled nonlinear crystals within a broad range of power levels. Efficiency of nonlinear radiation transformation at powers from 1 W to 10 kW was studied in three different configurations: with an external power-enhancement cavity and without the cavity in the case of single and double radiation pass through a nonlinear crystal. It is demonstrated that at power levels exceeding 1 kW, the efficiencies of methods with and without external power-enhancement cavities become comparable, whereas at even higher powers, SHG by a single or double pass through a nonlinear crystal becomes preferable because of the relatively high efficiency of nonlinear transformation and fairly simple implementation.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jun [School of Physics, Beijing Institute of Technology and Beijing Key Laboratory of Fractional Signals and Systems, Beijing 100081 (China); College of Physics and Electronic Engineering, Henan Normal University, 453007 Xinxiang, Henan (China); Zhang, Xiangdong, E-mail: zhangxd@bit.edu.cn [School of Physics, Beijing Institute of Technology and Beijing Key Laboratory of Fractional Signals and Systems, Beijing 100081 (China)
2015-09-28
Simultaneous negative refraction for both the fundamental frequency (FF) and second-harmonic (SH) fields in two-dimensional nonlinear photonic crystals have been found through both the physical analysis and exact numerical simulation. By combining such a property with the phase-matching condition and strong second-order susceptibility, we have designed a SH lens to realize focusing for both the FF and SH fields at the same time. Good-quality non-near field images for both FF and SH fields have been observed. The physical mechanism for such SH focusing phenomena has been disclosed, which is different from the backward SH generation as has been pointed out in the previous investigations. In addition, the effect of absorption losses on the phenomena has also been discussed. Thus, potential applications of these phenomena to biphotonic microscopy technique are anticipated.
New harmonic materials: index engineering. Thin-thick quadrature frequency conversion
International Nuclear Information System (INIS)
Eimerl, D.
1985-01-01
The quadrature conversion scheme is a method of generating the second harmonic. The scheme, which uses two crystals in series, has several advantages over single-crystal or other two crystal schemes. The most important is that it is capable of high conversion efficiency over a large dynamic range of drive intensity and detuning angle. Consider a pair of KDP crystals cut for type-II phase matching. In the quadrature scheme, the optic axes of the crystals are arranged so that the plans containing the direction of the laser beam and their optic axes (the kz planes) are mutually perpendicular. This arrangement has two important properties. First, in type-II phase matching, the incident wave is polarized at 45 deg to the kz plane of the crystal. This, in the quadrature scheme, if the incident wave is correctly polarized for efficient conversion in the first crystal, it is also correctly polarized for efficient conversion in the second crystal. Both crystals can therefore convert efficiently
Stimulation of Protein Expression Through the Harmonic Resonance of Frequency-Specific Music.
Orhan, Ibrahim Y; Gulbahar, Burak A
2016-12-01
The use of specific frequencies for specific individual amino acids may increase the potential energy of protein molecules in the medium [1]. The resonance would also increase the movement of particles in the cytosol, increasing the collisions necessary for the conduction of protein expression. The clash of two waves that share frequencies will exhibit an increase in energy through an increase in amplitude [2]. The increase in energy would in turn increase the number of collisions forming the tRNA-amino acid, increasing the amino acid acquiry for ribosomes to improve intracellular efficiency in gene expression. To test the hypothesis, Red Fluorescent Protein (RFP) in transformated BL-21 strains of E. coli and p53 protein of MCF-7 were examined after exposure to sounds of specific frequencies. Through the exposure of the experimental systems to a sequence of sounds that match the frequencies of specific amino acids, the levels of RFP exhibition respective to the control groups in the bacterial medium increased two-fold in terms of RFU. The experiments that targeted the p53 protein with the 'music' showed a decrease in the cell prevalence in the MCF-7 type breast cancer cells by 28%, by decreasing the speed of tumour formation. Exposure to 'music' that was designed through assigning a musical note for every single one of the twenty unique amino acids, produced both an analytical and a visible shift in protein synthesis, making it as potential tool for reducing procedural time uptake.
Koushki, A M; Sadighi-Bonabi, R; Mohsen-Nia, M; Irani, E
2018-04-14
In the present work, an efficient method is theoretically investigated for extending high-order harmonics and ultrashort attosecond pulse generation in N 2 and CO molecules by using the time-dependent density functional theory approach. Our results show that by utilizing chirped laser field in the presence of a low frequency field, not only is the harmonic cutoff extended remarkably but also the single short quantum trajectory is selected to contribute to the harmonic spectra. When a low frequency field is added to the two-color chirped laser field, the long quantum trajectories are suppressed and only the short quantum trajectories contribute to the higher harmonic emission mechanism. As a result, the spectral modulation is significantly decreased and an intense ultrashort pulse can be generated from the supercontinuum region of high harmonics. With such a scheme, the isolated ultrashort attosecond pulses can be generated in length, velocity, and acceleration gauges. Furthermore, these results are explained by using the classical and quantum time-frequency analyses.
International Nuclear Information System (INIS)
Gnesin, S; Coda, S; Goodman, T P; Decker, J; Peysson, Y; Mazon, D
2012-01-01
The fundamental mechanisms responsible for the interplay and synergy between the absorption dynamics of extraordinary-mode electron cyclotron waves at two different harmonic resonances (the 2nd and 3rd) are investigated in the TCV tokamak. An enhanced 3rd harmonic absorption in the presence of suprathermal electrons generated by 2nd harmonic heating is predicted by Fokker–Planck simulations, subject to complex alignment requirements in both physical space and momentum space. The experimental signature for the 2nd/3rd harmonic synergy is sought through the suprathermal bremsstrahlung emission in the hard x-ray range of photon energy. Using a synthetic diagnostic, the emission variation due to synergy is calculated as a function of the injected power and of the radial transport of suprathermal electrons. It is concluded that in the present experimental setup a synergy signature has not been unambiguously detected. The detectability of the synergy is then discussed with respect to variations and uncertainties in the plasma density and effective charge in view of future optimized experiments. (paper)
DEFF Research Database (Denmark)
Sun, Xiaofeng; Zeng, Jian; Chen, Zhe
2013-01-01
, and analyze the harmonic voltage propagation caused by the background harmonic voltage in power systems. Then, a new strategy is proposed for the site selection of resistive active power filter to damp the background harmonic voltage in power systems. Experiments have been performed to verify the theoretical......Series resonance between capacitance and line inductance may magnify background harmonic voltage and worsen the harmonic voltage distortion in power systems. To solve this problem, in this paper, the transmission line theory is used to set up the distributed parameter model of power system feeders...
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
Wintucky, Edwin G.; Simons, Rainee N.
2015-01-01
This paper presents the design, fabrication and test results for a novel waveguide multimode directional coupler (MDC). The coupler, fabricated from two dissimilar frequency band waveguides, is capable of isolating power at the second harmonic frequency from the fundamental power at the output port of a traveling-wave tube (TWT) amplifier. Test results from proof-of-concept demonstrations are presented for a Ku-band/Ka-band MDC and a Ka-band/E-band MDC. In addition to power measurements at harmonic frequencies, a potential application of the MDC is in the design of a satellite borne beacon source for atmospheric propagation studies at millimeter-wave (mm-wave) frequencies (Ka-band and E-band).
International Nuclear Information System (INIS)
Moutinho, Carlos
2015-01-01
This paper is focused on the control problems related to semi-active tuned mass dampers (TMDs) used to reduce harmonic vibrations, specially involving civil structures. A simplified version of the phase control law is derived and its effectiveness is investigated and evaluated. The objective is to improve the functioning of control systems of this type by simplifying the measurement process and reducing the number of variables involved, making the control system more feasible and reliable. Because the control law is of ON/OFF type, combined with appropriate trigger conditions, the activity of the actuation system may be significantly reduced, which may be of few seconds a day in many practical cases, increasing the durability of the device and reducing its maintenance. Moreover, due to the ability of the control system to command the motion of the inertial mass, the semi-active TMD is relatively insensitive to its initial tuning, resulting in the capability of self-tuning and in the possibility of controlling several vibration modes of a structure over a significant broadband frequency. (paper)
Gapontsev, Valentin P; Tyrtyshnyy, Valentin A; Vershinin, Oleg I; Davydov, Boris L; Oulianov, Dmitri A
2013-02-11
We present a method of third harmonic generation at 355 nm by frequency mixing of fundamental and second harmonic radiation of an ytterbium nanosecond pulsed all-fiber laser in a type-I phase-matched LiB(3)O(5) (LBO) crystal where originally orthogonal polarization planes of the fundamental and second harmonic beams are aligned by an optically active quartz crystal. 8 W of ultraviolet light at 355 nm were achieved with 40% conversion efficiency from 1064 nm radiation. The conversion efficiency obtained in a type-I phase-matched LBO THG crystal was 1.6 times higher than the one achieved in a type-II LBO crystal at similar experimental conditions. In comparison to half-wave plates traditionally used for polarization alignment the optically active quartz crystal has much lower temperature dependence and requires simpler optical alignment.
Kim, Hyun Keol; Montejo, Ludguier D; Jia, Jingfei; Hielscher, Andreas H
2017-06-01
We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n -th order absorption coefficients (FD-SP N ) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SP N based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SP N model with 3 rd order absorption coefficient (i.e., FD-SP 3 ) is used as a forward model to solve the inverse problem. The FD-SP 3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals. The forward results show that the FD-SP 3 model approximates the FD-ERT (S 12 ) solution within relatively high accuracy; the average error in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP 3 model than those with the SP 1 model. Therefore, this work shows that the FD-SP 3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S 12 ) and also it is more accurate than the FD-SP 1 .
International Nuclear Information System (INIS)
Chang, C.-W.; Liao, J.-D.
2008-01-01
In this study, the well-ordered alkanethiolate self-assembled monolayers (SAMs) of varied chain lengths and tail groups were employed as examples for nano-characterization on their mechanical properties. A novel nano-indentation technique with a constant harmonic frequency was applied on SAMs chemically adsorbed on Au to explore their contact mechanics, and furthermore to interpret how SAM molecules respond to an infinitesimal oscillation force without pressing them. Experimental results demonstrated that the harmonic contact stiffness along with the measured displacement of SAMs/Au was distinguishable using a dynamic contact modulus with the distinct feature of phase angles. Phase angles resulted from the relaxing continuation of an applied harmonic frequency and mostly influenced by the outermost tail group of SAM molecules. The harmonic contact stiffness of SAM molecules obviously increased with the densely packed alkyl chains and relatively intense agglomeration of the head group at the anchoring site. As a consequence, the result of this work is relevant to contact mechanics at the surface contact level for the distinction of molecular substances attached on a solid surface. Furthermore it is particularly anticipated to identify biological molecules of variable qualities under a fluid-like micro-environment
Energy Technology Data Exchange (ETDEWEB)
Chang, C.-W.; Liao, J.-D. [Department of Materials Science and Engineering, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan (China)], E-mail: jdliao@mail.ncku.edu.tw
2008-08-06
In this study, the well-ordered alkanethiolate self-assembled monolayers (SAMs) of varied chain lengths and tail groups were employed as examples for nano-characterization on their mechanical properties. A novel nano-indentation technique with a constant harmonic frequency was applied on SAMs chemically adsorbed on Au to explore their contact mechanics, and furthermore to interpret how SAM molecules respond to an infinitesimal oscillation force without pressing them. Experimental results demonstrated that the harmonic contact stiffness along with the measured displacement of SAMs/Au was distinguishable using a dynamic contact modulus with the distinct feature of phase angles. Phase angles resulted from the relaxing continuation of an applied harmonic frequency and mostly influenced by the outermost tail group of SAM molecules. The harmonic contact stiffness of SAM molecules obviously increased with the densely packed alkyl chains and relatively intense agglomeration of the head group at the anchoring site. As a consequence, the result of this work is relevant to contact mechanics at the surface contact level for the distinction of molecular substances attached on a solid surface. Furthermore it is particularly anticipated to identify biological molecules of variable qualities under a fluid-like micro-environment.
Bennett, Charles L [Livermore, CA
2009-10-20
A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.
Bounce-harmonic Landau Damping of Plasma Waves
Anderegg, Francois
2015-11-01
We present measurement of plasma wave damping, spanning the temperature regimes of direct Landau damping, bounce-harmonic Landau damping, inter-species drag damping, and viscous damping. Direct Landau damping is dominant at high temperatures, but becomes negligible as v vph / 5 . The measurements are conducted in trapped pure ion plasmas contained in Penning-Malmberg trap, with wave-coherent LIF diagnostics of particle velocities. Our focus is on bounce harmonics damping, controlled by an applied ``squeeze'' potential, which generates harmonics in the wave potential and in the particle dynamics. A particle moving in z experiences a non-sinusoidal mode potential caused by the squeeze, producing high spatial harmonics with lower phase velocity. These harmonics are Landau damped even when the mode phase velocity vph is large compared to the thermal velocity v , since the nth harmonic is resonant with a particle bouncing at velocity vb =vph / n . Here we increase the bounce harmonics through applied squeeze potential; but some harmonics are always present in finite length systems. For our centered squeeze geometry, theory shows that only odd harmonics are generated, and predicts the Landau damping rate from vph / n . Experimentally, the squeeze potential increases the wave damping and reduces its frequency. The frequency shift occurs because the squeeze potential reduces the number of particle where the mode velocity is the largest, therefore reducing the mode frequency. We observe an increase in the damping proportional to Vs2,and a frequency reduction proportional to Vs , in quantitative agreement with theory. Wave-coherent laser induced fluorescence allows direct observation of bounce resonances on the particle distribution, here predominantly at vph / 3 . A clear increase of the bounce harmonics is visible on the particle distribution when the squeeze potential is applied. Supported by NSF Grant PHY-1414570, and DOE Grants DE-SC0002451 and DE-SC0008693.
Beattie, Zachary T.; Jacobs, Peter G.; Riley, Thomas C.; Hagen, Chad C.
2015-01-01
Sleep apnea is a serious health condition that affects many individuals and has been associated with serious health conditions such as cardiovascular disease. Clinical diagnosis of sleep apnea requires that a patient spend the night in a sleep clinic while being wired up to numerous obtrusive sensors. We are developing a system that utilizes respiration rate and breathing amplitude inferred from non-contact bed sensors (i.e. load cells placed under bed supports) to detect sleep apnea. Multi-harmonic artifacts generated either biologically or as a result of the impulse response of the bed have made it challenging to track respiration rate and amplitude with high resolution in time. In this paper, we present an algorithm that can accurately track respiration on a second-by-second basis while removing noise harmonics. The algorithm is tested using data collected from 5 patients during overnight sleep studies. Respiration rate is compared with polysomnography estimations of respiration rate estimated by a technician following clinical standards. Results indicate that certain subjects exhibit a large harmonic component of their breathing signal that can be removed by our algorithm. When compared with technician transcribed respiration rates using polysomnography signals, we demonstrate improved accuracy of respiration rate tracking using harmonic artifact rejection (mean error: 0.18 breaths/minute) over tracking not using harmonic artifact rejection (mean error: −2.74 breaths/minute). PMID:26738176
International Nuclear Information System (INIS)
Fernandes, A.; Maiorino, J.R.
1989-01-01
This work presents a method to solve the neutron transport equation in thre space dimensions. The angular flux is aproximated by spherical harmonics and the finite element method is applied to the space component. The program originated by the analytical development is being tested and some results are presented. (author) [pt
Lipovsky, Bradley P.; Dunham, Eric M.
2015-02-01
Oscillatory seismic signals arising from resonant vibrations of hydraulic fractures are observed in many geologic systems, including volcanoes, glaciers and ice sheets, and hydrocarbon and geothermal reservoirs. To better quantify the physical dimensions of fluid-filled cracks and properties of the fluids within them, we study wave motion along a thin hydraulic fracture waveguide. We present a linearized analysis, valid at wavelengths greater than the fracture aperture, that accounts for quasi-static elastic deformation of the fracture walls, as well as fluid viscosity, inertia, and compressibility. In the long-wavelength limit, anomalously dispersed guided waves known as crack or Krauklis waves propagate with restoring force from fracture wall elasticity. At shorter wavelengths, the waves become sound waves within the fluid channel. Wave attenuation in our model is due to fluid viscosity, rather than seismic radiation from crack tips or fracture wall roughness. We characterize viscous damping at both low frequencies, where the flow is always fully developed, and at high frequencies, where the flow has a nearly constant velocity profile away from viscous boundary layers near the fracture walls. Most observable seismic signals from resonating fractures likely arise in the boundary layer crack wave limit, where fluid-solid coupling is pronounced and attenuation is minimal. We present a method to estimate the aperture and length of a resonating hydraulic fracture using both the seismically observed quality factor and characteristic frequency. Finally, we develop scaling relations between seismic moment and characteristic frequency that might be useful when interpreting the statistics of hydraulic fracture events.
Electromagnetic cyclotron harmonic waves
International Nuclear Information System (INIS)
Ohnuma, T.; Watanabe, T.; Hamamatsu, K.
1981-09-01
Electromagnetic electron cyclotron harmonic waves just below the electron cyclotron harmonics are investigated numerically and experimentally. Backward waves which are observed to propagate nearly perpendicular to the magnetic field just below the electron cyclotron frequency in a high density magnetoplasma are confirmed to be in accord with the theoretical electromagnetic cyclotron waves. (author)
Matte, G.M.; Neer, P.M.L.J. van; Danilouchkine, M.G.; Huijssen, J.; Verweij, M.; Jong, N. de
2011-01-01
Abstract—Second-harmonic imaging is currently one of the standards in commercial echographic systems for diagnosis, because of its high spatial resolution and low sensitivity to clutter and near-field artifacts. The use of nonlinear phenomena mirrors is a great set of solutions to improve
Matte, Guillaume M.; van Neer, Paul L.M.J.; Danilouchkine, Mike G.; Huijssen, Jacob; Verweij, Martin D.; de Jong, N.
2011-01-01
Second-harmonic imaging is currently one of the standards in commercial echographic systems for diagnosis, because of its high spatial resolution and low sensitivity to clutter and near-field artifacts. The use of nonlinear phenomena mirrors is a great set of solutions to improve echographic image
International Nuclear Information System (INIS)
Biso, Maurizio; Ansaldo, Alberto; Ricci, Davide
2012-01-01
Bucky gel actuators are one of the most promising type of electrochemical actuators based on carbon nanotubes (CNTs). They are lightweight, they are able to work in air without any liquid electrolyte and require just few volts to operate. In order to find real world applications where bucky gel actuators can outperform conventional motors, there are still some issues to be addressed. One key aspect in CNT-based electrochemical actuators is that their actuation speed is limited by the ability of charging and discharging the device without exceeding the electrochemical stability window of the electrolyte. This speed is macroscopically related with the product of the resistance and the capacitance of the equivalent circuit (circuit time constant), and with the ion diffusion speed inside the active electrodes. To enhance the actuator performance it is necessary to increase the ion drift current in the electrolyte avoiding to significantly raise the voltage at the electrodes and shorten the ion path necessary to charge the bucky gel electrodes. By proper material processing, we have successfully addressed this issue. A reduced thickness of the actuators to one third of the original size results in a one order of magnitude increase both of the strain at higher frequencies and of the maximum operating frequency. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Energy Technology Data Exchange (ETDEWEB)
Biso, Maurizio; Ansaldo, Alberto; Ricci, Davide [Robotics, Brain and Cognitive Sciences Department, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genoa (Italy)
2012-12-15
Bucky gel actuators are one of the most promising type of electrochemical actuators based on carbon nanotubes (CNTs). They are lightweight, they are able to work in air without any liquid electrolyte and require just few volts to operate. In order to find real world applications where bucky gel actuators can outperform conventional motors, there are still some issues to be addressed. One key aspect in CNT-based electrochemical actuators is that their actuation speed is limited by the ability of charging and discharging the device without exceeding the electrochemical stability window of the electrolyte. This speed is macroscopically related with the product of the resistance and the capacitance of the equivalent circuit (circuit time constant), and with the ion diffusion speed inside the active electrodes. To enhance the actuator performance it is necessary to increase the ion drift current in the electrolyte avoiding to significantly raise the voltage at the electrodes and shorten the ion path necessary to charge the bucky gel electrodes. By proper material processing, we have successfully addressed this issue. A reduced thickness of the actuators to one third of the original size results in a one order of magnitude increase both of the strain at higher frequencies and of the maximum operating frequency. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Harmonics and energy management
International Nuclear Information System (INIS)
Andresen, M.
1993-01-01
To summarize what this paper has presented: Voltage and current non-sinusoidal wave shapes exist in our power system. These harmonics result from the prolific use of non-linear loads. The use of these types of loads is increasing dramatically, partly due to the push to implement energy management techniques involving harmonic generating equipment. Harmonic analysis can identify specific harmonics, their frequency, magnitude, and phase shift referenced to the fundamental. Harmonic distortion forces the use of true RMS multimeters for measurement accuracy. High levels of neutral current and N-G voltages are now possible. Transformers may overheat and fail even though they are below rated capacity. Low power factors due to harmonics cannot be corrected by the installation of capacitors, and knowledge of the fundamental VARs or the displacement power factor is needed to use capacitors alone for power factor correction. The harmonic related problems presented are by no means an exhaustive list. Many other concerns arise when harmonics are involved in the power system. The critical issue behind these problems is that many of the devices being recommended from an energy management point of view are contributing to the harmonic levels, and thus to the potential for harmonic problems. We can no longer live in the sinusoidal mentality if we are to be effective in saving energy and reducing costs
Harmonic arbitrary waveform generator
Roberts, Brock Franklin
2017-11-28
High frequency arbitrary waveforms have applications in radar, communications, medical imaging, therapy, electronic warfare, and charged particle acceleration and control. State of the art arbitrary waveform generators are limited in the frequency they can operate by the speed of the Digital to Analog converters that directly create their arbitrary waveforms. The architecture of the Harmonic Arbitrary Waveform Generator allows the phase and amplitude of the high frequency content of waveforms to be controlled without taxing the Digital to Analog converters that control them. The Harmonic Arbitrary Waveform Generator converts a high frequency input, into a precision, adjustable, high frequency arbitrary waveform.
International Nuclear Information System (INIS)
Albers, R.C.; Gubernatis, J.E.
1981-01-01
The efficiency of four different Brillouin-zone integration schemes including the uniform mesh, special point method, special directions method, and Holas method are compared for calculating moments of the harmonic phonon frequencies of the solid one-component plasma. Very accurate values for the moments are also presented. The Holas method for which weights and integration points can easily be generated has roughly the same efficiency as the special directions method, which is much superior to the uniform mesh and special point methods for this problem
DEFF Research Database (Denmark)
Jensen, Ole Bjarlin; Andersen, Peter E.; Sumpf, Bernd
2009-01-01
More than 1.5 W of green light at 531 nm is generated by singlepass second harmonic generation in periodically poled MgO:LiNbO3. The pump laser is a high power tapered laser with a distributed Bragg reflector etched in the ridge section of the laser to provide wavelength selectivity. The output...... power of the single-frequency tapered laser is 9.3 W in continuous wave operation. A conversion efficiency of 18.5 % was achieved in the experiments....
International Nuclear Information System (INIS)
Lin, Qui-xun; Van Wechel, T.D.
1987-01-01
A single gap harmonic buncher has been constructed as a pretandem buncher. Over 85% of a proton dc beam has been bunched into pulses. The width (fwhm) of the pulses is 0.7 ns. The buncher is based on that built at Argonne. Changes were made to the buncher's configuration so that the buncher could be tuned to the desired four harmonic frequencies. A method of calibrating and setting the relative phases and amplitudes of the four harmonic frequencies has been used to obtain an optimum sawtooth-like bunching waveform
Energy Technology Data Exchange (ETDEWEB)
Ban, H. Y.; Kavuri, V. C., E-mail: venk@physics.upenn.edu; Cochran, J. M.; Pathak, S.; Chung, S. H.; Yodh, A. G. [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Schweiger, M.; Arridge, S. R. [Department of Computer Science, University College London, London WC1E 7JE (United Kingdom); Xie, L. [Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Busch, D. R. [Division of Neurology, Children’s Hospital of Philadelphia, Philadelphia, Pennsylvania 19104 (United States); Katrašnik, J. [Faculty of Electrical Engineering, University of Ljubljana, Ljubljana 1000 (Slovenia); Lee, K. [Daegu Gyeongbuk Institute of Science and Technology, Daegu 711-813 (Korea, Republic of); Choe, R. [Department of Biomedical Engineering, University of Rochester, Rochester, New York 14642 (United States); Czerniecki, B. J. [Department of Surgery, Hospital of the University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
2016-07-15
Purpose: The authors introduce a state-of-the-art all-optical clinical diffuse optical tomography (DOT) imaging instrument which collects spatially dense, multispectral, frequency-domain breast data in the parallel-plate geometry. Methods: The instrument utilizes a CCD-based heterodyne detection scheme that permits massively parallel detection of diffuse photon density wave amplitude and phase for a large number of source–detector pairs (10{sup 6}). The stand-alone clinical DOT instrument thus offers high spatial resolution with reduced crosstalk between absorption and scattering. Other novel features include a fringe profilometry system for breast boundary segmentation, real-time data normalization, and a patient bed design which permits both axial and sagittal breast measurements. Results: The authors validated the instrument using tissue simulating phantoms with two different chromophore-containing targets and one scattering target. The authors also demonstrated the instrument in a case study breast cancer patient; the reconstructed 3D image of endogenous chromophores and scattering gave tumor localization in agreement with MRI. Conclusions: Imaging with a novel parallel-plate DOT breast imager that employs highly parallel, high-resolution CCD detection in the frequency-domain was demonstrated.
Brunstrom, J M; Roberts, B
2001-07-01
When a partial of a periodic complex is mistuned, its change in pitch is greater than expected. Two experiments examined whether these partial-pitch shifts are related to the computation of global pitch. In experiment 1, stimuli were either harmonic or frequency-shifted (25% of F0) complexes. One partial was mistuned by +/- 4% and played with leading and lagging portions of 500 ms each, relative to the other components (1 s), in both monaural and dichotic contexts. Subjects indicated whether the mistuned partial was higher or lower in pitch when concurrent with the other components. Responses were positively correlated with the direction of mistuning in all conditions. In experiment 2, stimuli from each condition were compared with synchronous equivalents. Subjects matched a pure tone to the pitch of the mistuned partial (component 4). The results showed that partial-pitch shifts are not reduced in size by asynchrony. Similar asynchronies are known to produce a near-exclusion of a mistuned partial from the global-pitch computation. This mismatch indicates that global and partial pitch are derived from different processes. The similarity of the partial-pitch shifts observed for harmonic and frequency-shifted stimuli suggests that they arise from a grouping mechanism that is sensitive to spectral regularity.
