Diagonal Matrix Elements Research Articles

Full waveform inversion using a decomposed single frequency component from a spectrogram

Although many full waveform inversion methods have been developed to construct velocity models of subsurface, various approaches have been presented to obtain an inversion result with long-wavelength features even though seismic data lacking low-frequency components were used. In this study, a new full waveform inversion algorithm was proposed to recover a long-wavelength velocity model that reflects the inherent characteristics of each frequency component of seismic data using a single-frequency component decomposed from the spectrogram. We utilized the wavelet transform method to obtain the spectrogram, and the decomposed signal from the spectrogram was used as transformed data. The Gauss–Newton method with the diagonal elements of an approximate Hessian matrix was used to update the model parameters at each iteration. Based on the results of time–frequency analysis in the spectrogram, numerical tests with some decomposed frequency components were performed using a modified SEG/EAGE salt dome (A–A′) line to demonstrate the feasibility of the proposed inversion algorithm. This demonstrated that a reasonable inverted velocity model with long-wavelength structures can be obtained using a single frequency component. It was also confirmed that when strong noise occurs in part of the frequency band, it is feasible to obtain a long-wavelength velocity model from the noise data with a frequency component that is less affected by the noise. Finally, it was confirmed that the results obtained from the spectrogram inversion can be used as an initial velocity model in conventional inversion methods.

A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

This paper investigates adaptive active control projective synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system for the identical structural chaotic systems. It is the first time that the active synchronization, the projective synchronization, and the adaptive synchronization are combined to achieve the synchronization of chaotic systems, which extend the control capability of achieving chaotic synchronization. By using a constant diagonal matrix, the active control is developed. Especially, when designing the controller, we just need to ensure that the diagonal elements of the diagonal matrix are less than or equal 0. So, the synchronization of chaotic systems can be realized more easily. Furthermore, by proposing an active controller, in combination with several different control schemes, we lower the complexity of the design process of the controller. More importantly, the larger the absolute value of product of the diagonal elements of diagonal matrix is, the smoother the curve of chaotic synchronization is and the shorter the time of chaotic synchronization is. In our paper, we take Lorenz system as an example to verify the effectiveness of the proposed synchronization scheme. Theoretical analysis and numerical simulations demonstrate the feasibility of this control method.

Fluorescence in a Quantum System with Violated Symmetry

The model of a single multilevel one-electron atom with violated symmetry such that its transition dipole-moment operator has constant diagonal matrix elements, among which not all are pairwise equal to each other, has been studied. It has been shown that the expression for the far electromagnetic field of such an atom does not contain any appreciable contributions from the diagonal matrix elements of the transition dipole moment in an explicit form; thus, these matrix elements have an effect on fluorescence via the time dependence of non-diagonal matrix elements due to quantum non-linear processes of higher orders. It has also been demonstrated that a two-level quantum system, whose transition dipole operator has constant unequal diagonal matrix elements, can continuously fluoresce under excitation with monochromatic laser radiation at a much lower frequency than the frequency of the exciting radiation. The possibility of the experimental detection and practical application of this effect are discussed.

Refraction traveltime tomography based on damped wave equation for irregular topographic model

Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography.This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem.As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.

Atypicality of Most Few-Body Observables.

The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a major candidate to explain thermalization in isolated quantum systems. According to the typicality argument, the maximum variations of such matrix elements should decrease exponentially with increasing the size of the system, which implies the ETH. We show, however, that the typicality argument does not apply to most few-body observables for few-body Hamiltonians when the width of the energy shell decreases at most polynomially with increasing the size of the system.

Quadrupole collectivity in Ca42 from low-energy Coulomb excitation with AGATA

A Coulomb-excitation experiment to study electromagnetic properties of Ca42 was performed using a 170-MeV calcium beam from the TANDEM XPU facility at INFN Laboratori Nazionali di Legnaro. γ rays from excited states in Ca42 were measured with the AGATA spectrometer. The magnitudes and relative signs of ten E2 matrix elements coupling six low-lying states in Ca42, including the diagonal E2 matrix elements of 21+ and 22+ states, were determined using the least-squares code gosia. The obtained set of reduced E2 matrix elements was analyzed using the quadrupole sum rule method and yielded overall quadrupole deformation for 01,2+ and 21,2+ states, as well as triaxiality for 01,2+ states, establishing the coexistence of a weakly deformed ground-state band and highly deformed slightly triaxial sideband in Ca42. The experimental results were compared with the state-of-the-art large-scale shell-model and beyond-mean-field calculations, which reproduce well the general picture of shape coexistence in Ca42.

