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STUDY OF PI+ PI- SCATTERING IN PI- P ---> PI+ PI- X0 VIA A CHEW-LOW EXTRAPOLATION
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A Practical Approach To Pole Extrapolation
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Timing Discriminator Uses Leading-Edge Extrapolation
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Correct Analytic Extrapolations to Small w^2 and t I: the pi-N System
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Correct ANalytic Extrapolations to Small w^2 and t II: the pi pi System
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Methods of Extrapolating the T-Expansion Series
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Onset conditions of helical cores in tokamaks for extrapolation to ITER
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Discrete-Direct Calibration Real Space Validation and Predictor-Corrector Extrapolation.
Abstract not provided.
DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation.
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An experimental and analytical study on the development of extrapolation method for the creep-fatigue life of Alloy 617 to low strain ranges and long hold times at 950°C
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Mechanistic modeling of creep and aging for time extrapolation in LPBF 316 SS
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Influence of Suction Conditions and Refrigerant Fluid on Scroll Compressor Mass Flow Rate and Extrapolation Strategies
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Semiempirical Theories of the Affinities of Negative Atomic Ions
The determination of the electron affinities of negative atomic ions by means of direct experimental investigation is limited. To supplement the meager experimental results, several semiempirical theories have been advanced. One commonly used technique involves extrapolating the electron affinities along the isoelectronic sequences, The most recent of these extrapolations Is studied by extending the method to Include one more member of the isoelectronic sequence, When the results show that this extension does not increase the accuracy of the calculations, several possible explanations for this situation are explored. A different approach to the problem is suggested by the regularities appearing in the electron affinities. Noting that the regular linear pattern that exists for the ionization potentials of the p electrons as a function of Z, repeats itself for different degrees of ionization q, the slopes and intercepts of these curves are extrapolated to the case of the negative Ion. The method is placed on a theoretical basis by calculating the Slater parameters as functions of q and n, the number of equivalent p-electrons. These functions are no more than quadratic in q and n. The electron affinities are calculated by extending the linear relations that exist for the neutral atoms and positive ions to the negative ions. The extrapolated. slopes are apparently correct, but the intercepts must be slightly altered to agree with experiment. For this purpose one or two experimental affinities (depending on the extrapolation method) are used in each of the two short periods. The two extrapolation methods used are: (A) an isoelectronic sequence extrapolation of the linear pattern as such; (B) the same extrapolation of a linearization of this pattern (configuration centers) combined with an extrapolation of the other terms of the ground configurations. The latter method Is preferable, since it requires only experimental point for each period. The results agree within experimental error with all data, except with the most recent value of C, which lies 10% lower.
Proton radius from electron scattering data
Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle. Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. Methods: We make use of stepwise regression techniques using the F-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. Results: Starting with the precision, low four-momentum transfer (Q 2 ) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the F-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on GE from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-Q 2 data on G E to select functions which extrapolate to high Q 2 , we find that a Pad´e (N = M = 1) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, G E (Q 2 ) = (1 + Q 2 /0.66 GeV 2 ) -2 . Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extreme low-Q 2 data or by use of the Pad´e approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering result and the muonic hydrogen result are consistent. Lastly, it is the atomic hydrogen results that are the outliers.
Pressure effects on the relaxation of an excited nitromethane molecule in an argon bath
Classical molecular dynamics simulations were performed to study the relaxation of nitromethane in an Ar bath (of 1000 atoms) at 300 K and pressures 10, 50, 75, 100, 125, 150, 300, and 400 atm. The molecule was instantaneously excited by statistically distributing 50 kcal/mol among the internal degrees of freedom. At each pressure, 1000 trajectories were integrated for 1000 ps, except for 10 atm, for which the integration time was 5000 ps. The computed ensemble-averaged rotational energy decay is ∼100 times faster than the vibrational energy decay. Both rotational and vibrational decay curves can be satisfactorily fit with the Lendvay-Schatz function, which involves two parameters: one for the initial rate and one for the curvature of the decay curve. The decay curves for all pressures exhibit positive curvature implying the rate slows as the molecule loses energy. The initial rotational relaxation rate is directly proportional to density over the interval of simulated densities, but the initial vibrational relaxation rate decreases with increasing density relative to the extrapolation of the limiting low-pressure proportionality to density. The initial vibrational relaxation rate and curvature are fit as functions of density. For the initial vibrational relaxation rate, the functional form of the fit arises from a combinatorial model for the frequency of nitromethane “simultaneously” colliding with multiple Ar atoms. Roll-off of the initial rate from its low-density extrapolation occurs because the cross section for collision events with L Ar atoms increases with L more slowly than L times the cross section for collision events with one Ar atom. The resulting density-dependent functions of the initial rate and curvature represent, reasonably well, all the vibrational decay curves except at the lowest density for which the functions overestimate the rate of decay. The decay over all gas phase densities is predicted by extrapolating the fits to condensed-phase densities.
The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study
The metastable ring structure of the ozone 1{sup 1}A{sub 1} ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two {sup 1}A{sub 1} states. In the present work, valence correlated energies of the 1{sup 1}A{sub 1} state and the 2{sup 1}A{sub 1} state were calculated at the 1{sup 1}A{sub 1} open minimum, the 1{sup 1}A{sub 1} ring minimum, the transition state between these two minima, the minimum of the 2{sup 1}A{sub 1} state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 1{sup 1}A{sub 1} state, the present calculations yield the estimates of (ring minimum—open minimum) ∼45–50 mh and (transition state—open minimum) ∼85–90 mh. For the (2{sup 1}A{sub 1}–{sup 1}A{sub 1}) excitation energy, the estimate of ∼130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (2{sup 1}A{sub 1}–{sup 1}A{sub 1}) is found to be between 1 and 10 mh. The geometry of the transition state on the 1{sup 1}A{sub 1} surface and that of the minimum on the 2{sup 1}A{sub 1} surface nearly coincide. More accurate predictions of the energy differences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.
Lab-Scale, Closed-Loop Experimental Characterization, Model Refinement, and Validation of a Hydrokinetic Energy-Harvesting Ocean Kite
This paper presents a study wherein we experimentally characterize the dynamics and control system of a lab-scale ocean kite, and then refine, validate, and extrapolate this model for use in a full-scale system. Ocean kite systems, which harvest tidal and ocean current resources through high-efficiency cross-current motion, enable energy extraction with an order of magnitude less material (and cost) than stationary systems with the same rated power output. However, an ocean kite represents a nascent technology that is characterized by relatively complex dynamics and requires sophisticated control algorithms. In order to characterize the dynamics and control of ocean kite systems rapidly, at a relatively low cost, the authors have developed a lab-scale, closed-loop prototyping environment for characterizing tethered systems, whereby 3D printed systems are tethered and flown in a water channel environment. While this system has been shown to be capable of yielding similar dynamic characteristics to some full-scale systems, there are also fundamental limitations to the geometric scales and flow speeds within the water channel environment, making many other real-world scenarios impossible to replicate from the standpoint of dynamic similarity. Here, to address these scenarios, we show how the lab-scale framework is used to refine and validate a scalable dynamic model of a tethered system, which can then be extrapolated to full-scale operation. In this work, we present an extensive case study of this model refinement, validation, and extrapolation on an ocean kite system intended for operation in the Gulf Stream or similar current environments.