Rapidly convergent expansion method for calculating the effective conductivity of three-dimensional lattices of symmetric inclusions

1999 ◽  
Vol 86 (7) ◽  
pp. 3773-3779 ◽  
Author(s):  
Constantin Simovski ◽  
Sailing He
Keyword(s):  
Effective Conductivity ◽  
Three Dimensional ◽  
Expansion Method ◽  
Convergent Expansion

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 Nonlinear effects of locally heterogeneous hydraulic conductivity fields on regional stream–aquifer exchanges

2015 ◽  
Vol 19 (11) ◽  
pp. 4531-4545 ◽  
Author(s):  
J. Zhu ◽  
C. L. Winter ◽  
Z. Wang
Keyword(s):  
Groundwater Flow ◽  
Effective Conductivity ◽  
Model Simulation ◽  
Three Dimensional ◽  
Small Scale ◽  
Heihe River ◽  
Effective Parameters ◽  
Aquifer Systems ◽  
Basin Scale ◽  
Local Grid

Abstract. Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream–aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream–aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream–aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow paths in groundwater fluxes that in turn reduce aquifer–stream exchanges. Since surface water–groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management.

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.

Development of Three-Dimensional Neutron Kinetics Code Based on High Order Nodal Expansion Method in Hexagonal-Z Geometry

2018 ◽  
Author(s):  
Guo Chao ◽  
Liu Yu ◽  
He Hangxing ◽  
Liu Luguo ◽  
Wang Xiaoyu ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Benchmark Problems ◽  
Weighting Method ◽  
Control Rod ◽  
Order Polynomial ◽  
Runge Kutta ◽  
Nodal Expansion Method

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

Self-Similar Crack Expansion Method for Three-Dimensional Cracks Under Mixed-Mode Loading Conditions

1998 ◽  
Vol 65 (3) ◽  
pp. 557-565 ◽  
Author(s):  
Yonglin Xu ◽  
B. Moran ◽  
T. Belytschko
Keyword(s):  
Numerical Method ◽  
Mixed Mode ◽  
Three Dimensional ◽  
Expansion Method ◽  
Shear Loading ◽  
Boundary Integral ◽  
Normal Displacement ◽  
Loading Conditions ◽  
Mixed Mode Loading ◽  
Self Similar

Three-dimensional planar cracks under mixed-mode loading conditions are investigated by using the selfsimilar crack expansion method with the boundary integral equation technique. For a planar crack under general loading (tensile and shear) conditions, the normal displacement and tangential displacements on the crack surface exhibit uncoupled characteristics. However, the tangential displacements in the two directions are generally coupled. In this paper, two coupled boundary integral equations for a crack subject to shear loading are solved using the analytically numerical method, where the integrals on elements’ are estimated by using the explicit expression of the close form of the integrals. Combination of the self-similar crack expansion method and the analytically numerical method results in good accuracy, with errors in stress intensity factors of penny-shaped cracks and elliptical cracks less than one percent. This numerical analysis is applicable to the analysis of cracks with arbitrary geometry.

Electromagnetic properties of photonic crystals with diamond structure containing defects

2003 ◽  
Vol 18 (9) ◽  
pp. 2214-2220 ◽  
Author(s):  
Shingo Kanehira ◽  
Soshu Kirihara ◽  
Yoshinari Miyamoto ◽  
Kazuaki Sakoda ◽  
Mitsuo Wada Takeda
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Photonic Band Gap ◽  
Three Dimensional ◽  
Expansion Method ◽  
Electromagnetic Properties ◽  
Diamond Structure ◽  
Multiple Reflections ◽  
Air Cavity ◽  
Photonic Band

Three-dimensional photonic crystals with a diamond structure, which are composed of the TiO2-based ceramic particles dispersed in an epoxy lattice, were fabricated by stereolithography. The diamond structure showed a photonic band gap in the 14.3–17.0 GHz range along the Γ-K 〈110〉 direction, which is close to the band calculation using the plain wave expansion method. Two types of lattice defects—air cavity and dielectric cavity—were introduced into the diamond structure by removing a unit cell of diamond structure or inserting a block of the lattice medium into the air cavity. The transmission of millimeter waves affected by multiple reflections at the defects was measured in the photonic band gap. Resonant frequencies in the defects were calculated and compared with the measurement results.

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