Sisakun, Siphan
2000-12-01
The purpose of this study is to explore the ability of four acoustic parameters, mean fundamental frequency, jitter, shimmer, and harmonics-to-noise ratio, to detect vocal fatigue in student singers. The participants are 15 voice students, who perform two distinct tasks, data collection task and vocal fatiguing task. The data collection task includes the sustained vowel /a/, reading a standard passage, and self-rate on a vocal fatigue form. The vocal fatiguing task is the vocal practice of musical scores for a total of 45 minutes. The four acoustic parameters are extracted using the software EZVoicePlus. The data analyses are performed to answer eight research questions. The first four questions relate to correlations of the self-rating scale and each of the four parameters. The next four research questions relate to differences in the parameters over time using one-factor repeated measures analysis of variance (ANOVA). The result yields a proposed acoustic profile of vocal fatigue in student singers. This profile is characterized by increased fundamental frequency; slightly decreased jitter; slightly decreased shimmer; and slightly increased harmonics-to-noise ratio. The proposed profile requires further investigation.
Higher order harmonics of reactor neutron equation
International Nuclear Information System (INIS)
Li Fu; Hu Yongming; Luo Zhengpei
1996-01-01
The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out
DEFF Research Database (Denmark)
Dowlatabadi, Mohammadkazem Bakhshizadeh; Iman-Eini, Hossein; Blaabjerg, Frede
2015-01-01
Asymmetric multilevel inverters with a main and auxiliary power circuit can yield maximum number of voltage levels against the number of semiconductor devices. Most of the output power will be produced by the main inverter, which works at low frequency and the auxiliary inverters only improve the...
Multimegawatt relativistic harmonic gyrotron traveling-wave tube amplifier experiments
International Nuclear Information System (INIS)
Menninger, W.L.; Danly, B.G.; Temkin, R.J.
1996-01-01
The first multimegawatt harmonic relativistic gyrotron traveling-wave tube (gyro-twt) amplifier experiment has been designed, built, and tested. Results from this experimental setup, including the first ever reported third-harmonic gyro-twt results, are presented. Operation frequency is 17.1 GHz. Detailed phase measurements are also presented. The electron beam source is SNOMAD-II, a solid-state nonlinear magnetic accelerator driver with nominal parameters of 400 kV and 350 A. The flat-top pulsewidth is 30 ns. The electron beam is focused using a Pierce geometry and then imparted with transverse momentum using a bifilar helical wiggler magnet. Experimental operation involving both a second-harmonic interaction with the TE 21 mode and a third-harmonic interaction with the TE 31 mode, both at 17 GHz, has been characterized. The third-harmonic interaction resulted in 4-MW output power and 50-dB single-pass gain, with an efficiency of up to ∼8%. The best measured phase stability of the TE 31 amplified pulse was ±10 degree over a 9-ns period. The phase stability was limited because the maximum RF power was attained when operating far from wiggler resonance. The second harmonic, TE 21 had a peak amplified power of 2 MW corresponding to 40-dB single-pass gain and 4% efficiency. The second-harmonic interaction showed stronger superradiant emission than the third-harmonic interaction. Characterizations of the second- and third-harmonic gyro-twt experiments presented here include measurement of far-field radiation patterns, gain and phase versus interaction length, phase stability, and output power versus input power
Second harmonic inversion for ultrasound contrast harmonic imaging
Energy Technology Data Exchange (ETDEWEB)
Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico [THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam (Netherlands); Cachard, Christian; Basset, Olivier, E-mail: mirza.pasovic@creatis.insa-lyon.fr [CREATIS-LRMN, Universite de Lyon, INSA-Lyon, Universite Lyon 1, Inserm U630, CNRS UMR 5220 (France)
2011-06-07
Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f{sub 0} and the same amplitude P{sub 0} to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.
Second harmonic inversion for ultrasound contrast harmonic imaging
International Nuclear Information System (INIS)
Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico; Cachard, Christian; Basset, Olivier
2011-01-01
Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f 0 and the same amplitude P 0 to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Liu, Xinran; Kofman, Jonathan
2017-07-10
A new fringe projection method for surface-shape measurement was developed using four high-frequency phase-shifted background modulation fringe patterns. The pattern frequency is determined using a new fringe-wavelength geometry-constraint model that allows only two corresponding-point candidates in the measurement volume. The correct corresponding point is selected with high reliability using a binary pattern computed from intensity background encoded in the fringe patterns. Equations of geometry-constraint parameters permit parameter calculation prior to measurement, thus reducing measurement computational cost. Experiments demonstrated the ability of the method to perform 3D shape measurement for a surface with geometric discontinuity, and for spatially isolated objects.
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2017-05-15
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
Energy Technology Data Exchange (ETDEWEB)
Olivain, J [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1966-06-01
The generation of harmonics of the electron cyclotron half-frequency in a double-beam interaction experiment has been studied. A theoretical discussion is presented in which the transverse velocity distributions are represented by Dirac delta functions. The experimental measurements show the structure of the waves generated, for the fundamental mode (( {omega}={omega}/2).ce), i. e., their azimuthal wave number, wave length and radial profile of the oscillating potential, density and current. The quasi-electrostatic character of these waves has been established from these results by evaluating the ratio: vectorial product ({nabla}, E) / scalar product ({nabla}, E) which is always much smaller than unity. Measurements have also been made of the amplitudes and line-widths of several harmonics as well as the growth rate of the first of them. Finally, a number of observations have been made which show that nonlinear wave interactions play an important role in this system and which suggest an interpretation based on this mechanism for the generation of high order harmonics. (author) [French] Nous presentons les resultats obtenus sur la generation d'harmoniques de la demi-frequence giromagnetique electronique dans une experience interraction 'double-faisceau'. Nous discutons theoriquement ce systeme dans lequel les vitesses transversales sont introduites sous forme de distributions de Dirac. Les mesures experimentales ont permis, par le mode fondamental (({omega}={omega})/2.ce), de connaitre la structure des ondes engendrees (nombre d'onde 2 azimutal - longueur d'onde - profil radial du potentiel oscillant, amplitude des perturbations de potentiel, de densite et de courant). Le caractere quasi-electrostatique de ces ondes a pu etre etabli a partir de ces resultats en evaluant le rapport: produit vectoriel ({nabla}, E) / produit scalaire ({nabla}, E) qui reste toujours tres inferieur a l'unite. Les mesures ont egalement porte sur l'amplitude et la largeur des raies ainsi
Dual aperture dipole magnet with second harmonic component
Praeg, Walter F.
1985-01-01
An improved dual aperture dipole electromagnet includes a second-harmonic frequency magnetic guide field winding which surrounds first harmonic frequency magnetic guide field windings associated with each aperture. The second harmonic winding and the first harmonic windings cooperate to produce resultant magnetic waveforms in the apertures which have extended acceleration and shortened reset portions of electromagnet operation.
International Nuclear Information System (INIS)
Sarkar, P.; Bhattacharyya, S.P.
1995-01-01
The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab
Huang, Yongjun; Flores, Jaime Gonzalo Flor; Cai, Ziqiang; Yu, Mingbin; Kwong, Dim-Lee; Wen, Guangjun; Churchill, Layne; Wong, Chee Wei
2017-06-29
For the sensitive high-resolution force- and field-sensing applications, the large-mass microelectromechanical system (MEMS) and optomechanical cavity have been proposed to realize the sub-aN/Hz 1/2 resolution levels. In view of the optomechanical cavity-based force- and field-sensors, the optomechanical coupling is the key parameter for achieving high sensitivity and resolution. Here we demonstrate a chip-scale optomechanical cavity with large mass which operates at ≈77.7 kHz fundamental mode and intrinsically exhibiting large optomechanical coupling of 44 GHz/nm or more, for both optical resonance modes. The mechanical stiffening range of ≈58 kHz and a more than 100 th -order harmonics are obtained, with which the free-running frequency instability is lower than 10 -6 at 100 ms integration time. Such results can be applied to further improve the sensing performance of the optomechanical inspired chip-scale sensors.
Second harmonic generation in a bounded magnetoplasma
International Nuclear Information System (INIS)
Thomas, D.G.
1975-01-01
An experimental study of second harmonic generation in a magnetized plasma contained in a cylindrical cavity resonator shows how the harmonic power varies with fundamental power, background gas pressure, and magnetization. Two cavities were designed. For each the TM010 resonance was in the S-band and the TM011 resonance in the C-band. Both frequencies were harmonically related when the d.c. discharge sustaining the plasma was adjusted to give plasma frequencies of approximately 0.7 GHz and 1.53 GHz. The experimental results show the harmonic power approximately proportional to the square of the fundamental power from 5 to 100 mw, and a decreasing function of pressure from 10 to 150 millitorr. Experiments at constant plasma frequency and varying magnetic field from 0 to 3000 Gauss show a sharp drop in harmonic power to undetectable levels when the electron cyclotron frequency approximates either the fundamental or second harmonic frequencies. These effects are attributed, respectively, to the coupling of fundamental power to other modes and to cavity detuning away from the harmonic. With the plasma frequency adjusted to maintain simultaneous resonance of fundamental and harmonic, a harmonic signal maximum occurred when the upper hybrid frequency approximated the harmonic frequency. Several anomalies, apparently related to the magnetization, background gas, and electron density distribution were observed. Otherwise, the results are qualitatively consistent with the first order theory for a cold, collisional plasma
Rodriguez, Alejandro W; Ilic, Ognjen; Bermel, Peter; Celanovic, Ivan; Joannopoulos, John D; Soljačić, Marin; Johnson, Steven G
2011-09-09
We demonstrate the possibility of achieving enhanced frequency-selective near-field radiative heat transfer between patterned (photonic-crystal) slabs at designable frequencies and separations, exploiting a general numerical approach for computing heat transfer in arbitrary geometries and materials based on the finite-difference time-domain method. Our simulations reveal a tradeoff between selectivity and near-field enhancement as the slab-slab separation decreases, with the patterned heat transfer eventually reducing to the unpatterned result multiplied by a fill factor (described by a standard proximity approximation). We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group.
Bennett, Charles L.
2016-03-22
A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. When released, the inlet valve head undergoes a single oscillation past the equilibrium position to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.
Waveguide harmonic damper for klystron amplifier
International Nuclear Information System (INIS)
Kang, Y.
1998-01-01
A waveguide harmonic damper was designed for removing the harmonic frequency power from the klystron amplifiers of the APS linac. Straight coaxial probe antennas are used in a rectangular waveguide to form a damper. A linear array of the probe antennas is used on a narrow wall of the rectangular waveguide for damping klystron harmonics while decoupling the fundamental frequency in dominent TE 01 mode. The klystron harmonics can exist in the waveguide as waveguide higher-order modes above cutoff. Computer simulations are made to investigate the waveguide harmonic damping characteristics of the damper
International Nuclear Information System (INIS)
Takahashi, Hiroaki; Watanabe, Ryosuke; Miyauchi, Yoshihiro; Mizutani, Goro
2011-01-01
In this report, local electronic structures of steps and terraces on rutile TiO 2 single crystal faces were studied by second harmonic and sum frequency generation (SHG/SFG) spectroscopy. We attained selective measurement of the local electronic states of the step bunches formed on the vicinal (17 18 1) and (15 13 0) surfaces using a recently developed step-selective probing technique. The electronic structures of the flat (110)-(1x1) (the terrace face of the vicinal surfaces) and (011)-(2x1) surfaces were also discussed. The SHG/SFG spectra showed that step structures are mainly responsible for the formation of trap states, since significant resonances from the trap states were observed only from the vicinal surfaces. We detected deep hole trap (DHT) states and shallow electron trap (SET) states selectively from the step bunches on the vicinal surfaces. Detailed analysis of the SHG/SFG spectra showed that the DHT and SET states are more likely to be induced at the top edges of the step bunches than on their hillsides. Unlike the SET states, the DHT states were observed only at the step bunches parallel to [1 1 1][equivalent to the step bunches formed on the (17 18 1) surface]. Photocatalytic activity for each TiO 2 sample was also measured through methylene blue photodegradation reactions and was found to follow the sequence: (110) < (17 18 1) < (15 13 0) < (011), indicating that steps along [0 0 1] are more reactive than steps along [1 1 1]. This result implies that the presence of the DHT states observed from the step bunches parallel to [1 1 1] did not effectively contribute to the methylene blue photodegradation reactions.
International Nuclear Information System (INIS)
Eich, S.; Stange, A.; Carr, A.V.; Urbancic, J.; Popmintchev, T.; Wiesenmayer, M.; Jansen, K.; Ruffing, A.; Jakobs, S.; Rohwer, T.; Hellmann, S.; Chen, C.; Matyba, P.; Kipp, L.; Rossnagel, K.; Bauer, M.; Murnane, M.M.; Kapteyn, H.C.; Mathias, S.; Aeschlimann, M.
2014-01-01
Highlights: • We present a scheme to generate high intensity XUV pulses from HHG with variable time-bandwidth product. • Shorter-wavelength driven high-harmonic XUV trARPES provides higher photon flux and increased energy resolution. • High-quality high-harmonic XUV trARPES data with sub 150 meV energy and sub 30 fs time resolution is presented. - Abstract: Time- and angle-resolved photoemission spectroscopy (trARPES) using femtosecond extreme ultraviolet high harmonics has recently emerged as a powerful tool for investigating ultrafast quasiparticle dynamics in correlated-electron materials. However, the full potential of this approach has not yet been achieved because, to date, high harmonics generated by 800 nm wavelength Ti:Sapphire lasers required a trade-off between photon flux, energy and time resolution. Photoemission spectroscopy requires a quasi-monochromatic output, but dispersive optical elements that select a single harmonic can significantly reduce the photon flux and time resolution. Here we show that 400 nm driven high harmonic extreme-ultraviolet trARPES is superior to using 800 nm laser drivers since it eliminates the need for any spectral selection, thereby increasing photon flux and energy resolution to <150 meV while preserving excellent time resolution of about 30 fs
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
This paper completes a descrption of the quantization procedure in the harmonic superspace approach. The Feynman rules for N=2 matter and Yang-Mills theories are derived and the various examples of harmonic supergraph calculations are given. Calculations appear to be not more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any troubles, a non-locality in these disappears on-shell. The important property is that the quantum corrections are always writen as integrals over the full harmonic superspace even though the initial action is an integral over the analytic subspace. As a by-product our results imply a very simple proof of finiteness of a wide class of the N=4, d=2 non-linear Σ-models. The most general self-couplings of hypermultiplets including those with broken SU(2) are considered.The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established
DEFF Research Database (Denmark)
Garofalo, Fabio; Laurell, Thomas; Bruus, Henrik
2017-01-01
of the hard-to-measure mechanical indicators is correlated to that of the easy-to-measure electrical indicators, and, by introducing optimality criteria, it is clarified to which extent the latter suffices to identify optimal driving frequencies as the geometric configuration and the material parameters vary....... The latter have been varied by considering both Pyrex and aluminium nitroxide top-lid materials....
Harmonic operation of high gain harmonic generation free electron laser
International Nuclear Information System (INIS)
Deng Haixiao; Chinese Academy of Sciences, Beijing; Dai Zhimin
2008-01-01
In high gain harmonic generation (HGHG) free electron laser (FEL), with the right choice of parameters of the modulator undulator, the dispersive section and the seed laser, one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation, instead of the fundamental frequency of the radiator radiation in conventional HGHG, thus the radiator undulator is in harmonic operation (HO) mode. In this paper, we investigate HO of HGHG FEL. Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given. It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level. Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy. (authors)
Harmonically excited orbital variations
International Nuclear Information System (INIS)
Morgan, T.
1985-01-01
Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs
International Nuclear Information System (INIS)
Smithe, D.N.; Colestock, P.L.; Kashuba, R.J.; Kammash, T.
1987-04-01
A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Maxwell-Vlasov equations under typical Ion Cyclotron Range of Frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm-plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field, and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k/sub parallel/ is performed to yield the full three-dimensional field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between antenna and the resonance layer. 48 figs
Harmonic space and quaternionic manifolds
International Nuclear Information System (INIS)
Galperin, A.; Ogievetsky, O.; Ivanov, E.
1992-10-01
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs
One dimension harmonic oscillator
International Nuclear Information System (INIS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.
1977-01-01
The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr
Harmonic response of coupled and uncoupled granular YBCO
International Nuclear Information System (INIS)
Torralba, Maria Veronica S; Sarmago, Roland V
2004-01-01
The harmonic responses of granular YBCO were obtained via mutual inductance measurements. Two samples, one with and another without intergranular coupling, were investigated in terms of the harmonic components of magnetization at various field amplitudes and frequencies. By comparing the behaviour of the features in the harmonics to that of the peaks in the fundamental response, we explicitly identified which features in the harmonics originate from intragranular harmonic generation and which arise due to a contribution of intergranular coupling. Harmonic responses were obtained despite the absence of vortices and even harmonics were detected in a purely AC magnetic field
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
Helson, Henry
2010-01-01
This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Harmonic oscillator in Snyder space
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
College geometry an introduction to the modern geometry of the triangle and the circle
Altshiller-Court, Nathan
2007-01-01
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Understanding fifth-harmonic generation in CLBO
Patankar, S.; Yang, S. T.; Moody, J. D.; Bayramian, A. J.; Swadling, G. F.; Barker, D.; Datte, P.; Mennerat, G.; Norton, M.; Carr, C. W.; Begishev, I. A.; Bromage, J.; Ross, J. S.
2018-02-01
We report on results of fifth harmonic generation in Cesium Lithium Borate (CLBO) using a three-crystal cascaded frequency conversion scheme designed to study the energy balance of the final sum frequency generation stage. The experimental setup independently combines the first and fourth harmonic of a Nd:Glass laser in a 5mm thick CLBO crystal. Energy balance between the incoming and output energy is close to unity when the CLBO is out of phase matching and approximately 80% when the crystal is in phase matching. A detailed analysis of the residual fundamental and fourth harmonic energy indicates 5th harmonic light is being generated but only 26% is unaccounted for. We attribute the missing light to linear transmission loss in the CLBO oven. The ratio of the output to input energy is unity when the missing 5th harmonic is incorporated into the calculations. Two-dimensional plane wave mixing simulations show agreement with the results at lower intensities.
Directory of Open Access Journals (Sweden)
Piotr FOLĘGA
2014-03-01
Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.
Twenty-Four Tuba Harmonics Using a Single Pipe Length
Holmes, Bud; Ruiz, Michael J.
2017-01-01
Harmonics arise naturally from the resonances in strings and pipes. A video demonstration (Ruiz 2016 "YouTube: Tuba Harmonics" (https://youtu.be/souhEzOP9c4)) is provided where a tubist (coauthor Holmes) produces a phenomenal 24 harmonics using a single tuba pipe length by controlling the buzz of his lips. The frequencies of the…
Audibility of high harmonics in a periodic pulse
Duifhuis, H.
1970-01-01
A periodic pulse consisting of sufficiently narrow pulses has a frequency spectrum which contains all harmonics with equal amplitude. Owing to the limited resolving power of the hearing organ, only the low harmonics can be perceived separately. The high harmonics are heard together as one complex
Rodger, Alison
1995-01-01
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans
International Nuclear Information System (INIS)
Yuece, Cem
2003-01-01
In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained
DEFF Research Database (Denmark)
Wang, Xiongfei; Blaabjerg, Frede; Chen, Zhe
2012-01-01
This paper proposes a harmonic impedance synthesis technique for voltage-controlled distributed generation inverters in order to damp harmonic voltage distortion on a distribution network. The approach employs a multiloop control scheme, where a selective harmonic load current feedforward loop...... at the dominant harmonic frequencies. Thus, the harmonic voltage drop on the grid-side inductance and the harmonic resonances throughout a distribution feeder with multiple shunt-connected capacitors can be effectively attenuated. Simulation and laboratory test results validate the performance of the proposed...
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Directory of Open Access Journals (Sweden)
Dismas K. Choge
2018-04-01
Full Text Available We demonstrate a compact blue and orange-two color continuous wave laser source emitting at 487 nm and from 597.4 to 600.3 nm, respectively. The temperature tunable coherent orange radiation is achieved by frequency mixing 974 nm laser diode (LD and a C-band amplified spontaneous emission laser source while the temperature insensitive blue radiation is generated by second-order quasi-phase-matching frequency doubling of 974 nm LD. We implement the simultaneous nonlinear processes in a single magnesium oxide doped periodically poled lithium niobate bulk crystal without the need of an aperiodic design.
Computational modeling of geometry dependent phonon transport in silicon nanostructures
Cheney, Drew A.
Recent experiments have demonstrated that thermal properties of semiconductor nanostructures depend on nanostructure boundary geometry. Phonons are quantized mechanical vibrations that are the dominant carrier of heat in semiconductor materials and their aggregate behavior determine a nanostructure's thermal performance. Phonon-geometry scattering processes as well as waveguiding effects which result from coherent phonon interference are responsible for the shape dependence of thermal transport in these systems. Nanoscale phonon-geometry interactions provide a mechanism by which nanostructure geometry may be used to create materials with targeted thermal properties. However, the ability to manipulate material thermal properties via controlling nanostructure geometry is contingent upon first obtaining increased theoretical understanding of fundamental geometry induced phonon scattering processes and having robust analytical and computational models capable of exploring the nanostructure design space, simulating the phonon scattering events, and linking the behavior of individual phonon modes to overall thermal behavior. The overall goal of this research is to predict and analyze the effect of nanostructure geometry on thermal transport. To this end, a harmonic lattice-dynamics based atomistic computational modeling tool was created to calculate phonon spectra and modal phonon transmission coefficients in geometrically irregular nanostructures. The computational tool is used to evaluate the accuracy and regimes of applicability of alternative computational techniques based upon continuum elastic wave theory. The model is also used to investigate phonon transmission and thermal conductance in diameter modulated silicon nanowires. Motivated by the complexity of the transmission results, a simplified model based upon long wavelength beam theory was derived and helps explain geometry induced phonon scattering of low frequency nanowire phonon modes.
Sub-harmonic broadband humps and tip noise in low-speed ring fans.
Moreau, Stéphane; Sanjose, Marlène
2016-01-01
A joint experimental and numerical study has been achieved on a low-speed axial ring fan in clean inflow. Experimental evidence shows large periodic broadband humps at lower frequencies than the blade passing frequencies and harmonics even at design conditions. These sub-harmonic humps are also found to be sensitive to the fan process and consequently to its tip geometry. Softer fans yield more intense humps more shifted to lower frequencies with respect to the fan harmonics. Unsteady turbulent flow simulations of this ring fan mounted on a test plenum have been achieved by four different methods that have been validated by comparing with overall performances and detailed hot-wire velocity measurements in the wake. Noise predictions are either obtained directly or are obtained through Ffowcs Williams and Hawkings' analogy, and compared with narrowband and third-octave power spectra. All unsteady simulations correctly capture the low flow rates, the coherent vortex dynamics in the tip clearance and consequently the noise radiation dominated by the tip noise in the low- to mid-frequency range. Yet, only the scale-adaptive simulation and the lattice Boltzmann method simulations which can describe most of the turbulent structures accurately provide the proper spectral shape and levels, and consequently the overall sound power level.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Computer model for harmonic ultrasound imaging.
Li, Y; Zagzebski, J A
2000-01-01
Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.
Pairwise harmonics for shape analysis
Zheng, Youyi
2013-07-01
This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of shape descriptors that are more global, discriminative, and can effectively capture the variations in the underlying geometry. Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more efficient algorithms than the state-of-the-art methods for three applications: intrinsic reflectional symmetry axis computation, matching shape extremities, and simultaneous surface segmentation and skeletonization. © 2012 IEEE.
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Symmetric airfoil geometry effects on leading edge noise.
Gill, James; Zhang, X; Joseph, P
2013-10-01
Computational aeroacoustic methods are applied to the modeling of noise due to interactions between gusts and the leading edge of real symmetric airfoils. Single frequency harmonic gusts are interacted with various airfoil geometries at zero angle of attack. The effects of airfoil thickness and leading edge radius on noise are investigated systematically and independently for the first time, at higher frequencies than previously used in computational methods. Increases in both leading edge radius and thickness are found to reduce the predicted noise. This noise reduction effect becomes greater with increasing frequency and Mach number. The dominant noise reduction mechanism for airfoils with real geometry is found to be related to the leading edge stagnation region. It is shown that accurate leading edge noise predictions can be made when assuming an inviscid meanflow, but that it is not valid to assume a uniform meanflow. Analytic flat plate predictions are found to over-predict the noise due to a NACA 0002 airfoil by up to 3 dB at high frequencies. The accuracy of analytic flat plate solutions can be expected to decrease with increasing airfoil thickness, leading edge radius, gust frequency, and Mach number.
Harmonic ratcheting for fast acceleration
Cook, N.; Brennan, J. M.; Peggs, S.
2014-04-01
A major challenge in the design of rf cavities for the acceleration of medium-energy charged ions is the need to rapidly sweep the radio frequency over a large range. From low-power medical synchrotrons to high-power accelerator driven subcritical reactor systems, and from fixed focus alternating gradient accelerators to rapid cycling synchrotrons, there is a strong need for more efficient, and faster, acceleration of protons and light ions in the semirelativistic range of hundreds of MeV/u. A conventional way to achieve a large, rapid frequency sweep (perhaps over a range of a factor of 6) is to use custom-designed ferrite-loaded cavities. Ferrite rings enable the precise tuning of the resonant frequency of a cavity, through the control of the incremental permeability that is possible by introducing a pseudoconstant azimuthal magnetic field. However, rapid changes over large permeability ranges incur anomalous behavior such as the "Q-loss" and "f-dot" loss phenomena that limit performance while requiring high bias currents. Notwithstanding the incomplete understanding of these phenomena, they can be ameliorated by introducing a "harmonic ratcheting" acceleration scheme in which two or more rf cavities take turns accelerating the beam—one turns on when the other turns off, at different harmonics—so that the radio frequency can be constrained to remain in a smaller range. Harmonic ratcheting also has straightforward performance advantages, depending on the particular parameter set at hand. In some typical cases it is possible to halve the length of the cavities, or to double the effective gap voltage, or to double the repetition rate. This paper discusses and quantifies the advantages of harmonic ratcheting in general. Simulation results for the particular case of a rapid cycling medical synchrotron ratcheting from harmonic number 9 to 2 show that stability and performance criteria are met even when realistic engineering details are taken into consideration.
International Nuclear Information System (INIS)
McGuire, John Andrew
2004-01-01
The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of ∼ 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm -1 occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach
Energy Technology Data Exchange (ETDEWEB)
McGuire, John Andrew [Univ. of California, Berkeley, CA (United States)
2004-11-24
The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of {approx} 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm^{-1} occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach.
