Radial Symmetry Effects in Area Moments of Inertia

2002 ◽  
Author(s):  
E. Terence Foster
Keyword(s):  
Radial Symmetry ◽  
Moments Of Inertia

The Deformation Structure of the Nuclei 32S and 36Ar

2017 ◽  
Vol 13 (2) ◽  
pp. 4678-4688
Author(s):  
K. A. Kharroube
Keyword(s):  
Single Particle ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Moments Of Inertia ◽  
Deformation Structures ◽  
Particle Potential ◽  
Nilsson Model ◽  
Single Particle Potential ◽  
Axes Of Symmetry ◽  
Good Agreement

We applied two different approaches to investigate the deformation structures of the two nuclei S32 and Ar36 . In the first approach, we considered these nuclei as being deformed and have axes of symmetry. Accordingly, we calculated their moments of inertia by using the concept of the single-particle Schrödinger fluid as functions of the deformation parameter β. In this case we calculated also the electric quadrupole moments of the two nuclei by applying Nilsson model as functions of β. In the second approach, we used a strongly deformed nonaxial single-particle potential, depending on Î² and the nonaxiality parameter γ , to obtain the single-particle energies and wave functions. Accordingly, we calculated the quadrupole moments of S32 and Ar36 by filling the single-particle states corresponding to the ground- and the first excited states of these nuclei. The moments of inertia of S32 and Ar36 are then calculated by applying the nuclear superfluidity model. The obtained results are in good agreement with the corresponding experimental data.

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

Pollen characterization of ornamental species of Mammillaria Haw. (Cactaceae/Cactoideae)

2019 ◽  
Vol 6 (1) ◽  
pp. 13 ◽  
Author(s):  
Denise M. D. S. Mouga ◽  
Gabriel R. Schroeder ◽  
Nilton P. Vieira Junior ◽  
Enderlei Dec
Keyword(s):  
Pollen Morphology ◽  
Pollen Grains ◽  
Radial Symmetry ◽  
Morphological Data ◽  
Medium Size ◽  
Ornamental Species

The pollen morphology of thirteen species of Cactaceae was studied: M. backebergiana F.G. Buchenau, M. decipiens Scheidw, M. elongata DC, M. gracilis Pfeiff., M. hahniana Werderm., M. marksiana Krainz, M. matudae Bravo, M. nejapensis R.T. Craig & E.Y. Dawson, M. nivosa Link ex Pfeiff., M. plumosa F.A.C. Weber, M. prolifera (Mill.) Haw, M. spinosissima var. “A Peak” Lem. and M. voburnensis Scheer. All analysed pollen grains are monads, with radial symmetry, medium size (M. gracilis, M. marksiana, M. prolifera, large), tricolpates (dimorphs in M. plumosa [3-6 colpus] and M. prolifera [3-6 colpus]), with circular-subcircular amb (quadrangular in M. prolifera and M. plumosa with six colpus). The pollen grains presented differences in relation to the shape and exine thickness. The exine was microechinate and microperforated. The pollen morphological data are unpublished and will aid in studies that use pollen samples. These pollen grains indicate ornamental cacti.

scholarly journals Infinitely many positive solutions of nonlinear Schrödinger equations

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Riccardo Molle ◽  
Donato Passaseo
Keyword(s):  
Positive Solutions ◽  
Radial Symmetry ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

AbstractThe paper deals with the equation $$-\Delta u+a(x) u =|u|^{p-1}u $$ - Δ u + a ( x ) u = | u | p - 1 u , $$u \in H^1({\mathbb {R}}^N)$$ u ∈ H 1 ( R N ) , with $$N\ge 2$$ N ≥ 2 , $$p> 1,\ p< {N+2\over N-2}$$ p > 1 , p < N + 2 N - 2 if $$N\ge 3$$ N ≥ 3 , $$a\in L^{N/2}_{loc}({\mathbb {R}}^N)$$ a ∈ L loc N / 2 ( R N ) , $$\inf a> 0$$ inf a > 0 , $$\lim _{|x| \rightarrow \infty } a(x)= a_\infty $$ lim | x | → ∞ a ( x ) = a ∞ . Assuming that the potential a(x) satisfies $$\lim _{|x| \rightarrow \infty }[a(x)-a_\infty ] e^{\eta |x|}= \infty \ \ \forall \eta > 0$$ lim | x | → ∞ [ a ( x ) - a ∞ ] e η | x | = ∞ ∀ η > 0 , $$ \lim _{\rho \rightarrow \infty } \sup \left\{ a(\rho \theta _1) - a(\rho \theta _2) \ :\ \theta _1, \theta _2 \in {\mathbb {R}}^N,\ |\theta _1|= |\theta _2|=1 \right\} e^{\tilde{\eta }\rho } = 0 \quad \text{ for } \text{ some } \ \tilde{\eta }> 0$$ lim ρ → ∞ sup a ( ρ θ 1 ) - a ( ρ θ 2 ) : θ 1 , θ 2 ∈ R N , | θ 1 | = | θ 2 | = 1 e η ~ ρ = 0 for some η ~ > 0 and other technical conditions, but not requiring any symmetry, the existence of infinitely many positive multi-bump solutions is proved. This result considerably improves those of previous papers because we do not require that a(x) has radial symmetry, or that $$N=2$$ N = 2 , or that $$|a(x)-a_\infty |$$ | a ( x ) - a ∞ | is uniformly small in $${\mathbb {R}}^N$$ R N , etc. ....