Improved non-dimensional dynamic influence function method for vibration analysis of arbitrarily shaped plates with simply supported edges

An analytical method for free vibration analysis of arbitrarily shaped plates with simply supported edges is presented using the non-dimensional dynamic influence function (NDIF) method, which was introduced by the author. A major difficulty in the theoretical formulation of the proposed method is to analytically measure the values of diagonal elements of the system matrix that gives the eigenvalues and mode shapes of the plate of interest. In addition, particular attentions are given to remove the spurious eigenvalues of the plate. Various case studies show that the proposed method yields very accurate eigenvalues and mode shapes compared with other analytical and numerical methods in spite of its theoretical simplicity.

Accuracy and bias of genomic prediction with different de-regression methods

Genomic selection has become increasingly important in the breeding of animals and plants. The response variable is an important factor, influencing the accuracy of genomic selection. The de-regressed proof (DRP) based on traditional estimated breeding value (EBV) is commonly used as response variable. In the current study, simulated data from 16th QTL-MAS Workshop and real data from Chinese Holstein cattle were used to compare accuracy and bias of genomic prediction with two methods of calculating DRP. Our results with simulated data showed that the correlation between genomic EBV and true breeding value achieved using the Jairath method (DRP_J) was superior to that achieved using the Garrick method (DRP_G) for simulated trait 1 but the reverse was true for simulated trait 3, and these two methods performed comparably for simulated trait 2. For all three simulated traits, DRP_J yielded larger bias of genomic prediction. However, DRP_J outperformed DRP_G in both accuracy and unbiasedness for four milk production traits in Chinese Holstein. In the estimation of genomic breeding value using genomic BLUP model, two methods for weighting diagonal elements of incidence matrix associated with residual error were also compared. With increasing the proportion of genetic variance unexplained by markers, the accuracy of genomic prediction was decreased and the bias was increased. Weighting by the reliability of DRP produced accuracy comparable to the evaluation where the proportion of genetic variance unexplained by markers was considered, but with smaller bias in general.

Research on Dynamic Graph Target Tracking Method Fusing the Color Local Entropy

Focusing on the problems of target deformation, occlusion, background interference and rotation, a robust video tracking method is proposed in this paper, which is based on the superpixels and dynamic graph matching. Firstly, to make the superpixels edge fit better and structure tighter, the local gradient feature is fused into the simple linear iterative clustering (SLIC) method. Secondly, the candidate target superpixels set is generated by Graph Cuts and to obtain more accurate foreground superpixels set, the LASVM classification results are fused into the Graph Cuts energy function. Thirdly, in order to make the proposed tracker more robust, the color local entropy is fused into the diagonal elements of the affinity matrix. Experiment results show that the proposed algorithm has strong robustness and better tracking accuracy.

Study of Thermal and Coherent A1g Phonons in Bismuth Telluride

Totally symmetric A1g phonons are studied for the equilibrium and coherent states of a Bi2Te3 lattice. Equilibrium phonons were investigated in the frequency domain by the method of spontaneous Raman scattering, whereas coherent phonons were studied by the method of active femtosecond spectroscopy in the time domain. In the latter case, femtosecond laser pulses were used both for generating and detecting coherent A1g phonons having a well-defined phase allowing the selective optical control of the lattice dynamics. A comparison of the results obtained in the frequency and time domains suggests that diagonal and nondiagonal elements of the density matrix of lattice excitations relax with the same characteristic time to the equilibrium and zero values, respectively.

Reorientation-effect measurement of the first 2+ state in 12C: Confirmation of oblate deformation

A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ−ray spectrometer at the TRIUMF/ISAC II facility has permitted the determination of the 〈21+‖E2ˆ‖21+〉 diagonal matrix element in 12C from particle−γ coincidence data and state-of-the-art no-core shell model calculations of the nuclear polarizability. The nuclear polarizability for the ground and first-excited (21+) states in 12C have been calculated using chiral NN N4LO500 and NN+3NF350 interactions, which show convergence and agreement with photo-absorption cross-section data. Predictions show a change in the nuclear polarizability with a substantial increase between the ground state and first excited 21+ state at 4.439 MeV. The polarizability of the 21+ state is introduced into the current and previous Coulomb-excitation reorientation-effect analyses of 12C. Spectroscopic quadrupole moments of QS(21+)=+0.053(44) eb and QS(21+)=+0.08(3) eb are determined, respectively, yielding a weighted average of QS(21+)=+0.071(25) eb, in agreement with recent ab initio calculations. The present measurement confirms that the 21+ state of 12C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei.

