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A UNIFIED ALGORITHM FOR PHASE AND CROSS-TALK CALIBRATION OF POLARIMETRIC DATA - THEORY AND OBSERVATIONS

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1994年第1期32卷 89-99页

作者： QUEGAN, S Department of Applied and Computational Mathematics University of Sheffield Sheffield UK

A unified approach to phase and cross-talk calibration of polarimetric data which can be applied to calibrating scattering matrix data or to extraction of the descriptors of distributed targets is described. It relies on the scene being dominated by targets with uncorrelated like and cross-polarized backscattering coefficients, but provides cross-talk calibration of targets for which this is not true. The algorithm needs unsymmetrized data, but uses only quantities derived from the covariance matrix of large areas. It makes no assumptions about system reciprocity, permits ready interpretation of the terms in the calibration procedure, allows comparison of the relative magnitude of the system-induced mixing of terms in the observed covariance matrix, is noniterative, and produces indicators which allow testing of whether it meets its own underlying assumptions. The linear distortion model is shown to lead to an inconsistent system of equations;this inconsistency can be removed by introducing an extra parameter which has properties expected of system noise. The modulus of the copolarized correlation coefficient, which is important in polarimetric classification and as a phase descriptor, is shown to be invariant under all effects embodied in the linear distortion model. Calibration of the scattering matrix data is based on a minimum least squares principle. This suggests that current methods of symmetrization are not optimal. The same analysis shows that estimates of parameters needed to form an equivalent reciprocal system are also nonoptimal. The method is more general than the well-known van Zyl algorithm for cross-talk removal, and permits an analysis of the conditions under which the van Zyl algorithm will yield valid results. Correction of phase distortion induced by channel imbalance is treated as an optional extra step relying on a known HH-VV phase difference in some region of the image. Results from the algorithm are discussed using scattering matrix data fr

关键词： Calibration Scattering Covariance matrix Phase distortion Data mining Layout Backscatter System testing Equations Crosstalk

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PROGRESS IN THE INTERPRETATION OF HF SEA ECHO - HF RADAR AS A REMOTE-SENSING TOOL

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IEE PROCEEDINGS-F RADAR AND SIGNAL PROCESSING 1990年第2期137卷 139-147页

作者： WYATT, LR Department of Applied and Computational Mathematics University of Sheffield Sheffield UK

When HF radar systems are used for surveillance or tracking of ships or aircraft the strong signal from the ocean surface is termed clutter since it obscures the required signals. Over 30 years ago it was recognised that this sea ‘clutter’had characteristics that could be related to the ocean wave spectrum and the idea of using HF radar for remote sensing was born. This paper describes recent work on the inversion of the Doppler spectrum of HF radar echoes from the ocean surface to provide measurements of the ocean wave directional spectrum.

关键词： ocean waves ocean surface electromagnetic wave reflection Surface waves, tides, and sea level remote sensing Radar equipment, systems and applications HF radar echo Other topics in Earth sciences Doppler spectrum inversion radar cross-sections radar clutter ship tracking Oceanographic and hydrological techniques and equipment HF sea echo ocean wave directional spectrum clutter radar applications remote sensing tool aircraft tracking Instrumentation and techniques for geophysical, hydrospheric and lower atmosphere research Radar theory oceanographic techniques

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Error Analysis of One-Leg Methods forDifferential-Algebraic Equations of Index 2

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Communications in Nonlinear Science and Numerical Simulation 1999年第3期4卷 230-233页

作者： Aiguo XIAO and Shoufu LI(department of mathematics and Institute for computational and applied mathematics,Xiangtan University, Xiangtan 411105, China)E-mail: xianag@*** Department of Mathematics and Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 411105 China

IntroductionConsiderthefOllowingsystemofDAEsinHessenbergformwheretheinitialvalues(yo,to)areassumedtobeconsistent,i.e.(g.f)(yo,ic)==0,g(yo)=***,wesupposethat(1)hasauniquesolution(y(x),z(x)),andjandgaresufficientlydiffe... 详细信息

关键词： differential-algebraic equations index 2 one-leg methods error

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SELF-ADAPTIVE NEAR-OPTIMAL CONTROL OF DIFFUSION EQUATIONS

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1980年第6期127卷 290-295页

作者： ZINOBER, ASI Department of Applied & Computational Mathematics University of Sheffield Sheffield UK

The self-adaptive near-optimal control of diffusion equations is described. The variable structure feedback design is independent of the initial conditions and the plant parameter values. Rather than identifying the precise parameter values by adaptive correction, the online self-adaptive closed-loop controller organises itself by identifying certain dynamic characteristics associated with sliding motion. Digital simulation results are presented for both linear and nonlinear systems, and the effect of parameter variations and external disturbances are discussed. The system responses are close to the time-optimal paths.

关键词： parameter variations variable structure systems diffusion equations near optimal control sliding motion online control closed loop control Self-adjusting control systems Optimal control control system synthesis variable structure feedback design self-adjusting systems optimal control system responses linear systems nonlinear systems self adaptive control external disturbances dynamic characteristics

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Elimination of spiral waves and spatiotemporal chaos by the pulse with a specific spatiotemporal configuration

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Chinese Physics B 2008年第5期17卷 1925-1934页

作者：袁国勇杨世平王光瑞陈式刚 Department of Physics Hebei Normal University Institute of Applied Physics and Computational Mathematics

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.

