L1 generalized inverse beam-forming algorithm resolving coherent/incoherent, distributed and multipole sources

To resolve coherent/incoherent, distributed/compact, and multipole aerodynamic-sound sources with phased-array pressure data, a new source-detection algorithm is developed based on L₁ generalized inverse techniques. To extract each coherent signal, a cross spectral matrix is decomposed into eigenmodes. Subsequently, the complex source-amplitude distribution that recovers each eigenmode is solved using generalized inverse techniques with reference solutions which include multipoles as well as a monopole. Namely, the source distribution consisting of pre-defined source types is solved as an L₁ norm problem using iteratively re-weighted least squares (IRLS). The capabilities of the proposed algorithm are demonstrated using various benchmark problems to compare the results with several existing beam-forming algorithms, and it is found that distributed sources as well as dipoles with arbitrary orientation can be identified regardless of coherency with another source. The resolution is comparable to existing deconvolution techniques, such as DAMAS or CLEAN, and the computational cost is only several times more than that of DAMAS2. The proposed algorithm is also examined using previous model-scale test data taken in an open-jet wind-tunnel for a study on jet-flap interaction, and some indication of dipole radiation is discerned near the flap edge.     

On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

On spectral representations for the functions Wi(v, q2) (i = 1, 2) describing electroproduction process

It is shown that the Deser, Gilbert, Sudarshan representation (DGSR) does not follow from microcausality and spectrality only. Examples of the functions W_i(v, q²) satisfying the microcausality and spectrality conditions are given which cannot be written as the DGSR with spectral function h(a, α) that is a temperature distribution. Instead of the DGSR the spectral representation for W_i(v, q²) has been proved (eq. (3)) which follows only from microcausality and spectrality.     

ON THE BACKBENDING MECHANISM OF MUITIBAND STRUCTURE IN NUCLEUS 185Pt

The observation of multi-band structure in nucleus ¹⁸⁵Pt reported recently,once again raises the open question about whether the alignment of proton h_9/2 pair or neutron i_13/2 pair should be responsible to the backbending in five band.Blocking experiments prefer the proton h_9/2 pair while the Total Rothian Surface calculation supports neutron i_13/2 pair.Based on the analysis of assumptions implied in both approaches,a new theoretical calculation which includes the dynamic effect of band crossing is presented.Such a calculation indicates that the alignment of proton h pair should be the main cause for the observed backbendings.     

Fast approximate technique for the cumulative wavenumber model to modeling radiative transfer in a mixture of real gas media

In the cumulative wavenumber (CW) model, the total range of the absorption cross-section Cη is subdivided into the supplementary absorption cross-section of gray gases C_j, j=1,…,n, where n is the number of gray gases; and the wavenumber region is subdivided into intervals Δ_i=[η_i−1, η_i], i=1, 2,…,p, where p is the number of intervals. The intersection of the two spectral subdivisions is used to define the modeling of the fractional gray gas D_ij. In the CW model, we solve the radiative transfer equation (RTE) in every subinterval D_ij; then it is necessary to solve n x p times the spectral form of the RTE for complete spectral integration. In this work, the CW model is used with a numerical approximation technique based on additive properties of radiative intensity to reduce the solution of RTE to n new fractional gray gas D_j for complete spectral integration. The CW model was first coupled with the discrete ordinates method and the accuracy of the simplified technique and the algorithm was first examined for one-dimensional homogeneous media; results are compared with line-by-line calculations and it is found that the CW model with the simplified technique is exact for the homogeneous media examined. Also, the fast approach is tested in the diffuse reflecting boundaries case. The CW model is implemented in a bi-dimensional enclosure containing real gases in isothermal cases. Afterwards, this approximate technique is extended to non-isothermal and non-homogeneous cases; the results are compared with line-by-line calculations taken from literature and good agreement was found. The results obtained using the acceleration technique for the CW model agree with the results of original CW model. With this acceleration technique the CPU time decreases p times. Spectral database HITRAN and HITEMP are used to obtain the molecular absorption spectrum of the gases.     

