Gaussian Character Research Articles

About the Gaussian-Schell pulse train spectrum

The Gaussian-Schell (G-S) pulse model describes variations in Gaussian shaped light pulses. Recent studies proposed random functions fitted to G-S pulses in a non-stationary context. More specifically, this paper provides a cyclo-stationary model. The associated power spectrum is derived. A correlation between pulses is shown to remove the power spectrum Gaussian character.

Colored multiplicative and additive non-Gaussian noise-driven dynamical system: Mean first passage time

We have studied the barrier crossing dynamics in presence of non-Gaussian noises. It has been observed that multiplicative colored non-Gaussian noise can induce resonant activation (RA). The conspicuous dependence of mean first passage time (MFPT) on correlation time ( τ 2 ) of additive colored noise having fixed variance have been analyzed. Beyond a critical value of τ 2 the MFPT increases for a given rate of increase of noise strength with τ 2 if the additive colored noise is non-Gaussian. The MFPT first decreases with increase of the non-Gaussian parameter (measures deviation from Gaussian character) of multiplicative colored noise followed by an increase exhibiting a minimum. The appearance of the minimum critically depends on the additive noise.

Gaussian and non-Gaussian speckle fluctuations in the diffusing-wave spectroscopy signal of a coarsening foam

All previous applications of diffusing-wave spectroscopy to aqueous foams have relied on the assumption that the electric field of the detected light is a Gaussian random variable and hence that the Siegert relation applies. We test this crucial assumption by simultaneous measurement of both second- and third-order temporal intensity correlations. We find that the electric field is Gaussian for typical experimental geometries equivalent to illumination and detection with a plane wave, both for backscattering and transmission through an optically thick slab. However, we find that the Gaussian character breaks down for point-in-point-out backscattering geometries in which the illumination spot size is not sufficiently large in comparison with the size of the intermittent rearrangement events.

Effect of component separation on the temperature distribution of the cosmic microwave background

We present a study of the effect of component separation on the recovered cosmic microwave background (CMB) temperature distribution, considering Gaussian and non-Gaussian input CMB maps. In particular, the non-Gaussian maps have been generated as a mixture of a Gaussian CMB map and a cosmic strings map in different proportions. First, we extract the CMB component from simulated multifrequency Planck data (in small patches of the sky) using the maximum-entropy method (MEM), Wiener filter (WF) and a method based on the subtraction of foreground templates plus a linear combination of frequency channels (LCFC). We then apply a wavelet-based method to study the Gaussianity of the recovered CMB and compare it with the same analysis for the input map. When the original CMB map is Gaussian (and assuming that point sources have been removed), we find that neither MEM nor WF introduce non-Gaussianity in the CMB reconstruction. Regarding the LCFC, the Gaussian character is also preserved provided that the appropriate combination of frequency channels is used. On the contrary, if the input CMB map is non-Gaussian, all the studied methods produce a reconstructed CMB with lower detections of non-Gaussianity than the original map. This effect is mainly due to the presence of instrumental noise in the data, which clearly affects the quality of the reconstructions. In this case, MEM tends to produce slightly higher non-Gaussian detections in the reconstructed map than WF whereas the detections are lower for the LCFC. We have also studied the effect of point sources in the MEM reconstruction. If no attempt to remove point sources is performed, they clearly contaminate the CMB reconstruction, introducing spurious non-Gaussianity. When the brightest point sources are removed from the data using the Mexican Hat Wavelet, the Gaussian character of the CMB is preserved. However, when analysing larger regions of the sky, the variance of our estimators will be appreciably reduced and, in this case, we expect the point source residuals to introduce spurious non-Gaussianity in the CMB distribution. Therefore, a careful subtraction (or masking) of point source emission is crucial in order to be able to perform Gaussian analysis of the CMB.

The correction of short-range Mie scattering laser lidar returns based on the Gaussian character of laser beam

A new method for correcting Mie scattering laser lidar short-range returns by virtue of Gaussian emission was described. Firstly, basing on the Gaussian character of laser beam, the lidar returns were corrected. Secondly, on the assumptionof an almost homogenous atmosphere, the corrected logarithmic range-adjusted power curve S(r) was fitted with conic section, then the corresponding influences of overlapping area were corrected. Some examples show that the corrected results are much closer to the real atmospheric conditions.