Determination of nonlinear resistance voltage-current relationships by measuring harmonics
Stafford, J. M.
1971-01-01
Test configuration measures harmonic signal amplitudes generated in nonlinear resistance. Vacuum-type voltmeter measures low frequency sinusoidal input signal amplitude and wave-analyzer measures amplitude of harmonic signals generated in junction. Input signal harmonics amplitude must not exceed that of harmonics generated in nonlinear resistance.
Unlocking higher harmonics in atomic force microscopy with gentle interactions.
Santos, Sergio; Barcons, Victor; Font, Josep; Verdaguer, Albert
2014-01-01
In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.
Stability and nonlinear dynamics of gyrotrons at cyclotron harmonics
International Nuclear Information System (INIS)
Saraph, G.P.; Nusinovich, G.S.; Antonsen, T.M. Jr.; Levush, B.
1992-01-01
Gyrotrons operating at higher harmonics of the cyclotron frequency can overcome the frequency limitations caused by achievable strength of the magnetic field. However, the excitation of modes at the fundamental frequency exhibit a major problem for stable operation of harmonic gyrotron at high power with high efficiency. Therefore the issues of stability of gyrotron operation at the cyclotron harmonics and nonlinear dynamics of mode interaction are of great importance. The results of the authors stability analysis and multimode simulation are presented here. A detailed nonlinear theory of steady state single mode operation at cyclotron harmonics has been presented previously, taking into account beam-wave coupling and nonlinear gain function at cyclotron harmonics. A set of equations describing low gain regime interaction of modes resonant at different cyclotron harmonics was studied before. The multifrequency time-dependent nonlinear analysis presented here is based on previous gyrotron studies and beam-wave interaction at cyclotron harmonics. The authors have determined the parameter space for stable single mode operation at the second harmonic. The nonlinear dynamics of mode evolution and mode interaction for a harmonic gyrotron is presented. A new nonlinear effect in which the parasite at the fundamental harmonic helps excite the operating mode at the second harmonic has been demonstrated
Investigation of an Ultrafast Harmonic Resonant RF Kicker
Energy Technology Data Exchange (ETDEWEB)
Huang, Yulu [Univ. of Chinese Academy of Sciences (CAS), Beijing (China)
2016-10-01
square pulse, and get a Flat-Top waveform which will give a uniform kick over the bunch length of the kicked electron bunches, thus the transverse emittance of these kicked electron bunches can be maintained. By using two identical kickers with the betatron phase advance of 180 degree or its odd multiples, the residual kick voltage wave slopes at the unkicked bunch position will be totally cancelled out. Flat-Top waveform combined with two kicker scheme, the transverse emittance of the cooling electron bunches will be conserved during the whole injection, recirculation, and ejection processes. In the cavity design part, firstly, the cavity geometry is optimized to get high transverse shunt impedance thus less than 100 W of RF losses on the cavity wall can be achieved for all these 10 harmonic modes. To support all these 10 harmonic modes, group of four QWRs are adopted with the mode distribution of 5:3:1:1. In the multi-frequency cavities such as the five-mode-cavity and the three-mode-cavity, tunings are required to achieve the design frequencies for each mode. Slight segments of taper design on the inner conductor help to get the frequencies to be exactly on the odd harmonic modes. Stub tuners equal to the number of resonant modes are inserted to the outer conductor wall to compensate the frequency shifts due manufacturing errors and other perturbations during the operation such as the change of the cavity temperature. Single loop couple is designed for all harmonic modes in each cavity. By adjusting its loop size, position and rotation, it is possible to get the fundamental mode critical coupled and other higher harmonic modes slightly over coupled. A broadband circulator will be considered for absorbing the reflected power. Finally in this part, multipole field components due to the asymmetric cylindrical structure around the beam axis of the cavity as well as the beam-induced higher order mode (HOM) issues will be analyzed and discussed in this thesis. A half
Harmonics mitigation on industrial loads using series and parallel ...
African Journals Online (AJOL)
Most industrial loads are inductive in nature and therefore absorb Volts Ampere Reactance (VARs) leading to lagging power factor. Some inductive loads also produce current and voltage signals with frequencies in integer multiples of the 50 or 60 Hz fundamental frequencies called harmonics. Harmonics in power system ...
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter β. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of β on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved β values can be obtained by considering the diffraction effects.
Petrovic, Goran; Kilic, Tomislav; Terzic, Bozo
2009-04-01
In this paper a sensorless speed detection method of induction squirrel-cage machines is presented. This method is based on frequency determination of the stator neutral point voltage primary slot harmonic, which is dependent on rotor speed. In order to prove method in steady state and dynamic conditions the simulation and experimental study was carried out. For theoretical investigation the mathematical model of squirrel cage induction machines, which takes into consideration actual geometry and windings layout, is used. Speed-related harmonics that arise from rotor slotting are analyzed using digital signal processing and DFT algorithm with Hanning window. The performance of the method is demonstrated over a wide range of load conditions.
International Nuclear Information System (INIS)
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing; Barnard, Dan
2015-01-01
The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α 2 ≃ 2α 1
Jeong, Hyunjo; Zhang, Shuzeng; Barnard, Dan; Li, Xiongbing
2015-09-01
The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α2 ≃ 2α1.
Harmonic distortion in microwave photonic filters.
Rius, Manuel; Mora, José; Bolea, Mario; Capmany, José
2012-04-09
We present a theoretical and experimental analysis of nonlinear microwave photonic filters. Far from the conventional condition of low modulation index commonly used to neglect high-order terms, we have analyzed the harmonic distortion involved in microwave photonic structures with periodic and non-periodic frequency responses. We show that it is possible to design microwave photonic filters with reduced harmonic distortion and high linearity even under large signal operation.
Collective excitations of harmonically trapped ideal gases
Van Schaeybroeck, B.; Lazarides, A.
2009-01-01
We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show
Audibility of harmonics in periodic "white noise"
Duifhuis, H.
1973-01-01
The finding that spectrally suppressed high harmonics (n>16) in a periodic pulse are perceptible has been related [H. Duifhuis, J. Acoust. Soc. Amer. 48, 888–893 (1970); 49, 1155–1163 (1971)] to the ear's limited resolving power in peripheral frequency analysis. The limited frequency resolution
The Harmonics of Kansei Images
DEFF Research Database (Denmark)
Su, Jianning; Restrepo-Giraldo, John Dairo
2008-01-01
sensibility it elicits on a person (kansei), is a key factor in the design of tools to support designers in delivering the right product’s appearance. This paper presents an approach to mathematically represent a product’s kansei based on the frequency signature (harmonics) of a shape. This mathematical...... representation should allow the automatic indexing and retrieval of images from a repository of design precedents. This is done through a series of experiments aiming at determining the relation between images, kansei words and the frequency signatures of those images. Tests suggest the method is promising...... and can be used for indexing images in Content Based Image Retrieval Systems....
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
International Nuclear Information System (INIS)
Belendez, Augusto; Pascual, Carolina
2007-01-01
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A
International Nuclear Information System (INIS)
Obe, Emeka S.; Binder, A.
2011-01-01
A detailed model in direct-phase variables of a synchronous reluctance motor operating at mains voltage and frequency is presented. The model includes the stator and rotor slot openings, the actual winding layout and the reluctance rotor geometry. Hence, all mmf and permeance harmonics are taken into account. It is seen that non-negligible harmonics introduced by slots are present in the inductances computed by the winding function procedure. These harmonics are usually ignored in d-q models. The machine performance is simulated in the stator reference frame to depict the difference between this new direct-phase model including all harmonics and the conventional rotor reference frame d-q model. Saturation is included by using a polynomial fitting the variation of d-axis inductance with stator current obtained by finite-element software FEMAG DC (registered) . The detailed phase-variable model can yield torque pulsations comparable to those obtained from finite elements while the d-q model cannot.
Quantitative modeling of the third harmonic emission spectrum of plasmonic nanoantennas.
Hentschel, Mario; Utikal, Tobias; Giessen, Harald; Lippitz, Markus
2012-07-11
Plasmonic dimer nanoantennas are characterized by a strong enhancement of the optical field, leading to large nonlinear effects. The third harmonic emission spectrum thus depends strongly on the antenna shape and size as well as on its gap size. Despite the complex shape of the nanostructure, we find that for a large range of different geometries the nonlinear spectral properties are fully determined by the linear response of the antenna. We find excellent agreement between the measured spectra and predictions from a simple nonlinear oscillator model. We extract the oscillator parameters from the linear spectrum and use the amplitude of the nonlinear perturbation only as scaling parameter of the third harmonic spectra. Deviations from the model only occur for gap sizes below 20 nm, indicating that only for these small distances the antenna hot spot contributes noticeable to the third harmonic generation. Because of its simplicity and intuitiveness, our model allows for the rational design of efficient plasmonic nonlinear light sources and is thus crucial for the design of future plasmonic devices that give substantial enhancement of nonlinear processes such as higher harmonics generation as well as difference frequency mixing for plasmonically enhanced terahertz generation.
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
Harmonics in large offshore wind farms
DEFF Research Database (Denmark)
Kocewiak, Lukasz Hubert
and nature of various harmonic components. A comprehensive comparison of harmonic voltages and currents based on probability distribution estimation and appropriate statistics calculation (mean, variance, probability density function, etc.) is applied. Such approach gives a better overview and comparison...... and analysis, and ϐinally ending up on modelling and models application. Different aspects of validation in time domain, frequency domain, and by application of statistical methods are mentioned in relation to respective problems. Measurements constitute a core part in industry-oriented research. Due...... that it is of great importance to know the nature of generated harmonics in large offshore wind farms in order to apply the most suitable data processing technique. Time-frequency analysis based on multiresolution wavelet transform is used in order to perform time-frequency domain analysis helpful to distinguish...
Directory of Open Access Journals (Sweden)
Kweon-Ho Nam
Full Text Available Despite considerable research efforts on the relationship between arterial geometry and cardiovascular pathology, information is lacking on the pulsatile geometrical variation caused by arterial distensibility and cardiomotility because of the lack of suitable in vivo experimental models and the methodological difficulties in examining the arterial dynamics. We aimed to investigate the feasibility of using a chick embryo system as an experimental model for basic research on the pulsatile variation of arterial geometry. Optical microscope video images of various arterial shapes in chick chorioallantoic circulation were recorded from different locations and different embryo samples. The high optical transparency of the chorioallantoic membrane (CAM allowed clear observation of tiny vessels and their movements. Systolic and diastolic changes in arterial geometry were visualized by detecting the wall boundaries from binary images. Several to hundreds of microns of wall displacement variations were recognized during a pulsatile cycle. The spatial maps of the wall motion harmonics and magnitude ratio of harmonic components were obtained by analyzing the temporal brightness variation at each pixel in sequential grayscale images using spectral analysis techniques. The local variations in the spectral characteristics of the arterial wall motion were reflected well in the analysis results. In addition, mapping the phase angle of the fundamental frequency identified the regional variations in the wall motion directivity and phase shift. Regional variations in wall motion phase angle and fundamental-to-second harmonic ratio were remarkable near the bifurcation area. In summary, wall motion in various arterial geometry including straight, curved and bifurcated shapes was well observed in the CAM artery model, and their local and cyclic variations could be characterized by Fourier and wavelet transforms of the acquired video images. The CAM artery model with
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Harmonic Mitigation Methods in Large Offshore Wind Power Plants
DEFF Research Database (Denmark)
Kocewiak, Łukasz Hubert; Chaudhary, Sanjay; Hesselbæk, Bo
2013-01-01
Various sources of harmonic problems in large wind power plants (WPPs) and optimized harmonic mitigation methods are presented in this paper. The harmonic problems such as sources of harmonic emission and amplification as well as harmonic stability are identified. Also modern preventive...... and remedial harmonic mitigation methods in terms of passive and active filtering are described. It is shown that WPP components such as long HVAC cables and park transformers can introduce significant low-frequency resonances which can affect wind turbine control system operation and overall WPP stability...... as well as amplification of harmonic distortion. It is underlined that there is a potential in terms of active filtering in modern grid-side converters in e.g. wind turbines, STATCOMs or HVDC stations utilized in modern large WPPs. It is also emphasized that the grid-side converter controller should...
Effects of harmonic roving on pitch discrimination
DEFF Research Database (Denmark)
Santurette, Sébastien; de Kérangal, Mathilde le Gal; Joshi, Suyash Narendra
2015-01-01
Performance in pitch discrimination tasks is limited by variability intrinsic to listeners which may arise from peripheral auditory coding limitations or more central noise sources. The present study aimed at quantifying such “internal noise” by estimating the amount of harmonic roving required...... to impair pitch discrimination performance. Fundamental-frequency difference limens (F0DLs) were obtained in normal-hearing listeners with and without musical training for complex tones filtered between 1.5 and 3.5 kHz with F0s of 300 Hz (resolved harmonics) and 75 Hz (unresolved harmonics). The harmonicity...... that could be used to quantify the internal noise and provide strong constraints for physiologically inspired models of pitch perception....
XUV pulse effect on signal modulations of harmonic spectra from H ...
Indian Academy of Sciences (India)
LIQIANG FENG
2018-03-24
Mar 24, 2018 ... 2Laboratory of Modern Physics, Liaoning University of Technology, ... Molecular high-order harmonic generation; amplitude modulation of harmonics; frequency .... Here, mp, R and z are the mass of H or T, the internu-.
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Evaluation of Harmonics Impact on Digital Relays
Directory of Open Access Journals (Sweden)
Kinan Wannous
2018-04-01
Full Text Available This paper presents the concept of the impact of harmonic distortion on a digital protection relay. The aim is to verify and determine the reasons of a mal-trip or failure to trip the protection relays; the suggested solution of the harmonic distortion is explained by a mathematical model in the Matlab Simulink programming environment. The digital relays have been tested under harmonic distortions in order to verify the function of the relays algorithm under abnormal conditions. The comparison between the protection relay algorithm under abnormal conditions and a mathematical model in the Matlab Simulink programming environment based on injected harmonics of high values is provided. The test is separated into different levels; the first level is based on the harmonic effect of an individual harmonic and mixed harmonics. The test includes the effect of the harmonics in the location of the fault point into distance protection zones. This paper is a new proposal in the signal processing of power quality disturbances using Matlab Simulink and the power quality impact on the measurements of the power system quantities; the test simulates the function of protection in power systems in terms of calculating the current and voltage values of short circuits and their faults. The paper includes several tests: frequency variations and decomposition of voltage waveforms with Fourier transforms (model and commercial relay, the effect of the power factor on the location of fault points, the relation between the tripping time and the total harmonic distortion (THD levels in a commercial relay, and a comparison of the THD capture between the commercial relay and the model.
Development of a second-harmonic buncher for the RILAC
International Nuclear Information System (INIS)
Kohara, S.; Goto, A.; Miyazawa, Y.; Chiba, T.; Hemmi, M.; Chiba, Y.; Ikezawa, E.; Kase, M.; Yano, Y.
1994-01-01
A second-harmonic buncher has been constructed and installed on the injection beam line of the RIKEN variable-frequency heavy-ion linac (RILAC) to increase beam intensity. It has a good impedance matching to power feed line without adjusting device in the required wide frequency range. Beam intensity was increased by 50% with both the fundamental-frequency and the second-harmonic bunchers. Its structure, rf characteristics and beam test are described. (author)
Harmonic-hopping in Wallacea's bats.
Kingston, Tigga; Rossiter, Stephen J
2004-06-10
Evolutionary divergence between species is facilitated by ecological shifts, and divergence is particularly rapid when such shifts also promote assortative mating. Horseshoe bats are a diverse Old World family (Rhinolophidae) that have undergone a rapid radiation in the past 5 million years. These insectivorous bats use a predominantly pure-tone echolocation call matched to an auditory fovea (an over-representation of the pure-tone frequency in the cochlea and inferior colliculus) to detect the minute changes in echo amplitude and frequency generated when an insect flutters its wings. The emitted signal is the accentuated second harmonic of a series in which the fundamental and remaining harmonics are filtered out. Here we show that three distinct, sympatric size morphs of the large-eared horseshoe bat (Rhinolophus philippinensis) echolocate at different harmonics of the same fundamental frequency. These morphs have undergone recent genetic divergence, and this process has occurred in parallel more than once. We suggest that switching harmonics creates a discontinuity in the bats' perception of available prey that can initiate disruptive selection. Moreover, because call frequency in horseshoe bats has a dual function in resource acquisition and communication, ecological selection on frequency might lead to assortative mating and ultimately reproductive isolation and speciation, regardless of external barriers to gene flow.
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
Nonlinearly driven harmonics of Alfvén modes
Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.
2014-01-01
In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.
Nonlinearly driven harmonics of Alfvén modes
Energy Technology Data Exchange (ETDEWEB)
Zhang, B., E-mail: bozhang@austin.utexas.edu; Breizman, B. N.; Zheng, L. J.; Berk, H. L. [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2014-01-15
In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.
Institute of Scientific and Technical Information of China (English)
李金泽; 李宝才; 翟学明
2016-01-01
在基于行波自然频率的输电线路单端故障定位方法中，主自然频率值的准确度是进行故障点精确定位的关键。目前的主自然频率的提取大多采用小波变换、MUSIC 方法，小波分析受所选小波基影响较大，MUSIC 的参数选择对频谱估计影响较大，它们都未能很好地解决这一问题。提出一种基于故障线路自然频率的单端测距新方法。该方法在提取主自然频率过程中首先对行波信号进行 EEMD 分解，并用 ICA 方法进行正交化处理，从而抑制 WVD 本身存在交叉项的问题，然后对各个分量进行 WVD 转换并叠加，获得正交的自然频率谱；进而综合考虑基波和多次谐波求取全局主自然频率。EMTDC 仿真实验验证了该算法在不同故障类型、故障距离、过渡电阻和噪声情况下的可行性及其精度。%In the single terminal fault locating method of transmission line based on traveling wave natural frequency, the accuracy of extracting primary natural frequency is the key to caring out to pinpoint trouble spots in. Currently, wavelet transform and MUSIC method are commonly used for extracting primary natural frequency. Wavelet analysis is influenced by the selected wavelets and the parameters’ selection greatly impacts spectral estimation in MUSIC, which can’t solve this problem well. A new single ended fault location method of extracting faulted line natural frequencies is described. The traveling wave signal is decomposed by EEMD and orthogonal process is made with ICA method to suppress the WVD's problem of cross-term, and then each component of WVD is converted and superimposed to obtain the natural frequency spectrum orthogonal. Then the global primary natural frequency is obtained considering the fundamental and harmonics. Simulation experiment by EMTDC confirms the feasibility and accuracy of the proposed algorithm under different fault types, fault distance, transition resistance
Energy Technology Data Exchange (ETDEWEB)
Schneidmiller, E.A.; Yurkov, M.V.
2012-05-15
Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned X-ray FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of X-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned X-ray FEL facilities. In particular, LCLS after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25-30 keV providing multi-gigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other X-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact X-ray FELs (driven by electron beams with a relatively low energy), allowing the use of the standard undulator technology instead of small-gap in-vacuum devices. Finally, in this paper we discover that in a part of the
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Secondary Voltage Control for Harmonics Suppression in Islanded Microgrids
DEFF Research Database (Denmark)
Wang, Xiongfei; Guerrero, Josep M.; Blaabjerg, Frede
2011-01-01
in islanded microgrids. In addition to the centralized controller for fundamental frequency voltage component, a selective harmonic compensator is implemented in the secondary voltage control system. With the help of Park transformation, the cyclic references generated by the selective harmonic compensator...
Harmonic supergraphs. Green functions
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Gievetsky, V.; Sokatchev, E.
1985-01-01
The quantization procedure in the harmonic superspace approach is worked out. Harmonic distributions are introduced and are used to construct the analytic superspace delta-functions and the Green functions for the hypermultiplet and the N=2 Yang-Mills superfields. The gauge fixing is described and the relevant Faddeev-Popov ghosts are defined. The corresponding BRST transformations are found. The harmonic superspace quantization of the N=2 gauge theory turns out to be rather simple and has many parallels with that for the standard (N=0) Yang-Mills theory. In particular, no ghosts-forghosts are needed
Linking high harmonics from gases and solids.
Vampa, G; Hammond, T J; Thiré, N; Schmidt, B E; Légaré, F; McDonald, C R; Brabec, T; Corkum, P B
2015-06-25
When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion creates high-order harmonics of the fundamental laser frequency. This sub-cycle effect generates coherent soft X-rays and attosecond pulses, and provides a means to image molecular orbitals. Recently, high harmonics have been generated from bulk crystals, but what mechanism dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per ångström. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid to be tomographically reconstructed.
Energy Technology Data Exchange (ETDEWEB)
Thomas, Alexander Roy [Univ. of Michigan, Ann Arbor, MI (United States); Krushelnick, Karl [Univ. of Michigan, Ann Arbor, MI (United States)
2016-09-08
We have studied ion motion effects in high harmonic generation, including shifts to the harmonics which result in degradation of the attosecond pulse train, and how to mitigate them. We have examined the scaling with intensity of harmonic emission. We have also switched the geometry of the interaction to measure, for the first time, harmonics from a normal incidence interaction. This was performed by using a special parabolic reflector with an on axis hole and is to allow measurements of the attosecond pulses using standard techniques. Here is a summary of the findings: First high harmonic generation in laser-solid interactions at 10^{21} Wcm^{-2}, demonstration of harmonic focusing, study of ion motion effects in high harmonic generation in laser-solid interactions, and demonstration of harmonic amplification.
Analysing harmonic motions with an iPhone’s magnetometer
Yavuz, Ahmet; Kağan Temiz, Burak
2016-05-01
In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.
MMS Observations of Harmonic Electromagnetic Cyclotron Waves
Usanova, M.; Ahmadi, N.; Ergun, R.; Trattner, K. J.; Fuselier, S. A.; Torbert, R. B.; Mauk, B.; Le Contel, O.; Giles, B. L.; Russell, C. T.; Burch, J.; Strangeway, R. J.
2017-12-01
Harmonically related electromagnetic ion cyclotron waves with the fundamental frequency near the O+ cyclotron frequency were observed by the four MMS spacecraft on May 20, 2016. The wave activity was detected by the spacecraft on their inbound passage through the Earth's morning magnetosphere during generally quiet geomagnetic conditions but enhanced solar wind dynamic pressure. It was also associated with an enhancement of energetic H+ and O+ ions. The waves are seen in both magnetic and electric fields, formed by over ten higher order harmonics, most pronounced in the electric field. The wave activity lasted for about an hour with some wave packets giving rise to short-lived structures extending from Hz to kHz range. These observations are particularly interesting since they suggest cross-frequency coupling between the lower and higher frequency modes. Further work will focus on examining the nature and role of these waves in the energetic particle dynamics from a theoretical perspective.
Superstrings and harmonic superspace
International Nuclear Information System (INIS)
Kallosh, R.E.; AN SSSR, Moscow. Fizicheskij Inst.)
1987-01-01
The paper on superstrings and harmonic superspace is a contribution to the book dedicated to E.S. Fradkin on his sixtieth birthday. The purpose of the paper is to propose a description of N = 2,3 superspace which could be used for the investigation of the effective d = 10 harmonic superspace corresponding to the heterotic superstring. A description is given of the structure of semi-simple Lie algebras in the Cartan-Weyl basis, as well as the general properties of the even, compact part of harmonic superspace. The main properties of the four-dimensional N = 2 SYM theory are discussed, along with the N = 3, d = 4 super Yang-Mills theory. Finally the relation between the harmonic superspace and the heterotic E 8 x E 8 superstring is examined. (U.K.)
Harmonic excitations in quasicrystals
International Nuclear Information System (INIS)
Luck, J.M.
1986-03-01
The harmonic excitations (phonons) of quasicrystals are studied in a simple one-dimensional model. The spectrum is a Cantor set, which exhibits selfsimilarity properties. The eigenstates are generically ''critical'', i.e. neither extended nor localized
Multidimensional high harmonic spectroscopy
International Nuclear Information System (INIS)
Bruner, Barry D; Soifer, Hadas; Shafir, Dror; Dudovich, Nirit; Serbinenko, Valeria; Smirnova, Olga
2015-01-01
High harmonic generation (HHG) has opened up a new frontier in ultrafast science where attosecond time resolution and Angstrom spatial resolution are accessible in a single measurement. However, reconstructing the dynamics under study is limited by the multiple degrees of freedom involved in strong field interactions. In this paper we describe a new class of measurement schemes for resolving attosecond dynamics, integrating perturbative nonlinear optics with strong-field physics. These approaches serve as a basis for multidimensional high harmonic spectroscopy. Specifically, we show that multidimensional high harmonic spectroscopy can measure tunnel ionization dynamics with high precision, and resolves the interference between multiple ionization channels. In addition, we show how multidimensional HHG can function as a type of lock-in amplifier measurement. Similar to multi-dimensional approaches in nonlinear optical spectroscopy that have resolved correlated femtosecond dynamics, multi-dimensional high harmonic spectroscopy reveals the underlying complex dynamics behind attosecond scale phenomena. (paper)
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Gauge field geometry from complex and harmonic analyticities
International Nuclear Information System (INIS)
Gal'perin, A.S.; Ivanov, E.A.; Ogievetsky, V.I.; Sokatchev, E.
1987-01-01
The analyticity preservation principle is employed to demonstrate and impressive affinity between field theories with intrinsic analytic structure and superfield gauge theories. The defining constraints of the former theories are interpreted as the integrability conditions for the existence of appropriate analytic subspaces and are solved by passing to the basis with manifest analyticity. We prefer to work within the analytic basis. This allows, e.g., to replace the nonlinear splitting problem of twistor approach by solving a linear equation
International Nuclear Information System (INIS)
Saraph, G.P.; Antonsen, T.M. Jr.; Nusinovich, G.S.; Levush, B.
1995-01-01
Mode competition can present a major hurdle in achieving stable, efficient operation of a gyrotron at the cyclotron harmonics. A type of mode interaction in which three modes at different cyclotron harmonics are parametrically coupled together is analyzed here. This coupling can lead to parametric excitation or suppression of a mode; cyclic mode hopping; or the coexistence of three modes. Simulation results are presented for the parametric instability involving modes at the fundamental, second harmonic, and third harmonic of the cyclotron frequency. It is shown that the parametric excitation can lead to stable, efficient operation of a high-power gyrotron at the third harmonic. Based on this phenomenon, two practical designs are presented here for the third harmonic operation at 94 and 210 GHz. copyright 1995 American Institute of Physics
Microgrid Reactive and Harmonic Power Sharing Using Enhanced Virtual Impedance
DEFF Research Database (Denmark)
He, Jinwei; Wei Li, Yun; Guerrero, Josep M.