Simulation of elasto optical properties of K2SO4 crystals

The electronic optical spectra of the mechanically free and stressed crystals of potassium sulfate, K₂SO₄, in the orthorhombic phase Pnma have been calculated by the Cambridge Serial Total Energy Package (CASTEP) code. On the basis of these calculations, the components of stress elasto optical tensors based on the changes of refractive index n (π_im) and birefringence Δn () (i, k, m=1, 2, …, 6) have been obtained for the indices i, k ,m=1, 2, 3. Absolute magnitudes of the calculated tensor π_im are probably underestimated because the magnitudes of the calculated elastic stiffness tensor c_rm are found to be overestimated about two times. Features of the spectral dependences n(E) and k(E) of refractive and absorption indices of the mechanically free and stressed potassium sulfate crystals have been analyzed.     

The inverse problem for the third order equation uxxx + q(x)ux + r(x)u = −iζ3u

The spectral problem u_xxx + q(x)u_x + r(x)u = ?iξ³u is considered. A set of spectral data which is sufficient for the reconstruction of the potentials q(x) and r(x) is found and the problem of this reconstruction, this inverse problem solved.     

Practical improvements to real and imaginary spectral based modal parameter measurements of SDOF systems

For a single degree of freedom system, especially with non-light damping, the use of the real spectral part of either the displacement or velocity responses (or the transfer functions based on them) has the advantages of determining the natural frequency (f_n) directly, independent of the response parameter, and providing an accurate measurement for damping (ζ). However, this method is sensitive to spectral phase errors due to temporal misalignment of the signal or due to net inter-channel delay differences caused by signal filtering. Two techniques are presented to correct for these errors; one based on the correct temporal alignment of the impulsive part, and the other on the infimum of the imaginary spectral part. These are first demonstrated using a numerical model, and are shown to facilitate the correct measurement of f_n and bring ζ within the expected error limits due to quantisation. Secondly, they are applied to an experimental system and are seen to greatly improve the consistency between measurements using different methods.     

Spectral estimation of NMR relaxation

In this paper, spectral estimation of NMR relaxation is constructed as an extension of Fourier Transform (FT) theory as it is practiced in NMR or MRI, where multidimensional FT theory is used. nD NMR strives to separate overlapping resonances, so the treatment given here deals primarily with monoexponential decay. In the domain of real error, it is shown how optimal estimation based on prior knowledge can be derived. Assuming small Gaussian error, the estimation variance and bias are derived. Minimum bias and minimum variance are shown to be contradictory experimental design objectives. The analytical continuation of spectral estimation is constructed in an optimal manner. An important property of spectral estimation is that it is phase invariant. Hence, hypercomplex data storage is unnecessary. It is shown that, under reasonable assumptions, spectral estimation is unbiased in the context of complex error and its variance is reduced because the modulus of the whole signal is used. Because of phase invariance, the labor of phasing and any error due to imperfect phase can be avoided. A comparison of spectral estimation with nonlinear least squares (NLS) estimation is made analytically and with numerical examples. Compared to conventional sampling for NLS estimation, spectral estimation would typically provide estimation values of comparable precision in one-quarter to one-tenth of the spectrometer time when S/N is high. When S/N is low, the time saved can be used for signal averaging at the sampled points to give better precision. NLS typically provides one estimate at a time, whereas spectral estimation is inherently parallel. The frequency dimensions of conventional nD FT NMR may be denoted D₁, D₂, etc. As an extension of nD FT NMR, one can view spectral estimation of NMR relaxation as an extension into the zeroth dimension. In nD NMR, the information content of a spectrum can be extracted as a set of n-tuples (ω₁, … ω_n), corresponding to the peak maxima. Spectral estimation of NMR relaxation allows this information content to be extended to a set of (n + 1)-tuples (λ, ω₁, … ω_n), where λ is the relaxation rate.     

