Note on the determination of the best-fitting plane for a given set of directions

1961 ◽  
Vol 49 (1) ◽  
pp. 13-14 ◽  
Author(s):  
A. R. Ritsema ◽  
J. G. J. Scholte
Keyword(s):  
Best Fitting

Determination of the Interference Geometry Between Two Convex Objects

2006 ◽  
Author(s):  
Lianzhen Luo ◽  
Meyer Nahon
Keyword(s):  
Contact Force ◽  
Contact Area ◽  
Contact Dynamics ◽  
Continuous Contact ◽  
Application Point ◽  
Haptic Interactions ◽  
Fitting Method ◽  
Best Fitting ◽  
Arbitrary Objects

The determination of the interference geometry between two arbitrary objects is an essential problem encountered in the simulation of continuous contact dynamics and haptic interactions. In these applications, with known material properties, the interbody contact force is only a function of the interference geometry between two objects. Here a theoretical basis and algorithms for the calculation of the interference geometry, such as overlap region, contact area and normal, and interference volume, are presented. Two methods to obtain the contact area and normal are analyzed: an area-weighted method and a best-fitting method. The geometric properties of the area-weighted method are presented and the degenerate cases related to both methods are discussed. Methods to calculate the application point of an interbody contact force are discussed. Some numerical simulation results are presented based on the implementation of the geometric algorithms, which are verified by comparison with hand calculation. The continuity of contact normal and its application point are demonstrated for a case in which the contacting objects smoothly move with respect to each other in the simulation.

Least-squares Analysis of Fabric Data: A Note on Conical, Cylindroidal and Near–cylindroidal Folds

1971 ◽  
Vol 8 (6) ◽  
pp. 694-697 ◽  
Author(s):  
C. S. Venkitasubramanyan
Keyword(s):  
Least Squares ◽  
Stereographic Projection ◽  
Rotation Axis ◽  
Computational Procedure ◽  
Apical Angle ◽  
Small Circle ◽  
Best Fitting ◽  
Fabric Diagrams ◽  
The Mean

A cylinder and a plane may be considered as special limiting cases for a right circular cone as the semi-apical angle approaches 0° and 90° respectively (Loudon 1964, Kelley 1966). If these forms are viewed as surfaces generated by an array of lines in space, the rotation axis for the array (the axis of the "cone") can be determined from the orientations of the surface-generating lines by a single computational procedure, using least-squares criterion. The mean angle between the rotation axis and the surface-generating lines will be the semi-apical angle of the cone. However, if this method for determination of the semi-apical angle of the cone, and therefore the best-fitting small circle, is extended to fabric diagrams, in which an array of lines may only statistically describe a great circle or small circle on a stereographic projection, ambiguities arise in certain cases and the semi-apical angle obtained may not be the true semi-apical angle. The difficulty arises because the poles to foliation surfaces are arbitrarily assigned "senses".

scholarly journals Application of Numerical Analysis of the Shape of Electron Paramagnetic Resonance Spectra for Determination of the Number of Different Groups of Radicals in the Burn Wounds

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Paweł Olczyk ◽  
Katarzyna Komosinska-Vassev ◽  
Paweł Ramos ◽  
Łukasz Mencner ◽  
Krystyna Olczyk ◽  
...  
Keyword(s):  
Electron Paramagnetic Resonance ◽  
Repair Process ◽  
Spectral Shape ◽  
Dipolar Interactions ◽  
Epr Spectrum ◽  
Paramagnetic Resonance ◽  
Burn Wounds ◽  
Best Fitting ◽  
Electron Paramagnetic

Background. The evidence exists that radicals are crucial agents necessary for the wound regeneration helping to enhance the repair process. Materials and methods. The lineshape of the electron paramagnetic resonance (EPR) spectra of the burn wounds measured with the low microwave power (2.2 mW) was numerically analyzed. The experimental spectra were fitted by the sum of two and three lines. Results. The number of the lines in the EPR spectrum corresponded to the number of different groups of radicals in the natural samples after thermal treatment. The component lines were described by Gaussian and Lorentzian functions. The spectra of the burn wounds were superposition of three lines different in shape and in linewidths. The best fitting was obtained for the sum of broad Gaussian, broad Lorentzian, and narrow Lorentzian lines. Dipolar interactions between the unpaired electrons widened the broad Gaussian and broad Lorentzian lines. Radicals with the narrow Lorentzian lines existed mainly in the tested samples. Conclusions. The spectral shape analysis may be proposed as a useful method for determining the number of different groups of radicals in the burn wounds.

scholarly journals Star Formation in the Local Universe from the CALIFA sample: calibration and contribution of disks to the SFR density

