Direct Curve Fitting Research Articles

Design flood recalculation under land surface change

Under the influence of land surface variation, observed flood series are no longer stationary. Therefore, conventional flood frequency analysis methods based on the independent and identically distributed hydrological time series are not authentic, and design flood, which is the core of flood control planning, obtained by conventional methods is inevitably being questioned. In this study, we selected Wangkuai reservoir and Xidayang reservoir catchments in Daqinghe watershed affected by human activities to recalculate design floods. We firstly summarized land-use change and construction of hydraulic structures in the two catchments and found that land-use had changed a lot during 1970–1980, and numerous hydraulic structures had been built which had a significant influence on land surface in both catchments. Then, we used both reconstruction of flood series based on rainfall–runoff relationship and probability distribution methods to reconstruct the annual maximum peak flow series and calculated the design flood peaks under current and past land surface. Finally, we compared the design floods by the two methods with those derived from the direct curve fitting method without taking the land surface change into account, and we found that design flood peak and volume decreased due to land surface change in Wangkuai reservoir catchment and Xidayang reservoir catchment. The results were of great significance for flood control in these two catchments.

Fatigue damage evaluation of broad-band Gaussian and non-Gaussian wind load effects by a spectral method

This study presents fatigue damage evaluation of broad-band Gaussian and non-Gaussian wind load effects by a spectral method proposed in Benasciutti and Tovo (2005) [4]. The wind load effects considered are alongwind, crosswind and their coupled responses of tall buildings, and wind pressures on claddings. Following this spectral method, the rainflow counting damage is approximated by a linear combination of its upper and lower bounds. A refined formulation for determining the combination factor is proposed, which depends on bandwidth parameters in terms of process spectral moments. For non-Gaussian wind load effects, research emphasis is placed on the modeling of translation function which relates the non-Gaussian process with an underlying Gaussian process and is essential for non-Gaussian fatigue damage evaluation. Both moment-based translation model and the model by a direct curve fitting are addressed for a wide range of non-Gaussian characteristics, including a newly developed translation model for hardening non-Gaussian processes. The effectiveness and accuracy of the spectral method for broad-band Gaussian and non-Gaussian processes are demonstrated through comparison with the results from time domain rainflow counting method.

A new method to estimate parameters of the growth model for metastatic tumours

PurposeKnowledge of natural tumour growth is valuable for understanding tumour biology, optimising screening programs, prognostication, optimal scheduling of chemotherapy, and assessing tumour spread. However, mathematical modelling in individuals is hampered by the limited data available. We aimed to develop a method to estimate parameters of the growth model and formation rate of metastases in individual patients.Materials and methodsData from one patient with liver metastases from a primary ileum carcinoid and one patient with lung metastases from a primary renal cell carcinoma were used to demonstrate this new method. Metastatic growth models were estimated by direct curve fitting, as well as with the new proposed method based on the relationship between tumour growth rate and tumour volume. The new model was derived from the Gompertzian growth model by eliminating the time factor (age of metastases), which made it possible to perform the calculations using data from all metastases in each patient. Finally, the formation time of each metastasis and, consecutively, the formation rate of metastases in each patient were estimated.ResultsWith limited measurements in clinical studies, fitting different growth curves was insufficient to estimate true tumour growth, even if patients were followed for several years. Growth of liver metastases was well described with a general growth model for all metastases. However, the lung metastases from renal cell carcinoma were better described by heterogeneous exponential growth with various growth rates.ConclusionAnalysis of the regression of tumour growth rate with the logarithm of tumour volume can be used to estimate parameters of the tumour growth model and metastasis formation rates, and therefore the number and size distribution of metastases in individuals.

Curve Fitting Approach of Saddle-Shaped Curve for Automated Welding/Cutting

Curve fitting, or interpolation algorithm is core technology for Computer Numerical Control (CNC) systems. A saddle-shaped curve is formed by intersection of two tubes. The trajectory interpolation of saddle-shaped curve is usually carried out through approximating the curve as segments of straight line for automated CNC welding/cutting. This paper proposes a new saddle curve curve fitting algorithm for automated welding/cutting system with non-Cartesian coordinate system. Simulation of the direct curve fitting algorithm has demonstrated that the algorithm has high curve interpolation precision and high feedrate stability.

