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The shape of spherical quartics
2003
Computer Aided Geometric Design
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With the help of the generalized stereographic projection (Dietz et al., 1993), we construct a two-parameter family of spherical quartics solving this problem. ...
We study the shape of these solutions and derive criteria which guarantee solutions without cusps or self-intersections. ...
In particular, we are indebted to one of them for providing the proof of Proposition 2. Wenping Wang's work is supported by a grant (HKU 7032/99E) of Hong Kong Research Grant Council. ...
doi:10.1016/j.cagd.2003.07.003
fatcat:7hqs457g4jh2jlkhezhmop7byy
Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles
2009
Physical Review Letters
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Finally, we find that the degree of hypostaticity is determined by the number of quartic modes of the packing. ...
We study the structural and mechanical properties of jammed ellipse packings, and find that the nature of the jamming transition in these systems is fundamentally different from that for spherical particles ...
We find significant differences between the behavior near jamming of ellipse-shaped and spherical particles: (i) The lowest-energy vibrational excitations are composed of predominantly rotational particle ...
doi:10.1103/physrevlett.102.255501
pmid:19659093
fatcat:tbiyzhzrareotkbxqxudwv6dai
The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions
[article]
2021
arXiv
pre-print
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In contrast, β≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. ...
We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero ...
The average quartic eigenmode frequency scales as ω 0 ∼ ( A − 1) −1/3 , which is different than the scaling behavior of the quartic modes in jammed packings of rigid, frictionless non-spherical particles ...
arXiv:2108.09616v1
fatcat:l264eyayzfc7vfshfi3o4tlvhq
Jammed packings of 3D superellipsoids with tunable packing fraction, contact number, and ordering
2019
Soft Matter
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We consider more than 200 different particle shapes by varying the three shape parameters... ...
We carry out numerical studies of static packings of frictionless superellipsoidal particles in three spatial dimensions. ...
Quartic modes always correspond to the lowest frequency modes, and the translational content of these eigenmodes is small for nearly spherical particle shapes, and increases with asphericity. ...
doi:10.1039/c9sm01932d
pmid:31742301
pmcid:PMC6902436
fatcat:s5tnewwngzb2dgmyvpxovas5qi
Jammed packings of 3D superellipsoids with tunable packing fraction, contact number, and ordering
[article]
2019
arXiv
pre-print
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Over the full range of orientational order, we find that the number of quartic modes of the dynamical matrix for the packings always matches the number of missing contacts relative to the isostatic value ...
We consider more than 200 different particle shapes by varying the three shape parameters that define superellipsoids. ...
In addition, we acknowledge the High-performance Computing Platform of Peking University. We also thank S. Li at Peking University for helpful discussions. ...
arXiv:1909.12191v1
fatcat:j6j65dhl2bb4pnfppn42rxuh6m
On Spherical Quartics, with a Quadruple Cyclic Arc, and a Triple Focus
1880
Proceedings of the London Mathematical Society
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If cP < 1, there may be two cusped quartics in the group, pear-shaped ( Fig. 1) , and cardioidal (Fig. 2) ; these are of the fifth class. ...
Such a group of spherical quartics may be thus defined: * = (l+dx)(l+x*+y')+\(l+x'+y*)* : (A), if x, y denote by Gudermann's system of spherical coordinates the tangents of arcs, intercepted on the arcs ...
doi:10.1112/plms/s1-12.1.168
fatcat:j5l7wsjafzdpnl2uktm4e6buz4
Second shape transition temperature: prolate noncollective to oblate noncollective
1997
Zeitschrift für Physik A Hadrons and Nuclei
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For temperatures between T c1 (I) and T c2 (I), rotation of the hot spherical shape produces a prolate shape rotating about its symmetry axis. This is the opposite of the classical response. ...
Many nuclei have a temperature interval where the rotation of a hot spherical equilibrium shape generates a prolate equilibrium shape rotating around its symmetry axis. PACS: 21.60. ...
For temperatures between T c1 (I) and T c2 (I), rotation of the hot spherical shape produces a prolate shape rotating about its symmetry axis. This is the opposite of the classical response. ...
doi:10.1007/s002180050287
fatcat:xkfaat4jwzg3vbbo445e6khrta
Bridging particle deformability and collective response in soft solids
[article]
2021
arXiv
pre-print
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We find that jammed packings of deformable particles with excess shape degrees of freedom possess low-frequency quartic vibrational modes that stabilize the packings even though they possess fewer interparticle ...
We find that the mechanical response of jammed packings of deformable particles with shape degrees of freedom differs significantly from that of jammed packings of rigid-shape particles, which emphasizes ...