Anisotropic resonator analysis using the Fourier–Bessel mode solver

A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday’s and Ampere’s laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier–Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

Tracing the evolution of nuclear forces under the similarity renormalization group

I examine the evolution of nuclear forces under the similarity renormalization group (SRG) using traces of the many-body configuration-space Hamiltonian. While SRG is often said to “soften” the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly smaller changes. By employing traces, I argue that this is a very natural outcome as one diagonalizes a matrix, and helps one to understand the success of SRG.

Conceptual DFT analysis of the fragility spectra of atoms along the minimum energy reaction coordinate.

Theoretical justification has been provided to the method for monitoring the sequence of chemical bonds' rearrangement along a reaction path, by tracing the evolution of the diagonal elements of the Hessian matrix. Relations between the divergences of Hellman-Feynman forces and the energy and electron density derivatives have been demonstrated. By the proof presented on the grounds of the conceptual density functional theory formalism, the spectral amplitude observed on the atomic fragility spectra [L. Komorowski et al., Phys. Chem. Chem. Phys. 18, 32658 (2016)] reflects selectively the electron density modifications in bonds of an atom. In fact the spectral peaks for an atom reveal changes of the electron density occurring with bonds creation, breaking, or varying with the reaction progress.

The Effect of PolSAR Image De-speckling on Wetland Classification: Introducing a New Adaptive Method

ABSTRACTSpeckle noise significantly degrades the radiometric quality of PolSAR image and, consequently, decreases the classification accuracy. This article proposes a new speckle reduction method for PolSAR imagery based on an adaptive Gaussian Markov Random Field model. We also introduce a new span image, called pseudo-span, obtained by the diagonal elements of the coherency matrix based on the least square analysis. The proposed de-speckling method was applied to full polarimetric C-band RADARSAT-2 data from the Avalon area, Newfoundland, Canada. The efficiency of the proposed method was evaluated in 2 different levels: de-speckled images and classified maps obtained by the Random Forest classifier. In terms of de-speckling, the proposed method illustrated approximately 19%, 43%, 46%, and 50% improvements in equivalent number of looks values, in comparison with SARBM3D, Enhanced Lee, Frost, and Kuan filter, respectively. Also, improvements of approximately 19%, 9%, 55%, and 32% were obtained in the overall classification accuracy using de-speckled PolSAR image by the proposed method compared with SARBM3D, Enhanced Lee, Frost, and Kuan filter, respectively. This new adaptive de-speckling method illustrates to be an efficient approach in terms of both speckle noise suppression and details/edges preservation, while having a great influence on the overall wetland classification accuracy.

Weighted Least Squared Approach to Fault Detection and Isolation for GPS Integrity Monitoring

Reliability of a global navigation satellite system is one of great importance for global navigation purposes. Therefore, an integrity monitoring system is an inseparable part of aviation navigation system. Failures or faults due to malfunctions in the systems should be detected to keep the integrity of the system intact. In order to solve the problem that least squares method detects and isolates a satellite fault for GPS integrity monitoring, in this paper, a weighted least squares algorithm is proposed for satellite fault detection and isolation. The algorithm adopts the diagonal elements of the covariance matrix of GPS measurement equation as the weighted factor. Firstly, the weighted least squares approach for satellite fault detection establishes the test statistic by the sum of the squares of the pseudo-range residuals of each satellite for GPS. Then, the detection threshold is obtained by the false alarm rate of the fault detection, probability density function and visiable satellite number.The effectiveness of the proposed approach is illustrated in a problem of GPS (Global Positioning System) autonomous integrity monitoring system. Through the real raw measured GPS data，based on least squares RAIM method and the weighted least squares RAIM approach, the performance of the two algorithms is compared. The results show that the proposed RAIM approach is superior to the least squares RAIM algorithm in the sensitivity of fault detection and fault isolation performance for GPS integrity monitoring.

Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.