SU-FF-T-253: Surface and Implanted Dosimeters: From a Phantom to Patients

Purpose: Empirical dosemeasurement with physical detectors is an essential aspect of quality assurance in radiation therapy. Factors such as patient setup, treatment plan error, and physiologic motion work to degrade the accuracy of dose delivery in moving from in vitro to in vivodosemeasurements.Method and Materials: This analysis draws from published measurements with diode dosimeters and the authors' experience with an implantable dosimeter system. The spread in measured values for three situations will be evaluated: (1) a solid‐state dosimeter on a fixed phantom with a single field exposure, (2) a solid‐state dosimeter attached to the skin surface of a patient, (3) a solid‐state dosimeter implanted into the GTV of a tumor for the full course of external beam treatment.Results: Histograms plotted for the three measurement situations show an increase in the variance of recorded values in moving from a fixed phantom to the interior of the patient. In particular, data from implanted sensors for breast and prostate patients both show a substantial number of dose deviations (from the treatment plan) above 5% and also at 8% and above. In addition to daily variations in delivered dose, with an essentially Gaussian character, offsets from a mean of zero were seen in the implanted dosimeter data. Conclusion: This study highlights the chain of approximations occurring between the last empirical check of dose accuracy, at the machine level, and the actual delivered dose at depth in the patient. The data from the three evaluation setups is sensible in that one finds a series of expanding Gaussian distributions in going from a very well controlled to a less well controlled setup. The frequency of errors in excess of 5% for sensors at depth in patients suggests that clinically relevant deviations in dose at depth may be common.

Nonlocality of two- and three-mode continuous variable systems

We address nonlocality of a class of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing strong nonlocality are considered, in which the dichotomic Bell operator is represented by displaced parity and by pseudospin operator respectively. Three-mode states are also considered as a conditional source of two-mode non Gaussian states, whose nonlocal properties are analyzed. We found that the non Gaussian character of the conditional states allows violation of Bell's inequalities (by parity and pseudospin tests) stronger than with a conventional twin-beam state. However, the non Gaussian character is not sufficient to reveal nonlocality thorough a dichotomized quadrature measurement strategy.

Conditioning two-party quantum teleportation within a three-party quantum channel

We consider an arbitrary continuous-variable three-party Gaussian quantum state which is used to perform quantum teleportation of a pure Gaussian state between two of the parties (Alice and Bob). In turn, the third party (Charlie) can condition the process by means of local operations and classical communication. We find the best measurement that Charlie can implement on his own mode that preserves the Gaussian character of the three-mode state and optimizes the teleportation fidelity between Alice and Bob.

Transverse nuclear spin relaxation due to director fluctuations in liquid crystals. II. Second-order contributions of the fluctuating director

Recently, we have introduced a slow-motional theory for transverse nuclear spin relaxation due to director fluctuations [D. Frezzato, G. Kothe, and G. J. Moro, J. Phys. Chem. B 105, 1281 (2001)]. This method is now generalized to second-order contributions of the fluctuating director. We consider the specific case in which the director is aligned orthogonal to the magnetic field. By exploiting the Gaussian character of director fluctuations, the stochastic Liouville equation for the coupled spin and director dynamics is solved in terms of a characteristic function whose time dependence is determined by a nonlinear integral equation. A convenient solution of the integral equation is obtained by decomposing the characteristic function according to the relaxation rates of the director fluctuations. In a first application, we evaluate the free induction decay and the corresponding absorption spectrum for quadrupolar probe nuclei in nematic liquid crystals. It is shown that the transverse magnetization is well represented by a monoexponential decay, i.e., a Lorentzian lineshape in the frequency domain. Explicit relations are derived for the linewidths and frequency shifts under slow-motional conditions where the Redfield theory cannot be applied anymore.

Distilling Gaussian states with Gaussian operations is impossible.

We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.

Statistical cosmology with quadratic density fields

Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations grow linearly. During this phase, the Gaussian character of the fluctuations is preserved. Later on, when the fluctuations have an amplitude of the order of the mean density or larger, non-linear effects cause departures from Gaussianity. In Fourier space, non-linearity is responsible for coupling Fourier modes and altering the initially random distribution of phases that characterizes Gaussian initial conditions. In this paper, we investigate some of the effects of quadratic non-linearity on basic statistical properties of cosmological fluctuations. We demonstrate how this form of non-linearity can affect asymptotic properties of density fields such as homogeneity, ergodicity, and behaviour under smoothing. We also show how quadratic density fluctuations give rise to a particular relationship between the phases of different Fourier modes which, in turn, leads to the generation of a non-vanishing bispectrum. We thus elucidate the relationship between higher-order power spectra and phase distributions.

A simple test of the Gaussian character of noise

The test consists in the measurement of the noise intensity at the output of a bandpass filter, and the estimation of the accuracy of the measurement. The confidence interval for the estimate is calculated under the assumption that the noise is stationary and Gaussian. This assumption is called “zero-hypothesis”. If a considerable part of the experimental data is outside the confidence interval, then the zero-hypothesis does not hold. The effect of noise being non-Gaussian is investigated analytically. Experimental data of 1/ f noise in GaAs epitaxial films are presented and discussed.