As shown in Fig. 2 (a), we find that the number of missing contacts in jammed DP packings always matches the number of quartic modes N q across a wide range of shape parameters. ...
arXiv:2012.02915v2
fatcat:trvawy265fgblmduha2ifem5mi
Effect of anharmonicities in the critical number of trapped condensed atoms with an attractive two-body interaction
2002
Physical Review A. Atomic, Molecular, and Optical Physics
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As an example of how a cubic or quartic anharmonic term can affect the maximum number of particles, we consider the trap parameters and the results given by Roberts et al. [Phys. Rev. ...
We determine the quantitative effect, in the maximum number of particles and other static observables, due to small anharmonic terms added to the confining potential of an atomic condensed system with ...
L.T. also thanks the Conselho Nacional de Desenvolvimento Científico e Tecnológico ͑CNPq͒ of Brazil for support. ...
doi:10.1103/physreva.66.043605
fatcat:f2psqy36ovh6jptyfrbw2y5n7a
Optical cross-connect system based on the White cell and three-state microelectromechanical system: experimental demonstration of the quartic cell
2006
Applied Optics
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We describe in detail the implementation of an underpopulated quartic White cell configuration. We discuss the aberrations associated with the output of the system. ...
We present a proof of concept (design, simulations, and experimental results) for an optical crossconnection device based on the optical White cell and a three-state microelectromechanical system tilting ...
We thank William Thalgott and Feras Abou Galala for their time and expertise to construct the pseudo-MEMS and cut the silicon wafers, respectively. ...
doi:10.1364/ao.45.004658
pmid:16799680
fatcat:6djaz7ru5zg3bpeq7mjbbvdxti
The Schrödinger equation on a Lagrange mesh
2017
Journal of Physics, Conference Series
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The accuracy of the matrix elements is tested with the quartic anharmonic oscillator and a double ring-shaped harmonic oscillator potentials. ...
generalized spherical coordinates Gaotsiwe J Rampho -Recent citations Lagrange-mesh solution of the Schrödinger equation in generalized spherical coordinates Gaotsiwe J Rampho -This content was downloaded ...
discussed for the quartic anharmonic oscillator in two dimensions and the double ring-shaped harmonic oscillator in three dimensions. ...
doi:10.1088/1742-6596/905/1/012037
fatcat:dknj2zyucnagxjftetsmon6o5a
Page 9943 of Mathematical Reviews Vol. , Issue 2004m
[page]
2004
Mathematical Reviews
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2004m:41003 41A10 65D05 65D18
Jiittler, Bert (A-LINZ-AG; Linz);
Wang, Wenping [Wang, Wen Ping'| (PRC-HK-CIS; Hong Kong)
The shape of spherical quartics. ...
Given two points and associated tangent vectors (first deriva- tives) on a sphere, the focus is on the interpolation of this data with a spherical quartic. ...
Method of solving triplets consisting of a singlet and airspaced doublet with given primary aberrations
1998
Journal of Modern Optics
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The roots give the element powers. Second, the lens shapes are obtained by solving the quartic polynomial equation which is obtained by combining the equations of spherical aberration and coma. ...
The triplet is required to yield specified amounts of lens power and four primary aberrations: spherical aberration, coma, longitudinal chromatic aberration and secondary spectrum. ...
Second, the lens shapes are obtained b y solving the quartic polynomial equation which is obtained by combining the equations of S 1 and S2. ...
doi:10.1080/095003498150547
fatcat:um6k7t2urbej5dtdjpwh46qws4
Method of solving triplets consisting of a singlet and air-spaced doublet with given primary aberrations
1998
Journal of Modern Optics
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The roots give the element powers. Second, the lens shapes are obtained by solving the quartic polynomial equation which is obtained by combining the equations of spherical aberration and coma. ...
The triplet is required to yield specified amounts of lens power and four primary aberrations: spherical aberration, coma, longitudinal chromatic aberration and secondary spectrum. ...
Second, the lens shapes are obtained b y solving the quartic polynomial equation which is obtained by combining the equations of S 1 and S2. ...
doi:10.1080/09500349808231743
fatcat:qvvq7aeebbcktncdpxsphaym7i
Stationary states in two-dimensional systems driven by bivariate Lévy noises
2014
Physical Review E
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2014 pre-print arXiv:1406.7103v1 fatcat:2z5tsqmibjdnlbvzn5pegodu64
Moreover, stationary states can have local minima at the origin. The shape of stationary states reflects symmetries of the underlying noise, i.e. its spectral measure. ...
In 2D systems, intriguing properties of stationary states originate not only due to heavy tails of noise pulses, which are distributed according to α-stable densities, but also because of properties of ...
The studied model is presented in Section II. Section III discusses obtained, mainly numerically, results. The paper is closed with concluding remarks (Section IV). ...
doi:10.1103/physreve.90.032128
pmid:25314416
fatcat:ezuw7xpx7fbo5lspvorbrbakcq
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