Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Review of time-domain polarization measurements for assessing insulation condition in aged transformers

This paper presents a review of the time-domain polarization measurement techniques for the condition assessment of aged transformer insulation. The polarization process is first described with appropriate dielectric response theories and then commonly used polarization methods are described with special emphasis on the most widely used return voltage(rv) measurement. Most recent emphasis has been directed to techniques of determining moisture content of insulation indirectly by measuring rv parameters. The major difficulty still lies with the accurate interpretation of return voltage results. This paper investigates different thoughts regarding the interpretation of rv results for different moisture and ageing conditions. Other time domain polarization measurement techniques and their results are also presented in this paper.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Calibration of time domain reflectometry (DTR) for soil moisture measurements in cultivated peat soils

Tiivistelmä: TDR-mittausten kalibrointi viljeltyjen turvemaiden kosteuden mittaamiseen

Electrical conductivity of soil irrigated with swine wastewater estimated by time-domain reflectometry¹

Wastewater application to soil is an alternative for fertilization and water reuse. However, particular care must be taken with this practice, since successive wastewater applications can cause soil salinization. Time-domain reflectometry (TDR) allows for the simultaneous and continuous monitoring of both soil water content and apparent electrical conductivity and thus for the indirect measurement of the electrical conductivity of the soil solution. This study aimed to evaluate the suitability of TDR for the indirect determination of the electrical conductivity (ECse) of the saturated soil extract by using an empirical equation for the apparatus TDR Trase 6050X1. Disturbed soil samples saturated with swine wastewater were used, at soil proportions of 0, 0.45, 0.90, 1.80, 2.70, and 3.60 m³ m-3. The probes were equipped with three handmade 0.20 cm long rods. The fit of the empirical model that associated the TDR measured values of electrical conductivity (EC TDR) to ECse was excellent, indicating this approach as suitable for the determination of electrical conductivity of the soil solution.

Water percolation estimated with time domain reflectometry (TDR) in drainage lysimeters

Due to the difficulty of estimating water percolation in unsaturated soils, the purpose of this study was to estimate water percolation based on time-domain reflectometry (TDR). In two drainage lysimeters with different soil textures TDR probes were installed, forming a water monitoring system consisting of different numbers of probes. The soils were saturated and covered with plastic to prevent evaporation. Tests of internal drainage were carried out using a TDR 100 unit with constant dielectric readings (every 15 min). To test the consistency of TDR-estimated percolation levels in comparison with the observed leachate levels in the drainage lysimeters, the combined null hypothesis was tested at 5 % probability. A higher number of probes in the water monitoring system resulted in an approximation of the percolation levels estimated from TDR - based moisture data to the levels measured by lysimeters. The definition of the number of probes required for water monitoring to estimate water percolation by TDR depends on the soil physical properties. For sandy clay soils, three batteries with four probes installed at depths of 0.20, 0.40, 0.60, and 0.80 m, at a distance of 0.20, 0.40 and 0.6 m from the center of lysimeters were sufficient to estimate percolation levels equivalent to the observed. In the sandy loam soils, the observed and predicted percolation levels were not equivalent even when using four batteries with four probes each, at depths of 0.20, 0.40, 0.60, and 0.80 m.

Efficient self-synchronised blind audio watermarking system based on time domain and FFT amplitude modification

Many audio watermarking schemes divide the audio signal into several blocks such that part of the watermark is embedded into each of them. One of the key issues in these block-oriented watermarking schemes is to preserve the synchronisation, i.e. to recover the exact position of each block in the mark recovery process. In this paper, a novel time domain synchronisation technique is presented together with a new blind watermarking scheme which works in the Discrete Fourier Transform (DFT or FFT) domain. The combined scheme provides excellent imperceptibility results whilst achieving robustness against typical attacks. Furthermore, the execution of the scheme is fast enough to be used in real-time applications. The excellent transparency of the embedding algorithm makes it particularly useful for professional applications, such as the embedding of monitoring information in broadcast signals. The scheme is also compared with some recent results of the literature.

