ON THE DOI MODEL FOR THE SUSPENSIONS OF ROD-LIKE MOLECULES IN COMPRESSIBLE FLUIDS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250027 ◽  
Author(s):  
HANTAEK BAE ◽  
KONSTANTINA TRIVISA
Keyword(s):  
Dimensional Space ◽  
Initial Density ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Polymeric Fluids ◽  
Atmospheric Sciences ◽  
Practical Applications ◽  
Doi Model ◽  
Time Existence ◽  
Three Dimensional Space

Polymeric fluids arise in many practical applications in biotechnology, medicine, chemistry, industrial processes, and atmospheric sciences. In this paper, the Doi model for the suspensions of rod-like molecules in a compressible fluid is investigated. The model under consideration describes the interaction between the orientation of rod-like polymer molecules on the microscopic scale and the macroscopic properties of the fluid in which these molecules are contained. Prescribing arbitrarily the initial density of the fluid, the initial velocity, and the initial orientation distribution in suitable spaces, we establish the global-in-time existence of a weak solution to our model defined on a bounded domain in the three-dimensional space. The proof relies on the construction of an approximate sequence of solutions by introducing appropriate regularization and the establishment of compactness.

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.

scholarly journals Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

1993 ◽  
Vol 21 (4) ◽  
pp. 233-250 ◽  
Author(s):  
David D. Sam ◽  
E. Turan Onat ◽  
Pavel I. Etingof ◽  
Brent L. Adams
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Measurement Data ◽  
Orientation Distribution ◽  
Harmonic Polynomials ◽  
Crystallite Orientation ◽  
Orientation Measurement ◽  
Three Dimensional Space

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.

scholarly journals A Study on Intelligent GIS Installation System Based on Six-DOF Parallel Multi-axis Motion Control

2021 ◽  
Vol 2074 (1) ◽  
pp. 012066
Author(s):  
Ti Liu ◽  
Hongwei Mao ◽  
Dong Lei ◽  
Boming Li ◽  
Dahong Fu
Keyword(s):  
Motion Control ◽  
Power Transmission ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Positioning System ◽  
Practical Applications ◽  
Visual Positioning ◽  
Six Dof ◽  
Six Degree Of Freedom ◽  
Three Dimensional Space

Abstract Aiming at the connection of pipelines during the GIS installation process of power transmission and transformation projects, this subject designs and produces an intelligent GIS installation system based on 6-DOF parallel multi-axis motion control, which is applied to practical applications. The intelligent installation system can realize six independent motions and their combined motions in three-dimensional space. Relying on the multi-dimensional visual positioning system, through the six-degree-of-freedom parallel multi-axis motion control system, the precise docking during the installation of the precision GIS cavity can be realized.

New Books

1933 ◽  
Vol 26 (7) ◽  
pp. 444-447
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Careful Attention ◽  
Practical Applications ◽  
Computational Skill ◽  
Three Dimensional Space

This book is a revised and enlarged edition of an earlier volume. The authors have herein given careful attention to training the pupil in the analysis of three dimensional space. In order to develop computational skill, the authors have included a large number of carefully graded practical applications involving both arithmetical and algebraical computation.

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>

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