2013-01-01
To address the load sharing problem in islanding microgrids, this paper proposes an improved approach which regulates the distributed generation (DG) unit interfacing virtual impedance at fundamental and selected harmonic frequencies. In contrast to the conventional virtual impedance control where...... only a line current feed-forward term is added to the DG voltage reference, the proposed virtual impedances at fundamental and harmonic frequencies are realized using DG line current and point of common coupling (PCC) voltage feed-forward terms, respectively. With this modification, the mismatched DG...... feeder impedances can be properly compensated, resulting in accurate reactive and harmonic power sharing at the same time. In addition, this paper shows that the microgrid PCC harmonic voltages can be mitigated by reducing the magnitude of DG unit equivalent harmonic impedance. Finally, an improved...
Sanroman-Junquera, Margarita; Mora-Jimenez, Inmaculada; Garcia-Alberola, Arcadio; Caamano, Antonio J; Trenor, Beatriz; Rojo-Alvarez, Jose L
2018-04-01
Spatial and temporal processing of intracardiac electrograms provides relevant information to support the arrhythmia ablation during electrophysiological studies. Current cardiac navigation systems (CNS) and electrocardiographic imaging (ECGI) build detailed 3-D electroanatomical maps (EAM), which represent the spatial anatomical distribution of bioelectrical features, such as activation time or voltage. We present a principled methodology for spectral analysis of both EAM geometry and bioelectrical feature in CNS or ECGI, including their spectral representation, cutoff frequency, or spatial sampling rate (SSR). Existing manifold harmonic techniques for spectral mesh analysis are adapted to account for a fourth dimension, corresponding to the EAM bioelectrical feature. Appropriate scaling is required to address different magnitudes and units. With our approach, simulated and real EAM showed strong SSR dependence on both the arrhythmia mechanism and the cardiac anatomical shape. For instance, high frequencies increased significantly the SSR because of the "early-meets-late" in flutter EAM, compared with the sinus rhythm. Besides, higher frequency components were obtained for the left atrium (more complex anatomy) than for the right atrium in sinus rhythm. The proposed manifold harmonics methodology opens the field toward new signal processing tools for principled EAM spatiofeature analysis in CNS and ECGI, and to an improved knowledge on arrhythmia mechanisms.
Improving the voltage quality of an inverter via by-passing the harmonic current components
DEFF Research Database (Denmark)
Zhong, Qing-Chang; Blaabjerg, Frede; Guerrero, Josep M.
2012-01-01
In this paper, a control strategy is proposed to improve the total harmonic distortion (THD) of the output voltage of an inverter. The physical interpretation of the control strategy is to connect shunt resonant filters at harmonic frequencies to the output so that the harmonic current components...
Transfer functions of US transducers for harmonic imaging and bubble respons
van Neer, Paul L.M.J.; Matte, Guillaume; Sijl, J.; Borsboom, Jerome M.G.; de Jong, N.
2007-01-01
Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics
Coherent harmonic production using a two-section undulator FEL
Energy Technology Data Exchange (ETDEWEB)
Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others
1995-12-31
We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.
Acceleration test with mixed higher harmonics in HIMAC
International Nuclear Information System (INIS)
Kanazawa, M.; Sugiura, A.; Misu, T.
2004-01-01
In HIMAC synchrotron, beam tests with a magnetic ally loaded cavity have been performed. This cavity has very low Q-value of about 0.5, and can be added higher harmonics with fundamental acceleration frequency. In our tested system for higher harmonics, wave form of a DDS (Direct Digital Synthesizer) can be rewrite, and arbitrary wave form can be used for beam acceleration. In the beam test, second and third harmonic wave were added on the fundamental acceleration frequency, and increases of the accelerated beam intensity have been achieved. In this paper, results of the beam test and the acceleration system are presented. (author)
DEFF Research Database (Denmark)
Lowes, F.J.; Olsen, Nils
2004-01-01
Most modern spherical harmonic geomagnetic models based on satellite data include estimates of the variances of the spherical harmonic coefficients of the model; these estimates are based on the geometry of the data and the fitting functions, and on the magnitude of the residuals. However...
International Nuclear Information System (INIS)
Alberti, S.; Pedrozzi, M.; Tran, M.Q.; Hogge, J.P.; Tran, T.M.; Muggli, P.; Joedicke, B.; Mathews, H.G.
1990-04-01
A quasi-optical gyrotron (QOG) designed for operation at the fundamental (Ω ce ≅100 GHz) exhibits simultaneous emission at Ω ce and 2Ω ce (second harmonic). For a beam current of 4 A, 20% of the total RF power is emitted at the second harmonic. The experimental measurements show that the excitation of the second harmonic is only possible when the fundamental is present. The frequency of the second harmonic is locked by the frequency of the fundamental. Experimental evidence shows that when the second harmonic is not excited, total efficiency is enhanced. (author) 6 refs., 5 figs., 1 tab
Harmonization versus Mutual Recognition
DEFF Research Database (Denmark)
Jørgensen, Jan Guldager; Schröder, Philipp
The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired with the oppor......The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired...... countries and three firms, where firms first lobby for the policy coordination regime (harmonization versus mutual recognition), and subsequently, in case of harmonization, the global standard is auctioned among the firms. We discuss welfare effects and conclude with policy implications. In particular......, harmonized standards may fail to harvest the full pro-competitive effects from trade liberalization compared to mutual recognition; moreover, the issue is most pronounced in markets featuring price competition....
Second harmonic generation imaging
2013-01-01
Second-harmonic generation (SHG) microscopy has shown great promise for imaging live cells and tissues, with applications in basic science, medical research, and tissue engineering. Second Harmonic Generation Imaging offers a complete guide to this optical modality, from basic principles, instrumentation, methods, and image analysis to biomedical applications. The book features contributions by experts in second-harmonic imaging, including many pioneering researchers in the field. Written for researchers at all levels, it takes an in-depth look at the current state of the art and possibilities of SHG microscopy. Organized into three sections, the book: Provides an introduction to the physics of the process, step-by-step instructions on how to build an SHG microscope, and comparisons with related imaging techniques Gives an overview of the capabilities of SHG microscopy for imaging tissues and cells—including cell membranes, muscle, collagen in tissues, and microtubules in live cells—by summarizing experi...
International Nuclear Information System (INIS)
Au, R.; Fowler, M.; Hanawa, H.; Riedel, J.; Qua, Z.G.
1984-01-01
In early 1983 it was decided to mount coils on arms separated by 120 degrees and buck them out so that the third harmonic dphi/dt component would be cancelled and thus the first and second field harmonics could be very accurately measured. The original intention was to do as others had done, namely, use fast ADC's to read the voltages, and computer process the result to get the Fourier components. However, because of the 100 to 1 dynamic range of the fast ADC's and the likelihood that noise would be a problem, the authors decided to do things differently. Using a fast Fourier transform analyzer was considered, but this instrument is very expensive, so they decided to use a completely electronic analog approach: The authors decided to use active bandpass filters to render the harmonic components
Benefits from the BESSY FEL Higher Harmonic Radiation
Goldammer, K
2005-01-01
In the FEL process, bunching and coherent radiation is produced at the fundamental frequency as well as its higher harmonics. BESSY proposes a linac-based cascaded High-Gain Harmonic-Generation (HGHG) free electron laser (FEL) multi-user facility. The BESSY soft X-ray FEL will be seeded by three lasers spanning the spectral range of 230nm to 460nm. Two to four HGHG stages downconvert the seed wavelength to the desired radiation range of 1.24nm to 51nm using higher harmonic bunching. As a surplus, higher harmonic radiation is intrinsically produced in each FEL stage. Radiation on a higher harmonic of the FEL frequency is of high interest because it yields the possibility to reduce the number of FEL stages. This paper details extensive studies of the higher harmonic content of the BESSY FEL radiation. Important aspects of FEL interaction on higher harmonics as resulting from theory and from numerical simulations are discussed. For the case of the BESSY FEL, methods for improving the harmonic content are present...
General Criterion for Harmonicity
Proesmans, Karel; Vandebroek, Hans; Van den Broeck, Christian
2017-10-01
Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring," namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.
Recent topics in differential and analytic geometry
Ochiai, T
1990-01-01
Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters con
Comparing Harmonic Similarity Measures
de Haas, W.B.; Robine, M.; Hanna, P.; Veltkamp, R.C.; Wiering, F.
2010-01-01
We present an overview of the most recent developments in polyphonic music retrieval and an experiment in which we compare two harmonic similarity measures. In contrast to earlier work, in this paper we specifically focus on the symbolic chord description as the primary musical representation and
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom
2017-01-01
-robust to noise, or very computationally inten- sive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the liter- ature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also...
Pruitt, Kathryn Ringler
2012-01-01
This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the "best" metrical foot is chosen…
Gluck, P.; Krakower, Zeev
2010-01-01
We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)
Young children's harmonic perception.
Costa-Giomi, Eugenia
2003-11-01
Harmony and tonality are two of the most difficult elements for young children to perceive and manipulate and are seldom taught in the schools until the end of early childhood. Children's gradual harmonic and tonal development has been attributed to their cumulative exposure to Western tonal music and their increasing experiential knowledge of its rules and principles. Two questions that are relevant to this problem are: (1) Can focused and systematic teaching accelerate the learning of the harmonic/tonal principles that seem to occur in an implicit way throughout childhood? (2) Are there cognitive constraints that make it difficult for young children to perceive and/or manipulate certain harmonic and tonal principles? A series of studies specifically addressed the first question and suggested some possible answers to the second one. Results showed that harmonic instruction has limited effects on children's perception of harmony and indicated that the drastic improvement in the perception of implied harmony noted approximately at age 9 is due to development rather than instruction. I propose that young children's difficulty in perceiving implied harmony stems from their attention behaviors. Older children have less memory constraints and more strategies to direct their attention to the relevant cues of the stimulus. Younger children focus their attention on the melody, if present in the stimulus, and specifically on its concrete elements such as rhythm, pitch, and contour rather than its abstract elements such as harmony and key. The inference of the abstract harmonic organization of a melody required in the perception of implied harmony is thus an elusive task for the young child.
Symmetries in physics and harmonics
International Nuclear Information System (INIS)
Kolk, D.
2006-01-01
In this book the symmetries of elementary particles are described in relation to the rules of harmonics in music. The selection rules are described in connections with harmonic intervals. Also symmetry breaking is considered in this framework. (HSI)
Phase matching of high-order harmonics in a semi-infinite gas cell
International Nuclear Information System (INIS)
Steingrube, Daniel S.; Vockerodt, Tobias; Schulz, Emilia; Morgner, Uwe; Kovacev, Milutin
2009-01-01
Phase matching of high-order harmonic generation is investigated experimentally for various parameters in a semi-infinite gas-cell (SIGC) geometry. The optimized harmonic yield is identified using two different noble gases (Xe and He) and its parameter dependence is studied in a systematic way. Beside the straightforward setup of the SIGC, this geometry promises a high photon flux due to a large interaction region. Moreover, since the experimental parameters within this cell are known accurately, direct comparison to simulations is performed. Spectral splitting and blueshift of high-order harmonics are observed.
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Harmonic Patterns in Forex Trading
Nemček, Sebastian
2013-01-01
This diploma thesis is committed to examination of validity of Harmonic Patterns in Forex trading. Scott Carney described existing and introduced new Harmonic Patterns in 1999 in his book Harmonic Trader. These patterns use the Fibonacci principle to analyze price action and to provide both bullish and bearish trading signals. The goal of this thesis is to find out whether harmonic trading strategy on selected pairs is profitable in FX market, which patterns are the most profitable and what i...
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
2×1 Microstrip Patch Array Antenna with Harmonic Suppression Capability for Rectenna
Directory of Open Access Journals (Sweden)
Nur Aisyah Amir
2017-12-01
Full Text Available This paper is an extension of work originally presented in 2016 IEEE Asia-Pacific Conference on Applied Electromagnetics (APACE. A 2×1 microstrip patch array antenna integrated with photonic bandgap (PBG and stubs is designed and analyzed. The performance of the PBG and stubs structure are explained and analyzed in terms of the elimination of the resonance at the harmonic frequencies of the antenna. The proposed antenna is designed on FR-4 substrate with thickness of 1.6 mm and operated at 2.45 GHz frequency suitable for rectenna design application. From the simulated result, the first harmonic frequency (5.4 GHz, the second harmonic frequency (6.6 GHz and the third harmonic frequency (7.8 GHz are successfully suppressed. For instance, the radiation to the forward of the stubs-PBG antenna is suppressed at more than 15 dB at the second and third harmonic frequencies.
Overhead distribution line models for harmonics studies
Energy Technology Data Exchange (ETDEWEB)
Nagpal, M.; Xu, W.; Dommel, H.W.
1994-01-01
Carson's formulae and Maxwell's potential coefficients are used for calculating the per unit length series impedances and shunt capacitances of the overhead lines. The per unit length values are then used for building the models, nominal pi-circuit, and equivalent pi-circuit at the harmonic frequencies. This paper studies the accuracy of these models for presenting the overhead distribution lines in steady-state harmonic solutions at frequencies up to 5 kHz. The models are verified with a field test on a 25 kV distribution line and the sensitivity of the models to ground resistivity, skin effect, and multiple grounding is reported.
Harmonic surface wave propagation in plasma
International Nuclear Information System (INIS)
Shivarova, A.; Stoychev, T.
1980-01-01
Second order harmonic surface waves generated by one fundamental high-frequency surface wave are investigated experimentally in gas discharge plasma. Two types of harmonic waves of equal frequency, associated with the linear dispersion relation and the synchronism conditions relatively propagate. The experimental conditions and the different space damping rates of the waves ensure the existence of different spatial regions (consecutively arranged along the plasma column) of a dominant propagation of each one of these two waves. Experimental data are obtained both for the wavenumbers and the space damping rates by relatively precise methods for wave investigations such as the methods of time-space diagrams and of phase shift measurements. The results are explained by the theoretical model for nonlinear mixing of dispersive waves. (author)
Atto second high harmonic sources
International Nuclear Information System (INIS)
Nam, Chang Hee
2008-01-01
High harmonic generation is a powerful method to produce attosecond pulses. The high harmonics, emitted from atoms driven by intense femtosecond laser pulses, can from an attosecond pulse train with equally spaced harmonic spectrum or an isolated single attosecond pulse with broad continuum spectrum. Using high power femtosecond laser technology developed at CXRC, we have investigated the spectral and temporal characteristics of high harmonics obtained from gaseous atoms. The spectral structure of harmonics could be manipulated by controlling laser chirp, and continuous tuning of harmonic wavelengths was achieved. For rigorous temporal characterization of attosecond harmonic pulses a cross correlation technique was applied to the photoionization process by harmonic and IR femtosecond pulses and achieved the complete temporal reconstruction of attosecond pulse trains, revealing the detailed temporal structure of the attosecond chirp by material dispersion. The duration of attosecond high harmonic pulses is usually much longer than that of transform limited pulses due to the inherent chirp originating from the harmonic generation process. The attosecond chirp compensation in the harmonic generation medium itself was demonstrated, thereby realizing the generation of near transform limited attosecond pulses. The interference of attosecond electron wave packets, generated from an atom by attosecond harmonic pulses, will be also presented
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Three-dimensional analysis of harmonic generation in high-gain free-electron lasers
International Nuclear Information System (INIS)
Huang, Zhirong; Kim, Kwang-Je
2000-01-01
In a high-gain free-electron laser (FEL) employing a planar undulator, strong bunching at the fundamental wavelength can drive substantial bunching and power levels at the harmonic frequencies. In this paper we investigate the three-dimensional evolution of harmonic radiation based on the coupled Maxwell-Klimontovich equations that take into account nonlinear harmonic interactions. Each harmonic field is a sum of a linear amplification term and a term driven by nonlinear harmonic interactions. After a certain stage of exponential growth, the dominant nonlinear term is determined by interactions of the lower nonlinear harmonics and the fundamental radiation. As a result, the gain length, transverse profile, and temporal structure of the first few harmonics are eventually governed by those of the fundamental. Transversely coherent third-harmonic radiation power is found to approach 1% of the fundamental power level for current high-gain FEL projects
High-order harmonics generation from overdense plasmas
International Nuclear Information System (INIS)
Quere, F.; Thaury, C.; Monot, P.; Martin, Ph.; Geindre, J.P.; Audebert, P.; Marjoribanks, R.
2006-01-01
Complete test of publication follows. When an intense laser beam reflects on an overdense plasma generated on a solid target, high-order harmonics of the incident laser frequency are observed in the reflected beam. This process provides a way to produce XUV femtosecond and attosecond pulses in the μJ range from ultrafast ultraintense lasers. Studying the mechanisms responsible for this harmonic emission is also of strong fundamental interest: just as HHG in gases has been instrumental in providing a comprehensive understanding of basic intense laser-atom interactions, HHG from solid-density plasmas is likely to become a unique tool to investigate many key features of laser-plasma interactions at high intensities. We will present both experimental and theoretical evidence that two mechanisms contribute to this harmonic emission: - Coherent Wake Emission: in this process, harmonics are emitted by plasma oscillations in te overdense plasma, triggered in the wake of jets of Brunel electrons generated by the laser field. - The relativistic oscillating mirror: in this process, the intense laser field drives a relativistic oscillation of the plasma surface, which in turn gives rise to a periodic phase modulation of the reflected beam, and hence to the generation of harmonics of the incident frequency. Left graph: experimental harmonic spectrum from a polypropylene target, obtained with 60 fs laser pulses at 10 19 W/cm 2 , with a very high temporal contrast (10 10 ). The plasma frequency of this target corresponds to harmonics 15-16, thus excluding the CWE mechanism for the generation of harmonics of higher orders. Images on the right: harmonic spectra from orders 13 et 18, for different distances z between the target and the best focus. At the highest intensity (z=0), harmonics emitted by the ROM mechanism are observed above the 15th order. These harmonics have a much smaller spectral width then those due to CWE (below the 15th order). These ROM harmonics vanish as soon
Intelligent harmonic load model based on neural networks
Ji, Pyeong-Shik; Lee, Dae-Jong; Lee, Jong-Pil; Park, Jae-Won; Lim, Jae-Yoon
2007-12-01
In this study, we developed a RBFNs(Radial Basis Function Networks) based load modeling method with harmonic components. The developed method implemented by using harmonic information as well as fundamental frequency and voltage which are essential input factors in conventional method. Thus, the proposed method makes it possible to effectively estimate load characteristics in power lines with harmonics. The RBFNs have certain advantage such as simple structure and rapid computation ability compared with multilayer perceptron which is extensively applied for load modeling. To show the effectiveness, the proposed method has been intensively tested with various dataset acquired under the different frequency and voltage and compared it with conventional methods such as polynominal 2nd equation method, MLP and RBF without considering harmonic components.
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
Harmonic analysis of electrified railway based on improved HHT
Wang, Feng
2018-04-01
In this paper, the causes and harms of the current electric locomotive electrical system harmonics are firstly studied and analyzed. Based on the characteristics of the harmonics in the electrical system, the Hilbert-Huang transform method is introduced. Based on the in-depth analysis of the empirical mode decomposition method and the Hilbert transform method, the reasons and solutions to the endpoint effect and modal aliasing problem in the HHT method are explored. For the endpoint effect of HHT, this paper uses point-symmetric extension method to extend the collected data; In allusion to the modal aliasing problem, this paper uses the high frequency harmonic assistant method to preprocess the signal and gives the empirical formula of high frequency auxiliary harmonic. Finally, combining the suppression of HHT endpoint effect and modal aliasing problem, an improved HHT method is proposed and simulated by matlab. The simulation results show that the improved HHT is effective for the electric locomotive power supply system.
Human sperm steer with second harmonics of the flagellar beat.
Saggiorato, Guglielmo; Alvarez, Luis; Jikeli, Jan F; Kaupp, U Benjamin; Gompper, Gerhard; Elgeti, Jens
2017-11-10
Sperm are propelled by bending waves traveling along their flagellum. For steering in gradients of sensory cues, sperm adjust the flagellar waveform. Symmetric and asymmetric waveforms result in straight and curved swimming paths, respectively. Two mechanisms causing spatially asymmetric waveforms have been proposed: an average flagellar curvature and buckling. We image flagella of human sperm tethered with the head to a surface. The waveform is characterized by a fundamental beat frequency and its second harmonic. The superposition of harmonics breaks the beat symmetry temporally rather than spatially. As a result, sperm rotate around the tethering point. The rotation velocity is determined by the second-harmonic amplitude and phase. Stimulation with the female sex hormone progesterone enhances the second-harmonic contribution and, thereby, modulates sperm rotation. Higher beat frequency components exist in other flagellated cells; therefore, this steering mechanism might be widespread and could inspire the design of synthetic microswimmers.
Probabilistic aspects of harmonic emission of large offshore wind farms
Energy Technology Data Exchange (ETDEWEB)
Jensen, Christian F. [Energinet.dk, Fredericia (Denmark); Bak, Claus L. [Aalborg Univ. (Denmark). Dept. of Energy Technology; Kocewiak, Lukasz; Hjerrild, Jesper [DONG Energy, Skaerbaek (Denmark); Berthelsen, Kasper K. [Aalborg Univ. (Denmark). Dept. of Mathematical Sciences
2011-07-01
In this article, a new probabilistic method of assessment of harmonic emission of large offshore wind farms is presented. Based on measurements from the British wind farm Burbo Banks, probability density functions are estimated for the dominating low order harmonic currents injected by a single turbine. The degree and type of dependence between the harmonic emission and the operating point of a single turbine is established. A model of Burbo Banks, suitable for harmonic load flow studies, is created in DIgSILENT Power Factory along with a DPL-script that deals with the probabilistic issues of the harmonic emission. The simulated harmonic distortion at the PCC is compared to measurement. This reveals some difficulties regarding harmonic load flow studies. The harmonic background distortion in the grid to where the wind farms is connected must be included in the study. Furthermore, a very detailed representation of the frequency dependent short circuit impedance must be used before sufficiently accurate results can be obtained from the model. (orig.)
Wolff, Thomas H; Shubin, Carol
2003-01-01
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for fu...
The Harmonization of Accounting
Directory of Open Access Journals (Sweden)
Hajnal Noémi
2017-11-01
Full Text Available The development and configuration of the regulatory framework of the accounting systems in Romania and Hungary took place in different ways. Among the reasons for the diversities in these countries’ accounting systems, the following can be certainly mentioned: different purposes of taxation, legal structure, the accountancy’s connection with the corporate law and family law, diversification on corporate financing policy, and cultural heterogeneity. Both countries quickly caught up with the international accounting harmonization standards. The adaptation of the international accounting standards has many advantages and disadvantages; these have been discussed in several previous researches. This paper aims at comparing the Romanian and Hungarian states’ accounting regulations from the early 1990s, which were implemented in order to harmonize the states’ accountancy regulations with the international standards, and their impact on the economy, based on secondary analysis.
Squeezing and entanglement in doubly resonant, type II, second-harmonic generation
DEFF Research Database (Denmark)
Andersen, Ulrik Lund; Buchhave, Preben
2003-01-01
We investigate, theoretically, the generation of bright and vacuum-squeezed light as well as entanglement in intracavity, type II, phase-matched second-harmonic generation. The cavity in which the crystal is embedded is resonant at the fundamental frequency but not at the second-harmonic frequenc...
Harmonic generation effect in high-Tc films
International Nuclear Information System (INIS)
Khare, Neeraj; Shrivastava, S.K.; Padmanabhan, V.P.N.; Khare, Sangeeta; Gupta, A.K.
1997-01-01
Harmonic generation in thick BPSCCO and thin YBCO films are reported. The application of an ac field (H ac > H c1 ) of frequency f causes the generation of odd harmonics of frequency (2n+1)f. The application of dc field in addition to the ac field causes the appearance of even harmonics also in the BPSCCO film. However, the appearance of even harmonics is not observed in YBCO film with high J c ∼ 1.6x10 6 A/cm 2 and appearance of second harmonic with small magnitude is observed in YBCO film with low J c ∼ 2x10 3 A/cm 2 . The variation of amplitudes of these harmonics are studied as a function of magnitude of ac and dc field and the results are explained in the framework of critical state model. A high-T c film magnetometer based on the measurement of the amplitude of second harmonic has been developed whose field sensitivity is ∼ 1.5x10 -8 T. (author)
Directory of Open Access Journals (Sweden)
Chuang Qian
2016-12-01
Full Text Available As the field of high-precision applications based on carriers continues to expand, the development of low-cost, small, modular receivers and their application in diverse scenarios and situations with complex data quality has increased the requirements of carrier-phase data preprocessing. A new geometry-based cycle slip detection and repair method based on Global Position System (GPS + BeiDou Navigation Satellite System (BDS is proposed. The method uses a Time-differenced Carrier Phase (TDCP model, which eliminates the Inner-System Bias (ISB between GPS and BDS, and it is conducive to the effective combination of GPS and BDS. It avoids the interference of the noise of the pseudo-range with cycle slip detection, while the cycle slips are preserved as integers. This method does not limit the receiver frequency number, and it is applicable to single-frequency data. The process is divided into two steps to detect and repair cycle slip. The first step is cycle slip detection, using the Improved Local Analysis Method (ILAM to find satellites that have cycle slips; The second step is to repair the cycle slips, including estimating the float solution of changes in ambiguities at the satellites that have cycle slips with the least squares method and the integer solution of the cycle slips by rounding. In the process of rounding, in addition to the success probability, a decimal test is carried out to validate the result. Finally, experiments with filed test data are carried out to prove the effectiveness of this method. The results show that the detectable cycle slips number with GPS + BDS is much greater than that with GPS. The method can also detect the non-integer outliers while fixing the cycle slip. The maximum decimal bias in repair is less than that with GPS. It implies that this method takes full advantages of multi-system.
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
[Harmonization of TSH Measurements.
Takeoka, Keiko; Hidaka, Yoh; Hishinuma, Akira; Ikeda, Katsuyoshi; Okubo, Shigeo; Tsuchiya, Tatsuyuki; Hashiguchi, Teruto; Furuta, Koh; Hotta, Taeko; Matsushita, Kazuyuki; Matsumoto, Hiroyuki; Murakami, Masami; Maekawa, Masato
2016-05-01
The measured concentration of thyroid stimulating hormone (TSH) differs depending on the reagents used. Harmonization of TSH is crucial because the decision limits are described in current clinical practice guide- lines as absolute values, e.g. 2.5 mIU/L in early pregnancy. In this study, we tried to harmonize the report- ed concentrations of TSH using the all-procedure trimmed mean. TSH was measured in 146 serum samples, with values ranging from 0.01 to 18.8 mIU/L, using 4 immunoassays. The concentration of TSH was highest with E test TOSOH and lowest with LUMIPULSE. The concentrations with each reagent were recalculated with the following formulas: E test TOSOH 0.855x-0.014; ECLusys 0.993x+0.079; ARCHITECT 1.041x- 0.010; and LUMIPULSE 1.096x-0.015. Recalculation eliminated the between-assay discrepancy. These formulas may be used until harmonization of TSH is achieved by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC).