A comparison of JKR-based methods to analyze quasi-static and dynamic indentation force curves

The Johnson–Kendall–Roberts (JKR) theory of elastic contact, extended to take viscoelastic effects into account, is used to evaluate work of adhesion and modulus of elastomeric films. In this paper, we present a comparison of five approaches to analyze quasi-static and dynamic JKR force curve data obtained using instrumented indentation. The load-displacement experiments were performed using a 200-μm radius borosilicate glass sphere against poly(dimethyl siloxane) (PDMS). By applying a small oscillation to the tip during indentation, dynamic stiffness vs load data were also obtained for frequencies between 25 and 160 Hz. Direct curve fitting as well as simplified 2- and 3-point analysis methods were used to compare modulus values obtained from load-displacement and stiffness-load data. Fit methods not requiring determination of the initial point of tip–sample contact (“zero” displacement) provided modulus values closest to those obtained by direct curve fitting. The dynamic stiffness-load data revealed a frequency dependent modulus; load-displacement measurements obtained simultaneously were consistent with the relaxed, or low-frequency, modulus of the PDMS sample. These experiments demonstrate that both the frequency dependent and relaxed modulus can be obtained from a single experiment.

Control of frequency chirp in nanosecond-pulsed laser spectroscopy 1 Optical-heterodyne chirp analysis techniques

We evaluate ways to analyze optical-heterodyne measurements of frequency chirp in pulsed, single-longitudinal-mode output from lasers (or other coherent light sources) that operate on nanosecond time scales. The instantaneous frequency is extracted from the beat signal generated between a continuous-wave reference beam and the output of the pulsed source. Three analysis techniques are tested: Fourier-transform, direct curve fitting, and electronic mixing. We use synthetic beat waveforms based on actual experimental parameters to evaluate the three methods and apply these chirp-measurement techniques to an injection-seeded optical parametric oscillator system.

The Effect of Crack-Tip Interactions on the Curve-Fitting of Isopachics

Recent work by the authors has allowed the estimation of crack-tip SIFs by direct curvefitting of a cardioid form to measured isopachics from thermoelastic stress analysis. However, some of the curve-fits indicated that the cardioid form was inappropriate for the base model. One of the possible explanations for this is that the cardioid form is only suitable for an isolated crack-tip stress field. In the experimental data for the previous studies, a crack was placed centrally in a plate and there will therefore have been two (potentially) interacting crack-tips involved. The object of the current paper is to determine numerically, the stress field for such a crack system and to quantify the effect of any interactions on the curve-fitting procedure.

Determination of the Topological Shape of Integral Membrane Protein Light-Harvesting Complex LH2 from Photosynthetic Bacteria in the Detergent Solution by Small-Angle X-Ray Scattering

The topological shape of the integral membrane protein light-harvesting complex LH2 from photosynthetic bacteria Rhodobacter spheroides 2.4.1 in detergent solution has been determined from synchrotron small-angle X-ray scattering data using direct curve-fitting by the ellipsoid, ab initio shape determination methods of simulated annealing algorithm and multipole expansion, respectively. The results indicate that the LH2 protein in aqueous solution is encapsulated by a monolayered detergent shell. The detergent-stabilized structure has the shape of an oblate plate, with a thickness of 40 Å, a long axis of 110 Å, and a short axis of 85 Å. After correction for the detergent shell, the shape of the LH2 core is also an oblate plate with a height of 40 Å, a long axis of 80 Å, and a short axis of 55 Å. In contrast to the cylindrical crystal structure with a height of 40 Å and a diameter of 68 Å, the molecular shape of the LH2 complex in detergent solution clearly deviates from the ringlike crystal structure, with an eccentricity found to be 0.59—consistent with the result of single molecular spectroscopy study of the isolated single LH2 molecules.

Kinetic analysis of immunointeractions with covalently immobilized fatty acid-binding protein using a grating coupler sensor

Application of a grating coupler sensor (GCS) to the real time investigation of the interaction kinetics of covalently immobilized recombinant bovine heart-type fatty acid-binding protein (H-FABP) and corresponding antibody is described. The immobilization of the antigen is performed by activating the matrix hydroxyl groups with p-toluenesulfonyl chloride (TSC) and afterwards coupling the protein by reaction with its nucleophilic aminogroups. Covalent coupling via TSC permits reproducible measurements of immunointeractions on the same grating coupler sensor chip and complete regeneration after each binding cycle with glycine-hydrochloride. We demonstrate the analysis of binding data obtained on a GCS by linearization as well as direct curve fitting using the integrated rate equation for the determination of apparent rate and affinity constants. With both analysis methods we studied H-FABP/monoclonal anti-H-FABP-antibody interactions and obtained an average apparent association rate constant k a=4.2×10 3 M −1 s −1, a dissociation rate constant of k d=1.3×10 −4 s −1 and an equilibrium constant of K D=3×10 −8 M.

Noninvasive assessment of the ventricular relaxation time constant (tau) in humans by Doppler echocardiography.