2014 ◽  
Vol 10 (S309) ◽  
pp. 305-305
Author(s):  
Cristina Catalán-Torrecilla ◽  
Armando Gil de Paz ◽  
África Castillo-Morales ◽  
Jorge Iglesias-Páramo ◽  
Sebastián F. Sánchez ◽  
...  
Keyword(s):  
Star Formation ◽  
Formation Rate ◽  
Physical Property ◽  
Wide Field ◽  
Local Universe ◽  
Spatially Resolved ◽  
Best Fitting ◽  
Nearby Galaxies ◽  
First Time

AbstractThe study of the star formation rate (SFR) is crucial for understanding the birth and evolution of the galaxies (Kennicutt 1998), with this aim in mind, we make use of a well-characterized sample of 380 nearby galaxies from the CALIFA survey that fill the entire color-magnitude diagram in the Local Universe. The availability of wide-field CALIFA IFS ensures a proper determination of the underlying stellar continuum and, consequently, of the extiction-corrected Hα luminosity. We compare our integrated Hα-based SFRs with single and hybrids tracers at other wavelengths found in the literature (Calzetti 2013). Then, we provide a new set of single-band and hybrid calibrators anchored to the extinction-corrected Hα luminosities. In the case of the hybrid calibrators we determine the best fitting aIR coefficients for different combinations of observed (UV or Hα) and dust-reprocessed (22μm or TIR) SFR contributions (where SFR ∝ Lobs + aIR × L[IR]). This analysis allow us to provide, for the first time, a set of hybrid calibrations for different morphological types and masses. These are particularly useful in case that the sample to be analyzed shows a different bias in terms of morphology or, more commonly, luminosity or stellar mass. We also study the dependence of this coefficient with color and ionized-gas attenuation. The distributions of aIR values are quite wide in all cases. We found that not single physical property can by itself explain the variation found in aIR.Finally, we explore the spatial distribution of the SFR by measuring the contribution of disks to the total SFR in the Local Universe. Our preliminary spatially-resolved analysis shows that the disk to total (disk + spheroidal component) SFR ratio is on average ∼ 88%. The use of the 2D spectroscopic data is critical to properly determine the Hα luminosity function and SFR density in the Local Universe per galaxy components, the ultimate goal of this project.

scholarly journals Stellar profile independent determination of the dark matter distribution of the Fornax Local Group dwarf spheroidal galaxy

2020 ◽  
Vol 501 (2) ◽  
pp. 2332-2351
Author(s):  
Sasha R Brownsberger ◽  
Lisa Randall
Keyword(s):  
Dark Matter ◽  
Cold Dark Matter ◽  
Local Group ◽  
Axial Ratio ◽  
Dwarf Spheroidal Galaxies ◽  
Stellar Velocity ◽  
Best Fitting ◽  
Kinematic Models ◽  
Velocity Dispersions

ABSTRACT We detail a method to measure the correspondence between dark matter (DM) models and observations of stellar populations within Local Group dwarf spheroidal galaxies (LG dSphs) that assumes no parametric stellar distribution. Solving the spherical or cylindrical Jeans equations, we calculate the consistency of DM and stellar kinematic models with stellar positions and line-of-sight velocities. Our method can be used to search for signals of standard and exotic DM distributions. Applying our methodology to the Fornax LG dSph and using statistical bootstrapping, we find: (i) that oblate or prolate cored DM haloes match the stellar data, respectively, ≃60 or ≃370 times better than oblate or prolate cusped DM haloes for isotropic and isothermal stellar velocity dispersions, (ii) that cusped spherical DM haloes and cored spherical DM haloes match the Fornax data similarly well for isotropic stellar velocity dispersions, (iii) that the semiminor to semimajor axial ratio of spheroidal DM haloes are more extreme than 80 per cent of those predicted by Lambda cold dark matter with baryon simulations, (iv) that oblate cored or cusped DM haloes are, respectively, ≃5 or ≃30 times better matches to Fornax than prolate cored or cusped DM haloes, and (v) that Fornax shows no evidence of a disc-like structure with more than two per cent of the total DM mass. We further note that the best-fitting cusped haloes universally favour the largest mass and size fit parameters. If these extreme limits are decreased, the cusped halo likelihoods decrease relative to those of cored haloes.

scholarly journals The MUSE-Wide Survey: A determination of the Lyman α emitter luminosity function at 3 < z < 6

2019 ◽  
Vol 621 ◽  
pp. A107 ◽  
Author(s):  
Edmund Christian Herenz ◽  
Lutz Wisotzki ◽  
Rikke Saust ◽  
Josephine Kerutt ◽  
Tanya Urrutia ◽  
...  
Keyword(s):  
Luminosity Function ◽  
Dynamic Range ◽  
Supporting Evidence ◽  
Full Sample ◽  
Low Surface Brightness ◽  
Best Fitting ◽  
Parametric Statistical Test ◽  
Maximum Likelihood Technique ◽  
Non Parametric

