Inverse Aspect Research Articles

A HIGH ORDER NUMERICAL SCHEME FOR FRACTAL-FRACTIONAL LASER SYSTEM WITH CHAOS STUDY

The primary goal of this research is to look into the dynamical behavior of a fractional and fractal-fractional (FF) order laser chaotic model. The model is first considered with Caputo’s fractional derivative. An iterative technique based on the Laplace transform and its inverse aspect is used to achieve a particular solution for the fractional model. The existence of a unique solution is examined for the fractional laser chaotic model. Next, the laser chaotic model is addressed with a FF approach in the Caputo sense. The approximate results are achieved for the proposed fractional and FF models by using the Atangana–Seda numerical methods. The dynamical structures are plotted at various values of fractional and FF parameters.

Investigation of the Pronoun “We” within the Framework of Enunciation Theory

In this paper, the matter of subjectivity, which is of paramount importance in Turkish, yet studied in a limited number of research, was discussed centering on the pronoun “we”. In this regard, the pronoun’s semantic content was defined, emphasizing its relation to other pronouns. In doing so, the Benveniste’ Enunciation Theory was applied. Initially, the definition of the pronoun “we” was resolved, then the conflict between the pronouns “we”/”I” was analyzed further. After observing how the pronoun “we” is used with titles, its use in fictional works, theses, scientific research, and group studies was also examined. Additionally, how the pronoun “we” was reached in the inner speech was also investigated, and the process of replacing “we” with “you”; “we”/”you” (plural, polite)/”you” (second person singular)=subordinate parent relationship; we”/”you” (plural, polite)/”you” (second person singular)=equality relationship were revealed. Therefore, it was observed that these uses show a semantic change from both negative to positive and from positive to negative, which are two aspects of inversion. Besides, it was revealed how the pronoun “we” acquires its semantic sense when the third singular person speaks on behalf of multiple persons. Finally, the observed use of “we” referring to uncertain “I” and, the speaker’s strategies of avoiding responsibility and getting lost in “we” were explained. The “we” as used by spokespersons in political texts/discourses was also mentioned in this context, and the use of “we are” was emphasized.

Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws

The Rayleigh wave has been frequently applied in geological seismic inspection and ultrasonic non-destructive testing, due to its low attenuation and dispersion. A thorough and effective utilization of Rayleigh wave requires better understanding of its scattering phenomenon. The paper analyzes the scattering of Rayleigh wave at the canyon-shaped flaws on the surface, both in forward and inverse aspects. Firstly, we suggest a modified boundary element method (BEM) incorporating the far-field displacement patterns into the traditional BEM equation set. Results show that the modified BEM is an efficient and accurate approach for calculating far-field reflection coefficients. Secondly, we propose an inverse reconstruction procedure for the flaw shape using reflection coefficients of Rayleigh wave. By theoretical deduction, it can be proved that the objective function of flaw depth d(x1) is approximately expressed as an inverse Fourier transform of reflection coefficients in wavenumber domain. Numerical examples are given by substituting the reflection coefficients obtained from the forward analysis into the inversion algorithm, and good agreements are shown between the reconstructed flaw images and the geometric characteristics of the actual flaws.

Hamiltonian identification in presence of large control field perturbations

Quantum system inversion concerns learning the characteristics of the underlying Hamiltonian by measuring suitable observables from the responses of the system’s interaction with members of a set of applied fields. Various aspects of inversion have been confirmed in theoretical, numerical and experimental works. Nevertheless, the presence of noise arising from the applied fields may contaminate the quality of the results. In this circumstance, the observables satisfy probability distributions, but often the noise statistics are unknown. Based on a proposed theoretical framework, we present a procedure to recover both the unknown parts of the Hamiltonian and the unknown noise distribution. The procedure is implemented numerically and seen to perform well for illustrative Gaussian, exponential and bi-modal noise distributions.

Forward and inverse modelling of post-seismic deformation

We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.

