scholarly journals An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Ranjan Sharma ◽  
Naresh Dadhich ◽  
Shyam Das ◽  
Sunil D. Maharaj
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Interior Solution ◽  
Uniform Density ◽  
Charged Fluid ◽  
Charged Fluid Sphere ◽  
Physical Conditions ◽  
Charged Star ◽  
Three Dimensional Space

AbstractWe wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz (Astrophys Astron 3:325, 1982) for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya–Tikekar parameter, k, indicating deviation from sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions required for a relativistic charged fluid sphere as an interior to a charged star. We also obtain and discuss charged analogue of the Buchdahl compactness bound.

The Osculatory Packing of a Three Dimensional Sphere

1973 ◽  
Vol 25 (2) ◽  
pp. 303-322 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Dimensional Euclidean Space ◽  
Dimensional Sphere ◽  
Specific Knowledge ◽  
Precise Information ◽  
Practical Applications ◽  
Physical Problems ◽  
Three Dimensional Space

Packings by unequal spheres in three dimensional space have interested many authors. This is to some extent due to the practical applications of such investigations to engineering and physical problems (see, for example, [16; 17; 31]). There are a few general results known concerning complete packings by spheres in N-dimensional Euclidean space, due mainly to Larman [20; 21]. For osculatory packings, although there is a great deal of specific knowledge about the two-dimensional situation, the results for higher dimensions, such as [4], rely on general methods which do not give particularly precise information.

Interpolation of Spatial Displacements Using the Clifford Algebra of E4

1999 ◽  
Vol 121 (1) ◽  
pp. 39-44 ◽  
Author(s):  
K. R. Etzel ◽  
J. M. McCarthy
Keyword(s):  
Clifford Algebra ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Coordinate Frame ◽  
Spatial Motion ◽  
Hypercomplex Numbers ◽  
Key Frames ◽  
Spatial Displacements ◽  
Three Dimensional Space

In this paper we show that the Clifford Algebra of four dimensional Euclidean space yields a set of hypercomplex numbers called “double quaternions.” Interpolation formulas developed to generate Bezier-style quaternion curves are shown to be applicable to double quaternions by simply interpolating the components separately. The resulting double quaternion curves are independent of the coordinate frame in which the key frames are specified. Double quaternions represent rotations in E4 which we use to approximate spatial displacements. The result is a spatial motion interpolation methodology that is coordinate frame invariant to a desired degree of accuracy within a bounded region of three dimensional space. Examples demonstrate the application of this theory to computing distances between spatial displacement, determining the mid-point between two displacements, and generating the spatial motion interpolating a set of key frames.

scholarly journals Lax Triples for Integrable Surfaces in Three-Dimensional Space

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jan L. Cieśliński ◽  
Artur Kobus
Keyword(s):  
Dimensional Space ◽  
Linear Equations ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Chiral Model ◽  
Lax Representation ◽  
Integrable Deformation ◽  
Principal Chiral Model ◽  
Orthogonal Systems ◽  
Three Dimensional Space

We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean spaceE3. We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameterλare trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the groupSpin(6). Finally, the obtained results are interpreted in the context of the soliton surfaces approach.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

scholarly journals Quantitative image analysis of microbial communities with BiofilmQ

2021 ◽  
Author(s):  
Raimo Hartmann ◽  
Hannah Jeckel ◽  
Eric Jelli ◽  
Praveen K. Singh ◽  
Sanika Vaidya ◽  
...  
Keyword(s):  
Image Analysis ◽  
Microbial Communities ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Software Tool ◽  
Image Cytometry ◽  
Quantitative Image Analysis ◽  
Space And Time ◽  
Quantitative Image ◽  
Three Dimensional Space

AbstractBiofilms are microbial communities that represent a highly abundant form of microbial life on Earth. Inside biofilms, phenotypic and genotypic variations occur in three-dimensional space and time; microscopy and quantitative image analysis are therefore crucial for elucidating their functions. Here, we present BiofilmQ—a comprehensive image cytometry software tool for the automated and high-throughput quantification, analysis and visualization of numerous biofilm-internal and whole-biofilm properties in three-dimensional space and time.

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