We investigate the Lyman α emitter (LAE) luminosity function (LF) within the redshift range 2.9 ≤ z ≤ 6 from the first instalment of the blind integral field spectroscopic MUSE-Wide survey. This initial part of the survey probes a region of 22.2 arcmin2 in the CANDELS/GOODS-S field (24 MUSE pointings with 1h integrations). The dataset provided us with 237 LAEs from which we construct the LAE LF in the luminosity range 42.2 ≤ log LLyα[erg s−1] ≤ 43.5 within a volume of 2.3 × 105 Mpc3. For the LF construction we utilise three different non-parametric estimators: the classical 1/Vmax method, the C− method, and an improved binned estimator for the differential LF. All three methods deliver consistent results, with the cumulative LAE LF being Φ(log L Lyα[erg s−1] = 43.5) ≃ 3 × 10−6 Mpc−3 and Φ(log L Lyα[erg s−1] = 42.2) ≃ 2 × 10−3 Mpc−3 towards the bright and faint end of our survey, respectively. By employing a non-parametric statistical test, and by comparing the full sample to subsamples in redshift bins, we find no supporting evidence for an evolving LAE LF over the probed redshift and luminosity range. Using a parametric maximum-likelihood technique we determine the best-fitting Schechter function parameters α = 1.84+04.2−0.41 and L∗[erg s−0.1] = 42.2−0.16+0.22 with the corresponding normalisation logϕ*[Mpc−3]= − 2.71. However, the dynamic range in Lyα luminosities probed by MUSE-Wide leads to a strong degeneracy between α and L*. Moreover, we find that a power-law parameterisation of the LF appears to be less consistent with the data compared to the Schechter function, even so when not excluding the X-Ray identified AGN from the sample. When correcting for completeness in the LAE LF determinations, we take into account that LAEs exhibit diffuse extended low surface brightness halos. We compare the resulting LF to one obtained by applying a correction assuming compact point-like emission. We find that the standard correction underestimates the LAE LF at the faint end of our survey by a factor of 2.5. Contrasting our results to the literature we find that at 42.2 ≤ log LLyα[erg s−1] ≲ 42.5 previous LAE LF determinations from narrow-band surveys appear to be affected by a similar bias.

Potential Energy Curve and Dissociation Energy for the SnCl Molecule

1993 ◽  
Vol 58 (7) ◽  
pp. 1485-1490 ◽  
Author(s):  
Narayanan Rajamanickam ◽  
Natarajan Ponraj ◽  
Ponpandian Durai Ezhilarasan ◽  
Veluchamy Arumugachamy ◽  
Manuel Fernandez Gomez ◽  
...  
Keyword(s):  
Potential Energy ◽  
Dissociation Energy ◽  
Ground State ◽  
Potential Energy Curve ◽  
Energy Curve ◽  
Empirical Potential ◽  
Best Fitting ◽  
Expansion Coefficients ◽  
Electronic Ground

The potential energy curve for the electronic ground state of the SnCl molecule has been constructed by the Rydberg-Klein-Rees method in the modification by Vanderslice and collaborators. Empirical potential functions, of five parameters by Hulburt and Hirschfelder, of three parameters by Lippincott and collaborators, and that by Szoke and Baitz using the electronegativity are examined for their adequacy to represent the true curve. The five parameters by Hulburt-Hirschfelder function, U(r) = De[(1 - e-x)2 + c x3 e-2x (1 + bx)], was found to be the best fitting function and it was used for the determination of the dissociation energy. The estimated value attained for dissociation energy is 346 ± 8 kJ mol-1. For this value of dissociation energy, the estimated values for parameters and expansion coefficients are c = 0.06864, b = -0.363738, a0 = 2.759 . 103 m-1, a1 = 2.876 and a2 = 4.013, a0, a1 and a2, being the Dunham's coefficients.

scholarly journals GIS analysis of geological surfaces orientations: the qgSurf plugin for QGIS

2019 ◽  
Author(s):  
Mauro Alberti
Keyword(s):  
Quantitative Analysis ◽  
Southern Italy ◽  
Gis Analysis ◽  
Southern Apennines ◽  
Geological Structures ◽  
Theoretical Orientations ◽  
Best Fitting ◽  
Best Fit

GIS techniques enable the quantitative analysis of geological structures. In particular, topographic traces of geological lineaments can be compared with the theoretical ones for geological planes, to determine the best fitting theoretical planes. qgSurf, a Python plugin for QGIS, implements this kind of processing, in addition to the determination of the best-fit plane to a set of topographic points, the calculation of the distances between topographic traces and geological planes and also basic stereonet plottings. By applying these tools to a case study of a Cenozoic thrust lineament in the Southern Apennines (Calabria, Southern Italy), we deduce the approximate orientations of the lineament in different fault-delimited sectors and calculate the misfits between the theoretical orientations and the actual topographic traces.

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