Additional Correction Term Research Articles

Correction of systematic effects in digitizing oscilloscopes

This paper presents a procedure to improve the accuracy of a digital sampling oscilloscope in the acquisition of complex waveforms. The approach assumes knowledge of the spectral composition of the analyzed waveform, which must be within the oscilloscope bandwidth. Using suitable calibration data, additive correction terms are calculated which compensate for vertical gain inaccuracies due to in-band variations of the oscilloscope frequency response. A criterion is also given to determine when the correction uncertainty is acceptable.

EXPERIMENTS WITH TWO DIFFERENT APPROACHES TO GRIDDING TERRESTRIAL GRAVITY ANOMALIES AND THEIR EFFECT ON REGIONAL GEOID COMPUTATION

This paper compares the gridding of two types of terrestrial gravity anomaly prior to the computation of regional gravimetric geoid models over Australia. The aim is to investigate the effects of high-frequency components (by way of the terrain correction) on the resulting grid of mean gravity anomalies, and hence the geoid. The gravity anomaly types investigated comprise simple Bouguer anomalies and refined Bouguer anomalies, both computed using a constant topographic mass density. Irrespective of which anomaly type is used for gridding, the relevant additional correction terms are applied to yield an approximation of the mean Helmert anomaly. Regional gravimetric geoid models are then computed over Australia and compared with one another and with GPS-levelling points on the Australian Height Datum. This shows that the application of terrain corrections before or after gravity gridding has only a relatively small effect on the computed geoid in Australia.

EXPERIMENTS WITH TWO DIFFERENT APPROACHES TO GRIDDING TERRESTRIAL GRAVITY ANOMALIES AND THEIR EFFECT ON REGIONAL GEOID COMPUTATION

This paper compares the gridding of two types of terrestrial gravity anomaly prior to the computation of regional gravimetric geoid models over Australia. The aim is to investigate the effects of high-frequency components (by way of the terrain correction) on the resulting grid of mean gravity anomalies, and hence the geoid. The gravity anomaly types investigated comprise simple Bouguer anomalies and refined Bouguer anomalies, both computed using a constant topographic mass density. Irrespective of which anomaly type is used for gridding, the relevant additional correction terms are applied to yield an approximation of the mean Helmert anomaly. Regional gravimetric geoid models are then computed over Australia and compared with one another and with GPS-levelling points on the Australian Height Datum. This shows that the application of terrain corrections before or after gravity gridding has only a relatively small effect on the computed geoid in Australia.

東北日本の異常震域に対応するための距離減衰式の補正係数

東北日本の異常震域に対応するための距離減衰式の補正係数

Rotamer-Specific Potentials of Mean Force for Residue Pair Interactions

We present an approach for the development of knowledge-based mean-force potentials for representing residue−residue interactions in proteins at the amino acid level of resolution which take into account the rotamer states of the residues. The rotamer-specific potentials which consist of an additional correction term to the current database-derived statistical potentials are expressed in terms of distance-dependent mean force potentials (MFP). To describe the relative geometry of two residues we used a set of six distances between different pairs of atoms. The distant-dependent MFPs are calculated from computer simulations of each pair of amino acids at the atomic level using the weighted-histogram analysis method. The umbrella sampling for each of 52003 different rotamer pairs was performed with a force-bias Monte Carlo algorithm using molecular mechanics potentials with statistically derived restraint terms. Our simulations show that the MFPs are very sensitive to the rotamer states of the amino acid residues. Preliminary tests of the potential's performance show that it can reproduce side-chain packing with reasonable accuracy.

Multigrid high-order mesh refinement techniques for composite grid electrostatics calculations

A new method for performing high-order mesh-refinement multigrid computations in real space is presented. The method allows for accurate linear scaling electrostatics calculations over composite domains with local nested fine patches. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of refinement patches of increasing resolution. Conservation forms are generated on coarse scales by additional defect correction terms that counter the local excess fluxes at the boundaries. Formulas are given for arbitrary order, extending the existing technique of Bai and Brandt. Test calculations are presented for a singular source in three dimensions that illustrate the multigrid convergence properties, numerical accuracy, and correct order of the approach. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1731–1739, 1999

High-Resolution Modeling of the Advance of the Younger Dryas Ice Sheet and Its Climate in Scotland