Diagonal rejection-based minimum variance distortionless response for fiber underwater acoustic array

The high mounting precision of the fiber underwater acoustic array leads to an array manifold without perturbation. Besides, the targets are either static or slowly moving in azimuth in underwater acoustic array signal processing. Therefore, the covariance matrix can be estimated accurately by prolonging the observation time. However, this processing is limited to poor bearing resolution due to small aperture, low SNR and strong interferences. In this paper, diagonal rejection (DR) technology for Minimum Variance Distortionless Response (MVDR) was developed to enhance the resolution performance. The core idea of DR is rejecting the main diagonal elements of the covariance matrix to improve the output signal to interference and noise ratio (SINR). The definition of SINR here implicitly assumes independence between the spatial filter and the received observations at which the SINR is measured. The power of noise converges on the diagonal line in the covariance matrix and then it is integrated into the output beams. With the diagonal noise rejected by a factor smaller than 1, the array weights of MVDR will concentrate on interference suppression, leading to a better resolution capability. The algorithm was theoretically proved with optimal rejecting coefficient derived under both infinite and finite snapshots scenarios. Numerical simulations were conducted with an example of a linear array with eight elements half-wavelength spaced. Both resolution and Direction-of-Arrival (DOA) performances of MVDR and DR-based MVDR (DR–MVDR) were compared under different SNR and snapshot numbers. A conclusion can be drawn that with the covariance matrix accurately estimated, DR–MVDR can provide a lower sidelobe output level and a better bearing resolution capacity than MVDR without harming the DOA performance.

Theoretical Investigation of the Electronic, Structural, Optical and Thermodynamic Properties of LaxSr1-xTiO3 (x=0, 0.125, 0.25)

Lanthanum doped strontium titanate (La1-xSrxTiO­3, La-STO) materials are essential for solid oxide fuel cell (SOFC) electrodes and high-temperature gas sensors.[1] In the literature, their electronic structures and optical properties have been investigated intensively by density functional theory (DFT). However, the obtained information is theoretically limited to low temperature because the traditional DFT approach doesn’t include temperature effects. Since many of the applications of these materials for SOFCs and sensors are 400-800°C range, it is very important to know how their properties change when operating at high-temperatures. To better understand the thermodynamic behavior of La-STO with different La-doping levels at high temperatures, the ab initio thermodynamics calculations which combine first-principles DFT with lattice phonon dynamics have been employed in this study to calculate their electronic structures and thermodynamic evolutions versus temperature.[2-5] The obtained results show that with increasing La-doping level, the corresponding structures of La-STO become unstable with an increasing number of soft modes, especially when the La content over Sr is higher than 25%.[6] The La-STOs are conductors even at T=0K due to the electron of La filling in the conduction band of STO, which is consistent with experimental results. The results also reveal that although the GGA+U method could predict the band-gap of STO closer to the experimental measurements, the predicted lattice parameters of La-STO are larger than experimental values and result in more phonon soft modes. These deviations demonstrate the limitations of such U corrections for property extrapolation to high temperatures in comparison with the standard GGA approach. From the calculated optical dielectric tensors of La-STO, one can see that in the optical frequency range, there is a major difference between pure STO and La-doped STO consistent with the dielectric nature of STO and the finite electrical conductivity in La-doped STO associated with electrons in the conduction band, and consistent with expectations from experiments and simple Drude theory arguments. The reason is that STO possesses a band-gap, while La-doped STOs do not have a band-gap, as the extra electrons occupy the conduction band of STO. Due to the reduced symmetry for the La-doped STO systems, the diagonal elements (εXX, εYY, εZZ) of the dielectric matrix are not equal for some of La-STOs. Related to the DFT energy of pure STO, the calculated thermodynamic properties show that with increasing La-doping levels, the ΔH(T) and ΔG(T) decrease at given temperature T. With increasing T, the ΔH(T) of each La-STO increases while its ΔG(T) decreases because of the effects of TΔS(T) term. These results are useful for understanding the thermodynamic behaviors of La-STO materials at high temperatures and guide further studies of SOFC electrodes and sensor materials.

A theoretical study of the dissociative recombination of SH+ with electrons through the 2Π states of SH.

A quantitative theoretical study of the dissociative recombination of SH+ with electrons has been carried out. Multireference, configuration interaction calculations were used to determine accurate potential energy curves for SH+ and SH. The block diagonalization method was used to disentangle strongly interacting SH valence and Rydberg states and to construct a diabatic Hamiltonian whose diagonal matrix elements provide the diabatic potential energy curves. The off-diagonal elements are related to the electronic valence-Rydberg couplings. Cross sections and rate coefficients for the dissociative recombination reaction were calculated with a stepwise version of the multichannel quantum defect theory, using the molecular data provided by the block diagonalization method. The calculated rates are compared with the most recent measurements performed on the ion Test Storage Ring (TSR) in Heidelberg, Germany.