A ten-faced hexangulaconulariid from Cambrian Stage 2 of South China

2021 ◽  
pp. 1-8
Author(s):  
Junfeng Guo ◽  
Jian Han ◽  
Heyo Van Iten ◽  
Zuchen Song ◽  
Yaqin Qiang ◽  
...  
Keyword(s):  
New Genus ◽  
Radial Symmetry ◽  
New Taxon ◽  
Three Gorges ◽  
Substantial Variation ◽  
The Three Gorges ◽  
Apical Half ◽  
Lateral Margins ◽  
Number Of Faces ◽  
Extinct Group

Abstract Hexangulaconulariids (Cambrian stages 1–2) are an extinct group of medusozoan polyps having a biradially symmetrical, fan-shaped periderm that is distinct from those of medusozoan polyps showing three-, four-, five-, or six-fold radial symmetry. Hexangulaconulariids exhibit substantial variation in gross morphology, including variation in the number of faces on each of the two major sides of the periderm. An intermediate taxon of hexangulaconulariids with ten faces (five on each major side) was expected. Here we describe a new hexangulaconulariid, Decimoconularia isofacialis new genus new species from Bed 5 of the Yanjiahe Formation (Cambrian Stage 2) in the Three Gorges area of Hubei Province, China. The new taxon differs from other hexangulaconulariids (Arthrochites, Hexaconularia, and Septuconularia) mainly in possessing a total of ten faces. The two lateral margins are each marked by a ridge in about the apertural half of the periderm and by a collinear furrow in about the apical half, while the five faces on each major side are bounded by a furrow in about the apertural half and by a collinear ridge in about the apical half. Among hexangulaconulariids, Decimoconularia and Septuconularia may be more closely related to each other than either genus is to Arthrochites or Hexaconularia. UUID: http://zoobank.org/ca270a3b-25ee-4d1f-bdeb-91a963370e70

scholarly journals Method for assessment of matching of total ankle joint endoprostheses based on CT data

2020 ◽  
Vol 6 (3) ◽  
pp. 396-397
Author(s):  
Heiner Martin ◽  
Josephine Wittmüß ◽  
Thomas Mittlmeier ◽  
Niels Grabow
Keyword(s):  
Cross Sections ◽  
Spline Functions ◽  
Moments Of Inertia ◽  
Cad System ◽  
Principal Moments Of Inertia ◽  
Principal Axes ◽  
Ct Data ◽  
The One ◽  
Relative Differences ◽  
Systemic Design

AbstractThe investigation of matching of endoprosthesis tibial components to the bone cross section is of interest for the manufacturer as well as for the surgeon. On the one hand, a systemic design of the prosthesis and the assortment is possible, on the other hand, a better matching implantation is enabled on the basis of experience of this study. CT sections were segmented manually using a CAD system and fitted by spline functions, then superseded with cross sections of the tibial component of a modified Hintermann H3 prosthesis. The principal moments of inertia, the direction of the principal axes and the area of the section were evaluated. Based on the relative differences of the principal moments of inertia, recommendations for application of the different prosthesis size and its selection with the surgery can be made.

scholarly journals Reconciling galaxy cluster shapes, measured by theorists versus observers

2020 ◽  
Vol 500 (2) ◽  
pp. 2627-2644
Author(s):  
David Harvey ◽  
Andrew Robertson ◽  
Sut-Ieng Tam ◽  
Mathilde Jauzac ◽  
Richard Massey ◽  
...  
Keyword(s):  
Hubble Space Telescope ◽  
Orientation Angle ◽  
Galaxy Cluster ◽  
Galactic Nuclei ◽  
Weak Lensing ◽  
Strongly Correlated ◽  
The Bahamas ◽  
Cluster Galaxy ◽  
Moments Of Inertia ◽  
X Ray

ABSTRACT If properly calibrated, the shapes of galaxy clusters can be used to investigate many physical processes: from feedback and quenching of star formation, to the nature of dark matter. Theorists frequently measure shapes using moments of inertia of simulated particles’. We instead create mock (optical, X-ray, strong-, and weak-lensing) observations of the 22 most massive ($\sim 10^{14.7}\, \mathrm{ M}_\odot$) relaxed clusters in the BAHAMAS simulations. We find that observable measures of shape are rounder. Even when moments of inertia are projected into 2D and evaluated at matched radius, they overestimate ellipticity by 56 per cent (compared to observable strong lensing) and 430 per cent (compared to observable weak lensing). Therefore, we propose matchable quantities and test them using observations of eight relaxed clusters from the Hubble Space Telescope (HST) and Chandra X-Ray Observatory. We also release our HST data reduction and lensing analysis software to the community. In real clusters, the ellipticity and orientation angle at all radii are strongly correlated. In simulated clusters, the ellipticity of inner (&lt;rvir/20) regions becomes decoupled: for example, with greater misalignment of the central cluster galaxy. This may indicate overly efficient implementation of feedback from active galactic nuclei. Future exploitation of cluster shapes as a function of radii will require better understanding of core baryonic processes. Exploitation of shapes on any scale will require calibration on simulations extended all the way to mock observations.

73.22 More Moments of Inertia without Integration

1989 ◽  
Vol 73 (464) ◽  
pp. 127
Author(s):  
Nick Lord
Keyword(s):  
Moments Of Inertia

scholarly journals Designing of Drive Systems in the Aspect of the Desired Spectrum of Operation

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2562
Author(s):  
Tomasz Dzitkowski ◽  
Andrzej Dymarek ◽  
Jerzy Margielewicz ◽  
Damian Gąska ◽  
Lukasz Orzech ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Dynamic Parameters ◽  
Synthesis Algorithm ◽  
Moments Of Inertia ◽  
Driving System ◽  
Six Degrees Of Freedom ◽  
Resonance Frequencies ◽  
Drive Systems ◽  
Power Component

A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis.

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