scholarly journals Application of the implicit Fourier-expansion method to the calculation of three-dimensional equilibria by the iterative method

1984 ◽  
Vol 31 (2-3) ◽  
pp. 227-233 ◽  
Author(s):  
Aleksei I. Shestakov
Keyword(s):  
Iterative Method ◽  
Fourier Expansion ◽  
Three Dimensional ◽  
Expansion Method

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

scholarly journals A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Niklas Ericsson
Keyword(s):  
Fourier Expansion ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Countable Family ◽  
Angular Variable ◽  
Two Dimensional ◽  
Sobolev Norms ◽  
Well Posed ◽  
Variational Formulations

Abstract We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.

Chaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microfluidic device

2016 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Yasser Aboelkassem
Keyword(s):  
Mathematical Modeling ◽  
Stream Function ◽  
Microfluidic Device ◽  
Fourier Expansion ◽  
Expansion Method ◽  
Small Oscillation ◽  
Chaotic Mixing ◽  
Mixing Efficiency ◽  
Induced Flow ◽  
Mixing Patterns

AbstractChaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microffluidic device is presented in this article. Mathematical modeling for the induced flow motions by moving a Stokeslet along the x-axis is derived using Fourier expansion method. The solution is formulated in terms of the velocity stream function. The model is then used to explore different stirring dynamics as function of the Stokeslet parameters. For instance, the effects of using various oscillation amplitudes and force strengths are investigated. Mixing patterns using Poincaré maps are obtained numerically and have been used to characterize the mixing efficiency. Results have shown that, for a given Stokeslet’s strength, efficient mixing can be obtained when small oscillation amplitudes are used. The present mixing platform is expected to be useful for many of biomicrofluidic applications.

Three-dimensional-positioning based on echolocation using a simple iterative method

2015 ◽  
Vol 69 (3) ◽  
pp. 680-684 ◽  
Author(s):  
Natee Thong-un ◽  
Shinnosuke Hirata ◽  
Minoru Kuribayashi Kurosawa
Keyword(s):  
Iterative Method ◽  
Three Dimensional

Terahertz wave properties of alumina microphotonic crystals with a diamond structure

2008 ◽  
Vol 23 (4) ◽  
pp. 1036-1041 ◽  
Author(s):  
Hideaki Kanaoka ◽  
Soshu Kirihara ◽  
Yoshinari Miyamoto
Keyword(s):  
Photonic Band Gap ◽  
Three Dimensional ◽  
Expansion Method ◽  
Linear Shrinkage ◽  
Terahertz Wave ◽  
Diamond Structure ◽  
Terahertz Time Domain Spectroscopy ◽  
3D Cad ◽  
Unit Cells ◽  
Wave Properties

Fabrication and terahertz wave properties of alumina microphotonic crystals with a diamond structure were investigated. The three-dimensional diamond structure was designed on a computer using 3D-CAD software. The designed lattice constant was 500 μm. The structure consisted of 8 × 8 × 4 unit cells. Acrylic diamond structures with an alumina dispersion of 40 vol% were formed by using microstereolithography. Fabricated precursors were dewaxed at 600 °C and sintered at 1500 °C. The linear shrinkage ratio was about 25%. The relative density reached 97.5%. The electromagnetic wave properties were measured by terahertz time-domain spectroscopy. A complete photonic band gap was observed at the frequency range from 0.40 THz to 0.47 THz, and showed good agreement with the simulation results calculated by the plane wave expansion method. Moreover, localized modes were obtained at the frequencies 0.42 THz and 0.46 THz by introducing an air defect in the diamond structure. They corresponded to the simulation by the transmission line modeling method.

High extraction efficiency in GaN-based light-emitting diodes with air-hole photonic crystal slab

2014 ◽  
Vol 28 (21) ◽  
pp. 1450173 ◽  
Author(s):  
Dan Liu ◽  
Hui Liu ◽  
Jin Hou ◽  
Yihua Gao
Keyword(s):  
Photonic Crystal ◽  
Light Emitting Diodes ◽  
Extraction Efficiency ◽  
Three Dimensional ◽  
Expansion Method ◽  
Light Emitting ◽  
Hole Radius ◽  
Parameters Tuning ◽  
Gan Led ◽  
Air Hole

In this paper, extraction efficiency in simplified and layered light-emitting diodes (LEDs) of GaN photonic crystal with periodic air holes is studied by three-dimensional finite-difference time-domain method. Photonic band structures of the photonic crystal are obtained by plane-wave expansion method. The results about simplified GaN -LED show that extraction efficiency is very sensitive to the structure parameters tuning, and increases considerably inside the transverse-electric-like gap region. A maximum extraction efficiency above 90% can be achieved. The effects of the PC thickness and air-hole radius on relative extraction efficiency of layered GaN -LED are analyzed. They show optimal values to obtain high relative extraction efficiency.

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