Gliding and Quasi-harmonic Tremor Behaviour of Raung Volcano: November 2014 Crisis Period Case Study
Directory of Open Access Journals (Sweden)
Vico Luthfi Ipmawan
2018-01-01
Full Text Available DOI: 10.17014/ijog.5.1.13-21The seismic activity of Raung Volcano was raised on 11 November 2014. As many as 1709 tremors were recorded followed by continuous tremors appearing in late November 2014. Quasi-harmonic and gliding tremors appeared in a spectrogram on 12 November 2014. The quasi-harmonic tremors refer to tremors that have no fully harmonic form in spectrum. The gliding harmonic tremors refer to harmonic tremors that have frequency jumps with either positive or negative increment. After signal restitution processing, the Maximum Entropy Spectral Analysis (MESA method was applied in Raung recordings resulting the spectrum and the spectrogram of tremors. The quasi-harmonic tremors have the monotonic spectrum in its head and centre segment, and the harmonic one in its tails. There are twenty-four spectrums that show frequency changes between the monotonic and harmonic. The similarity between the fundamental frequency range of the monotonic and harmonic ones suggests that both signals are excited from a common resonator. The alternating of monotonic and harmonic respectively over this period is qualitatively similar with Julian’s synthetic time series about the nonlinear oscillator model. It is suggested that Raung Volcano magma pressure is sizeable to make a chaotic vibration. A pressure increasing in Raung magmatic conduit causes the increasing of P-wave velocity and makes a positive gliding frequency.
Effect of harmonic rank on the streaming of complex tones
DEFF Research Database (Denmark)
Madsen, Sara Miay Kim; Dau, Torsten; Moore, Brian C.J.
2015-01-01
The effect of the rank of the harmonics on sequential stream segregation of complex tones was investigated for normal-hearing participants with no musical training. It was hypothesized that stream segregation would be greater for tones with high pitch salience, as assessed by fundamental frequency....... There was a significant trend for less stream segregation with increasing harmonic rank. The amount of stream segregation was inversely correlated with the f0 difference limens, consistent with the hypothesis....
High order harmonic generation from plasma mirror
International Nuclear Information System (INIS)
Thaury, C.
2008-09-01
When an intense laser beam is focused on a solid target, its surface is rapidly ionized and forms a dense plasma that reflects the incident field. For laser intensities above few 10 15 W/cm 2 , high order harmonics of the laser frequency, associated in the time domain to a train of atto-second pulses (1 as = 10 18 s), can be generated upon this reflection. Because such a plasma mirror can be used with arbitrarily high laser intensities, this process should eventually lead to the production of very intense pulses in the X-ray domain. In this thesis, we demonstrate that for laser intensities about 10 19 W/cm 2 , two mechanisms can contribute to the generation of high order harmonics: the coherent wake emission and the relativistic emission. These two mechanisms are studied both theoretically and experimentally. In particular, we show that, thanks to very different properties, the harmonics generated by these two processes can be unambiguously distinguished experimentally. We then investigate the phase properties of the harmonic, in the spectral and in the spatial domain. Finally, we illustrate how to exploit the coherence of the generation mechanisms to get information on the dynamics of the plasma electrons. (author)
Image Formation in Second-Harmonic Near-Field Microscopy
DEFF Research Database (Denmark)
Bozhevolnyi, Sergey I.; Lozovski, Valeri Z.; Pedersen, Kjeld
1999-01-01
contributions in the effective current, i.e., the currents generated by the self-consistent fields at the fundamental and second-harmonic frequencies. The self-consistent problem for both frequencies is solved exactly by use of the diagram technique adapted from quantum electrodynamics. Preliminary numerical...
Simultaneous operation of a free-electron laser on two harmonically related wavelengths
International Nuclear Information System (INIS)
Burke, A.T.; Ride, S.K.
1992-01-01
The interaction of light waves at the fundamental and the third harmonic frequencies in a free-electron laser (FEL) oscillator is explored using the 1-D finite pulse mode-code BFELP. The code, which assumes that only the TEM 00 transverse mode is present at both harmonic frequencies, tracks the temporally-finite pulse electric field amplitudes of the fundamental and the third harmonic which interact with an rf-linac-generated electron micropulse inside a wiggler. The evolution of the pulse profiles, with possibly different mirror reflectivities at each frequency, after many passes through the wiggler and the optical resonator, has been generated for various initial conditions. Results include pulse-dependent third-harmonic coherent-spontaneous emission (CSE) with, and without, multiple-pass interference effects; the effects of sidebands at the fundamental on third-harmonic CSE; and, lasing competition between the fundamental and third harmonic in overlapping spatial regions of the electron micropulse
Symmetry properties of second harmonics generated by antisymmetric Lamb waves
Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen
2018-03-01
Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.
Plasma wave and second harmonic generation
International Nuclear Information System (INIS)
Sodha, M.S.; Sharma, J.K.; Tewari, D.P.; Sharma, R.P.; Kaushik, S.C.
1978-01-01
An investigation is made of a plasma wave at pump wave frequency and second harmonic generation caused by a self induced transverse inhomogeneity introduced by a Gaussian electromagnetic beam in a hot collisionless plasma. In the presence of a Gaussian beam the carriers get redistributed from the high field region to the low field region by ponderomative force and a transverse density gradient is established in the plasma. When the electric vector of the main beam is parallel to this density gradient, a plasma wave at the pump wave frequency is generated. In addition to this the transverse intensity gradient of the electromagnetic wave also contributes significantly to the plasma wave generation. The power of the plasma wave exhibits a maximum and minimum with the power of the pump wave (at z = 0). The generated plasma wave interacts with the electromagnetic wave and leads to the generation of a second harmonic. Furthermore, if the initial power of the pump wave is more than the critical power for self-focusing, the beam gets self-focused and hence the generated plasma wave and second harmonic which depend upon the background electron concentration and power of the main beam also get accordingly modified. (author)
Next generation data harmonization
Armstrong, Chandler; Brown, Ryan M.; Chaves, Jillian; Czerniejewski, Adam; Del Vecchio, Justin; Perkins, Timothy K.; Rudnicki, Ron; Tauer, Greg
2015-05-01
Analysts are presented with a never ending stream of data sources. Often, subsets of data sources to solve problems are easily identified but the process to align data sets is time consuming. However, many semantic technologies do allow for fast harmonization of data to overcome these problems. These include ontologies that serve as alignment targets, visual tools and natural language processing that generate semantic graphs in terms of the ontologies, and analytics that leverage these graphs. This research reviews a developed prototype that employs all these approaches to perform analysis across disparate data sources documenting violent, extremist events.
Harmonic mode-locking using the double interval technique in quantum dot lasers.
Li, Yan; Chiragh, Furqan L; Xin, Yong-Chun; Lin, Chang-Yi; Kim, Junghoon; Christodoulou, Christos G; Lester, Luke F
2010-07-05
Passive harmonic mode-locking in a quantum dot laser is realized using the double interval technique, which uses two separate absorbers to stimulate a specific higher-order repetition rate compared to the fundamental. Operating alone these absorbers would otherwise reinforce lower harmonic frequencies, but by operating together they produce the harmonic corresponding to their least common multiple. Mode-locking at a nominal 60 GHz repetition rate, which is the 10(th) harmonic of the fundamental frequency of the device, is achieved unambiguously despite the constraint of a uniformly-segmented, multi-section device layout. The diversity of repetition rates available with this method is also discussed.
Effect of Context on the Contribution of Individual Harmonics to Residue Pitch.
Gockel, Hedwig E; Alsindi, Sami; Hardy, Charles; Carlyon, Robert P
2017-12-01
There is evidence that the contribution of a given harmonic in a complex tone to residue pitch is influenced by the accuracy with which the frequency of that harmonic is encoded. The present study investigated whether listeners adjust the weights assigned to individual harmonics based on acquired knowledge of the reliability of the frequency estimates of those harmonics. In a two-interval forced-choice task, seven listeners indicated which of two 12-harmonic complex tones had the higher overall pitch. In context trials (60 % of all trials), the fundamental frequency (F0) was 200 Hz in one interval and 200 + ΔF0 Hz in the other. In different (blocked) conditions, either the 3rd or the 4th harmonic (plus the 7th, 9th, and 12th harmonics), were replaced by narrowband noises that were identical in the two intervals. Feedback was provided. In randomly interspersed test trials (40 % of all trials), the fundamental frequency was 200 + ΔF0/2 Hz in both intervals; in the second interval, either the third or the fourth harmonic was shifted slightly up or down in frequency with equal probability. There were no narrowband noises. Feedback was not provided. The results showed that substitution of a harmonic by noise in context trials reduced the contribution of that harmonic to pitch judgements in the test trials by a small but significant amount. This is consistent with the notion that listeners give smaller weight to a harmonic or frequency region when they have learned that this frequency region does not provide reliable information for a given task.
DEFF Research Database (Denmark)
Sun, Xiaofeng; Han, Ruijing; Shen, Hong
2016-01-01
voltages. This paper proposes a double-resistive active power filter (D-RAPF) system consisting of a terminal-RAPF and an attenuation-RAPF for each individual harmonic. The terminal-RAPF operating as the characteristic impedance of the feeder is installed at the end bus to suppress harmonic propagation......Harmonic propagation between power-factor correction capacitors and system inductors seriously deteriorates power quality in a radial power distribution feeder. Installation of a resistive active power filter (RAPF) at the end bus only suppresses harmonic propagation, not attenuates harmonic...... at all harmonic frequencies. The attenuation-RAPF, whose control gain can be set according to the requirements of the harmonic voltage distortion limit, is installed at a specific position for each individual harmonic to attenuate the corresponding harmonic voltages. The D-RAPF system not only suppresses...
Precise Model Analysis for 3-phase High Power Converter using the Harmonic State Space Modeling
DEFF Research Database (Denmark)
Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede
2015-01-01
This paper presents about the generalized multi-frequency modeling and analysis methodology, which can be used in control loop design and stability analysis. In terms of the switching frequency of high power converter, there can be harmonics interruption if the voltage source converter has a low...... switching frequency ratio or multi-sampling frequency. The range of the control bandwidth can include the switching component. Thus, the systems become unstable. This paper applies the Harmonic State Space (HSS) Modeling method in order to find out the transfer function for each harmonics terms...
Harmonic Resonances in Wind Power Plants
DEFF Research Database (Denmark)
Fernandez, Francisco Daniel Freijedo; Chaudhary, Sanjay; Teodorescu, Remus
2015-01-01
This work reviews the state-of-the-art in the field of harmonic resonance problems in Wind Power Plants (WPPs). Firstly, a generic WPP is modeled according to the equivalent circuits of its passive and active components. Main focus is put on modeling active components, i.e. the ones based on power...... converters. Subsequently, pros and cons of frequency and time domain analysis methods are outlined. The next sections are devoted to mitigation methods implemented in the power electronics converters. From the wind turbine perspective, different techniques to enhance the robustness of the controller...... are analyzed. Subsequently, the suitability for active damping of harmonics using STATCOM devices is assessed, with focus both on control techniques and power converter technologies....
Simulation of Second Harmonic Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2010-01-01
A non-linear ultrasound imaging simulation software should be capable of simulating the non-linear fields for any kind of transducer, focusing, apodization, and attenuation. At present, a major issue is the overlong simulation time of the non-linear software. An Angular Spectrum Approach (ASA......) using a quasi-linear approximation for solving the Westervelt equation can simulate the second harmonic pressure at any distance. Therefore, it shortens the execution time compared with the operator splitting method. The purpose of this paper is to implement the monochromatic solution for the second...... harmonic component based on ASA and Field II, and to compare with results from the simulation program Abersim. A linear array transducer with a center frequency of 4 MHz and 64 active elements is used as the transmitting source. The initial plane is 5 mm away from the transducer surface...
Investigation of Student Reasoning about Harmonic Motions
Tongnopparat, N.; Poonyawatpornkul, J.; Wattanakasiwich, P.
This study aimed to investigate student reasoning about harmonic oscillations. We conducted a semi-structured interview based on three situations of harmonic motions—(1) a mass attaching to spring and horizontally oscillating without damping, (2) the same situation but vertically oscillating and (3) a mass attaching to spring and oscillating in viscous liquid. Forty-five second-year students taking a vibrations and wave course at Chiang Mai University, Thailand participated in a fifteen-minute interview, which was video-recorded. The videos were transcribed and analyzed by three physics instructors. As results, we found that most students had misconceptions about angular frequency and energy mostly in the second and third situations.
Harmonics in a Wind Power Plant: Preprint
Energy Technology Data Exchange (ETDEWEB)
Preciado, V.; Madrigal, M.; Muljadi, E.; Gevorgian, V.
2015-04-02
Wind power generation has been growing at a very fast pace for the past decade, and its influence and impact on the electric power grid is significant. As in a conventional power plant, a wind power plant (WPP) must ensure that the quality of the power being delivered to the grid is excellent. At the same time, the wind turbine should be able to operate immune to small disturbances coming from the grid. Harmonics are one of the more common power quality issues presented by large WPPs because of the high switching frequency of the power converters and the possible nonlinear behavior from electric machines (generator, transformer, reactors) within a power plant. This paper presents a summary of the most important issues related to harmonics in WPPs and discusses practical experiences with actual Type 1 and Type 3 wind turbines in two WPPs.
Physics of tissue harmonic imaging by ultrasound
Jing, Yuan
Tissue Harmonic Imaging (THI) is an imaging modality that is currently deployed on diagnostic ultrasound scanners. In THI the amplitude of the ultrasonic pulse that is used to probe the tissue is large enough that the pulse undergoes nonlinear distortion as it propagates into the tissue. One result of the distortion is that as the pulse propagates energy is shifted from the fundamental frequency of the source pulse into its higher harmonics. These harmonics will scatter off objects in the tissue and images formed from the scattered higher harmonics are considered to have superior quality to the images formed from the fundamental frequency. Processes that have been suggested as possibly responsible for the improved imaging in THI include: (1) reduced sensitivity to reverberation, (2) reduced sensitivity to aberration, and (3) reduction in side lobes. By using a combination of controlled experiments and numerical simulations, these three reasons have been investigated. A single element transducer and a clinical ultrasound scanner with a phased array transducer were used to image a commercial tissue-mimicking phantom with calibrated targets. The higher image quality achieved with THI was quantified in terms of spatial resolution and "clutter" signals. A three-dimensional model of the forward propagation of nonlinear sound beams in media with arbitrary spatial properties (a generalized KZK equation) was developed. A time-domain code for solving the KZK equation was validated with measurements of the acoustic field generated by the single element transducer and the phased array transducer. The code was used to investigate the impact of aberration using tissue-like media with three-dimensional variations in all acoustic properties. The three-dimensional maps of tissue properties were derived from the datasets available through the Visible Female project. The experiments and simulations demonstrated that second harmonic imaging (1) suffers less clutter associated with
Geometry of isotropic convex bodies
Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen
2014-01-01
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...
Tissue Harmonic Synthetic Aperture Imaging
DEFF Research Database (Denmark)
Rasmussen, Joachim
The main purpose of this PhD project is to develop an ultrasonic method for tissue harmonic synthetic aperture imaging. The motivation is to advance the field of synthetic aperture imaging in ultrasound, which has shown great potentials in the clinic. Suggestions for synthetic aperture tissue...... system complexity compared to conventional synthetic aperture techniques. In this project, SASB is sought combined with a pulse inversion technique for 2nd harmonic tissue harmonic imaging. The advantages in tissue harmonic imaging (THI) are expected to further improve the image quality of SASB...
Optimization of weld bead geometry of MS plate
Indian Academy of Sciences (India)
The considered specimen was checked to harmonize the optimum setting between input factors, for example, welding current, open circuit voltage, and thickness of plate, with respect to obtaining prosperous weld strength as well as bead geometry quality characteristics, for example, tensile strength, bead width, ...
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan, Jeonbuk 570-749 (Korea, Republic of); Zhang, Shuzeng; Li, Xiongbing [School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075 (China); Barnard, Dan [Center for Nondestructive Evaluation, Iowa State University, Ames, IA 50010 (United States)
2015-09-15
The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α{sub 2} ≃ 2α{sub 1}.
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Automated detection and characterization of harmonic tremor in continuous seismic data
Roman, Diana C.
2017-06-01
Harmonic tremor is a common feature of volcanic, hydrothermal, and ice sheet seismicity and is thus an important proxy for monitoring changes in these systems. However, no automated methods for detecting harmonic tremor currently exist. Because harmonic tremor shares characteristics with speech and music, digital signal processing techniques for analyzing these signals can be adapted. I develop a novel pitch-detection-based algorithm to automatically identify occurrences of harmonic tremor and characterize their frequency content. The algorithm is applied to seismic data from Popocatepetl Volcano, Mexico, and benchmarked against a monthlong manually detected catalog of harmonic tremor events. During a period of heightened eruptive activity from December 2014 to May 2015, the algorithm detects 1465 min of harmonic tremor, which generally precede periods of heightened explosive activity. These results demonstrate the algorithm's ability to accurately characterize harmonic tremor while highlighting the need for additional work to understand its causes and implications at restless volcanoes.
Harmonic current prediction by impedance modeling of grid-tied inverters
DEFF Research Database (Denmark)
Pereira, Heverton A.; Freijedo, Francisco D.; Silva, M. M.
2017-01-01
and harmonic voltage profiles. Results reinforce that impedance models can represent with relatively accuracy the harmonic current emitted by the PV plants at the point of common coupling (PCC). Lastly, a stress test is performed to show how a variation in the harmonic voltage phase angle impacts the PV plant...... impedance models when used in harmonic integration studies. It is aimed to estimate the harmonic current contribution as a function of the background harmonic voltages components. Time domain simulations based on detailed and average models are compared with the impedance model developed in frequency domain....... In grids with harmonic voltages, impedance models can predict the current distortion for all active power injection scenarios. Furthermore, measurements in a 1.4 MW PV plant connected in a distributed grid are used to validate the simulation based on impedance models during different power injections...
International Nuclear Information System (INIS)
Ganeev, R. A.; Bom, L. B. Elouga; Kieffer, J.-C.; Ozaki, T.
2007-01-01
We demonstrate the intensity enhancement of single harmonics in high-order harmonic generation from laser plasma. We identified several targets (In, Sn, Sb, Cr, and Mn) that demonstrate resonance-induced enhancement of single harmonic, that are spectrally close to ionic transitions with strong oscillator strengths. We optimized and obtained enhancements of the 13th, 17th, 21st, 29th, and 33rd harmonics from the above targets, by varying the chirp of the 800 nm wavelength femtosecond laser. We also observe harmonic enhancement by using frequency-doubled pump laser (400 nm wavelength). For Mn plasma pumped by the 400 nm wavelength laser, the maximum order of the enhanced harmonic observed was the 17th order (λ=23.5 nm), which corresponds to the highest photon energy (52.9 eV) reported for an enhanced single harmonic
Harmonic Dark Pulse Emission in Erbium-Doped Fiber Laser
International Nuclear Information System (INIS)
Zian, Cheak Tiu; Arman, Zarei; Sin, Jin Tan; Harith, Ahmad; Sulaiman, Wadi Harun
2015-01-01
A harmonic dark pulse generation in an erbium-doped fiber laser is demonstrated based on a figure-of-eight configuration. It is found that the harmonic dark pulse can be shifted from the fundamental to the 5"t"h order harmonic by increasing the pump power with an appropriate polarization controller orientation. The fundamental repetition rate of 20 kHz is obtained at the pump power of 29 mW. The highest pulse energy of 42.6 nJ is obtained at the fundamental repetition rate. The operating frequency of the dark pulse trains shifts to 2"n"d, 3"r"d, 4"t"h and 5"t"h harmonic as the pump powers are increased to 34 mW, 50 mW, 59 mW and 137 mW, respectively. (paper)
Numerical modeling of Harmonic Imaging and Pulse Inversion fields
Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis
2003-10-01
Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.
Multi-order nonlinear diffraction in second harmonic generation
DEFF Research Database (Denmark)
Saltiel, S. M.; Neshev, D.; Krolikowski, Wieslaw
We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes.......We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes....
Zhang, Guobo; Chen, Min; Liu, Feng; Yuan, Xiaohui; Weng, Suming; Zheng, Jun; Ma, Yanyun; Shao, Fuqiu; Sheng, Zhengming; Zhang, Jie
2017-10-02
Relativistically intense laser solid target interaction has been proved to be a promising way to generate high-order harmonics, which can be used to diagnose ultrafast phenomena. However, their emission direction and spectra still lack tunability. Based upon two-dimensional particle-in-cell simulations, we show that directional enhancement of selected high-order-harmonics can be realized using blazed grating targets. Such targets can select harmonics with frequencies being integer times of the grating frequency. Meanwhile, the radiation intensity and emission area of the harmonics are increased. The emission direction is controlled by tailoring the local blazed structure. Theoretical and electron dynamics analysis for harmonics generation, selection and directional enhancement from the interaction between multi-cycle laser and grating target are carried out. These studies will benefit the generation and application of laser plasma-based high order harmonics.
Second harmonic generation microscopy
DEFF Research Database (Denmark)
Brüggemann, Dagmar Adeline; Brewer, Jonathan R.; Risbo, Jens
2010-01-01
Myofibers and collagen show non-linear optical properties enabling imaging using second harmonic generation (SHG) microscopy. The technique is evaluated for use as a tool for real-time studies of thermally induced changes in thin samples of unfixed and unstained pork. The forward and the backward...... scattered SHG light reveal complementary features of the structures of myofibers and collagen fibers. Upon heating the myofibers show no structural changes before reaching a temperature of 53 °C. At this temperature the SHG signal becomes extinct. The extinction of the SHG at 53 °C coincides with a low......-temperature endotherm peak observable in the differential scanning calorimetry (DSC) thermograms. DSC analysis of epimysium, the connective tissue layer that enfold skeletal muscles, produces one large endotherm starting at 57 °C and peaking at 59.5 °C. SHG microscopy of collagen fibers reveals a variability of thermal...
Azimuthal anisotropy: The higher harmonics
International Nuclear Information System (INIS)
Poskanzer, Arthur M.; STAR Collaboration
2004-01-01
We report the first observations of the fourth harmonic (v 4 ) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v 4 is about a factor of 10 smaller than v 2 . For the sixth (v 6 ) and eighth (v 8 ) harmonics upper limits on the magnitudes are reported
Harmonic Series Meets Fibonacci Sequence
Chen, Hongwei; Kennedy, Chris
2012-01-01
The terms of a conditionally convergent series may be rearranged to converge to any prescribed real value. What if the harmonic series is grouped into Fibonacci length blocks? Or the harmonic series is arranged in alternating Fibonacci length blocks? Or rearranged and alternated into separate blocks of even and odd terms of Fibonacci length?
Tuvan Throat Singing and Harmonics
Ruiz, Michael J.; Wilken, David
2018-01-01
Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the…
Characterization of Harmonic Signal Acquisition with Parallel Dipole and Multipole Detectors
Park, Sung-Gun; Anderson, Gordon A.; Bruce, James E.
2018-04-01
Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) is a powerful instrument for the study of complex biological samples due to its high resolution and mass measurement accuracy. However, the relatively long signal acquisition periods needed to achieve high resolution can serve to limit applications of FTICR-MS. The use of multiple pairs of detector electrodes enables detection of harmonic frequencies present at integer multiples of the fundamental cyclotron frequency, and the obtained resolving power for a given acquisition period increases linearly with the order of harmonic signal. However, harmonic signal detection also increases spectral complexity and presents challenges for interpretation. In the present work, ICR cells with independent dipole and harmonic detection electrodes and preamplifiers are demonstrated. A benefit of this approach is the ability to independently acquire fundamental and multiple harmonic signals in parallel using the same ions under identical conditions, enabling direct comparison of achieved performance as parameters are varied. Spectra from harmonic signals showed generally higher resolving power than spectra acquired with fundamental signals and equal signal duration. In addition, the maximum observed signal to noise (S/N) ratio from harmonic signals exceeded that of fundamental signals by 50 to 100%. Finally, parallel detection of fundamental and harmonic signals enables deconvolution of overlapping harmonic signals since observed fundamental frequencies can be used to unambiguously calculate all possible harmonic frequencies. Thus, the present application of parallel fundamental and harmonic signal acquisition offers a general approach to improve utilization of harmonic signals to yield high-resolution spectra with decreased acquisition time. [Figure not available: see fulltext.
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Harmonics in transmission power systems
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz
. The comparison shows that results obtained used both types of the cores are the same, so it is concluded that both cores can be used for harmonic measurements. Low-inductance resistors are introduced in the secondary circuits, in series with the metering and protective relaying. On those resistors, the harmonic......Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need...... end only so the ground is not used as a return path. A way to reduce the capacitive coupling is to provide shielding. Harmonic currents are measured using the conventional inductive voltage transformers. Both protective and metering cores were compared if they could be used for harmonic measurements...
Tuvan throat singing and harmonics
Ruiz, Michael J.; Wilken, David
2018-05-01
Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the listener hears two pitches simultaneously. Harmonics such as H8, H9, H10, and H12 form part of a pentatonic scale and are commonly selected for melody tones by Tuvan singers. A real-time spectrogram is provided in a video (Ruiz M J 2018 Video: Tuvan Throat Singing and Harmonics http://mjtruiz.com/ped/tuva/) so that Tuvan harmonics can be visualized as they are heard.
Phase-locked high-order-harmonic and sub-100-as pulse generation from stretched molecules
International Nuclear Information System (INIS)
Lan Pengfei; Lu Peixiang; Cao Wei; Wang Xinlin; Yang Guang
2006-01-01
High harmonic generation from diatomic molecules in a linearly polarized intense laser field is investigated and the emission time of the harmonics is discussed with the time-frequency analysis method. It is shown that high harmonic generation from molecules at equilibrium distance is similar to that from atoms. Only the harmonics in the cutoff are synchronized, i.e., well phase-locked, whereas the other harmonics are not phase-locked. For the molecule stretched well beyond its equilibrium distance, the harmonics exhibit distinct time-frequency characteristics. The harmonic spectrum can be extended to I p +8U p , where I p and U p are the ionization and ponderomotive potential, and the harmonics with energies below I p +3.17U p are not phase-locked and the harmonics with energies beyond I p +3.17U p are well phase-locked. Thus a large range of harmonics which are well phase-locked are produced, and a train of clean attosecond (as) pulses with a single 90-as pulse in each half optical cycle can be generated with a multicycle laser pulse. Using a few-cycle laser pulse, an isolated attosecond pulse with a duration of about 95 as is obtained
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo
2017-03-01
The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
Transmit beamforming for optimal second-harmonic generation.