Ice-sheet modeling tightly constrained by empirical studies provides an effective framework to reconstruct past climatic and environmental conditions. Scotland was severely affected by the abrupt climate change associated with the Younger Dryas Stade, during which an extensive ice sheet formed across the west highlands after a period of ice-free conditions. Here, a quasi-three-dimensional, time-dependent ice flow/mass-balance model is developed and applied to Scotland at 1 km resolution. The flow model is based on the driving stress approximation with an additional longitudinal correction term, essential at this scale of operation. Surface mass balance is driven by temperature and precipitation changes and further mass wastage is achieved through an empirically defined calving term. The ice dynamics and mass-balance components are coupled through the equation for mass continuity, which is integrated through time over a finite-difference grid which yields the geometric evolution of the ice sheet. Initial experiments reveal the model to be relatively insensitive to internal parameters but highly sensitive to mass balance. Furthermore, these experiments indicate that Scotland is readily susceptible to glaciation with large glaciers building up on the flanks of Ben Nevis after a temperature depression of 2.5°C, under present-day precipitation. The Younger Dryas is modeled using a GRIP temperature series locally adjusted for amplitude and a systematic series of runs enables the isolation of the climate which best matches mapped ice limits. This “optimum-fit” configuration requires an annual temperature cooling of 8°C and the introduction of substantial west–east and south–north precipitation gradients of 40 and 50%, respectively, to the present-day regime. Under these conditions, a series of substantial independent regional ice centers develop in agreement with trimline studies and after 550 years the modeled ice sheet closely resembles the maximum limits as indicated by field mapping. However, modeled ice continues to expand beyond 550 yr, in conflict with the mapped ice limits which suggest a prolonged period of stability. This discrepancy may be explained by the onset of extreme aridity ca. 400 yr into the Stade associated with a southern migration of the Polar Front, leading to a reduction in atmospheric circulation which effectively starved the ice sheet of its moisture source, preventing further expansion. Introduction of an additional 20% reduction in precipitation to the “optimum-fit” regime after 350 yr brings the modeled ice sheet to equilibrium, substantiating this conclusion.

The transformative complex absorbing potential method: a bridge between complex absorbing potentials and smooth exterior scaling

The derivation of the transformative complex absorbing potential (TCAP) method and its performance are discussed. This approach was developed in a previous paper (1995 J. Phys. B: At. Mol. Opt. Phys. 28 1475) and illustrates the relation between complex absorbing potentials (CAPs) and the smooth exterior scaling (SES) method. Starting from an energy-dependent CAP one arrives at an SES-like Hamiltonian via an elementary similarity transformation. Developing this idea further leads to the so-called TCAP equation. It differs from the SES Schrödinger equation in two respects. Firstly, the potential is not transformed and, secondly, an additional correction term appears. Neglecting this rather small term leads to a Hamilton operator that is easy to apply to time-dependent as well as time-independent problems. This Hamiltonian can be extended order by order ending up in the full SES Hamiltonian. By numerical application it is demonstrated that the TCAP approach is very efficient and can easily be generalized to the multi-dimensional case for which formulae are provided.

Anomalies in the Nuclear Dissociation Cross Sections of208Pbat 33 TeV

We have measured total nuclear disintegration cross sections for ${}^{208}\mathrm{Pb}$ ions at 33 TeV $(160\ensuremath{-}\mathrm{GeV}A)$ colliding with C, Si, Cu, Sn, and Pb. Using well established theory, we calculate the nuclear electromagnetic, electron electromagnetic, and the hadronic contributions and find that their sum underestimates the measured cross sections. An additive correction term linear in target ${Z}_{T}$ (i.e., ${120Z}_{T}\mathrm{mb}$) is necessary to bring agreement between theory and experiment. The source of this additional term is unknown.

AC transport with reservoirs of finite width

The linear response conductance coefficients are calculated in the scattering approach at finite frequency, damping and magnetic field for a microstructure in which the reservoirs are modeled as quantum wire leads of infinite length but finite width. Independent of frequency, inelastic scattering causes subbands with large group velocity to contribute more strongly to the conductance than channels of comparable transmission but slower propagation. At finite frequency and magnetic fields, additional correction terms appear. © 1997 Elsevier Science Ltd. All rights reserved.

Renormalization and chiral symmetry breaking in quenched QED in arbitrary covariant gauges.

We extend a previous Landau-gauge study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in strong-coupling, quenched QED_4 to arbitrary covariant gauges. We use the fermion-photon proper vertex proposed by Curtis and Pennington with an additional correction term included to compensate for the small gauge-dependence induced by the ultraviolet regulator. We discuss the chiral limit and the onset of dynamical chiral symmetry breaking in the presence of nonperturbative renormalization. We extract the critical coupling in several different gauges and find evidence of a small residual gauge-dependence in this quantity.

Relativistic self-interaction-free density-functional formalism.

We present a relativistic self-interaction-free density-functional formalism based on the local-density approximation with additional correction terms, and propose an algorithm for its numerical solution. The rigorous foundations of the scheme in density-functional threory and the resulting effective one-electron picture are discussed. Calculations for several atoms are shown as a practical example.