关键词： spiral wave spatiotemporal chaos elimination

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SEMIVECTORIAL POLARIZED H FIELD SOLUTIONS FOR DIELECTRIC WAVE-GUIDES WITH ARBITRARY INDEX PROFILES

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IEE PROCEEDINGS-J OPTOELECTRONICS 1988年第5期135卷 333-338页

作者： STERN, MS Department of Applied and Computational Mathematics University of Sheffield Sheffield UK

Following recent successes with semivectorial polarisedẼ field solutions for rib, channel, embedded, and buried waveguides a method is presented for the determination of corresponding polarisedH̃ field modes for similar and other rectangular waveguide structures which may contain any arbitrary distribution of horizontal and vertical dielectric discontinuities. The new finite difference schemes take full account of the discontinuities in the normal gradients of magnetic field components across all internal dielectric interfaces. The polarisedH̃ field results, which are presented for various rib and embedded wave-guide structures, are found to be in excellent agreement with the corresponding polarisedẼ field modes. Application of the zero divergence constraint prevents the occurrence of spurious modes.

关键词： polarised H̰ field modes Electromagnetic waves: theory semivectorial polarised Ḛ field solutions Optical waveguides Optical waveguides and couplers Waveguide and cavity theory electromagnetic field theory buried waveguides rib waveguides waveguide theory channel waveguides embedded waveguide structures dielectric waveguides

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Determining the resistance of X-pinch plasma

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Chinese Physics B 2013年第4期22卷 344-349页

作者：赵屾薛创朱鑫磊张然罗海云邹晓兵王新新宁成丁宁束小建 Department of Electrical Engineering Tsinghua University Institute of Applied Physics and Computational Mathematics

The current and the voltage of an X-pinch were measured. The inductance of the X-pinch was assumed to be a constant and estimated by the calculation of the magnetic field based on the well-known Biot–Savart’s Law. The voltage of the inductance was calculated with L · di/dt and subtracted from the measured voltage of the X-pinch. Then, the resistance of the X-pinch was determined and the following results were obtained. At the start of the current flow the resistance of the exploding wires is several tens of Ohms, one order of magnitude, higher than the metallic resistance of the wires at room temperature, and then it falls quickly to about 1 , which reflects the physical processes occurring in the electrically exploding wires, i.e., a current transition from the highly resistive wire core to the highly conductive plasma. It was shown that the inductive contribution to the voltage of the X-pinch is less than the resistive contribution. For the wires we used, the wires’ material and diameter have no strong influence on the resistance of the X-pinch, which may be explained by the fact that the current flows through the plasma rather than through the metallic wire itself. As a result, the current is almost equally divided between two parallel X-pinches even though the diameter and material of the wires used for these two X-pinches are significantly different.

关键词： electrical explosion of wires X-pinch Z-pinch

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Approximate analytical solutions and application to logistic models with fractional derivatives

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Partial Differential Equations in applied mathematics 2025年 13卷

作者： Aibinu, M.O. Momoniat, E. Department of Mathematics and Applied Mathematics University of Johannesburg P.O. Box 524 Auckland Park 2006 South Africa Data Science Across Disciplines Research Group (Institute for the Future of Knowledge) University of Johannesburg PO Box 524 Auckland Park 2006 South Africa Department of Mathematics University of Regina Regina SK S4S 0A2 Canada National Institute for Theoretical and Computational Sciences (NITheCS) South Africa

A powerful tool to investigate hypotheses, verify experimental results and simulate the dynamics of complex systems is mathematical modeling. Different versions and generalizations of the logistic growth model have been considered. The nonlinear nature of the most mathematical models has called for the introduction of diverse techniques to obtain their solutions. This paper introduces a generalized form of the logistic growth model, which incorporates and improves some existing models as special cases. Moreover, the paper presents an approximate analytical method that is potent in treating the nonlinear fractional differential equations with time delay and applies it to the logistic models. Lastly, the paper presents some numerical experiments and displays the dynamics of logistic models with Caputo-fractional derivative and time delay to show that the approximate analytical method always yields reliable solutions. © 2024

关键词： Approximate Fractional derivatives Logistic Model Sumudu transform

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The complex interplay between risk tolerance and the spread of infectious diseases

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Journal of the Royal Society Interface 2025年第225期22卷 20240486页

作者： Nguyen, Maximilian M. Freedman, Ari S. Cheung, Matthew A. Saad-Roy, Chadi M. Espinoza, Baltazar Grenfell, Bryan T. Levin, Simon A. Lewis-Sigler Institute Princeton University PrincetonNJ United States Department of Ecology and Evolutionary Biology Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Miller Institute for Basic Research in Science University of California Berkeley BerkeleyCA United States Department of Integrative Biology University of California BerkeleyCA United States Biocomplexity Institute University of Virginia CharlottesvilleVA United States

Risk-driven behaviour provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regard to risk tolerance. The interplay between behaviour and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioural composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behaviour, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the fraction of risk-averse people in the population and the duration of intervention usage reduce the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold and overshoot is eliminated. Finally, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse. © 2025 The Author(s).

关键词： epidemic size heterogeneous behaviour intervention adoption and usage risk tolerance

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Variational data assimilation for a nonlinear hydraulic model

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applied MATHEMATICAL MODELLING 1996年第9期20卷 675-682页

作者： Chertok, DL Lardner, RW Applied and Computational Mathematics Program Simon Fraser University Burnaby British Columbia Canada

A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate values of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a sufficient number of locations are available for assimilation.

关键词： parameter estimation data assimilation model identification

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