Hoilund-Kaupang, Halvard; Masoy, Svein-Erik
2011-08-01
A simulation study of transmit ultrasound beams from several transducer configurations is conducted to compare second-harmonic imaging at 3.5 MHz and 11 MHz. Second- harmonic generation and the ability to suppress near field echoes are compared. Each transducer configuration is defined by a chosen f-number and focal depth, and the transmit pressure is estimated to not exceed a mechanical index of 1.2. The medium resembles homogeneous muscle tissue with nonlinear elasticity and power-law attenuation. To improve computational efficiency, the KZK equation is utilized, and all transducers are circular-symmetric. Previous literature shows that second-harmonic generation is proportional to the square of the transmit pressure, and that transducer configurations with different transmit frequencies, but equal aperture and focal depth in terms of wavelengths, generate identical second-harmonic fields in terms of shape. Results verify this for a medium with attenuation f1. For attenuation f1.1, deviations are found, and the high frequency subsequently performs worse than the low frequency. The results suggest that high frequencies are less able to suppress near-field echoes in the presence of a heterogeneous body wall than low frequencies.
Energy Technology Data Exchange (ETDEWEB)
Perkins, R. J., E-mail: rperkins@pppl.gov; Hosea, J. C.; Jaworski, M. A.; Diallo, A.; Bell, R. E.; Bertelli, N.; Gerhardt, S.; Kramer, G. J.; LeBlanc, B. P.; Phillips, C. K.; Podestà, M.; Roquemore, L.; Taylor, G.; Wilson, J. R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Ahn, J.-W.; Gray, T. K. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); McLean, A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Sabbagh, S. [Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)
2015-04-15
The National Spherical Torus eXperiment (NSTX) can exhibit a major loss of high-harmonic fast wave (HHFW) power along scrape-off layer (SOL) field lines passing in front of the antenna, resulting in bright and hot spirals on both the upper and lower divertor regions. One possible mechanism for this loss is RF sheaths forming at the divertors. Here, we demonstrate that swept-voltage Langmuir probe characteristics for probes under the spiral are shifted relative to those not under the spiral in a manner consistent with RF rectification. We estimate both the magnitude of the RF voltage across the sheath and the sheath heat flux transmission coefficient in the presence of the RF field. Although precise comparison between the computed heat flux and infrared (IR) thermography cannot yet be made, the computed heat deposition compares favorably with the projections from IR camera measurements. The RF sheath losses are significant and contribute substantially to the total SOL losses of HHFW power to the divertor for the cases studied. This work will guide future experimentation on NSTX-U, where a wide-angle IR camera and a dedicated set of coaxial Langmuir probes for measuring the RF sheath voltage directly will quantify the contribution of RF sheath rectification to the heat deposition from the SOL to the divertor.
High order harmonic generation from plasma mirrors
International Nuclear Information System (INIS)
George, H.
2010-01-01
When an intense laser beam is focused on a solid target, the target's surface is rapidly ionized and forms dense plasma that reflects the incident field. For laser intensities above few 10 to the power of 15 Wcm -2 , high order harmonics of the laser frequency, associated in the time domain to a train of atto-second pulses (1 as 10 -18 s), can be generated upon this reflection. In this thesis, we developed numerical tools to reveal original aspects of harmonic generation mechanisms in three different interaction regime: the coherent wake emission, the relativistic emission and the resonant absorption. In particular, we established the role of these mechanisms when the target is a very thin foil (thickness of the order of 100 nm). Then we study experimentally the spectral, spatial and coherence properties of the emitted light. We illustrate how to exploit these measurements to get information on the plasma mirror dynamics on the femtosecond and atto-second time scales. Last, we propose a technique for the single-shot complete characterization of the temporal structure of the harmonic light emission from the laser-plasma mirror interaction. (author)
The IPNS second harmonic RF upgrade
International Nuclear Information System (INIS)
Middendorf, M.E.; Brumwell, F.R.; Dooling, J.C.; Horan, D.; Kustom, R.L.; Lien, M.K.; McMichael, G.E.; Moser, M.R.; Nassiri, A.; Wang, S.
2008-01-01
The intense pulsed neutron source (IPNS) rapid cycling synchrotron (RCS) is used to accelerate protons from 50 MeV to 450 MeV, at a repetition rate of 30 Hz. The original ring design included two identical rf systems, each consisting of an accelerating cavity, cavity bias supply, power amplifiers and low-level analog electronics. The original cavities are located 180 degrees apart in the ring and provide a total peak accelerating voltage of ∼21 kV over the 2.21-MHz to 5.14-MHz revolution frequency sweep. A third rf system has been constructed and installed in the RCS. The third rf system is capable of operating at the fundamental revolution frequency for the entire acceleration cycle, providing an additional peak accelerating voltage of up to ∼11 kV, or at the second harmonic of the revolution frequency for the first ∼4 ms of the acceleration cycle, providing an additional peak voltage of up to ∼11 kV for bunch shape control. We describe here the hardware implementation and operation to date of the third rf cavity in the second harmonic mode.
Transient regime in second harmonic generation
Szeftel, Jacob; Sandeau, Laure; Sandeau, Nicolas; Delezoide, Camille; Khater, Antoine
2013-09-01
The time growth of the electromagnetic field at the fundamental and double frequencies is studied from the very onset of the second harmonic generation (SHG) process for a set of dipoles lacking a symmetry centre and exhibiting a nonresonant coupling with a classical electromagnetic field. This approach consists first of solving the Schrödinger equation by applying a generalised Rabi rotation to the Hamiltonian describing the light-dipole interaction. This rotation has been devised for the resulting Hamiltonian to show up time-independent for both components of the electromagnetic field at the fundamental frequency and the second harmonic one. Then an energy conservation argument, derived from the Poynting theorem, is introduced to work out an additional relationship between the electromagnetic field and its associated electric polarisation. Finally this analysis yields the full time behaviour of all physical quantities of interest. The calculated results reproduce accurately both the observed spatial oscillations of the SHG intensity (Maker's fringes) and its power law dependence on the intensity of the incoming light at the fundamental frequency.
Harmonic lasing in x-ray free electron lasers
Directory of Open Access Journals (Sweden)
E. A. Schneidmiller
2012-08-01
Full Text Available Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed might be a cheap and efficient way of extension of wavelength ranges of existing and planned x-ray free electron laser (FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of x-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned x-ray FEL (XFEL facilities. In particular, Linac Coherent Light Source (LCLS after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25–30 keV providing multigigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow one to extend operating range (ultimately up to 100 keV, to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other x-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact x-ray FELs (driven by electron beams with a relatively low energy, allowing the use of the standard undulator technology instead of
Second harmonic generation in resonant optical structures
Eichenfield, Matt; Moore, Jeremy; Friedmann, Thomas A.; Olsson, Roy H.; Wiwi, Michael; Padilla, Camille; Douglas, James Kenneth; Hattar, Khalid Mikhiel
2018-01-09
An optical second-harmonic generator (or spontaneous parametric down-converter) includes a microresonator formed of a nonlinear optical medium. The microresonator supports at least two modes that can be phase matched at different frequencies so that light can be converted between them: A first resonant mode having substantially radial polarization and a second resonant mode having substantially vertical polarization. The first and second modes have the same radial order. The thickness of the nonlinear medium is less than one-half the pump wavelength within the medium.
Effects of low harmonics on tone identification in natural and vocoded speech.
Liu, Chang; Azimi, Behnam; Tahmina, Qudsia; Hu, Yi
2012-11-01
This study investigated the contribution of low-frequency harmonics to identifying Mandarin tones in natural and vocoded speech in quiet and noisy conditions. Results showed that low-frequency harmonics of natural speech led to highly accurate tone identification; however, for vocoded speech, low-frequency harmonics yielded lower tone identification than stimuli with full harmonics, except for tone 4. Analysis of the correlation between tone accuracy and the amplitude-F0 correlation index suggested that "more" speech contents (i.e., more harmonics) did not necessarily yield better tone recognition for vocoded speech, especially when the amplitude contour of the signals did not co-vary with the F0 contour.
Search for harmonic emission in solar type I radio bursts
Energy Technology Data Exchange (ETDEWEB)
Jaeggi, M.; Benz, A.O.
1982-03-01
We have made a statistical analysis of the harmonic emission of type I bursts, based upon the latest plasma wave theories for the emission mechanism. No systematic harmonic emission is found within the detection limit. This is also the case for a superposed epoch analysis of many bursts. The derived upper limit of the Langmuir wave energy density is Wsub(L)<5 10/sup -7/.lsub(km)/sup -1/ erg cm/sup -3/, where lsub(km) is the depth of the source. In a few single cases there is emission at the harmonic frequency but we could not exclude that this are change hits of an independent activity present at that frequency. These observations provide a considerable constraint on plasma emission models of type I bursts.
Fundamental and Harmonic Oscillations in Neighboring Coronal Loops
Li, Hongbo; Liu, Yu; Vai Tam, Kuan
2017-06-01
We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.
Harmonic Instability Source Identification in Large Wind Farms
DEFF Research Database (Denmark)
Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei
2017-01-01
A large-scale power electronics based power system like a wind farm introduces the passive and active impedances. The interactions between the active and passive impedances can lead to harmonic-frequency oscillations above the fundamental frequency, which can be called harmonic instability....... This paper presents an approach to identify which wind turbine and which bus has more contribution to the harmonic instability problems. In the approach, a wind farm is modeled as a Multi-Input Multi-Output (MIMO) dynamic system. The poles of the MIMO transfer matrix are used to predict the system...... instability and the eigenvalues sensitivity analysis in respect to the elements of the MIMO matrix locates the most influencing buses of the wind farm. Time-domain simulations in PSCAD software environment for a 400-MW wind farm validate that the presented approach is an effective tool to determine the main...
Coherence properties of the harmonic generation in intense laser field
International Nuclear Information System (INIS)
Salieres, P.
1995-01-01
In this thesis is presented an experimental and theoretical study of the harmonic generation in intense field and coherence properties of this radiation. The first part reminds the main harmonic specter characteristics. Follow then experimental studies of the tray extension with the laser lighting, the harmonic generation by ions, and the influence of the laser field on the efficiency of generation. The second part presents the quantum model of the harmonic generation in tunnel regime that we have used for the calculation of the dipoles. We compare dependence in lighting of some harmonic, by insisting on the characteristic behavior of the atomic phase. The theory of the propagation is presented in third part. After the reminder of the case of a perturbative polarization, we develop the case of the polarization in tunnel regime. With the help of numerical simulations, we show the influence of the atomic phase on the agreement of phase, and therefore on the efficiency of conversion and profiles of generation in the medium. The importance of the geometry of the interaction is underlined. The part IV presents the study of the spatial coherence of the harmonic radiation. We develop first consequences of the theory of the agreement of phase for profiles of emission. Then the comparison with experimental profiles is detailed in function of the different parameters( order of non linearity, laser lighting, position of the focus by report in the gaseous medium). The study of the spectral and temporal coherence of the part V begins with the experimental effect investigation of the ionization on specters of the harmonic of weak order. We present then theoretical predictions of the preceding model for spectral and temporal profiles of the harmonic of highest order, generated in tunnel regime. The part VI is devoted to the UVX source aspect of the harmonic radiation. General characteristics (number of photons, agreement) are first detailed, then we present the first experiences
Dynamics of injection locking in a solid-state laser with intracavity second-harmonic generation
International Nuclear Information System (INIS)
Zolotoverkh, I I; Lariontsev, E G
2000-01-01
The dynamics of oscillation in a solid-state laser with intracavity second-harmonic generation under the influence of an external signal at the second-harmonic frequency injected into its cavity in the presence of feedback at the double frequency is theoretically studied. Boundaries of the regions of injection locking for three stationary laser states differing in the nonlinear phase incursion caused by radiation conversion into the second harmonic are found. Relaxation oscillations in the stationary state of injection locking are studied. It is shown that the second relaxation frequency, which is related to phase perturbations of the second harmonic and perturbations of the phase difference of waves in a nonlinear crystal, is excited in a single-mode solid-state laser in addition to the fundamental frequency of relaxation oscillations. Conditions are found under which relaxation oscillations at the second relaxation frequency are excited. (lasers)
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
A PLL-based multirate structure for time-varying power systems harmonic/interharmonic estimation
Carvalho, de J.R.; Duque, C.A.; Ribeiro, M.V.; Cerqueira, A.S.; Baldwin, T.L.; Ribeiro, P.F.
2009-01-01
This paper describes a phase-locked-loop (PLL)-based power systems harmonic estimation algorithm, which uses an analysis filter bank and multirate processing. The filter bank is composed of bandpass filters. The initial center frequency of each filter is purposely chosen to be equal to harmonic
Bárány, Imre; Vilcu, Costin
2016-01-01
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Power quality issues current harmonics
Mikkili, Suresh
2015-01-01
Power Quality Issues: Current Harmonics provides solutions for the mitigation of power quality problems related to harmonics. Focusing on active power filters (APFs) due to their excellent harmonic and reactive power compensation in two-wire (single phase), three-wire (three-phase without neutral), and four-wire (three-phase with neutral) AC power networks with nonlinear loads, the text:Introduces the APF technology, describing various APF configurations and offering guidelines for the selection of APFs for specific application considerationsCompares shunt active filter (SHAF) control strategi
Application of harmonic pulse testing to water-oil displacement
Fokker, P.A.; Verga, F.
2011-01-01
Harmonic pulse testing is a well testing technique in which the injection or production rate is varied in a periodic way. The pressure response to the imposed rates, both in the pulser well and in the observer wells, can be analyzed in the frequency domain to evaluate the reservoir properties. The
A new analytical approximation to the Duffing-harmonic oscillator
International Nuclear Information System (INIS)
Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.
2009-01-01
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Sub-harmonic bunching with the AGOR cyclotron
Brandenburg, S; Roobol, LP; Stokroos, M; Marti, F
2001-01-01
A quasi-single gap buncher with saw-tooth voltage has been designed and is currently being built at the KVI. It operates at a sub-harmonic of the RF frequency and has a duty cycle of 80% at 15 MHz. We report on the design of the new buncher, and on results of tests with our sinusoidal buncher to
Almost-sure identifiability of multidimensional harmonic retrieval
Jiang, T; Sidiropoulos, ND; ten Berge, JMF
Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the
Presence of strong harmonics during visual entrainment: a magnetoencephalography study.
Heinrichs-Graham, Elizabeth; Wilson, Tony W
2012-09-01
Visual neurons are known to synchronize their firing with stimuli that flicker at a constant rate (e.g. 12Hz). These so-called visual steady-state responses (VSSR) are a well-studied phenomenon, yet the underlying mechanisms are widely disagreed upon. Furthermore, there is limited evidence that visual neurons may simultaneously synchronize at harmonics of the stimulation frequency. We utilized magnetoencephalography (MEG) to examine synchronization at harmonics of the visual stimulation frequency (18Hz). MEG data were analyzed for event-related-synchronization (ERS) at the fundamental frequency, 36, 54, and 72Hz. We found strong ERS in all bands. Only 31% of participants showed maximum entrainment at the fundamental; others showed stronger entrainment at either 36 or 54Hz. The cortical foci of these responses indicated that the harmonics involved cortices that were partially distinct from the fundamental. These findings suggest that spatially-overlapping subpopulations of neurons are simultaneously entrained at different harmonics of the stimulus frequency. Copyright © 2012 Elsevier B.V. All rights reserved.
On quantum harmonic oscillator being subjected to absolute
Indian Academy of Sciences (India)
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing ...
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
International Nuclear Information System (INIS)
Saraph, G.P.; Lawson, W.; Latham, P.E.; Cheng, J.; Castle, M.
1995-01-01
Two and three cavity, co-axial, relativistic gyroklystron amplifiers are investigated for driving future linear colliders. Detailed designs of gyroklystrons operating at fundamental (8.568 GHz), second (17.136 GHz), and fourth harmonic (34.272 GHz) frequencies are presented. Numerical simulations predict over 40% efficiency, 45-50 dB gain, and 100-160 MW power level for the fundamental and second harmonic designs. It is shown that introducing a penultimate (buncher) cavity significantly improves efficiency and gain of the second harmonic amplifier. The fourth harmonic design has a modest efficiency of 10-15%
Directory of Open Access Journals (Sweden)
Yun-Long Lu
2014-01-01
Full Text Available A miniaturized bandpass filter with harmonics suppression is presented. The proposed filter consists of two quarter-wavelength microstrip resonators, which are meandered for circuit size reduction. An interdigital capacitor, loading at zero-voltage point, is employed to provide the desired coupling between the resonators at operating frequency, whereas the coupling coefficient at the third harmonic is realized to be zero. Besides, the second and fourth harmonics are suppressed since λ/4 resonators are adopted. Benefiting from these properties, a miniaturized bandpass filter with the second, third, and fourth harmonics suppression was designed and implemented. The final measured and simulated results show good consistence with the theoretical counterparts.
Superharmonic imaging with chirp coded excitation: filtering spectrally overlapped harmonics.
Harput, Sevan; McLaughlan, James; Cowell, David M J; Freear, Steven
2014-11-01
Superharmonic imaging improves the spatial resolution by using the higher order harmonics generated in tissue. The superharmonic component is formed by combining the third, fourth, and fifth harmonics, which have low energy content and therefore poor SNR. This study uses coded excitation to increase the excitation energy. The SNR improvement is achieved on the receiver side by performing pulse compression with harmonic matched filters. The use of coded signals also introduces new filtering capabilities that are not possible with pulsed excitation. This is especially important when using wideband signals. For narrowband signals, the spectral boundaries of the harmonics are clearly separated and thus easy to filter; however, the available imaging bandwidth is underused. Wideband excitation is preferable for harmonic imaging applications to preserve axial resolution, but it generates spectrally overlapping harmonics that are not possible to filter in time and frequency domains. After pulse compression, this overlap increases the range side lobes, which appear as imaging artifacts and reduce the Bmode image quality. In this study, the isolation of higher order harmonics was achieved in another domain by using the fan chirp transform (FChT). To show the effect of excitation bandwidth in superharmonic imaging, measurements were performed by using linear frequency modulated chirp excitation with varying bandwidths of 10% to 50%. Superharmonic imaging was performed on a wire phantom using a wideband chirp excitation. Results were presented with and without applying the FChT filtering technique by comparing the spatial resolution and side lobe levels. Wideband excitation signals achieved a better resolution as expected, however range side lobes as high as -23 dB were observed for the superharmonic component of chirp excitation with 50% fractional bandwidth. The proposed filtering technique achieved >50 dB range side lobe suppression and improved the image quality without
Wiggler magnetic field assisted third harmonic generation in expanding clusters
Vij, Shivani
2018-04-01
A simple theoretical model is constructed to study the wiggler magnetic field assisted third harmonic generation of intense short pulse laser in a cluster in its expanding phase. The ponderomotive force of laser causes density perturbations in cluster electron density which couples with wiggler magnetic field to produce a nonlinear current that generates transverse third harmonic. An intense short pulse laser propagating through a gas embedded with atomic clusters, converts it into hot plasma balls via tunnel ionization. Initially, the electron plasma frequency inside the clusters ω pe > \\sqrt{3}{ω }1 (with ω 1 being the frequency of the laser). As the cluster expands under Coulomb force and hydrodynamic pressure, ω pe decreases to \\sqrt{3}{ω }1. At this time, there is resonant enhancement in the efficiency of the third harmonic generation. The efficiency of third harmonic generation is enhanced due to cluster plasmon resonance and by phase matching due to wiggler magnetic field. The effect of cluster size on the expansion rate is studied to observe that the clusters of different radii would expand differently. The impact of laser intensity and wiggler magnetic field on the efficiency of third harmonic generation is also explored.
Harmonic Scalpel Versus Electrocautery in Axillary Dissection in Carcinoma Breast.
Nawaz, Allah; Waqar, Sadaf; Khan, Ahsan; Mansoor, Rashid; Butt, Usman Ismat; Ayyaz, Mahmood
2015-12-01
To compare the results between harmonics scalpel and electrocautery use in axillary dissection for carcinoma breast. Randomized controlled trial. Department of Surgery, Services Hospital, Lahore, from December 2013 to June 2014. Eighty patients fulfilling the inclusion criteria were selected and equally divided in two groups. Axillary dissection for carcinoma breast was performed by using the harmonic scalpel in one group and by using electrocautery in the other group. Total mean axillary drain output and frequency of axillary numbness were noted in both groups and compared. All the patients were females with mean age of 53.52 ± 9.8. Mean axillary drain output in harmonic scalpel group was 167.75 ± 43.90 as compared to 310.00 ± 60.09 in electrocautery group while only 12.5% of patients were positive for axillary numbness in harmonic scalpel group as compared to 100% of patients who were positive for electrocautery group. Use of harmonic scalpel in axillary dissection resulted in decreased total mean axillary drain output and lowered frequency of axillary numbness when compared to utilizing electrocautery.
Harmonic scalpel versus electrocautery in axillary dissection in carcinoma breast
International Nuclear Information System (INIS)
Nawaz, A.; Khan, A.; Mansoor, R.; Butt, U.I.
2015-01-01
To compare the results between harmonics scalpel and electrocautery use in axillary dissection for carcinoma breast. Study Design: Randomized controlled trial. Place and Duration of Study: Department of Surgery, Services Hospital, Lahore, from December 2013 to June 2014. Methodology: Eighty patients fulfilling the inclusion criteria were selected and equally divided in two groups. Axillary dissection for carcinoma breast was performed by using the harmonic scalpel in one group and by using electrocautery in the other group. Total mean axillary drain output and frequency of axillary numbness were noted in both groups and compared. Results: All the patients were females with mean age of 53.52 ± 9.8. Mean axillary drain output in harmonic scalpel group was 167.75 ± 43.90 as compared to 310.00 ± 60.09 in electrocautery group while only 12.5% of patients were positive for axillary numbness in harmonic scalpel group as compared to 100% of patients who were positive for electrocautery group. Conclusion: Use of harmonic scalpel in axillary dissection resulted in decreased total mean axillary drain output and lowered frequency of axillary numbness when compared to utilizing electrocautery. (author)
Second harmonics HOE recording in Bayfol HX
Bruder, Friedrich-Karl; Fäcke, Thomas; Hagen, Rainer; Hönel, Dennis; Orselli, Enrico; Rewitz, Christian; Rölle, Thomas; Walze, Günther; Wewer, Brita
2015-05-01
mass replication. In this paper, we will discuss and illustrate recording parameters to influence 2nd harmonic efficiency in optimized photopolymer films and will explain preferred geometries for recording.
Classical and multilinear harmonic analysis
Muscalu, Camil
2013-01-01
This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this vo...
Explaining the harmonic sequence paradox.
Schmidt, Ulrich; Zimper, Alexander
2012-05-01
According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced. ©2011 The British Psychological Society.
Introduction to abstract harmonic analysis
Loomis, Lynn H
2011-01-01
Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Cohabiting with the harmonic pollution
International Nuclear Information System (INIS)
Garcia C, Antonio A
1999-01-01
The Norm IEEE 519 tries of the permissible limits of harmonic distortion in the point of common joining between the energy supplier company and the industry. However fulfilling these limits of distortion doesn't guarantee that the problem for the company has finished, on the contrary will have to counteract the effects created by the harmonic distortion toward the interior of its electric system and to cohabit with this distortion
Comparison of fundamental, second harmonic, and superharmonic imaging: a simulation study.
van Neer, Paul L M J; Danilouchkine, Mikhail G; Verweij, Martin D; Demi, Libertario; Voormolen, Marco M; van der Steen, Anton F W; de Jong, Nico
2011-11-01
In medical ultrasound, fundamental imaging (FI) uses the reflected echoes from the same spectral band as that of the emitted pulse. The transmission frequency determines the trade-off between penetration depth and spatial resolution. Tissue harmonic imaging (THI) employs the second harmonic of the emitted frequency band to construct images. Recently, superharmonic imaging (SHI) has been introduced, which uses the third to the fifth (super) harmonics. The harmonic level is determined by two competing phenomena: nonlinear propagation and frequency dependent attenuation. Thus, the transmission frequency yielding the optimal trade-off between the spatial resolution and the penetration depth differs for THI and SHI. This paper quantitatively compares the concepts of fundamental, second harmonic, and superharmonic echocardiography at their optimal transmission frequencies. Forward propagation is modeled using a 3D-KZK implementation and the iterative nonlinear contrast source (INCS) method. Backpropagation is assumed to be linear. Results show that the fundamental lateral beamwidth is the narrowest at focus, while the superharmonic one is narrower outside the focus. The lateral superharmonic roll-off exceeds the fundamental and second harmonic roll-off. Also, the axial resolution of SHI exceeds that of FI and THI. The far-field pulse-echo superharmonic pressure is lower than that of the fundamental and second harmonic. SHI appears suited for echocardiography and is expected to improve its image quality at the cost of a slight reduction in depth-of-field.