Nonlocal density functional calculation of gas phase heats of formation

AbstractA general procedure is presented for computing the gas phase heats of formation of a wide variety of organic compounds. ΔE for the formation of the molecule from its elements at 0 K is obtained from density functional calculations (Gaussian 92/DFT) for optimized geometries. This result is converted to ΔH at 298 K by assuming ideal behavior and adding the translational, rotational, and vibrational energies. Additive correction terms corresponding to the various coordination states of the carbons, nitrogens, and oxygens were developed using a database of 54 compounds. The experimental ΔH values of these compounds are then reproduced with an average absolute error of 3 kcal/mol and a standard deviation of 4 kcal/mol. For a group of 10 test cases that were not part of the database, the average absolute error is 3.5 kcal/mol and the standard deviation is 4.1 kcal/mol. © 1995 by John Wiley & Sons, Inc.

The Upward Bias in Measures of Information Derived from Limited Data Samples

Extracting information measures from limited experimental samples, such as those normally available when using data recorded in vivo from mammalian cortical neurons, is known to be plagued by a systematic error, which tends to bias the estimate upward. We calculate here the average of the bias, under certain conditions, as an asymptotic expansion in the inverse of the size of the data sample. The result agrees with numerical simulations, and is applicable, as an additive correction term, to measurements obtained under such conditions. Moreover, we discuss the implications for measurements obtained through other usual procedures.

Estimation of effective diffusion time in a rapid thermal diffusion using a solid diffusion source

Two-step rapid thermal diffusion (RTD) of phosphorus and boron using a solid diffusion source is described. From the application of the Boltzmann-Matano method to SIMS profiles of phosphorus and boron after RTD, it has been found that some additional correction terms to the effective diffusion time must be introduced. In the phosphorus diffusion case, the increment of the effective diffusion time due to the supersaturation of point defects during the cooling cycle is about 3 s. In the case of boron diffusion, the additional effective diffusion time is a strong function of diffusion temperature. This has been explained as the effect of initial growth of the boron-rich layer during the glass-transfer process. The introduction of additional correction terms to the effective diffusion time makes it possible to treat the RTD process in a similar manner to normal diffusion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Higer-Order Harmonics in Electromagnetic Scattering from a Nonlinear Anisotropic Cylinder

The general solution of the scattering of harmonic signals, by a medium which has nonlinear constitutive relations, contains higher harmonics. The scattering amplitude consists of the linear component and additional correction terms that depend on the amplitude of the incident wave. In this paper, we examine the effects of nonlinearities on the field components and on the radar cross section at the second and third harmonics.

Flory's equation of state for nonrandom polymer-solvent solutions: application of local compositions and the two-fluid theory of mixtures

A new expression is presented for the partition function of binary solutions containing a polymer. This leads to an equation of state for polymer solutions of Flory's type. This equation does not require an additional corrective term as in the previous publications. Theoretical expressions are derived for free energy, enthalpy, entropy, chemical potential and other partial molar quantities. The properties of five polymer-solvent systems are interpreted according to this theory

A new approximate expression for the response of a hot-wire anemometer

Bruun's (tabulated) universal function for the response of a hot-wire anemometer is examined in detail to see if the function has some unique relationship with King's law. As a result of the analysis, an approximate expression is derived and proposed for the response over a wide range of wind speeds. Although the expression is like King's law with an additional correction term and is thus quite simple in form, it agrees with Bruun's universal function (and also with the derivative, i.e. the velocity sensitivity) to within 3% over the range of wind speeds from 2 to 120 m/s. There is little doubt that the proposed response equation may serve as a helpful guide in calibrating a hot-wire probe, in constructing a simple linearizer circuit of high accuracy, and in linearization by means of a computer.

Characteristic functions and the aberrations of symmetric optical systems II Addition of aberrations

We describe a method for the calculation of the eikonal coefficients of a symmetric optical system composed of two symmetric subsystems. We consider coefficients of second to tenth order in the direction cosines. The system eikonal is seen to consist of an additive part and correction terms of sixth and higher order. We discuss the interpretation and the magnitude of the correction terms.

On the relativistic invariance of QED in the Coulomb gauge and field transformations

To establish the relativistic invariance of QED, the equal time commutators (T00(x), T00(x')), (T00(x), T0k(x')) and (T0k(x), T0l(x')) of the energy-momentum tensor density are explicitly worked out in the full theory by making use, in the process, of only the canonical commutation relations of the dynamical independent field components as obtained from the Coulomb gauge. In particular, the equal time commutator (T0k(x), T0l(x')) is shown to be modified (and explicitly worked out) from what one may expect naively with the additional correction term having just the right symmetry property to establish Lorentz covariance. Finally the infinitesimal Lorentz transformations of all the field components are worked out and the consistency of the Coulomb gauge in the new frame is verified.