Estimation of Pine Forest Height and Underlying DEM Using Multi-Baseline P-Band PolInSAR Data

On the basis of the Gaussian vertical backscatter (GVB) model, this paper proposes a new method for extracting pine forest height and forest underlying digital elevation model (FUDEM) from multi-baseline (MB) P-band polarimetric-interferometric radar (PolInSAR) data. Considering the linear ground-to-volume relationship, the GVB is linked to the interferometric coherences of different polarizations. Subsequently, an inversion algorithm, weighted complex least squares adjustment (WCLSA), is formulated, including the mathematical model, the stochastic model and the parameter estimation method. The WCLSA method can take full advantage of the redundant observations, adjust the contributions of different observations and avoid null ground-to-volume ratio (GVR) assumption. The simulated experiment demonstrates that the WCLSA method is feasible to estimate the pure ground and volume scattering contributions. Finally, the WCLSA method is applied to E-SAR P-band data acquired over Krycklan Catchment covered with mixed pine forest. It is shown that the FUDEM highly agrees with those derived by LiDAR, with a root mean square error (RMSE) of 3.45 m, improved by 23.0% in comparison to the three-stage method. The difference between the extracted forest height and LiDAR forest height is assessed with a RMSE of 1.45 m, improved by 37.5% and 26.0%, respectively, for model and inversion aspects in comparison to three-stage inversion based on random volume over ground (RVoG) model.

Parametric excitation of axisymmetric toroidal electrostatic mode by drift wave turbulences

The axisymmetric toroidal electrostatic mode discussed in this paper refers collectively to the nearly ideal electrostatic fluid mode with zero toroidal mode number in magnetically confined toroidal plasmas like tokamak, including geodesic acoustic mode, sound waves and the so-called nearly zero-frequency zonal flow. Use is made of cold ion fluid model in the toroidal coordinate system with a circular cross section to develop the theory of parametric excitation for the three above mentioned modes systematically to the first order of inverse large aspect ratio, which ends up with the four following observations: (1) The density zonal flow is only associated with the excitation of the first harmonic cosine sound wave and is independent of the potential zonal flow. (2) The geodesic acoustic mode is the high frequency branch of the dispersion in the form of coupling between the first harmonic sine sound wave and the nearly zero-frequency zonal flow due to geodesic curvature, while the low frequency branch of the same dispersion is identified to be the ‘toroidally modified nearly zero-frequency zonal flow’. (3) Only a weak coupling exists between the second harmonic sine sound wave and the nearly zero-frequency zonal flow. (4) All cosine sound waves and sine sound waves beyond the second harmonic are decoupled to the nearly zero-frequency zonal flow. A Gaussian type of drift wave energy spectrum with only a few parameters is introduced for calculation. Emphasis is laid on the effects resulting from the finite radial spectrum width such as double Landau-singularity, which reveal a significant modification to the δ -spectrum, thus resulting in serious restriction to the parametric excitation of geodesic acoustic mode and nearly zero-frequency zonal flow. Also discussed is the possibility of excitation of density zonal flow in the high q region. Numerical results are presented graphically and discussed in the reasonable physical regime. It is indicated that the geodesic acoustic mode and the nearly zero-frequency zonal flow cannot be parametrically excited at the same radii, and that if the geodesic acoustic mode is parametrically excited, the density zonal flow is expectedly to be observed.

Crop LAI inversion based on the passive microwave remote sensing technology

The multichannel dual-polarized radiation characteristic database of corn vegetation canopy was constructed by using the corn structure parameters field measured data and the Matrix-Doubling model,and the relations between the emissivity and the transmissivity of the corn canopy were obtained using regression analysis based on the database.These relationships were applied to the microwave radiation propagation equation to compute the microwave radiation bright temperature of the surface covered with corn canopy.The results show that the correlation of the measured LAI value and the model inversion LAI is higher than 0.9,which suggests that the multichannel passive microwave data have considerable application potential in the aspect of corn LAI inversion.