Photomultiplier nonlinear response in time-domain laser-induced luminescence spectroscopy

A new procedure to find the limiting range of the photomultiplier linear response of a low-cost, digital oscilloscope-based time-resolved laser-induced luminescence spectrometer (TRLS), is presented. A systematic investigation on the instrument response function with different signal input terminations, and the relationship between the luminescence intensity reaching the photomultiplier and the measured decay time are described. These investigations establish that setting the maximum intensity of the luminescence signal below 0.3V guarantees, for signal input terminations equal or higher than 99.7 ohm, a linear photomultiplier response.

Frequency-Domain and Wide-Pulse Time-Domain Measurements of Lanthanide Luminescence and Lanthanide-Based Resonance Energy Transfer

Resonance energy transfer (RET) is a non-radiative transfer of the excitation energy from the initially excited luminescent donor to an acceptor. The requirements for the resonance energy transfer are: i) the spectral overlap between the donor emission spectrum and the acceptor absorption spectrum, ii) the close proximity of the donor and the acceptor, and iii) the suitable relative orientations of the donor emission and the acceptor absorption transition dipoles. As a result of the RET process the donor luminescence intensity and the donor lifetime are decreased. If the acceptor is luminescent, a sensitized acceptor emission appears. The rate of RET depends strongly on the donor–acceptor distance (r) and is inversely proportional to r6. The distance dependence of RET is utilized in binding assays. The proximity requirement and the selective detection of the RET-modified emission signal allow homogeneous separation free assays. The term lanthanide-based RET is used when luminescent lanthanide compounds are used as donors. The long luminescence lifetimes, the large Stokes’ shifts and the intense, sharply-spiked emission spectra of the lanthanide donors offer advantages over the conventional organic donor molecules. Both the organic lanthanide chelates and the inorganic up-converting phosphor (UCP) particles have been used as donor labels in the RET based binding assays. In the present work lanthanide luminescence and lanthanide-based resonance energy transfer phenomena were studied. Luminescence lifetime measurements had an essential role in the research. Modular frequency-domain and time-domain luminometers were assembled and used successfully in the lifetime measurements. The frequency-domain luminometer operated in the low frequency domain ( 100 kHz) and utilized a novel dual-phase lock-in detection of the luminescence. One of the studied phenomena was the recently discovered non-overlapping fluorescence resonance energy transfer (nFRET). The studied properties were the distance and temperature dependences of nFRET. The distance dependence was found to deviate from the Förster theory and a clear temperature dependence was observed whereas conventional RET was completely independent of the temperature. Based on the experimental results two thermally activated mechanisms were proposed for the nFRET process. The work with the UCP particles involved the measurement of the luminescence properties of the UCP particles synthesized in our laboratory. The goal of the UCP particle research is to develop UCP donor labels for binding assays. In the present work the effect of the dopant concentrations and the core–shell structure on the total up-conversion luminescence intensity, the red–green emission ratio, and the luminescence lifetime was studied. Also the non-radiative nature of the energy transfer from the UCP particle donors to organic acceptors was demonstrated for the first time in aqueous environment and with a controlled donor–acceptor distance.

A Well Stated Time Domain Integral Representation for Elastodynamic Analysis and Applications

This article discusses three possible ways to derive time domain boundary integral representations for elastodynamics. This discussion points out possible difficulties found when using those formulations to deal with practical applications. The discussion points out recommendations to select the convenient integral representation to deal with elastodynamic problems and opens the possibility of deriving simplified schemes. The proper way to take into account initial conditions applied to the body is an interesting topict shown. It illustrates the main differences between the discussed boundary integral representation expressions, their singularities and possible numerical problems. The correct way to use collocation points outside the analyzed domain is carefully described. Some applications are shown at the end of the paper, in order to demonstrate the capabilities of the technique when properly used.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested