On the stability of time-varying systems using an observer for feedback control†

The effects upon stability are considered when an observer is incorporated in a time-varying system to estimate the immeasurable state variables in order to implement the feedback control law.     

Application of tilt modulation of the scatter cross-sections to distinguish between different non-Gaussian rough surfaces: unified full wave approach

The tilt modulations of the like- and cross-polarized cross-sections for arbitrarily oriented resolution cells are determined using the unified full-wave approach. A broad family of non-Gaussian rough surfaces characterized by the gamma surface height probability density functions of order K are considered. Furthermore a Pearson-Moskowitz surface height spectral density function is assumed for the sea surface. The surface height autocorrelation function is also assumed to be non-Gaussian. An arbitrarily oriented mean plane associated with the resolution cell is characterized by tilt angles in and perpendicular to a fixed reference plane of incidence. The ‘tilt modulation’ of the scattering cross-sections is determined as functions of the wavelength of the incident field 𝛌₀ and the backscatter angle 0ⁱ ₀. Each resolution cell represents the real (or synthetic) radar footprint. The size of the resolution cell, orientation, and the statistical characteristics of the non-Gaussian surface determine the radar cross-section. Radar remote sensing options are discussed to distinguish between random rough surfaces characterized by different probability density functions.     

Scattering cross sections for composite surfaces with large mean square slopes—full wave analysis

Abstract

In this work the full wave approach to rough surface scattering is applied to composite models of rough surfaces with large mean square slopes. It is shown that both specular point scattering as well as Bragg scattering are accounted for in the analysis and the results are compared with earlier solutions based on a combination of physical optics and perturbation theories. Using the full wave approach it is not essential to decompose the rough surface into individual surfaces with different roughness scales unless it is desired to separate the specular point contribution from the Bragg contribution to the scattering cross sections. Shadowing is accounted for in the analysis.     

Auto‐fluorescence for analysis of ripening in Thompson Seedless and colour in Crimson Seedless table grapes

Background and Aims: Ripening of table grapes is routinely followed by measurement of soluble solids, acidity, colour and firmness. Non‐destructive means to measure ripening can be of great value to determine optimal harvest time and to compare the effect of treatments on ripening. Methods and Results: The portable fluorescence detector (Multiplex III, Force A, France) generates 12 signals which are processed to ratios which compensate for the structural complexity of the cluster. Sampling was carried out in a Thompson Seedless vineyard in four blocks and over 9 weeks. The simple fluorescence ratio (SFR_R) (correlated to chlorophyll level) decreased exponentially with an R² value of 0.97, while flourscence excitation ratio (FER_RG) (correlated to anthocyanin level) displayed an increasing linear trend with an R² of 0.98. The flavonoids (FLAV) ratio which was shown to correlate to the level of flavonoids increased during the first 5 weeks of veraison and then reached a steady level. In an experiment on Crimson Seedless grapes, application of abscisic acid (ABA) resulted in a dose response using the anthocyanin (ANTH) ratio which is the log expression of FER_RG. In a further experiment on Crimson Seedless, the clusters were separated into three colour groups after veraison; ABA and Ethrel were applied, leaving untreated clusters in each colour group as control. The ANTH ratio was able to quantify a significant increase in colour for each group with respect to its control. Conclusions: The results suggest that portable fluorescence detectors may become important tools to study ripening of table grapes. Significance of the Study: This is the first report of the use of fluorescence to follow ripening of table grapes.     