Inverse problems for the Sturm–Liouville operator with discontinuity

In the previous works of the author (Applied Mathematics Letters. 2009;22:1315–1319, and Integral Equations and Operator Theory. 2009;65:593–604), provided that discontinuity parameters and boundary condition parameters are known a priori the inverse problems for the Sturm–Liouville operator with discontinuity inside a finite interval was studied. In fact, it is unnecessary to fix above mentioned parameters. In this work, we prove that the potential function and all parameters in discontinuity conditions and boundary conditions can be uniquely determined by a set of values of eigenfunctions in some interior point and one spectrum. We also establish Gesztesy–Simon type theorem and Ambarzumyan type theorem of inverse spectral aspects for discontinuous boundary value problem. The proofs in this work rely on the properties of analytic functions and Phragmén-Lindelöf theorem.

Forward simulation and inverse dipole localization with the lowest order Raviart—Thomas elements for electroencephalography

Electroencephalography is a non-invasive imaging modality in which a primary current density generated by the neural activity in the brain is to be reconstructed based on external electric potential measurements. This paper focuses on the finite element method (FEM) from both forward and inverse aspects. The goal is to establish a clear correspondence between the lowest order Raviart–Thomas basis functions and dipole sources as well as to show that the adopted FEM approach is computationally effective. Each basis function is associated with a dipole moment and a location. Four candidate locations are tested. Numerical experiments cover two different spherical multilayer head models, four mesh resolutions and two different forward simulation approaches, one based on FEM and another based on the boundary element method (BEM) with standard dipoles as sources. The forward simulation accuracy is examined through column- and matrix-wise relative errors as well as through performance in inverse dipole localization. A closed-form approximation of dipole potential was used as the reference forward simulation. The present approach is compared to the BEM and indirectly also to the recent FEM-based subtraction approach regarding both accuracy, computation time and accessibility of implementation.

WE-A-M100F-01: Central Nervous System Intensity Modulated Radiation Therapy

Intensity modulated radiation therapy(IMRT) for the central nervous system(CNS) is being used more frequently in radiationoncology clinics. There are two general situations that the treatment of CNS disease may benefit from the use of IMRT compared to conventional, three‐dimensional conformal radiation therapy: 1) when multiple critical structures confined within the intracranial vault are to be avoided, one may desire an optimal dose distribution that allows for the dose to these structures to be minimized, and 2) since high‐grade gliomas tend to recur locally, IMRT should allow for dose escalation proportional to the corresponding heterogeneous cell populations. Based on the anatomic location of the treatment volumes, one can envision examples where IMRT could be of benefit. Patients with a concave or irregularly‐shaped target in a frontal lobe may require IMRT in order to spare the adjacent globe and any uninvolved optic apparatus. In patients with well‐lateralized tumors involving the brain parenchyma, complete sparing of the contralateral hemisphere is desirable. Patients with infiltrative gliomas traditionally have large margins placed around the treatment volumes, and these may often encompass uninvolved critical normal structures. For such cases, IMRT may allow for non‐uniform reduction of the treatment volume around these normal structures. The primary goal of this presentation is to provide a practical overview of IMRT for the CNS. Though much attention has been given to the inverse planning and quality assurance aspects of IMRT, one should have an adequate understanding of the entire process; from proper patient selection to positioning/immobilization and continuing through treatment. A discussion of the steps of the CNSIMRT process will include: patient selection, immobilization, recommended imaging acquisitions, structure delineation, planning strategies/parameters, dose objectives, plan evaluation, QA, and potential delivery issues. Guidelines and practical examples for each component of this process will be presented. To gain further familiarization of CNSIMRT, one should review the corresponding technological and clinical outcome literature. Comparisons to conventional radiotherapy methods will be examined in terms of technique, dosimetry and clinical outcome. Finally, current research and future directions of CNSIMRT will be introduced such as the novel use of sophisticated imaging techniques for improved structure definition, patient positioning and dose modulation. Educational Objectives: 1. To understand the general practice of CNSIMRT from patient selection through actual treatment. 2. To become familiar with specific details pertaining to the CNSIMRT process through several illustrative examples. 3. To be introduced to some of the research and future directions of CNSIMRT. Research supported, in part, by Varian Medical Systems.