The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+

The rotation-vibration Hamiltonian for an equilateral triangular X₃ molecule is derived in terms of the three curvilinear stretching coordinates Δr_i, and expanded in the form of a power series in the variables y_i = 1 ? exp(-aΔr_i), where a is a molecular parameter obtained from the potential function. The reason for the use of the variable y_i is twofold: Stretching potentials exhibit a much stronger convergence in the y_i than in the Δr_i, and a Hamiltonian expressed in the y_i can be diagonalized in a straightforward fashion using a Morse-oscillator basis set as we do here. Using a published ab initio potential surface we have expanded it as a polynomial in the y_i, and have calculated variationally the rotation-vibration energies of H₃⁺ and D₃⁺ using a symmetry-adapted Morse-oscillator-rigid symmetric top basis set. The results indicate that an expansion of the potential function to quartic terms in the y_i might be adequate, and that satisfactorily converged energies can be obtained with a relatively small basis set. The molecule H₃⁺ is the simplest polyatomic molecule. Inspection of the Appendix of this paper shows that the rotation-vibration Hamiltonian used here is one of the more complicated ones.     

Optimizing Spatially Localized NMR

Fourier-series windowing, a technique used to obtain spatially localized in vivo NMR spectra, is extended to fields-of-view containing a number of arbitrarily shaped regions of interest. For each volume, k-space weighting functions are derived and then combined to give an overall k-space sampling pattern - the number of signal acquisitions per phase-encoding vector - which can then be used to obtain spatially localized spectra of optimal sensitivity, consistent with a specified degree of localization. The technique is compared with the related methods of chemical-shift imaging and spectral localization by imaging.     

Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies

Long bones are good waveguides to support the propagation of ultrasonic guided waves. The low-order guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system. It is generally assumed that an angle of incidence, θ_i, generates a specific phase velocity of interest, c_o, via Snell’s law, θ_i = sin⁻¹(v_w/c_o) where v_w is the velocity of the coupling medium. In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes. Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array. The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6-MHz source signal. An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels. The imaged Lamb plate modes were identified by the theoretical dispersion curves. The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about c_o. The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles. The phenomena were well predicted by the excitation function of the source influence theory. The low-order modes were better imaged at steering angle ?30° for both plates. The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study.     

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Spin relaxation is a sensitive probe of molecular structure and dynamics. Correlation of relaxation time constants, such as T₁ and T₂, conceptually similar to the conventional multidimensional spectroscopy, have been difficult to determine primarily due to the absense of an efficient multidimensional Laplace inversion program. We demonstrate the use of a novel computer algorithm for fast two-dimensional inverse Laplace transformation to obtain T₁–T₂ correlation functions. The algorithm efficiently performs a least-squares fit on two-dimensional data with a nonnegativity constraint. We use a regularization method to find a balance between the residual fitting errors and the known noise amplitude, thus producing a result that is found to be stable in the presence of noise. This algorithm can be extended to include functional forms other than exponential kernels. We demonstrate the performance of the algorithm at different signal-to-noise ratios and with different T₁–T₂ spectral characteristics using several brine-saturated rock samples.     

Al NMR studies of NpPd5Al2

We present ²⁷Al NMR studies for a single crystal of the Np-based superconductor NpPd₅Al₂. We have observed a five-line ²⁷Al NMR spectrum with a center line and four satellite lines separated by first-order nuclear quadrupole splittings. The Knight shift clearly drops below T_c. The temperature dependence of the ²⁷Al nuclear spin-lattice relaxation rate shows no coherence peak below T_c, indicating that NpPd₅Al₂ is an unconventional superconductor with an anisotropic gap. The analysis of the present NMR data provides evidence for strong-coupling d-wave superconductivity in NpPd₅Al₂.     