EFFECT OF HYDROGEN PEROXIDE ON SOUR CHERRY ANTHOCYANINS

Degradation of sour cherry anthocyanins was studied at different H₂O₂ concentrations (0.233‐11.63 mmol.L^?1) over the temperature range of 20‐55C. Degradation reaction fitted to a first order kinetic model progressed very rapidly even at low H₂O₂ concentrations. Thus, the t_1/2 values at 20C varied between 111‐20 h in the concentration range of 0.233‐2.327 mmol.L^?1 H₂O₂. The degradation of anthocyanins occurred at a faster rate with increasing temperature at 5.82 and 11.63 mmol.L^?1 H₂O₂ concentrations. Between 25‐55C, activation energies (E_a) were 9.53 and 10.60 kcal.mol^?1 for 5.82 and 11.63 mmol.L^?1 H₂O₂ concentrations, respectively. Higher E_a value at 11.63 mmol.L^?1 H₂O₂ concentration indicated that the effect of temperature increased at higher H₂O₂ concentrations. A quadratic relationship (y = ‐0.0031x²+ 0.0218x + 0.0008, R²= 0.996) was found between the degradation rates at 20C and H₂O₂ concentrations of 0.233‐2.327 mmol.L^?1. According to this equation, k of 1.12 × 10^?3 h^?1 and t_1/2 of 26 days at 20C may be expected at 0.5 ppm (0.0147 mmol.L^?1) H₂O₂ concentration, i.e., the max. allowable H₂O₂ level by FDA in the finished food packages.     

Comparison of unified full-wave solutions for normal incidence microwave backscatter from sea with physical optics and hybrid solutions

Abstract

The unified full-wave solution for electromagnetic wave scatter from a rough surface is expressed as an integral similar in form to physical optics solutions. However it correctly predicts return for small and intermediate roughness scales where the physical optics approach fails. This full-wave solution is used here to evaluate microwave sea surface backscatter at normal incidence for both the like-and cross-polarized linear components. Surface heights and slopes are assumed to be Gaussian, the sea is characterized by its surface height spectral density function and both perfectly and finitely conducting surfaces are considered. Results from this complete full-wave evaluation are compared with approximations, involving single-scale (specular point) and two-scale models. For both of these models, however, it is necessary to assume a spectral wavenumber, ν_d, where spectral splitting between the large and the small scales of the rough surface occurs. The full-wave solution is used as a guide in the selection of ν_d and to study the accuracy and sensitivity of the different approximations to ν_d. It is also shown that results for cross-polarized backscatter based on the physical optics or two-scale models are totally inadequate.     

COMPUTER SIMULATION OF RANDOM SIGNALS AND ROUGH SURFACES WITH GIVEN STATISTICAL CHARACTERISTICS

Recurrence relations are developed to determine the weighting coefficients used in the simulation of random signals and rough surfaces with given statistical characteristics. These results can provide (in real time) straightforward, accurate solutions to the system of non-linear, algebraic equations associated with the method of moving summations. Three possible numerical methods have been reported to obtain approximate solutions to the system of non-linear, algebraic equations. However, none of them is straightforward, and they all require a large amount of computing time. This work can be applied to the numerical solution of the generalized telegraphist's equations used to analyze vertically and horizontally polarized radio wave scattering problems from permeable media with random rough interfaces. © 1997 by John Wiley & Sons, Ltd.     

NUMERICAL SOLUTIONS FOR THE SCATTERED FIELDS FROM ROUGH SURFACES USING THE FULL WAVE GENERALIZED TELEGRAPHISTS' EQUATIONS

A numerical method is used to solve the integro-differential generalized telegraphists' equations for the total (single and multiple) diffusely scattered radiation wave amplitudes. These equations were derived using a full wave approach. The singularities of the scattering coefficients are removed on integrating by parts. A stationary phase approximation is used to obtain the far fields. The numerical solutions are obtained for one-dimensional deterministic surfaces. The numerical results for the total (single and multiple) diffusely scattered fields are in good agreement with the earlier single scatter analytical results when the maximum surface slope is less than 30 degrees. The earlier single scatter analytical solutions are based on the assumption that the total field impressed upon a rough surface is associated with the incident field only. This assumption is not made for the evaluation of the numerical results presented here. The earlier analytical results are in total agreement with the small perturbation results when the rough surface height and slopes are of the same order of smallness. © 1997 by John Wiley & Sons, Ltd.