MI-NLMS adaptive beamforming algorithm for smart antenna system applications

A Matrix Inversion Normalized Least Mean Square (MI-NLMS) adaptive beamforming algorithm was developed for smart antenna application. The MI-NLMS which combined the individual good aspects of Sample Matrix Inversion (SMI) and the Normalized Least Mean Square (NLMS) algorithms is described. Simulation results showed that the less complexity MI-NLMS yields 15 dB improvements in interference suppression and 5 dB gain enhancement over LMS algorithm, converges from the initial iteration and achieves 24% BER improvements at cochannel interference equal to 5. For the case of 4-element uniform linear array antenna, MI-NLMS achieved 76% BER reduction over LMS algorithm.

MO-E-T-6C-02: IMRT of the Central Nervous System

Most of the clinical work with intensity modulated radiation therapy(IMRT) has focused on its use for the treatment of patients with prostate or head/neck cancers. However, IMRT for the central nervous system(CNS) is becoming more commonplace in the radiationoncology community. There are two general situations that the treatment of CNS disease may benefit from the use of IMRT compared to conventional, three‐dimensional conformal radiation therapy: 1) since multiple critical structures are confined within the intracranial vault, one may reason that optimization of the dose distributions should allow the dose to these structures to be minimized, and 2) since high‐grade gliomas tend to recur locally, IMRT should allow for dose escalation proportional to the corresponding heterogeneous cell populations. Based on the anatomic location of the treatment volumes, one can visualize examples where IMRT could be of benefit. Patients with a concave or irregularly‐shaped target in a frontal lobe may require IMRT in order to spare the adjacent globe and any uninvolved optic apparatus. In patients with well‐lateralized tumors involving the brain parenchyma, complete sparing of the contralateral hemisphere is desirable. Patients with infiltrative gliomas traditionally have large margins placed around the treatment volumes, and these may often encompass uninvolved critical normal structures. In these cases, IMRT allows non‐uniform reduction of the treatment volume around these structures. The goals of this presentation are to provide an overview of the practice of IMRT for the CNS, to review the corresponding published data, and to discuss future directions of exploration for CNSIMRT. Though much attention has been given to the inverse planning and quality assurance aspects of IMRT, one should have an adequate understanding of the entire process; from proper patient selection to positioning/immobilization and continuing through the actual radiation treatments. A discussion of the steps to the CNSIMRT process will include: patient selection, immobilization, recommended imaging acquisitions, structure delineation, planning strategies/parameters, dose objectives, plan evaluation, QA, and potential delivery issues. Guidelines and practical examples for each component of this process will be presented. To gain further familiarization of CNSIMRT, a review of published data is recommended. The focus of the review should examine both technological and clinical outcome data. Comparisons to conventional radiotherapy methods will be examined in terms of technique, dosimetry and clinical outcome. Finally, current research and future directions of CNSIMRT will be introduced such as the novel use of sophisticated imaging techniques for improved structure definition and dose modulation. Educational Objectives: 1. To understand the general practice of CNSIMRT from patient selection through actual treatment. 2. To become familiar with specific details pertaining to the CNSIMRT process through several illustrative examples. 3. To be introduced to some of the research and future directions of CNSIMRT. Research supported, in part, by Varian Medical Systems.