Peakfitter — an integrated Excel-based Visual Basic program for processing multiple skewed and shifting Gaussian-like spectral peaks simultaneously: application to radio frequency glow discharge ion trap mass spectrometry

This article is an electronic publication in Spectrochimica Acta Electronica (SAE), a section of Spectrochimica Acta Part B (SAB). The hardcopy text is accompanied by an electronic archive, stored on the SAE homepage at (http://www.elsevier.nl/locate/sabe). The archive contains program and data files. The main article discusses the scientific spectroscopic and instrumental aspects of the subject and explains the purpose of the program and data files. The work deals with a Microsoft Excel Visual Basic program, Peakfitter, which can process multiple Gaussian-shaped spectral peaks quickly and easily. The program employs Microsoft Excel Solver to process any Gaussian-like spectra that can be opened in Microsoft Excel 97. Up to three peaks in one to 225 spectra, each containing up to 2000 data points can be processed per data file to give background corrected peak areas for both raw data and its associated fit data as calculated by the trapezoidal method or by simple successive addition of channel intensities across each peak. Concurrently output also includes fit peak heights for Gaussian-shaped spectral peaks. Use of other statistical distributions such as the Lorentzian model requires only slight modification to a template file. Hence, Peakfitter was actually written as two application programs, ‘Gaussfitter’ and ‘Lorenfitter’ to accommodate spectra of Gaussian or Lorentzian character, respectively. Written initially to process data from a radio frequency glow discharge ion trap mass spectrometer (rf-GD/ITMS), the program is useful for processing sequentially acquired spectra, which have a limited number of data points across each peak. The user may examine and manipulate program variables in cases where the raw data is skewed with respect to the fit data. An assessment of Peakfitter is given using rf-GD/ITMS elemental analysis and ion–molecule reaction data. Peakfitter’s (i.e. ‘Gaussfitter’s) utility in processing rf-GD/ITMS spectra is characterized by a slight enhancement in signal-to-noise ratio for fit data and (possibly more importantly) the ability to reliably process multiple peaks simultaneously. For the rf-GD/ITMS data, peak area calculation by simple summation of raw data channel intensities proved more useful than other combinations of calculating peak area (i.e. trapezoidal method applied to either fit or raw data or summation method applied to fit data).

Overtone Vibrational Dephasing of Chloroform Studied by Higher-Order Nonlinear Spectroscopy

Vibrational dephasing of the overtone bands of chloroform and its deuterated analogue has been studied by higher-order nonlinear spectroscopy. The overtone signals of v = 2 and 3 are based on the fifth- and seventh-order optical nonlinearity, respectively. The overtone vibrational dephasing signals as well as the fundamental ones are represented well by a single-exponential function. These dephasing signals are not explained by the stochastic theory with a time correlation function having a Gaussian or exponential character. Effects of resonant transfer and population relaxation are found not to be important for the deviation from the theoretical prediction. It is suggested that polyatomic natures of the molecule such as off-diagonal anharmonicity or coupling with combination bands may be responsible for this deviation.

The effect of apodisation and finite resolution on Fourier transform infrared and Raman spectra

The interferograms measured on Fourier transform infrared (FTIR) and Raman (FT-Raman) spectrometers are routinely apodised before the Fourier transform is carried out. The effects of finite resolution and different apodisation functions on synthetic bands of known Lorentz-Gauss character have been investigated. (The apodisation functions chosen were those commonly available on commercial FTIR and FT-Raman spectrometers). The effects are dramatic, the ratio of resolution/(true bandwidth) required to obtain less than 10% distortion (as judged by the peak height and width) in the band varied from 1 for boxcar to less than 0.2 for Norton-Beer (strong). Increasing Gaussian character of the band results in initially (i.e. at high resolution) the band being less altered by resolution and apodisation than a pure Lorentzian band. As the resolution is degraded, the band is more strongly affected. These results are explained in terms of the effect of truncation and distortion of the Fourier transform of the bandshape. A comparison of calculated and experimental results gave good agreement for the 1216 cm −1 band of chloroform in deuterochloroform. The experimental results also showed an increasing degree of Gaussian character as the resolution became comparable with the full width at half height of the band.

Nitrogen in diamond thin films

The local structure, dynamical properties and spin-lattice relaxation rate of nitrogen in diamond films produced by plasma-assisted chemical vapor deposition has been investigated by electron spin resonance in the temperature range 10–773 K. We find an isotropic g-value g = 2.0024 and hyperfine interaction constants A ‖ = 40.7 G and A ⊥ = 28.2 G consistent with an axial distortion along one of the four equivalent [111] directions. The peak to peak line width is ΔH pp = 3.0 G and the spin concentration is of the order of N s = 9 × 10 18 cm −3. The line shape has Lorentzian character in the center and Gaussian character in the wings. The high-temperature reorientation frequency was found to follow an Arrhenius-type behavior with ν 0 = 3.2 × 10 12 Hz and E JT = 0.69 eV. From the saturation behavior of the resonance line the spin-lattice relaxation time was found to be of the order to T 1e ≈ 1.0 × 10 −5 s at room temperature and T 1e ≈ 1.0 × 10 −3 s at 10 K.

