Mathematical Preliminaries

Arfken, George B.

doi:10.1016/b978-0-12-384654-9.00001-3

Cited by 673 publications

(1,050 citation statements)

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“…The forward model consists of an empirical telluric transmission spectrum T λ (Livingston & Wallace 1991), where λ is the wavelength measured at rest and in vacuum; a measured isotopologue methane gas cell spectrum G λ (Plavchan et al 2013) that was obtained from the NASA Jet Propulsion Laboratory (JPL) and is corrected using high-S/N observations of A-type telluric standards; a line-spread function (LSF) L that models broadening and distortions in the spectral line profiledue to both instrumental and atmospheric effects and that is represented by a weighted sum of the first five terms of the Hermite function (i.e., a normal distribution multiplied by Hermite polynomials; see Arfken et al 2012) where the weights are free parameters; a quadratic curve B λ that models the instrumental blaze function and variations in the NIR sky background; and an instrumental fringing term f λ that is represented by a multiplicative sinusoid function. The forward model F λ is then given by…”

Section: Radial Velocity Extractionmentioning

confidence: 99%

A High-Precision Near-Infrared Survey for Radial Velocity Variable Low-Mass Stars Using Cshell and a Methane Gas Cell

Gagné

Plavchan

Gao

et al. 2016

ApJ

233

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We present the results of a precise near-infrared (NIR) radial velocity (RV) survey of 32 low-mass stars with spectral types K2-M4 using CSHELL at the NASA InfraRed Telescope Facility in the K band with an isotopologue methane gas cell to achieve wavelength calibration and a novel, iterative RV extraction method. We surveyed 14 members of young (≈25-150 Myr) moving groups, the young field star εEridani, and 18 nearby (<25 pc) low-mass stars and achieved typical single-measurement precisions of 8-15 m s −1 with a long-term stability of 15-50 m s −1 over longer baselines. We obtain the best NIR RV constraints to date on 27 targets in our sample, 19 of which were never followed by high-precision RV surveys. Our results indicate that very active stars can display long-term RV variations as low as ∼25-50 m s −1 at ≈2.3125 μm, thus constraining the effect of jitter at these wavelengths. We provide the first multiwavelength confirmation of GJ876bc and independently retrieve orbital parameters consistent with previous studies. We recovered RV variabilities for HD160934AB and GJ725AB that are consistent with their known binary orbits, and nine other targets are candidate RV variables with a statistical significance of 3σ-5σ. Our method, combined with the new iSHELL spectrograph, will yield long-term RV precisions of 5 m s −1 in the NIR, which will allow the detection of super-Earths near the habitable zone of mid-M dwarfs.

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Section: Radial Velocity Extractionmentioning

confidence: 99%

A High-Precision Near-Infrared Survey for Radial Velocity Variable Low-Mass Stars Using Cshell and a Methane Gas Cell

Gagné

Plavchan

Gao

et al. 2016

ApJ

233

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“…where and γ are Euler's complete and incomplete Gamma functions, [61] respectively, the values of which are computed using the GNU Scientific Library. [62] In DFT calculations, the elements of the XC potential matrix K DFT need to be integrated numerically.…”

Section: Formation Of Matricesmentioning

confidence: 99%

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

et al. 2012

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ERKALE is a novel software program for computing X-ray properties, such as ground-state electron momentum densities, Compton profiles, and core and valence electron excitation spectra of atoms and molecules. The program operates at Hartree-Fock or density-functional level of theory and supports Gaussian basis sets of arbitrary angular momentum and a wide variety of exchange-correlation functionals. ERKALE includes modern convergence accelerators such as Broyden and ADIIS and it is suitable for general use, as calculations with thousands of basis functions can routinely be performed on desktop computers. Furthermore, ERKALE is written in an object oriented manner, making the code easy to understand and to extend to new properties while being ideal also for teaching purposes.

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“…The ordinary differential equations of static equilibrium are solved by using a perturbation technique. While the literature offers several methods, the Frobenius method (Arfken et al, 2000) was selected in this paper.…”

Section: Finite Element Discretizationmentioning

confidence: 99%

Time Domain Modeling and Simulation of Nonlinear Slender Viscoelastic Beams Associating Cosserat Theory and a Fractional Derivative Model

Borges

Faria

et al. 2017

Lat. Am. j. solids struct.

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A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.

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Mathematical Preliminaries

Cited by 673 publications

References 0 publications

A High-Precision Near-Infrared Survey for Radial Velocity Variable Low-Mass Stars Using Cshell and a Methane Gas Cell

A High-Precision Near-Infrared Survey for Radial Velocity Variable Low-Mass Stars Using Cshell and a Methane Gas Cell

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

Time Domain Modeling and Simulation of Nonlinear Slender Viscoelastic Beams Associating Cosserat Theory and a Fractional Derivative Model

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