Rank-Deficient and Discrete III-Posed Problems: Numerical Aspects of Linear Inversion

Rank-Deficient and Discrete III-Posed Problems: Numerical Aspects of Linear Inversion

Aspects of the elution order inversion by pressure changes in programmed-temperature gas chromatography

The phenomenon of elution order inversion in programmed-temperature gas chromatography, as a result of only changing the head pressure of the column while retaining the same temperature program, is known to be experimentally detectable. In this paper we analyze some theoretical aspects of this phenomenon. These aspects concern the dependence of the separation on the pressure program for a couple of analytes presenting a retention reversal in isothermal gas chromatography (GC). In the theoretical context, the reason why the pressure program will not have a uniform effect on the separation of all crossing-over couples from a mixture, and why it is not possible to obtain a simple correlation for the separation of a given couple under different pressure conditions is visualized. A complete simulation of the process is required to evaluate the effect of the chosen head pressure-temperature program on the separation of the solutes.

An Analytic Model of Cold Air Damming and Its Applications

Abstract It is shown that the geometric shape of the cold dome in the two-layer model of cold air damming of Xu can be described approximately by a cubic polynomial and thus a set of coupled algebraic equations can be derived to quantify the scale and intensity of cold air damming as functions of the external parameters that characterize the environmental flow. In particular, these functions are easily computed and plotted in the parameter space, showing quantitatively how the cold dome width (scaled by the Rossby radius of deformation) and mountain-parallel jet speed change with the Froude number, surface roughness, inertial aspect ratio, and incident angle of the upstream inflow. The results also show that the cold dome width and mountain-parallel jet speed are insensitive to the depth of the upper-layer cross-mountain flow if the cross-mountain flow is sufficiently deep. The surface roughness and inverse inertial aspect ratio are found to have nearly the same control on the cold dome width and mountain...

Bootstrap Currents and its Scaling in the Non-Circular Tokamaks.

The bootstrap current (BSC) in non-circular tokamaks is studied with a simplified analytic model, and the scaling formula is derived.The BSC rateIB/IP in the plasma with the elongation κ is proportionl to (eaκ)1/2βP, rather than ea1/2βp, where ea is the inverse aspect ratio.This is one of the reasons why the ITER BSC scaling was writen in a somewhat strange form, that is, (ea1/2, βP) 1.3.

Blind Tests of Inversion Package for Stratigraphic Interpretation

This paper presents the blind test experiment set up for the EAEG workshop on Practical Aspects of Seismic Inversion(Berlin, 1989). The target was to review the possibilities provided by seismic data inversion at the end of the 1980's. This blind test consisted in deriving an acoustic impedance cross-section from a poststack seismic section and an impedance log. The control of the solution was made by comparison of the solution with logs at different well locations, these logs being kept hidden before the workshop. We give a mathematical formulation of the considered seismic inverse problem and we describe in detail the blind test experiment. We present the results obtained during this blind test with two software packages: SPIDER (Elf Aquitaine) and INTEGRATE (Jason Geosystems). These results and other results presented during the workshop (see the papers in this issue) illustrate the effectiveness of seismic inversion and the importance of integrating geological information during the inversion process.

Computational and asymptotic aspects of velocity inversion

We discuss computational and asymptotic aspects of the Born inversion method and show how asymptotic analysis is exploited to reduce the number of integrations in an f-k like solution formula for the velocity variation. The output of this alternative algorithm produces the reflectivity function of the surface. This is an array of singular functions—Dirac delta functions which peak on the reflecting surfaces—each scaled by the normal reflection strength at the surface. Thus, imaging of a reflector is achieved by construction of its singular function and estimation of the reflection strength is deduced from the peak value of that function. By asymptotic analysis of the application of the algorithm to the Kirchhoff representation of the backscattered field, we show that the peak value of the output estimates the reflection strength even when the condition of small variation in velocity (an assumption of the original derivation) is violated. Furthermore, this analysis demonstrates that the method provides a migration algorithm when the amplitude has not been preserved in the data. The design of the computer algorithm is discussed, including such aspects as constraints due to causality and spatial aliasing. We also provide O‐estimates of computer time. This algorithm has been successfully implemented on both synthetic data and common‐midpoint stacked field data.