The time constant of ventricular relaxation (tau) is a quantitative measure of diastolic performance requiring intraventricular pressure recording. This study validates in humans an equation relating tau to left ventricular pressure at peak -dP/dt (P0), pressure at mitral valve opening (PMV), and isovolumic relaxation time (IVRTinv). The clinically obtainable parameters peak systolic blood pressure (Ps), mean left atrial pressure (PLA), and Doppler-derived IVRT (IVRTDopp) are then substituted into this equation to obtain tau Dopp noninvasively. High-fidelity left atrial and left ventricular pressure recordings with simultaneous Doppler by transesophageal echocardiography were obtained from 11 patients during cardiac surgery. Direct curve fitting to the left ventricular pressure trace by Levenberg-Marquardt regression assuming a zero asymptote generated tau LM, the "gold standard" against which tau calc (IVRT inv/[ln(P0)-ln(PMV)]) and tau Dopp [IVRTDopp/[ln(Ps)-ln(PLA)]] were compared. For 123 cycles analyzed in 18 hemodynamic states, mean tau LM was 53.8 +/- 12.9 ms. tau calc (51.5 +/- 11 ms) correlated closely with this standard (r = .87, SEE = 5.5 ms). Noninvasive tau Dopp (43.8 +/- 11 ms) underestimated tau LM but exhibited close linear correlation (n = 88, r = .75, SEE = 7.5 ms). Substituting PLA = 10 mm Hg into the equation yielded tau 10 (48.7 +/- 15 ms), which also closely correlated with the standard (r = .62, SEE = 11.6 ms). The previously obtained analytical expression relating IVRT, invasive pressures, and tau is valid in humans. Furthermore, a more clinically obtainable, noninvasive method of obtaining tau also closely predicts this important measure of diastolic function.

Computerized curve fitting in the analysis of hydrogen gas clearance curves.

Hydrogen gas clearance curves obtained from the rat gastric corpus were digitized into a computer and then analyzed by three methods: 1) linear regression of log-transformed data, 2) direct curve fitting with a modified Gauss-Newton nonlinear regression algorithm, and 3) Zierler's height-over-area algorithm. For linear regression of log-transformed data, if the initial base-line estimate was inaccurate or normal amounts of experimental noise were present, the log-transformed data was skewed, leading to deviation of the regression line and incorrect estimation of blood flow. By utilization of the direct-fit routine, the initial estimate of the parameters or experimental noise had little influence on the blood flow determination because of iterative improvement of the parameters. In a study of isoproterenol-stimulated gastric blood flow, Zierler's algorithm underestimated the blood flow estimate. We conclude that analysis of hydrogen gas clearance curves by linear regression of log-transformed data or by Zierler's algorithm may potentially introduce errors in blood flow estimates that may be avoided by analysis with a direct-fitting, nonlinear regression algorithm.

Microcomputers in enzymology. A versatile BASIC computer program for analyzing kinetic data.

Direct curve-fitting is uncontested as the method of choice for evaluating kinetic experiments. If carried out by computer, the numerical solution of such problems is superior to customary graphical procedures in any respect. However, most programs available to date, cannot be executed by small systems. We now describe a BASIC program for desk-top microcomputers that performs linear and non-linear regression analysis of kinetic data. It may be directly applied to a number of problems common in enzyme kinetics, and is easily modified to handle further ones. The performance of the program is illustrated by some typical applications; in addition, fundamental statistical methods are discussed that allow a critical examination of the results obtained.

A method for the deductive and unique determination of the values of three parameters involved in fractional functions applicable to relaxation kinetics.

A novel method is proposed to determine deductively and uniquely the values of three parameters, a, b, and c in a fractional function of the form, y=a+bx/(c+x) where x and y are experimentally obtainable variables. This type of equation is frequently encountered in chemistry and biochemistry involving relaxation kinetics. The method of least squares with the Taylor expansion is employed for direct curve fitting of observed data to the fractional function. Approximate values of the parameters, which are always necessary prior to commending the above procedure, can be obtained by the method of rearrangement after canceling the denominator of fractional functions. This procedure is very simple, but very effective for estimating provisional values of the parameters. Deductive and unique determination of the parameters involved in the fractional function shown above can be accomplished for the first time by the combination of these two procedures. This method is extended to include the analysis of relaxation kinetic data such as those of temperature-jump method where the determination of equilibrium concentrations of reactants in addition to the three parameters is also necessary.

Uniaxial loading of orthotropic materials.

A method is presented for correlation of elasticity measurements made in variously oriented tensile tests of anisotropic materials. Linear relationships are established between each measured quantity and a trigonometric function of the orientation. A set of test data for carbon phenolic, exhibiting typically large scatter which precludes direct curve fitting, is analyzed and it is shown that the three measurements made in each test are compatible with one set of material properties. The results show that carbon phenolic (a laminated-cloth composite) is orthotropic (nine constants), the properties varying with direction in the plane of the cloth.