Simple Correction Formula Research Articles

Quantitative characterization of crosstalk effects for friction force microscopy with scan-by-probe SPMs

If the photodetector and cantilever of an atomic force microscope (AFM) are not properly adjusted, crosstalk effects will appear. These effects disturb measurements of the absolute vertical and horizontal cantilever deflections, which are involved in friction force microscopy (FFM). A straightforward procedure is proposed to study quantitatively crosstalk effects observed in scan-by-probe SPMs. The advantage of this simple, fast, and accurate procedure is that no hardware change or upgrade is needed. The results indicate that crosstalk effects depend not only on the alignment of the detector but also on the cantilever properties, position, and detection conditions. The measurements may provide information on the origin of the crosstalk effect. After determination of its magnitude, simple correction formulas can be applied to correct the crosstalk effects and then the single-load wedge method, using a commercially available grating, can be employed for accurate calibration of the lateral force.

Unsteady-state lock-in thermography - Application to shunts in solar cells

This paper presents the fast implementation of Lock-in Thermography (LIT) before reaching steady-state conditions. The errors caused by the initial temperature drift are compensated by a simple correction formula based on the measurement of the temperature drift image. The effect of this correction has been studied on the in-phase, quadrature, amplitude and the phase signals of lock-in thermography. Simulations and experiments have been performed for this study while considering a specific application of LIT for the investigation of solar cells. This study shows that in our case the error caused by the temperature drift is basically a baseline shift in the in-phase and the quadrature signal, and does not significantly affect the relative shape and spatial resolution of these signals. However, for the amplitude and phase signal this correction is more significant and affects also the relative shape of the signals. Experimental results validate the correction method and its effectiveness in eliminating errors from LIT data measured before thermal equilibrium has been established.

Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.

Rotation–vibrational states of and the adiabatic approximation

We discuss recent progress in the calculation and identification of rotation-vibrational states of H3+ at intermediate energies up to 13,000 cm(-1). Our calculations are based on the potential energy surface of Cencek et al. which is of sub-microhartree accuracy. As this surface includes diagonal adiabatic and relativistic corrections to the fixed nuclei electronic energies, the remaining discrepancies between our calculated and experimental data should be due to the neglect of non-adiabatic coupling to excited electronic states in the calculations. To account for this, our calculated energy values were adjusted empirically by a simple correction formula. Based on our understanding of the adiabatic approximation, we suggest two new approaches to account for the off-diagonal adiabatic correction, which should work; however, they have not been tested yet for H3+. Theoretical predictions made for the above-barrier energy region of recent experimental interest are accurate to 0.35 cm(-1) or better.

Clinical Comparison of Contour and Applanation Tonometry and Their Relationship to Pachymetry

To compare intraocular pressure readings of recently introduced dynamic contour tonometry (DCT) with pneumatonometry (PTG) and Goldmann applanation tonometry (GAT) and to correlate central corneal thickness (CCT) with these readings. Prospective, cross-sectional observation and instrument validation study. We included 258 independent eyes with normal anterior segment examinations results, irrespective of glaucoma diagnosis or glaucoma suspect. After pachymetry, DCT, PTG, and GAT were performed in a randomized order. Intraocular pressures as measured by DCT, PTG, and GAT were compared with each other and with CCT. Eyes with thinner CCTs tended to yield lower intraocular pressure measurements by GAT. A significant correlation (Pearson product moment correlation, P<.001) between CCT and GAT was found with a regression of 0.25 mm Hg per 10 microm (R2 = 0.060). Variation of CCT had no significant effect on intraocular pressure measurements by PTG (P = .10; R2 = 0.01) and DCT (P = .80; R2<0.01). A piecewise regression model showed that GAT readings are not linearly correlated with CCT. Comparison of the slopes below and above 535 microm showed the highest significance (P<.001). Goldmann applanation tonometry readings are potentially influenced by CCT, whereas PTG and DCT seem to be less dependent on CCT. Correlation between CCT and GAT is not linear. A simple correction formula suggesting a linear relationship might not be correct.

Systematic errors in DFT calculations of haloalkane heats of formation.