Decay characteristics of bone marrow in the presence of a trabecular bone network: in vitro and in vivo studies showing a departure from monoexponential behavior.

In this study, we examine MRI T2' decay characteristics for bone marrow in trabecular bone networks, using an asymmetric spin-echo sequence to isolate the inhomogeneous decay due to susceptibility variations between bone and marrow or water. In in vitro measurements on trabecular bone specimens from human vertebral bodies, tibia, and radii, we find significant deviations from a monoexponential signal decay. The initial decay is seen to have a Gaussian decay character, switching to a primarily exponential decay at later decay times. A similar trend is observed in in vivo measurements in the distal radius. Unlike an exponential decay, which may be characterized by a single decay rate, this is indicative of a significant variation in the decay rate with time. The deviations from exponential decay are seen to be orientation dependent, being most significant when the primary trabecular orientation is perpendicular to the static magnetic field.

Quantitation of the global secondary structure of globular proteins by FTIR spectroscopy: Comparison with X-ray crystallographic structure

Fourier transform infrared spectroscopy (FTIR) is potentially a powerful tool for determining the global secondary structure of proteins in solution, providing the spectra are analyzed using a statistically and theoretically justified methodology. We have performed FTIR experiments on 14 globular proteins and two synthetic polypeptides whose X-ray crystal structures are known to exhibit varying types and amounts of secondary structures. Calculation of the component structural elements of the vibrational bands was accomplished using nonlinear regression analysis, by fitting both the amide I and amide II bands of the Fourier self-deconvoluted spectra, the second-derivative spectra, and the original spectra. The methodology was theoretically justified by comparing (via nonlinear regression analysis) the global secondary structure determined after deconvolving into component bands the vibrational amide I envelopes with the calculated structure determined by first principles from Ramachandran analysis of the X-ray crystallographic structure of 14 proteins from the Brookhaven protein data bank. Justification of the nonlinear regression analysis model with respect to experimental and instrumental considerations was achieved by the decomposition of all the bands of benzene and an aqueous solution of ammonium acetate into component bands while floating the Gaussian/Lorentzian character of the line shapes. The results for benzene yield all pure Lorentzian line shapes with no Gaussian character while the ammonium acetate spectra yielded all Gaussian line shapes with no Lorentzian character. In addition, all-protein spectra yielded pure Gaussian line shapes with no Lorentzian character. Finally, the model was statistically justified by recognizing random deviation patterns in the regression analysis from all fits and by the extra sum of squares F-test which uses the degrees of freedom and the root mean square values as a tool to determine the optimum number of component bands required for the nonlinear regression analysis. Results from this study demonstrate that the globular secondary structure calculated from the amide I envelope for these 14 proteins from FTIR is in excellent agreement with the values calculated from the X-ray crystallographic data using three-dimensional Ramachandran analysis, providing that the proper contribution from GLN and ASN side chains to the 1667 and 1650 cm −1 component bands has been taken into account. The standard deviation of the regression analysis for the per cent helix, extended, turn and irregular conformations was found to be 3.49%, 2.07%, 3.59% and 3.20%, respectively.

Mapping closure for probability distribution function in low frequency magnetized plasma turbulence

Recent numerical studies on the Hasegawa–Mima equation and its variants describing low frequency magnetized plasma turbulence indicate that the potential fluctuations have a Gaussian character whereas the vorticity exhibits non-Gaussian features. A theoretical interpretation for this observation using the recently developed mapping closure technique [Chen, Chen, and Kraichnan, Phys. Rev. Lett. 63, 2657 (1989)] has been provided here. It has been shown that non-Gaussian statistics for the vorticity arises because of a competition between nonlinear straining and diffusive damping whereas the Gaussianity of the statistics of φ arises because the only significant nonlinearity is associated with divergence free convection, which produces no strain terms.

Magnetic 3d-4f coupling in REBa 2Cu 3O 7−δ

We present specific heat and inelastic magnetic neutron scattering data on REBa 2Cu 3O 7−δ (Re = rare earth). Independent of the oxygen content drastic anomalies are observed in the temperature behaviour of the magnetic neutron scattering response. The quasielastic linewidth is nearly independent of temperature up to about 100 K and then increases linearly. Below T ≈ 100 K the quasielastic scattering changes continuously from Lorentzian to Gaussian character. Together with the systematic variation of the 4f ordering temperatures found by specific heat measurements this suggests an increase of an indirect 3d-4f coupling with decreasing atomic number of RE and could therefore also explain the anomalies in PrBa 2CuO 7−δ