Phase-dependent quantum interference between different pathways in bichromatic harmonic generation
International Nuclear Information System (INIS)
Jun, Cai; Li-Ming, Wang; Hao-Xue, Qiao
2009-01-01
This paper studies the harmonic generation of the hydrogen atom subjected to a collinear bichromatic laser field by numerically solving the time-dependent Schrödinger equation using the split-operator pseudo-spectral method. By adding a frequency variation to the additional field, the contributions of different pathways to particular order harmonic generation can be isolated. The quantum interference pattern between harmonic pathways, which influences the harmonic intensity, is found to be either constructive or destructive with respect to different relative phase of the two field components. Detailed description of up to the 35th-order harmonics and the harmonic pathways for a wide range of field parameters is presented. (atomic and molecular physics)
International Nuclear Information System (INIS)
Deng Ming-Xi; Gao Guang-Jian; Li Ming-Liang
2015-01-01
The experimental observation of cumulative second-harmonic generation of the primary circumferential guided wave propagation is reported. A pair of wedge transducers is used to generate the primary circumferential guided wave desired and to detect its fundamental-frequency and second-harmonic amplitudes on the outside surface of the circular tube. The amplitudes of the fundamental waves and the second harmonics of the circumferential guided wave propagation are measured for different separations between the two wedge transducers. At the driving frequency where the primary and the double-frequency circumferential guided waves have the same linear phase velocities, the clear second-harmonic signals can be observed. The quantitative relationships between the second-harmonic amplitudes and circumferential angle are analyzed. It is experimentally verified that the second harmonics of primary circumferential guided waves do have a cumulative growth effect with the circumferential angle. (paper)
Turbulence Scattering of High Harmonic Fast Waves
International Nuclear Information System (INIS)
M. Ono; J. Hosea; B. LeBlanc; J. Menard; C.K. Phillips; R. Wilson; P. Ryan; D. Swain; J. Wilgen; S. Kubota; and T.K. Mau
2001-01-01
Effect of scattering of high-harmonic fast-magnetosonic waves (HHFW) by low-frequency plasma turbulence is investigated. Due to the similarity of the wavelength of HHFW to that of the expected low-frequency turbulence in the plasma edge region, the scattering of HHFW can become significant under some conditions. The scattering probability increases with the launched wave parallel-phase-velocity as the location of the wave cut-off layer shifts toward the lower density edge. The scattering probability can be reduced significantly with higher edge plasma temperature, steeper edge density gradient, and magnetic field. The theoretical model could explain some of the HHFW heating observations on the National Spherical Torus Experiment (NSTX)
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Coherent harmonics generated by a super-short electron pulse
International Nuclear Information System (INIS)
Ding Wu
1996-01-01
A novel mechanism generating superradiance harmonics is found. In this superradiance harmonics, the temporal width of harmonics is extremely short, the ratio of high harmonic fundamental wave is much higher than the known superradiance harmonics
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
General Lp-harmonic Blaschke bodies
Indian Academy of Sciences (India)
Abstract. Lutwak introduced the harmonic Blaschke combination and the harmonic. Blaschke body of a star body. Further, Feng and Wang introduced the concept of the L p- harmonic Blaschke body of a star body. In this paper, we define the notion of general. L p-harmonic Blaschke bodies and establish some of its ...
General Lp-harmonic Blaschke bodies
Indian Academy of Sciences (India)
Lutwak introduced the harmonic Blaschke combination and the harmonic Blaschke body of a star body. Further, Feng and Wang introduced the concept of the -harmonic Blaschke body of a star body. In this paper, we define the notion of general -harmonic Blaschke bodies and establish some of its properties.
Audibility of harmonics in 'periodic white noise'
Duifhuis, H.; Tomesen, H.H.
1970-01-01
In a previous article (Duifhuis, 1970) results' concerning the audibility of harmonics in a periodic pulse have been presented. Each of the lower harmonics could be perceived separately, whereas the high harmonics were heard together as one complex signal. High harmonics, however, appeared to be
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Eliminating the Influence of Harmonic Components in Operational Modal Analysis
DEFF Research Database (Denmark)
Jacobsen, Niels-Jørgen; Andersen, Palle; Brincker, Rune
2007-01-01
structures, in contrast, are subject inherently to deterministic forces due to the rotating parts in the machinery. These forces are seen as harmonic components in the responses, and their influence should be eliminated before extracting the modes in their vicinity. This paper describes a new method based...... on the well-known Enhanced Frequency Domain Decomposition (EFDD) technique for eliminating these harmonic components in the modal parameter extraction process. For assessing the quality of the method, various experiments were carried out where the results were compared with those obtained with pure stochastic...
The Role of Higher Harmonics In Musical Interval Perception
Krantz, Richard; Douthett, Jack
2011-10-01
Using an alternative parameterization of the roughness curve we make direct use of critical band results to investigate the role of higher harmonics on the perception of tonal consonance. We scale the spectral amplitudes in the complex home tone and complex interval tone to simulate acoustic signals of constant energy. Our analysis reveals that even with a relatively small addition of higher harmonics the perfect fifth emerges as a consonant interval with more, musically important, just intervals emerging as consonant as more and more energy is shifted into higher frequencies.
DEFF Research Database (Denmark)
Freijedo Fernandez, Francisco Daniel; Chaudhary, Sanjay Kumar; Guerrero, Josep M.
2015-01-01
-domain. As an alternative, a power based averaged modelling is also proposed. Type IV wind turbine harmonic signature and STATCOM active harmonic mitigation are considered for the simulation case studies. Simulation results provide a good insight of the features and limitations of the proposed methodologies.......This paper approaches modelling methodologies for integration of wind turbines and STATCOM in harmonic resonance studies. Firstly, an admittance equivalent model representing the harmonic signature of grid connected voltage source converters is provided. A simplified type IV wind turbine modelling...... is then straightforward. This linear modelling is suitable to represent the wind turbine in the range of frequencies at which harmonic interactions are likely. Even the admittance method is suitable both for frequency and time domain studies, some limitations arise in practice when implementing it in the time...
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Harmonic emission due to the nonlinear coupling of a Gaussian laser and a plasma wave
Energy Technology Data Exchange (ETDEWEB)
Pathak, R; Jain, R K [Department of Mathematics, SSL Jain College, Vidisha, MP, 464001 (India); Parashar, J [Department of Physics, Samrat Ashok Technological Institute, Vidisha, MP, 464001 (India)
2010-04-15
A high-power Gaussian laser propagating through a plasma couples with a large-amplitude plasma wave and undergoes scattering to produce harmonics. The process is sensitive to the phase matching angle between the laser and plasma wave numbers and the plasma wave frequency. For larger harmonics, the phase matching angle is high. The efficiency of the process is comparatively high at higher plasma wave frequencies.
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
High-order harmonic generation in laser plasma plumes
Ganeev, Rashid A
2013-01-01
This book represents the first comprehensive treatment of high-order harmonic generation in laser-produced plumes, covering the principles, past and present experimental status and important applications. It shows how this method of frequency conversion of laser radiation towards the extreme ultraviolet range matured over the course of multiple studies and demonstrated new approaches in the generation of strong coherent short-wavelength radiation for various applications. Significant discoveries and pioneering contributions of researchers in this field carried out in various laser scientific centers worldwide are included in this first attempt to describe the important findings in this area of nonlinear spectroscopy. "High-Order Harmonic Generation in Laser Plasma Plumes" is a self-contained and unified review of the most recent achievements in the field, such as the application of clusters (fullerenes, nanoparticles, nanotubes) for efficient harmonic generation of ultrashort laser pulses in cluster-containin...
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.
Harmonic Emissions of Three-Phase Diode Rectifiers in Distribution Networks
DEFF Research Database (Denmark)
Zare, Firuz; Soltani, Hamid; Kumar, Dinesh
2017-01-01
Harmonic emissions have been changed in distribution networks, with respect to frequency range and magnitude, due to the penetration of modern power electronics systems. Two new frequency ranges: 2–9 kHz and 9–150 kHz have been identified as new disturbing frequency ranges affecting distribution ...
Studies of harmonic generation in free electron lasers
International Nuclear Information System (INIS)
Goldammer, K.
2007-01-01
Nonlinear harmonic generation is one of the most interesting aspects of Free Electron Lasers under study today. It provides for coherent, high intensity radiation at higher harmonics of the FEL resonant frequency. The sources, numerical simulation and applications of harmonic radiation in cascaded High Gain Harmonic Generation FELs were the subject of this thesis. Harmonic emission in FELs originates from harmonic microbunching of the particles and the particular electron trajectory during FEL interaction. Numerical FEL simulation codes model these analytical equations and predict the performance of Free Electron Lasers with good accuracy. This thesis has relied heavily upon the FEL simulation code Genesis 1.3 which has been upgraded in the framework of this thesis to compute harmonic generation in a self-consistent manner. Tests against analytical predictions suggest that the harmonic power levels as well as harmonic gain lengths are simulated correctly. A benchmark with the FEL simulation code GINGER yields excellent agreement of the harmonic saturation length and saturation power. The new version of the simulation code Genesis was also tested against measurements from the VUV-FEL FLASH at DESY. The spectral power distributions of fundamental and third harmonic radiation were recorded at 25.9 nm and 8.6 nm, respectively. The relative bandwidths (FWHM) were in the range of 2 % for both the fundamental as well as the third harmonic, which was accurately reproduced by time-dependent simulations with Genesis. The new code was also used to propose and evaluate a new design for the BESSY Soft X-Ray FEL, a cascaded High Gain Harmonic Generation FEL proposed by BESSY in Berlin. The original design for the BESSY High Energy FEL line requires four HGHG stages to convert the initial seed laser wavelength of 297.5 nm down to 1.24 nm. A new scheme is proposed that makes use of fifth harmonic radiation from the first stage and reduces the number of HGHG stages to three. It
Studies of harmonic generation in free electron lasers
Energy Technology Data Exchange (ETDEWEB)
Goldammer, K.
2007-11-12
Nonlinear harmonic generation is one of the most interesting aspects of Free Electron Lasers under study today. It provides for coherent, high intensity radiation at higher harmonics of the FEL resonant frequency. The sources, numerical simulation and applications of harmonic radiation in cascaded High Gain Harmonic Generation FELs were the subject of this thesis. Harmonic emission in FELs originates from harmonic microbunching of the particles and the particular electron trajectory during FEL interaction. Numerical FEL simulation codes model these analytical equations and predict the performance of Free Electron Lasers with good accuracy. This thesis has relied heavily upon the FEL simulation code Genesis 1.3 which has been upgraded in the framework of this thesis to compute harmonic generation in a self-consistent manner. Tests against analytical predictions suggest that the harmonic power levels as well as harmonic gain lengths are simulated correctly. A benchmark with the FEL simulation code GINGER yields excellent agreement of the harmonic saturation length and saturation power. The new version of the simulation code Genesis was also tested against measurements from the VUV-FEL FLASH at DESY. The spectral power distributions of fundamental and third harmonic radiation were recorded at 25.9 nm and 8.6 nm, respectively. The relative bandwidths (FWHM) were in the range of 2 % for both the fundamental as well as the third harmonic, which was accurately reproduced by time-dependent simulations with Genesis. The new code was also used to propose and evaluate a new design for the BESSY Soft X-Ray FEL, a cascaded High Gain Harmonic Generation FEL proposed by BESSY in Berlin. The original design for the BESSY High Energy FEL line requires four HGHG stages to convert the initial seed laser wavelength of 297.5 nm down to 1.24 nm. A new scheme is proposed that makes use of fifth harmonic radiation from the first stage and reduces the number of HGHG stages to three. It
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Spontaneous decoherence of coupled harmonic oscillators confined in a ring
Gong, ZhiRui; Zhang, ZhenWei; Xu, DaZhi; Zhao, Nan; Sun, ChangPu
2018-04-01
We study the spontaneous decoherence of coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry-breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the gauge couplings between the center-of-mass and the relative degrees of freedoms, which actually originate from the symmetries of the ring geometry and the corresponding nontrivial boundary conditions. In particular, such spontaneous decoherence does not occur at all at the thermodynamic limit because the nontrivial boundary conditions become the trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has a chance for its quantum properties to degrade even without applying an external symmetry-breaking field or surrounding environment.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
Dynamics of harmonic generation in atoms and molecules
International Nuclear Information System (INIS)
Boutu, W.
2007-09-01
Harmonics are generated when an ultra-short laser impulse with an energy of 10 14 W/cm 2 is focused on a gas jet. A radiation in the UV X range is then emitted in the direction of the incident laser beam. This radiation has a periodical spectral structure composed of odd harmonics of the fundamental frequency. The first part of this work is dedicated to the optimization of the harmonic radiation. We have studied an alternative and cheaper solution to the flexible mirror, we have used a set of concentric phase plates in order to control the spatial phase of the beam and create an enlarged square profile near the focusing spot. We show how different parameters like phase shift or luminous-flux density or jet position have an impact on the harmonic signal. This second part of this work deals with the generation of high order harmonics in N 2 and CO 2 molecules. The experimental setting is based on the RABITT method (reconstruction of the atto-second burst by interference of 2-photon transitions). We have observed the presence of a spectral minimum linked to a phenomena of quantum interferences between the molecule and the electron wave packet. Moreover, a shift in the spectral phase appears at the place of the interference. (A.C.)
Analysis of higher order harmonics with holographic reflection gratings
Mas-Abellan, P.; Madrigal, R.; Fimia, A.
2017-05-01
Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.
HARMONIZED EUROPE OR EUROPEAN HARMONY?
Directory of Open Access Journals (Sweden)
Cosmin Marinescu
2007-07-01
Full Text Available Recent evolutions in Europe raise questions on the viability of the present economic and social model that defines the European construction project. In this paper, the author will try to explain the viability of institutional European model that sticks between free market mechanisms and protectionism. The main challenge for the EU is about the possibility to bring together the institutional convergence and the welfare for all Europeans. This is the result of the view, still dominant, of European politics elite, according to which institutional harmonization is the solution of a more dynamic and prosper Europe. But, economic realities convince us that, more and more, a harmonized, standardized Europe is not necessarily identical with a Europe of harmony and social cooperation. If „development through integration” seems to be harmonization through „institutional transplant”, how could then be the European model one sufficiently wide open to market, which creates the prosperity so long waited for by new member countries?
Harmonic superspaces of extended supersymmetry
International Nuclear Information System (INIS)
Ivanov, E.; Kalitzin, S.; Nguyen Ai Viet; Ogievetsky, V.
1984-01-01
The main technical apparatus of the harmonic superspace approach to extended SUSY, the calculus of harmonic variables on homogeneous spaces of the SUSY automorphism groups, is presented in detail for N=2, 3, 4. The basic harmonics for the coset manifolds G/H with G=SU(2), H=U(1); G=SU(3), H=SU(2)xU(1) and H=U(1)xU(1); G=SU(4), H=SU(3)xU(1), H=SU(2)xSU(2)xU(1), H=SU(2)xU(1)xU(1) and H=U(1)xU(1)xU(1); G=USp(2), H=SU(2)xSU(2), H=SU(2)xU(1) and H=U(1)xU(1) are tabulated a number of useful relations among them
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
A proof-of-principle experiment of a novel harmonics separation optics for synchrotron facilities
Czech Academy of Sciences Publication Activity Database
Oberta, Peter; Mikulík, P.; Hrdý, Jaromír
2012-01-01
Roč. 19, č. 6 (2012), s. 1012-1014 ISSN 0909-0495 R&D Projects: GA MPO FR-TI1/412 Institutional research plan: CEZ:AV0Z10100522 Keywords : harmonics separation * diffractive-refractive optics * nclined geometry Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.186, year: 2012
Jin, Tao; Chen, Yiyang; Flesch, Rodolfo C. C.
2017-11-01
Harmonics pose a great threat to safe and economical operation of power grids. Therefore, it is critical to detect harmonic parameters accurately to design harmonic compensation equipment. The fast Fourier transform (FFT) is widely used for electrical popular power harmonics analysis. However, the barrier effect produced by the algorithm itself and spectrum leakage caused by asynchronous sampling often affects the harmonic analysis accuracy. This paper examines a new approach for harmonic analysis based on deducing the modifier formulas of frequency, phase angle, and amplitude, utilizing the Nuttall-Kaiser window double spectrum line interpolation method, which overcomes the shortcomings in traditional FFT harmonic calculations. The proposed approach is verified numerically and experimentally to be accurate and reliable.
Effect of self-focusing on resonant third harmonic generation of laser in a rippled density plasma
International Nuclear Information System (INIS)
Kaur, Sukhdeep; Sharma, A. K.; Yadav, Sushila
2010-01-01
Resonant third harmonic generation by a Gaussian laser beam in a rippled density plasma is studied. The laser ponderomotive force induces second harmonic longitudinal velocity on electrons that couples with the static density ripple to produce a density perturbation at 2ω,2k+q, where ω and k are the frequency and wave number of the laser and q is the ripple wave number of the laser. This density perturbation beats with electron oscillatory velocity at ω,k-vector to produce a nonlinear current driving the third harmonic generation. In the regime of quadratic nonlinearity, the self-focusing of the laser enhances the third harmonic power. However, at higher intensity, plasma density is significantly reduced on the axis, detuning the third harmonic resonance and weakening the harmonic yield. Self-focusing causes enhancement in the efficiency of harmonic generation.
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1987-01-01
In the present paper we show how the N = 2 superconformal group is realised in harmonic superspace and examine conformal invariance of N = 2 off-shell theories. We believe that the example of N = O self-dual Yang-Mills equations can serve as an instructive introduction to the subject of harmonic superspace and this is examined. The rigid N = 2 conformal supersymmetry and its local version, i.e. N = 2 conformal supergravity is also discussed. The paper is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. (author)
Elements of abstract harmonic analysis
Bachman, George
2013-01-01
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give
Harmonic modeling of induction motors
Energy Technology Data Exchange (ETDEWEB)
Pedra, J.; Sainz, L.; Corcoles, F. [Department of Electrical Engineering, ETSEIB-UPC, Av. Diagonal 647, 08028 Barcelona (Spain)
2006-07-15
The paper proposes an induction motor model for the study of harmonic load flow in balanced and unbalanced conditions. The parameters of this model are obtained from motor manufacturer data and the positive- and negative-sequence equivalent circuits of the single- and double-cage models. An approximate harmonic model based on motor manufacturer data only is also proposed. In addition, the paper includes manufacturer data and the calculated parameters of 36 induction motors of different rated powers. This database is used to analyze the proposed models. (author)
Spatial properties of odd and even low order harmonics generated in gas.
Lambert, G; Andreev, A; Gautier, J; Giannessi, L; Malka, V; Petralia, A; Sebban, S; Stremoukhov, S; Tissandier, F; Vodungbo, B; Zeitoun, Ph
2015-01-14
High harmonic generation in gases is developing rapidly as a soft X-ray femtosecond light-source for applications. This requires control over all the harmonics characteristics and in particular, spatial properties have to be kept very good. In previous literature, measurements have always included several harmonics contrary to applications, especially spectroscopic applications, which usually require a single harmonic. To fill this gap, we present here for the first time a detailed study of completely isolated harmonics. The contribution of the surrounding harmonics has been totally suppressed using interferential filtering which is available for low harmonic orders. In addition, this allows to clearly identify behaviors of standard odd orders from even orders obtained by frequency-mixing of a fundamental laser and of its second harmonic. Comparisons of the spatial intensity profiles, of the spatial coherence and of the wavefront aberration level of 5ω at 160 nm and 6ω at 135 nm have then been performed. We have established that the fundamental laser beam aberrations can cause the appearance of a non-homogenous donut-shape in the 6ω spatial intensity distribution. This undesirable effect can be easily controlled. We finally conclude that the spatial quality of an even harmonic can be as excellent as in standard generation.
Improving the performance of the power supply of the MGC-20 cyclotron harmonic coils
International Nuclear Information System (INIS)
Hagras, A.A.M
2008-01-01
Correction of lower harmonics of the MGC-20 cyclotron magnetic field is of great importance for its operation. Actually, stability of the acceleration process, attainment of the final energy of the accelerated beam and efficiency of the beam extraction system depend on the lower harmonics control. Error in the magnetic field lower harmonics can reduce the efficiency of the beam extraction resulting in complete disappearance of the extracted beam of the cyclotron. For control of the cyclotron MGC-20 magnetic field lower harmonics, the so called inner and outer harmonic coils are provided.These harmonic coils must be fed by a very high accuracy current source power supply. This power supply must be equipped with a high resolution measurement and control scheme to achieve the imposed requirements of adjustment of the first harmonic magnetic field.Harmonic coils are supplied with conventional SCR controlled converters with analog control strategy. Frequent interruption of operation and difficulties in the adjustment of harmonic coil current lead to economical and research - time losses.This research project aims to replace this conventional system with a more effective, accurate and less complicated digital control system based on Motorola DSP56F807 and high switching frequency power circuit. Actually all the bulky modules including the analog integrator, the signal monitoring and protection, the pulse phase modulator and the comparator are all replaced by a single module circuit.
Optimal Selective Harmonic Control for Power Harmonics Mitigation
DEFF Research Database (Denmark)
Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede
2015-01-01
of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...
Beam dynamics in CIME for third harmonic
International Nuclear Information System (INIS)
Chautard, F.; Bourgarel, M.P.
2000-01-01
This report presents the results from simulations for beam dynamics in CIME third harmonics. Details are given regarding the procedures to reach the adaptation at the inflector exit. The aim of these simulation is to determine, for any given ion, the beam correlations at the inflector exit as well as the current values in the isochronous coils for all the field levels. Although not all the steps of the simulation are thoroughly displayed, the report gathers all the the elements necessary for CIME control. Information useful for controlling the Very Low Energy line, the main field and the isochronous coils are also presented. The report has the following content: I. Introduction. II. The field maps and the used codes. A. The maps of CIME magnetic fields; B. The 3D map of CIME electric potentials; C. The maps of 3D electric potentials in the CIME central region; D. Code LIONS and sorting codes. III. Central region. A. An outlook. B.Central rays; IV. Determination of beam correlations. A. Analytical calculation of adaptation conditions; B. Calculation of adaptation conditions based on particle distributions; C. Creating the beam matrices. D. Calculation method for inverse return correlations. V. Results of simulations. VI. Interpolation of isochronous coils at the referential frequency. VII. The interpolation code PARAM. VIII. Conclusions. The paper is supplemented by 4 appendices. The harmonics 2, 4 and 5 are currently under way and the results will be reported in a future paper
Harmonic ultrasound fields through layered liquid media.
Li, Yadong; Chen, Quan; Zagzebski, James
2004-02-01
Harmonic field generation through a layered liquid media is studied experimentally and theoretically. Lateral and axial beam profiles of the fundamental to the 4th harmonic component of the field from a focused, 19-mm diameter transducer were measured using a calibrated hydrophone in a water tank. Measurements were performed before and after the insertion of a cylindrical phantom containing vegetable oil. A frequency domain numerical solution to the "KZK" equation was used to calculate the beam profile, taking into account the acoustic properties of the medium and phantom. Effects of nonlinear propagation, diffraction, attenuation, and reflection are include in the calculation. Agreement within 5% was obtained between measurements and theoretical predictions throughout the mid- and far-field of the transducer for both the uniform path and the layered media. Measurements also were carried out using an unfocused transducer as a receiver. The shape of the axial beam profile using this receiver agreed very well with the theoretical prediction using the "KZK" equation, after accounting for phase variations over the finite-sized detector in the calculated field.
Probabilistic Harmonic Modeling of Wind Power Plants
DEFF Research Database (Denmark)
Guest, Emerson; Jensen, Kim H.; Rasmussen, Tonny Wederberg
2017-01-01
A probabilistic sequence domain (SD) harmonic model of a grid-connected voltage-source converter is used to estimate harmonic emissions in a wind power plant (WPP) comprised of Type-IV wind turbines. The SD representation naturally partitioned converter generated voltage harmonics into those...... with deterministic phase and those with probabilistic phase. A case study performed on a string of ten 3MW, Type-IV wind turbines implemented in PSCAD was used to verify the probabilistic SD harmonic model. The probabilistic SD harmonic model can be employed in the planning phase of WPP projects to assess harmonic...
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
Resonant third harmonic generation of KrF laser in Ar gas
Energy Technology Data Exchange (ETDEWEB)
Rakowski, R. [Department of Experimental Physics, University of Szeged, 6720 Szeged, Dóm tér 9 (Hungary); Institute of Optoelectronics, Military University of Technology, Gen. S. Kaliskiego 2, 00–908 Warsaw (Poland); Barna, A. [Department of Experimental Physics, University of Szeged, 6720 Szeged, Dóm tér 9 (Hungary); Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, EURATOM Association HAS, 1121 Budapest, XII. Konkoly Thege Miklós út 29-33 (Hungary); Suta, T.; Földes, I. B. [Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, EURATOM Association HAS, 1121 Budapest, XII. Konkoly Thege Miklós út 29-33 (Hungary); Bohus, J.; Szatmári, S. [Department of Experimental Physics, University of Szeged, 6720 Szeged, Dóm tér 9 (Hungary); Mikołajczyk, J.; Bartnik, A.; Fiedorowicz, H. [Institute of Optoelectronics, Military University of Technology, Gen. S. Kaliskiego 2, 00–908 Warsaw (Poland); Verona, C. [Department of Mechanical Engineering, University “Tor Vergata”, Via Orazio Raimondo, 18–00173, Rome (Italy); Verona Rinati, G. [Department of Industrial Engineering, University “Tor Vergata”, Via Orazio Raimondo, 18–00173, Rome (Italy); Margarone, D. [Institute of Physics ASCR, v.v.i. (FZU), ELI-Beamlines Project, 182 21 Prague (Czech Republic); Nowak, T. [Institute of Nuclear Physics, PAN, E. Radzikowskiego 152, 31–342 Cracow (Poland); and others
2014-12-15
Investigations of emission of harmonics from argon gas jet irradiated by 700 fs, 5 mJ pulses from a KrF laser are presented. Harmonics conversion was optimized by varying the experimental geometry and the nozzle size. For the collection of the harmonic radiation silicon and solar-blind diamond semiconductor detectors equipped with charge preamplifiers were applied. The possibility of using a single-crystal CVD diamond detector for separate measurement of the 3rd harmonic in the presence of a strong pumping radiation was explored. Our experiments show that the earlier suggested 0.7% conversion efficiency can really be obtained, but only in the case when phase matching is optimized with an elongated gas target length corresponding to the length of coherence.
Strong nonlinear harmonic generation in a PZT/Aluminum resonator
Energy Technology Data Exchange (ETDEWEB)
Parenthoine, D; Haumesser, L; Meulen, F Vander; Tran-Huu-Hue, L-P, E-mail: parenthoine@univ-tours.f [University Francois Rabelais of Tours, U 930 Imagerie et Cerveau, CNRS 2448, ENIVL, rue de la Chocolaterie, BP 3410, 41034 Blois (France)
2009-11-01
In this work, the extentional vibration mode of a coupled PZT/ Aluminum rod resonator is studied experimentally. Geometrical characteristics of the PZT are its 27 mm length and its 4x4 mm{sup 2} cross section area. The excitation voltage consists in sinusoidal bursts in the frequency range (20-80 kHz). Velocity measurements are performed at both ends of this system, using a laser probe. Strong harmonic distortions in the mechanical response (up to -20 dB with respect to the primary wave amplitude) have been observed. The corresponding input levels are far lower than those which are necessary to observe quadratic second harmonic generation in a free PZT resonator. The strong nonlinear effect can be explained as a super-harmonic resonance of the system due to a specific ratio between the eigen frequencies of the two parts of the resonator. Evolution of fundamental and harmonic responses are observed as a function of input levels, highlighting hysteretic behavior.
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Harmonic structures and intrinsic torsion
DEFF Research Database (Denmark)
Conti, Diego; Madsen, Thomas Bruun
We discuss the construction of 8-manifolds with harmonic Sp(2)Sp(1)-structures. In particular, we find 10 new examples of nilmanifolds that admit a closed 4-form Omega whose stabiliser is Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough...
The relativistic harmonic oscillator reconsidered
International Nuclear Information System (INIS)
Hofsaess, T.