The B3LYP and B3PW91 density functionals were employed with a large [BS1 = 6-311+G(3df,2p)] and small [BS2 = 6-311G(d,p)] basis set to compute enthalpies of formation (at optimized MP2/6-31G(d) geometries and with scaled HF/6-31G(d) frequencies) in the following series of haloalkanes: (1) the 15 fluoro-, chloro-, and chlorofluoromethanes, (2) the 18 fluorinated and chlorinated ethanes. Similar to earlier higher level calculations on haloalkanes, the computed enthalpies exhibited very large, systematic deviations from experiment. It was found that these errors could be largely eliminated using a very simple Bond Additivity Correction (BAC) formula, Delta(f)H degrees (BAC) = Delta(f)H degrees (calc) - n(CX). Delta(CX) [X = F, Cl], in which the BAC parameters, Delta(CF) and Delta(CCl) were determined by fitting the equation to experimental data on the four fluoroethanes and chloroethanes, respectively. The resultant BAC corrected enthalpies of formation are in excellent agreement with experiment, with RMS deviations in the same range as quoted RMS errors in measured enthalpies. Therefore, this simple BAC procedure may be utilized to provide reliable semiquantitative estimates of enthalpies of formation in larger haloalkanes, for which higher level ab initio calculations are not feasible.

Improved triangle method for two-dimensional Brillouin zone integrations to determine physical properties

An improvement of the linear triangle method for two-dimensional Brillouin zone integrations is presented. A simple correction formula for this improvement is given and applied to several systems --- a three layer Fe(001) slab, a three layer slab of Si(001), and three layers of ${\mathrm{MgB}}_{2}(001)$---to investigate its validity and efficiency. This ``improved triangle method'' is seen to give better convergence behavior of the total energy, atomic force, and magnetic moment with respect to the number of k-points than do the normal triangle method and the special k-point method of Monkhorst and Pack.

INSIGHT INTO THE SENSITIVITY TO AXIAL COMPRESSIVE LOAD OF THE NATURAL FREQUENCIES OF STRUCTURES WHICH INCLUDE SHEAR DEFORMATION

The effect is considered of transverse shear deformation and rotatory inertia on the natural frequencies of loaded structures. The paper covers the many structures for which there is a linear or nearly linear relationship between the square of the natural frequencies and load factor regardless of whether or not shear deformation is included. Equations are derived and evaluated for predicting and/or correcting the errors caused by neglecting the shear deformation of such structures when calculating their natural frequencies under load. The equations are shown to give good predictions of the exact results for axially compressed prismatic plate assemblies, including two sandwich panels with low core density and shear stiffnesses. The equation, their results and the stiffened panel examples are presented so as to give qualitative insight and numerical guidance both on the consequences of neglecting shear deformation (and rotatory inertia) and on the accuracy of the simple correction formulas presented. In particular, they show that the percentage errors caused by neglecting shear deformation when calculating natural frequencies of loaded structures will be greater—often very much greater — than the percentage errors in unloaded natural frequencies or buckling loads caused by neglecting shear deformation.

Strouhal numbers of inclined flat plates

Abstract The shedding frequencies and associated Strouhal numbers of vortices behind a flat plate with beveled sharp edges have been studied experimentally at angles of attack α = 0°–90° and Reynolds numbers in the range 3.5 × 10 3 – 3.2 × 10 4 . The Reynolds number has no discernible effects on the relation between the Strouhal number and the angle of attack in the range α = 10°–90° with fully separated flow. As the plate incidence is gradually reducing in this range, the modified Strouhal number based on the effective plate width normal to the freestream is found to remain at a nearly constant level until the bevel angle is taken into effect, which causes a shift of the separation point from the front edge to the rear edge, resulting in a jump of the modified Strouhal number to another higher level of approximately constant value. Accordingly, by the use of a correction factor to account for the effect of bevel angle, a universal Strouhal number of 0.160 ± 0.003 can be obtained for α = 10°–90°. It is observed that at low angles of attack α = 0°–5°, the influence of Reynolds number becomes significant due to the occurrence of flow reattachment and is rather complex for plates with different bevel angles. It is also observed that the effect of blockage on Strouhal number measurements can be corrected by employing a simple correction formula.

Evaluating the effect of optimized cutoff values in the assessment of prognostic factors

In clinical research the assessment of prognostic factors is often based on the division of the patients into two groups: a high risk and a low risk group. A common strategy is to select an optimal cutoff value in the prognostic factor which defines the two groups. The effect is measured as difference between the groups. We provide simple correction formulae for the correct P-value of the selected two-sample statistic. Moreover, we discuss consequences of that optimization on both the estimator of the cutoff point and the estimated effect. An approximate confidence region for both parameters is given. The small sample behaviour is analysed by means of a Monte-Carlo study. The optimization of the cutoff value results in an overestimation of the difference between the prognostic groups. Extensions of our discussion to censored data are given, too. Finally, we apply our approach to an example from oncology.

Improved tetrahedron method for Brillouin-zone integrations.

Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same number of k points. (2) A simple correction formula goes beyond the linear approximation of matrix elements within the tetrahedra and also improves the results for metals significantly. For a required accuracy this reduces the number of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration weights calculated using the tetrahedron method once for a given band structure. This allows an efficient use of the tetrahedron method also in plane-wave-based electronic-structure methods.

New technique for finite difference analysis of optical waveguide problems

AbstractThe method of effective penetration depth is used to produce a novel scalar or polarized finite difference approach for the solution of optical rib waveguide field problems. The new method is quicker than previous finite difference approaches and requires less computer memory. Propagation constant values are presented for a range of semiconductor rib waveguides and are found to be indistinguishable from benchmark results produced using earlier methods of analysis. A simple polarization correction formula recently derived is confirmed by utilizing the good accuracy of these results. This enables discussion of the relationship between quasi‐TE, quasi‐TM and scalar modes, and a further substantial reduction of the cpu time.

Determination of the compensation band due to birefringence with dispersion and large phase differences

The simple measurement of birefringence by means of a tilting compensator becomes difficult and unreliable when large phase differences must be compensated in samples in which dispersion of birefringence differs from that of the compensator. The problem is treated experimentally and theoretically. The result is a simple correction formula with only one parameter. A method to obtain this parameter is presented. Measurements on polycarbonate, polyethylene and polyurethane support the assumptions of the theoretical calculations.

Rectangular waveguide characterization for reflectometry

Simple first-order correction formulas are developed to describe the combined effect of wall distortion and wall loss on the propagation constant and normalized impedance of nominally rectangular waveguides intended for use in reflectometry. A simple method of measuring the propagation constant at a single frequency is described, resulting in practical advantages in characterization of the waveguide at other frequencies. >

Temperature Effects on Volume Measurements

Volume measuring systems for triaxial tests are susceptible to changes in ambient temperature, and the volume change due to temperature can represent 10% or more of the measured value, depending on the magnitude of the total volume change. The automatic volume change logging system showed a clear dependence on temperature, a dependence related to the thermal expansion of the water in the system, the apparatus itself and any entrapped air. By using regression analysis on data accumulated over several tests, a simple temperature correction formula for volume change is derived.

Measurement of permittivity by means of an open resonator. I. Theoretical

The objective of this paper is to provide a reliable theoretical foundation for the open-resonator method of measuring permittivity and loss-tangent of dielectric materials. From an exact solution of Maxwell’s equations obtained by means of the complex-source-point method, simplified formulae for the six Cartesian components of the electromagnetic field are obtained. These are then used in a variational formula to obtain an accurate formula for the resonant frequency of an open resonator with spherical mirrors (of equal radius of curvature) having a parallel-plane slab of dielectric material located centrally between the two mirrors. It is assumed that the mirrors are sufficiently large for diffraction effects to be negligible. In the following companion paper II, experimental results are presented which verify the accuracy, within the usual limits of practical measurement, of the simple correction formulae deduced here.

The effect of the epithermal neutron flux distribution on the accuracy of absolute and comparator standardization methods in (n, γ) activation analysis

A description is given of the systematic errors which can be introduced when applying absolute or comparator standardization techniques to RNAA or ENAA at irradiation sites with a deviating 1/E1+α epithermal neutron flux distribution. A simple correction formula for a≠0 is presented and a survey is given of the present state-of-the-art for experimentala-monitoring and for the calculation or experimental determination of the effective resonance energy Ēr. Extensive error calculation leads to the conclusion that, with careful selection ofa monitors and of the nuclear data involved, the rather large errors (∼10% or more) are reduced, after correction fora, to uncertainties of about 2%.

Improved natural frequencies for plates with a free edge

A simple correction formula is developed for the square of natural frequencies of plates with a free edge. The theory is applied to torsional vibrations of a long plate strip and to vibrations of a circular plate with a free edge and a number of nodal diameters. The paper concludes with the remark that the theory may be extended mutatis mutandis to vibrations of shells with a free edge.

Dependence of Bandshape and Depolarization Ratio on Slitwidth

A simple correction formula is presented for obtaining true Lorentzian half-band widths from convolutions with triangular slits. The correction is shown to be applicable to a number of other convolutions. Also, the dependence of the depolarization ratio in terms of peak heights on slitwidth is investigated.

A direct method for the calculation of the edge capacitance of thick electrodes

A new method is presented for the evaluation of the edge-capacitance correction for electrodes of finite thickness. The corrections are divided into three separate components: electrode thickness, the lower edge of the electrodes, and the back of the electrodes. Simple correction formulae are derived for the first two components and a set of curves is provided which enables the direct evaluation of the third component from an equally simple formula. Numerical results show excellent agreement with those obtained by more tedious graphical methods.