Spectral restoration from low signal-to-noise,distorted NMR signals: application to hyphenated capillary electrophoresis-NMR

In capillary electrophoresis separations coupled to NMR signal detection using small solenoidal coils, electrophoretic currents cause substantial distortion in the NMR spectral linewidths and peak heights, distortions which cannot be fully counteracted through shimming. The NMR spectra also have a low signal-to-noise ratio due to the small amounts of material, typically <1nmol, associated with such microseparations. This study proposes a two-step, signal processing method to restore spectral lines from the distorted NMR spectrum. First, a reference signal is acquired to estimate the broadening function, as a combination of several Lorentzian functions, using a gradient descent method. Then multi-resolution wavelet analysis is applied to the distorted spectrum to determine an initial estimate of the frequencies of the spectral lines. Convergence to the final spectrum, a second set of Lorentzians, involves deconvolution with the estimated broadening function using a gradient descent method. Experimental CE-NMR data show that considerable improvements in spectral quality are possible using this approach, although fine splittings can not be resolved if the broadening function is large.     

A false color image fusion method based on multi-resolution color transfer in normalization YCBCR space

In this paper, a false color image fusion method for merging visible and infrared images is proposed. Firstly, the source images and reference image are decomposed respectively by Laplacian pyramid transform. Then the grayscale fused image and the difference images between the normalized source images are assigned to construct YC_BC_R components. In the color transfer step, all the three channels of the color space in each decomposition level are processed with the statistic color mapping according to the color characteristics of the corresponding sub-images of the reference image. Color transfer is designed based on the multi-resolution scheme in order to significantly improve the detailed information of the final image, and to reduce excessive saturation phenomenon to have a comparatively natural color appearance compared with the classical global-coloring algorithm. Moreover, the differencing operation between the normalized source images not only provides inter-sensor contrast to make popping the potential targets but also weakens the influence of the ambient illumination variety to a certain degree. Finally, the fused results and several metrics for evaluation of fused images subjectively and objectively illustrate that the proposed color image fusion algorithm can yield a more complete mental representation of the perceived scene, resulting in better situational awareness.     

Giant optical anisotropy in M-plane GaN/AlGaN quantum wells due to crystal-field effect

The optical polarization of GaN/AlGaN wurtzite quantum wells in various orientations is studied using an arbitrarily-oriented [hkil] Hamiltonian potential matrix. The optical matrix elements in the wurtzite quantum wells are calculated using the k⋅p finite difference scheme. The results reveal the presence of giant in-plane optical anisotropy (polarized normal to [0001]) in the M-plane (i.e., the -oriented layer plane) GaN/Al_0.2Ga_0.8N quantum well, due to the positive crystal-field split energy effect (ΔCR>0). The present theoretical results are consistent with the photoluminescence measurements presented in the literature [B. Rau, et al., Appl. Phys. Lett. 77 (2000) 3343].     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Simple algorithm for the correction of MRI image artefacts due to random phase fluctuations

PurposeFast Field-Cycling (FFC) MRI is a novel technology that allows varying the main magnetic field B₀ during the pulse sequence, from the nominal field (usually hundreds of millitesla) down to Earth's field or below. This technique uses resistive magnets powered by fast amplifiers. One of the challenges with this method is to stabilise the magnetic field during the acquisition of the NMR signal. Indeed, a typical consequence of field instability is small, random phase variations between each line of k-space resulting in artefacts, similar to those which occur due to homogeneous motion but harder to correct as no assumption can be made about the phase error, which appears completely random. Here we propose an algorithm that can correct for the random phase variations induced by field instabilities without prior knowledge about the phase error.MethodsThe algorithm exploits the fact that ghosts caused by field instability manifest in image regions which should be signal free. The algorithm minimises the signal in the background by finding an optimum phase correction for each line of k-space and repeats the operation until the result converges, leaving the background free of signal.ConclusionWe showed the conditions for which the algorithm is robust and successfully applied it on images acquired on FFC-MRI scanners. The same algorithm can be used for various applications other than Fast Field-Cycling MRI.