1978-01-01
The bound states of scalar quarks interacting through a scalar harmonic oscillator are investigated. In the presence of this interaction the dressed quark propagator differs substantially from the free one. This leads to a Bethe Salpeter equation which does not allow for any stable bound states of positive mass. (orig.) [de
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
N=2 conformal supersymmetry is realized in harmonic superspace, its peculiarities are analyzed. The coordinate group and analytical prepotentials for N=2 conformal supergravity are found. A new version of the N=2 Einstein supergravity with infinite number of auxiliary fields is suggested. A hypermultiplet without central charges and constraints is used as a compensator
Sums of Generalized Harmonic Series
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 9. Sums of Generalized Harmonic Series: For Kids from Five to Fifteen. Zurab Silagadze. General Article Volume 20 Issue 9 September 2015 pp 822-843. Fulltext. Click here to view fulltext PDF. Permanent link:
Psychophysical estimates of cochlear phase response: masking by harmonic complexes.
Lentz, J J; Leek, M R
2001-12-01
Harmonic complexes with identical component frequencies and amplitudes but different phase spectra may be differentially effective as maskers. Such harmonic waveforms, constructed with positive or negative Schroeder phases, have similar envelopes and identical long-term power spectra, but the positive Schroeder-phase waveform is typically a less effective masker than the negative Schroeder-phase waveform. These masking differences have been attributed to an interaction between the masker phase spectrum and the phase characteristic of the basilar membrane. To explore this relationship, the gradient of stimulus phase change across masker bandwidth was varied by systematically altering the Schroeder-phase algorithm. Observers detected a signal tone added in-phase to a single component of a masker whose frequencies ranged from 200 to 5000 Hz, with a fundamental frequency of 100 Hz. For signal frequencies of 1000-4000 Hz, differences in masking across the harmonic complexes could be as large as 5-10 dB for phase gradients changing by only 10%. The phase gradient that resulted in a minimum amount of masking varied with signal frequency, with low frequencies masked least effectively by stimuli with rapidly changing component phases and high frequencies masked by stimuli with more shallow phase gradients. A gammachirp filter was implemented to model these results, predicting the qualitative changes in curvature of the phase-byfrequency function estimated from the empirical data: In some cases, small modifications to the gammachirp filter produced better quantitative predictions of curvature changes across frequency, but this filter, as implemented here, was unable to accurately represent all the data.
Ferromagnetic rollers in a harmonic confinement
Kaiser, Andreas; Snezhko, Alexey; Aranson, Igor S.
We present the emergence of flocking and global rotation in a system of rolling ferromagnetic microparticles energized by a vertical alternating magnetic field confined in a harmonic potential. By combing experiments and discrete particle simulations, we have identified primary physical mechanisms leading to the emergence of large-scale collective motion: spontaneous symmetry breaking of the clock / counterclockwise particle rotation, collisional alignment of particle velocities, and random particle re-orientations due to shape imperfections. We also emphasize a subtle role of rotational noise: While the low-frequency flocking appears to be noise-insensitive, the reentrant flocking happens to be noise-activated. Moreover, we uncover a new relation between collective motion and synchronisation.
Passive wide spectrum harmonic filter for adjustable speed drives in oil and gas industry
Al Jaafari, Khaled Ali
Non-linear loads such as variable speed drives constitute the bulky load of oil and gas industry power systems. They are widely used in driving induction and permanent magnet motors for variable speed applications. That is because variable speed drives provide high static and dynamic performance. Moreover, they are known of their high energy efficiency and high motion quality, and high starting torque. However, these non-linear loads are main sources of current and voltage harmonics and lower the quality of electric power system. In fact, it is the six-pulse and twelve-pulse diode and thyristor rectifiers that spoil the AC power line with the dominant harmonics (5th, 7th, 11th). They provide DC voltage to the inverter of the variable speed drives. Typical problems that arise from these harmonics are Harmonic resonances', harmonic losses, interference with electronic equipment, and line voltage distortion at the Point of Common Coupling (PCC). Thus, it is necessary to find efficient, reliable, and economical harmonic filters. The passive filters have definite advantage over active filters in terms of components count, cost and reliability. Reliability and maintenance is a serious issue in drilling rigs which are located in offshore and onshore with extreme operating conditions. Passive filters are tuned to eliminate a certain frequency and therefore there is a need to equip the system with more than one passive filter to eliminate all unwanted frequencies. An alternative solution is Wide Spectrum Harmonic passive filter. The wide spectrum harmonic filters are becoming increasingly popular in these applications and found to overcome some of the limitations of conventional tuned passive filter. The most important feature of wide spectrum harmonic passive filters is that only one capacitor is required to filter a wide range of harmonics. Wide spectrum filter is essentially a low-pass filter for the harmonic at fundamental frequency. It can also be considered as a
Parametric decay below the upper hybrid frequency
Energy Technology Data Exchange (ETDEWEB)
Albers, E; Krause, K; Schlueter, H [Bochum Univ. (Germany, F.R.). Inst. fuer Experimentalphysik 2
1977-03-21
Parametric decay of the upper hybrid mode is observed between the electron cyclotron frequency and its first two harmonics. The decay products are identified as electron Bernstein and ion acoustic mode. The diagnostic results confirm the relevant dispersion relations.
Lenore White Harmon: One Woman's Career Development.
Fouad, Nadya A.
1997-01-01
Presents biographical information on Lenore White Harmon, noted professor, counselor, and researcher. In a question-and-answer section, Harmon describes her early career decisions, work history, research efforts, professional contributions, important influences and reflections on her career development. (KW)
Tides and tidal harmonics at Umbharat, Gujarat
Digital Repository Service at National Institute of Oceanography (India)
Suryanarayana, A.; Swamy, G.N.
A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Energy Technology Data Exchange (ETDEWEB)
Singh, Mamta; Gupta, D. N., E-mail: dngupta@physics.du.ac.in [Department of Physics and Astrophysics, University of Delhi, Delhi 110 007 (India); Suk, H. [Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 500 712 (Korea, Republic of)
2015-06-15
We propose an idea to enhance the efficiency of second- and third-harmonic generation by considering the amplitude-modulation of the fundamental laser pulse. A short-pulse laser of finite spot size is modeled as amplitude modulated in time. Amplitude-modulation of fundamental laser contributes in quiver velocity of the plasma electrons and produces the strong plasma-density perturbations, thereby increase in current density at second- and third-harmonic frequency. In a result, the conversion efficiency of harmonic generation increases significantly. Power conversion efficiency of harmonic generation process is the increasing function of the amplitude-modulation parameter of the fundamental laser beam. Harmonic power generated by an amplitude modulated laser is many folds higher than the power obtained in an ordinary case.
International Nuclear Information System (INIS)
Singh, Mamta; Gupta, D. N.; Suk, H.
2015-01-01
We propose an idea to enhance the efficiency of second- and third-harmonic generation by considering the amplitude-modulation of the fundamental laser pulse. A short-pulse laser of finite spot size is modeled as amplitude modulated in time. Amplitude-modulation of fundamental laser contributes in quiver velocity of the plasma electrons and produces the strong plasma-density perturbations, thereby increase in current density at second- and third-harmonic frequency. In a result, the conversion efficiency of harmonic generation increases significantly. Power conversion efficiency of harmonic generation process is the increasing function of the amplitude-modulation parameter of the fundamental laser beam. Harmonic power generated by an amplitude modulated laser is many folds higher than the power obtained in an ordinary case
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
Macedo, D.X.; Guedes, I.
2014-01-01
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)
Density and geometry of single component plasmas
International Nuclear Information System (INIS)
Speck, A.; Gabrielse, G.; Larochelle, P.; Le Sage, D.; Levitt, B.; Kolthammer, W.S.; McConnell, R.; Wrubel, J.; Grzonka, D.; Oelert, W.; Sefzick, T.; Zhang, Z.; Comeau, D.; George, M.C.; Hessels, E.A.; Storry, C.H.; Weel, M.; Walz, J.
2007-01-01
The density and geometry of p-bar and e + plasmas in realistic trapping potentials are required to understand and optimize antihydrogen (H-bar) formation. An aperture method and a quadrupole oscillation frequency method for characterizing such plasmas are compared for the first time, using electrons in a cylindrical Penning trap. Both methods are used in a way that makes it unnecessary to assume that the plasmas are spheroidal, and it is shown that they are not. Good agreement between the two methods illustrates the possibility to accurately determine plasma densities and geometries within non-idealized, realistic trapping potentials
Density and geometry of single component plasmas
Speck, A; Larochelle, P; Le Sage, D; Levitt, B; Kolthammer, W S; McConnell, R; Wrubel, J; Grzonka, D; Oelert, W; Sefzick, T; Zhang, Z; Comeau, D; George, M C; Hessels, E A; Storry, C H; Weel, M; Walz, J
2007-01-01
The density and geometry of p¯ and e+ plasmas in realistic trapping potentials are required to understand and optimize antihydrogen (H¯) formation. An aperture method and a quadrupole oscillation frequency method for characterizing such plasmas are compared for the first time, using electrons in a cylindrical Penning trap. Both methods are used in a way that makes it unnecessary to assume that the plasmas are spheroidal, and it is shown that they are not. Good agreement between the two methods illustrates the possibility to accurately determine plasma densities and geometries within non-idealized, realistic trapping potentials.
Harmonic disturbance location by applying Bayesian inference
Ye, G.; Xiang, Y.; Cuk, V.; Cobben, J.F.G.
2016-01-01
Harmonic pollution is one of the most important power quality issues in electric power systems. Correct location of the main harmonic disturbance source is a key step to solve the problem. This paper presents a method to detect the location of harmonic disturbance source in low voltage network
Detection of Harmonic Occurring using Kalman Filtering
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Shoro, Ghulam Mustafa; Imran, Raja Muhammed
2014-01-01
/current characteristic. These harmonics are not to be allowed to grow beyond a certain limit to avoid any grave consequence to the customer’s main supply. Filters can be implemented at the power source or utility location to eliminate these harmonics. In this paper we detect the instance at which these harmonics occur...
Third Harmonic Imaging using a Pulse Inversion
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
The pulse inversion (PI) technique can be utilized to separate and enhance harmonic components of a waveform for tissue harmonic imaging. While most ultrasound systems can perform pulse inversion, only few image the 3rd harmonic component. PI pulse subtraction can isolate and enhance the 3rd...
Freely floating structures trapping time-harmonic water waves (revisited)
Kuznetsov, Nikolay; Motygin, Oleg
2014-01-01
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of ...
On the moment of inertia of a quantum harmonic oscillator
International Nuclear Information System (INIS)
Khamzin, A. A.; Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-01-01
An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate
Lin, Ruixing; Xu, Lin; Zheng, Xian
2018-03-01
Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.
International Nuclear Information System (INIS)
Faghihi-Nik, M.; Ghorbanalilu, M.; Shokri, B.
2010-01-01
Complete text of publication follows. Generation of harmonic radiation is an important subject of laser plasma interaction and attracts great attention due to a wide range of applications. It has been seen that intense electromagnetic and quasi-static transverse magnetic fields are generated in laser plasma interaction. An extremely intense magnetic field (up to hundreds of MG) has been observed by experimental measurements in interaction of short laser pulses with plasma. These self-generated or applied magnetic fields affect the propagation of the laser pulses. In most laser interactions with homogeneous plasma, odd harmonics of laser frequency are generated. In this paper, we point out the possibility of even harmonics generation when a linearly polarized laser beam propagates in homogeneous plasma in the presence of a transverse magnetic field. It is shown that applying external field induces a transverse current density oscillating twice of the laser field which leds to generation of second harmonic radiation. This current density is derived using the perturbation method, and the steady state amplitude of the second harmonic obtained by solution of the wave equation. By the same procedure the current density and then the steady state amplitude of higher order harmonics are calculated. The efficiency of harmonic generation (the ratio of harmonic power to incident power) is a drastically function of the strength of external magnetic field. It is found that the efficiency of even harmonics is zero in the absence of magnetic field and increases as the magnetic field is increased. For odd harmonics, applying the external magnetic field enhances the generated harmonics as well. The conversion efficiency also increases with increase in plasma density and intensity of the laser beam.
Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.
Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene
2017-08-01
Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.
Research on Harmonic Characteristic of Electronic Current Transformer Based on the Rogowski Coil
Shen, Diqiu; Hu, Bei; Wang, Xufeng; Zhu, Mingdong; Wang, Liang; Lu, Wenxing
2017-05-01
The nonlinear load present in the power system will cause the distortion of AC sine wave and generate the harmonic, which havea severe impact on the accuracy of energy metering and reliability of relay protection. Tosatisfy the requirements of energy metering and relay protection for the new generation of intelligent substation, based on the working principle of Rogowski coil current transformer, mathematical model and transfer characteristics of Rogowski coil sensors were studied in this paper, and frequency response characteristics of Rogowski coil current transformer system were analysed. Finally, the frequency response characteristics of the Rogowski coil current transformer at 2 to 13 harmonics was simulated and experimented. Simulation and experiments show that Rogowski coil current transformer couldmeet 0.2 accuracy requirements of harmonic power measurement of power system, and measure the harmonic components of the grid reliably.
Harmonic Detection at Initialization With Kalman Filter
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Imran, Raja Muhammad; Shoro, Ghulam Mustafa
2014-01-01
Most power electronic equipment these days generate harmonic disturbances, these devices hold nonlinear voltage/current characteristic. The harmonics generated can potentially be harmful to the consumer supply. Typically, filters are integrated at the power source or utility location to filter out...... the affect of harmonics on the supply. For the detection of these harmonics various techniques are available and one of that technique is the Kalman filter. In this paper we investigate that what are the consequences when harmonic detection system based on Kalman Filtering is initialized...
Data harmonization and model performance
The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.
A Framework to Analyze the Stochastic Harmonics and Resonance of Wind Energy Grid Interconnection
Directory of Open Access Journals (Sweden)
Youngho Cho
2016-08-01
Full Text Available This paper addresses a modeling and analysis methodology for investigating the stochastic harmonics and resonance concerns of wind power plants (WPPs. Wideband harmonics from modern wind turbines (WTs are observed to be stochastic, associated with real power production, and they may adversely interact with the grid impedance and cause unexpected harmonic resonance, if not comprehensively addressed in the planning and commissioning of the WPPs. These issues should become more critical as wind penetration levels increase. We thus propose a planning study framework comprising the following functional steps: First, the best fitted probability density functions (PDFs of the harmonic components of interest in the frequency domain are determined. In operations planning, maximum likelihood estimations (MLEs followed by a chi-square test are used once field measurements or manufacturers’ data are available. Second, harmonic currents from the WPP are represented by randomly-generating harmonic components based on their PDFs (frequency spectrum and then synthesized for time domain simulations via inverse Fourier transform. Finally, we conduct a comprehensive assessment by including the impacts of feeder configurations, harmonic filters and the variability of parameters. We demonstrate the efficacy of the proposed study approach for a 100-MW offshore WPP consisting of 20 units of 5-MW full converter turbines, a realistic benchmark system adapted from a WPP under development in Korea and discuss lessons learned through this research.
International Nuclear Information System (INIS)
Oishi, Tetsutarou; Yoshinuma, Mikirou; Ida, Katsumi; Akiyama, Tsuyoshi; Minami, Takashi; Nagaoka, Kenichi; Shimizu, Akihiro; Okamura, Shoichi; Kado, Shinichiro
2008-01-01
The coherent MHD oscillation, which consists of the fundamental frequency of several kilohertz and its higher harmonics, (harmonic oscillation: HO) has been observed in Compact Helical System. HO consists of two pairs of harmonic series. One is located in the core region near the ι=0.5 rational surface (denoted as 'HO (core)'), the other is located in the edge region near the ι=1.0 rational surface (denoted as 'HO (edge)'). In the present study, bispectral analysis is applied to the fluctuation data, for which HO is measured by beam emission spectroscopy (BES) and using magnetic probes. The analysis has revealed that fundamental mode of HO in both the magnetic and core density fluctuations have phase correlation with the harmonics including fundamental oscillation, while HO in edge density fluctuation does not have such phase correlation. Mode numbers of HOs are identical for harmonic components having different frequencies, i.e., m/n=-2/1 for HO (core) and m/n=-1/1 for HO (edge). It suggests that the generation of harmonics cannot be interpreted simply as mode coupling because the summation rule for the wavenumber is not satisfied, even though the bicoherence value is significant. The bicoherence value and relative amplitude of higher harmonics correlate with each other, which suggests that bicoherence indicates the degree of distortion of the signals. (author)
Hu, Yi
2010-05-01
Recent research results show that combined electric and acoustic stimulation (EAS) significantly improves speech recognition in noise, and it is generally established that access to the improved F0 representation of target speech, along with the glimpse cues, provide the EAS benefits. Under noisy listening conditions, noise signals degrade these important cues by introducing undesired temporal-frequency components and corrupting harmonics structure. In this study, the potential of combining noise reduction and harmonics regeneration techniques was investigated to further improve speech intelligibility in noise by providing improved beneficial cues for EAS. Three hypotheses were tested: (1) noise reduction methods can improve speech intelligibility in noise for EAS; (2) harmonics regeneration after noise reduction can further improve speech intelligibility in noise for EAS; and (3) harmonics sideband constraints in frequency domain (or equivalently, amplitude modulation in temporal domain), even deterministic ones, can provide additional benefits. Test results demonstrate that combining noise reduction and harmonics regeneration can significantly improve speech recognition in noise for EAS, and it is also beneficial to preserve the harmonics sidebands under adverse listening conditions. This finding warrants further work into the development of algorithms that regenerate harmonics and the related sidebands for EAS processing under noisy conditions.
Variable frequency harmonic vibration suppression using active vibration absorption
Directory of Open Access Journals (Sweden)
Francisco Beltrán-Carbajal
2014-01-01
Full Text Available Los absorbedores dinámicos pasivos de vibraciones se han utilizado ampliamente para atenuación de vibraciones dañinas en muchos sistemas de ingeniería prácticos. La aplicabilidad de estos dispositivos de absorción pasiva de vibraciones se limita a un ancho de banda angosto y especifico de frecuencias de operación. En este artículo se propone un nuevo esquema de absorción activa de vibraciones que permite extender la capacidad de supresión de vibraciones de un absorbedor masa-resorte-amortiguador pasivo para cualquier frecuencia de excitación, incluyendo fuerzas de perturbación armónica resonantes de interés. Los fundamentos centrales de un absorbedor pasivo se explotan en la etapa de diseño del esquema de absorción propuesto. Así, el dispositivo de absorción activa aplica fuerzas sobre el sistema mecánico primario que contrarrestan las fuerzas de perturbación desconocidas, conservando la propiedad de atenuación de vibraciones del absorbedor pasivo. La fuerza de perturbación se estima en línea usando un observador de estado extendido propuesto en este trabajo. Se incluyen resultados en simulación para mostrar la eficiencia del esquema de absorción activa de vibraciones para rechazar vibraciones forzadas resonantes y caóticas completamente desconocidas afectando el sistema mecánico primario, y para probar la efectividad de la estimación de fuerzas de perturbación exógenas.
Microbubble generator excited by fluidic oscillator's third harmonic frequency
Czech Academy of Sciences Publication Activity Database
Tesař, Václav
2014-01-01
Roč. 92, č. 9 (2014), s. 1603-1615 ISSN 0263-8762 R&D Projects: GA ČR GA13-23046S Institutional support: RVO:61388998 Keywords : fluidic oscillator * microbubble generation * fluidic feedback loop Subject RIV: BK - Fluid Dynamics Impact factor: 2.348, year: 2014 http://dx.doi.org/10.1016/j.cherd.2013.12.004
Harmonic oscillator on a lattice
International Nuclear Information System (INIS)
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
Harmonic Lattice Dynamics of Germanium
Energy Technology Data Exchange (ETDEWEB)
Nelin, G
1974-07-01
The phonon dispersion relations of the DELTA-, LAMBDA-, and SIGMA-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field.
Harmonic Lattice Dynamics of Germanium
International Nuclear Information System (INIS)
Nelin, G.
1974-01-01
The phonon dispersion relations of the Δ-, Λ-, and Σ-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field
Frequency-chirped readout of spatial-spectral absorption features
International Nuclear Information System (INIS)
Chang, Tiejun; Mohan, R. Krishna; Harris, Todd L.; Merkel, Kristian D.; Tian Mingzhen; Babbitt, Wm. Randall
2004-01-01
This paper examines the physical mechanisms of reading out spatial-spectral absorption features in an inhomogeneously broadened medium using linear frequency-chirped electric fields. A Maxwell-Bloch model using numerical calculation for angled beams with arbitrary phase modulation is used to simulate the chirped field readout process. The simulation results indicate that any spatial-spectral absorption feature can be read out with a chirped field with the appropriate bandwidth, duration, and intensity. Mapping spectral absorption features into temporal intensity modulations depends on the chirp rate of the field. However, when probing a spatial-spectral grating with a chirped field, a beat signal representing the grating period can be created by interfering the emitted photon echo chirped field with a reference chirped field, regardless of the chirp rate. Comparisons are made between collinear and angled readout configurations. Readout signal strength and spurious signal distortions are investigated as functions of the grating strength and the Rabi frequency of the readout pulse. Using a collinear readout geometry, distortions from optical nutation on the transmitted field and higher-order harmonics are observed, both of which are avoided in an angled beam geometry
Toward transparent and self-activated graphene harmonic transponder sensors
Huang, Haiyu Harry; Sakhdari, Maryam; Hajizadegan, Mehdi; Shahini, Ali; Akinwande, Deji; Chen, Pai-Yen
2016-04-01
We propose the concept and design of a transparent, flexible, and self-powered wireless sensor comprising a graphene-based sensor/frequency-modulator circuitry and a graphene antenna. In this all-graphene device, the multilayered-graphene antenna receives the fundamental tone at C band and retransmits the frequency-modulated sensed signal (harmonic tone) at X band. The frequency orthogonality between the received/re-transmitted signals may enable high-performance sensing in severe interference/clutter background. Here, a fully passive, quad-ring frequency multiplier is proposed using graphene field-effect transistors, of which the unique ambipolar charge transports render a frequency doubling effect with conversion gain being chemically sensitive to exposed gas/molecular/chemical/infectious agents. This transparent, light-weight, and self-powered system may potentially benefit a number of wireless sensing and diagnosis applications, particularly for smart contact lenses/glasses and microscope slides that require high optical transparency.
Infrasonic harmonic tremor and degassing bursts from Halema'uma'u Crater, Kilauea Volcano, Hawaii
Fee, David; Garcés, Milton; Patrick, Matt; Chouet, Bernard; Dawson, Phil; Swanson, Donald A.
2010-01-01
The formation, evolution, collapse, and subsequent resurrection of a vent within Halema'uma'u Crater, Kilauea Volcano, produced energetic and varied degassing signals recorded by a nearby infrasound array between 2008 and early 2009. After 25 years of quiescence, a vent-clearing explosive burst on 19 March 2008 produced a clear, complex acoustic signal. Near-continuous harmonic infrasonic tremor followed this burst until 4 December 2008, when a period of decreased degassing occurred. The tremor spectra suggest volume oscillation and reverberation of a shallow gas-filled cavity beneath the vent. The dominant tremor peak can be sustained through Helmholtz oscillations of the cavity, while the secondary tremor peak and overtones are interpreted assuming acoustic resonance. The dominant tremor frequency matches the oscillation frequency of the gas emanating from the vent observed by video. Tremor spectra and power are also correlated with cavity geometry and dynamics, with the cavity depth estimated at ~219 m and volume ~3 x 106 m3 in November 2008. Over 21 varied degassing bursts were observed with extended burst durations and frequency content consistent with a transient release of gas exciting the cavity into resonance. Correlation of infrasound with seismicity suggests an open system connecting the atmosphere to the seismic excitation process at depth. Numerous degassing bursts produced very long period (0.03-0.1 Hz) infrasound, the first recorded at Kilauea, indicative of long-duration atmospheric accelerations. Kilauea infrasound appears controlled by the exsolution of gas from the magma, and the interaction of this gas with the conduits and cavities confining it.
The quantum harmonic oscillator on a circle and a deformed quantum field theory
International Nuclear Information System (INIS)
Rego-Monteiro, M.A.
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
Pulse Splitting for Harmonic Beamforming in Time-Modulated Linear Arrays
Directory of Open Access Journals (Sweden)
Lorenzo Poli
2014-01-01
Full Text Available A novel strategy for harmonic beamforming in time-modulated linear arrays is proposed. The pulse splitting technique is exploited to simultaneously generate two harmonic patterns, one at the central frequency and another at a preselected harmonic of arbitrary order, while controlling the maximum level of the remaining sideband radiations. An optimization strategy based on the particle swarm optimizer is developed in order to determine the optimal parameters describing the pulse sequence used to modulate the excitation weights of the array elements. Representative numerical results are reported and discussed to point out potentialities and limitations of the proposed approach.
Fractional high-harmonic combs by attosecond-precision split-spectrum pulse control
Directory of Open Access Journals (Sweden)
Laux Martin
2013-03-01
Full Text Available Few-cycle laser fields enable pulse-shaping control of high-order harmonic generation by time delaying variable broadband spectral sections. We report the experimental generation of fractional (noninteger high-harmonic combs by the controlled interference of two attosecond pulse trains. Additionally the energy of the high harmonics is strongly tuned with the relative time delay. We quantify the tuning to directly result from the controlled variation of the instantaneous laser frequency at the shaped driver pulse intensity maximum.
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Expansion into lattice harmonics in cubic symmetries
Kontrym-Sznajd, G.
2018-05-01
On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.
Complex harmonic modal analysis of rotor systems
International Nuclear Information System (INIS)
Han, Dong Ju
2015-01-01
Complex harmonic analysis for rotor systems has been proposed from the strict complex modal analysis based upon Floquet theory. In this process the harmonic balance method is adopted, effectively associated with conventional eigenvalue analysis. Also, the harmonic coefficients equivalent to dFRFs in harmonic mode has been derived in practice. The modes are classified from identifying the modal characteristics, and the adaptation of harmonic balance method has been proven by comparing the results of the stability analyses from Floque theory and the eigen analysis. The modal features of each critical speed are depicted in quantitatively and qualitatively by showing that the strengths of each component of the harmonic coefficients are estimated from the order of magnitude analysis according to their harmonic patterns. This effectiveness has been verified by comparing with the numerical solutions
A DC to 3-phase series-resonant converter with low harmonic distortion
Huisman, H.; Haan, de S.W.H.
1985-01-01
A type of dc to 3-phase series-resonant converter (s.r.converter) or potentially submegawatt industrial applications is presented. The converter provides variable-frequency sine-wave currents, with low harmonic distortion at the output terminals, and with the frequency ranging from -200 through dc
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.