Numerical implementation of the three‐dimensional one‐way wave propagator using the third‐order Thiele approximation on a hexagonal grid

1996 ◽  
Vol 100 (4) ◽  
pp. 2834-2834
Author(s):  
Mattheus J. N. van Stralen ◽  
Maarten V. de Hoop ◽  
Hans Blok
Keyword(s):  
Three Dimensional ◽  
Numerical Implementation ◽  
Third Order ◽  
Hexagonal Grid ◽  
The Third

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Synthesis and third-order nonlinear optical properties of novel ethynyl-linked heteropentamer composed of four porphyrins and one pyrene

2009 ◽  
Vol 13 (02) ◽  
pp. 275-282 ◽  
Author(s):  
Ning Sheng ◽  
Jing Sun ◽  
Yongzhong Bian ◽  
Jianzhuang Jiang ◽  
Dong Xu
Keyword(s):  
Optical Properties ◽  
Nonlinear Optical ◽  
Three Dimensional ◽  
Spectroscopic Methods ◽  
Third Order ◽  
Zinc Compounds ◽  
Nlo Properties ◽  
Metal Free ◽  
The Third ◽  
Wide Range

Novel heteropentameric porphyrins-pyrene arrays, in which four meso-tetraphenyl porphyrins are linked to the center unit of pyrene by four acetylenyl bonds, were designed and synthesized. The newly synthesized heteropentameric compounds have been characterized by a wide range of spectroscopic methods. The third-order nonlinear optical (NLO) properties of both the metal-free and zinc compounds of the three-dimensional arrays were investigated by Z-scan experiments, showing enhanced NLO properties compared with that of the porphyrin and pyrene monomers.

Equilibrium and Stability of a Three-Dimensional Toroidal MHD Configuration Near its Magnetic Axis

1976 ◽  
Vol 31 (11) ◽  
pp. 1277-1288 ◽  
Author(s):  
D. Lortz ◽  
J. Nührenberg
Keyword(s):  
Three Dimensional ◽  
Magnetic Axis ◽  
Stability Criteria ◽  
Sufficient Criterion ◽  
Third Order ◽  
Stagnation Points ◽  
The Third ◽  
Longitudinal Current ◽  
The Stability

Abstract The expansion of a three-dimensional toroidal magnetohydrostatic equilibrium around its magnetic axis is reconsidered. Equilibrium and stability plasma-β estimates are obtained in connection with a discussion of stagnation points occurring in the third-order flux surfaces. The stability criteria entering the β-estimates are: (i) a necessary criterion for localized disturbances, (ii) a new sufficient criterion for configurations without longitudinal current. Hamada coordinates are used to evaluate these criteria.

scholarly journals Детально-сравнительный анализ взаимодействия сверхзвукового потока с поперечной газовой струей при больших параметрах нерасчетности

2019 ◽  
Vol 89 (10) ◽  
pp. 1513
Author(s):  
А.О. Бекетаева ◽  
P. Bruel ◽  
А.Ж. Найманова
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Mach Disk ◽  
Navier Stokes ◽  
Third Order ◽  
Navier Stokes Equations ◽  
The Third ◽  
Eno Scheme

The interaction of the spatial supersonic turbulent gas flow with a sound jet injected perpendicularly was widely studied both numerically and experimentally. However, there are only a few studies of the detail analysis of the formation and distribution of vortex structures from moderate till high pressure ratio (the ratio of pressure in the jet to pressure in the main flow).The aim of this paper is the study and identify the system of the vortex forming behind the injected sound jet in a transverse supersonic flow from the point of view of the mixing efficiency. For that the three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The presence of well known vortex structures are shown: two oppositely rotating vortices in front of the jet; horseshoe vortex; two pairs of the vortex in the mixing zone of the jet and the main flow, where one of them is located in the wake behind the jet and other in the lateral line of the jet. Also, the pressure ratio parameters are determined at which the additional pairs of vortices appear. Where, the first of them is formed on the edge of the Mach disk as a result of the interaction of the decelerated jet flow behind the Mach disk with the high-speed ascending flow behind the barrel. And, the second is due to the interaction of the ascending jet flow with the main gas flow. As a result of comparative analysis the criterion of the pressure ratio parameters are found under which a clear picture of additional horn vortices is observed near the wall in the region behind the jet. The graph of the dependence of the angle of inclination of the bow shock wave on the parameter of pressure ratio is obtained. Satisfactory agreement of the pressure distribution on the wall in front of the jet in the symmetry plane with experimental data is established.

Third-order structure function relations for quasi-geostrophic turbulence

2007 ◽  
Vol 572 ◽  
pp. 255-260 ◽  
Author(s):  
ERIK LINDBORG
Keyword(s):  
Structure Function ◽  
Three Dimensional ◽  
Structure Functions ◽  
Order Structure ◽  
Third Order ◽  
Longitudinal Structure ◽  
The Third ◽  
Inverse Cascade ◽  
Geostrophic Turbulence ◽  
Potential Enstrophy

We derive two third-order structure function relations for quasi-geostrophic turbulence, one for the forward cascade of potential enstrophy and one for the inverse cascade of energy. These relations are the counterparts of Kolmovorov's (1941) four-fifths law for the third-order longitudinal structure functions of three-dimensional turbulence.

Synthesis, Crystal Structure and NLO of a Pb(II) Coordination Compound Based on HO-H2BDC

2012 ◽  
Vol 184-185 ◽  
pp. 1311-1316
Author(s):  
Xi Hui Liu ◽  
Xin Zhuo ◽  
Li Zhang
Keyword(s):  
Coordination Mode ◽  
3D Structure ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
Third Order ◽  
Absorption Effect ◽  
X Ray ◽  
The Third ◽  
Self Focusing ◽  
532 Nm

A new three-dimensional Pb(II) coordination polymer, [Pb3(O-BDC)2]n (1) (HO-H2BDC = 5-Hydroxy-1,3-benzenedicarboxylate), has been solvothermally synthesized from the reaction of HO-H2BDC, Pb(NO3)2•6H2O and NaAc. Single-crystal X-ray diffraction analysis reveal that polymer 1 exhibit a unprecedented 3D structure and ligand HO-H2BDC has been observed to exhibit a new coordination mode. The third-order nonlinear optical (NLO) properties in DMF solution have been studied by Z-scan technique using 8 ns laser at 532 nm. The results reveal that the new compound exhibits strong NLO absorption effect and self-focusing refractive performance (α2 = 1.2 × 10-10 mW-1; n2 = -2.4×10-17 m2•W-1).

Third Order ENO Scheme on Non-Uniform Grid for Supersonic Flows

2015 ◽  
Vol 789-790 ◽  
pp. 330-335
Author(s):  
Yekaterina Moisseyeva ◽  
Altynshash Naimanova ◽  
Yerzhan Belyayev ◽  
Nurtoleu Shakhan
Keyword(s):  
Three Dimensional ◽  
Cross Flow ◽  
Uniform Grid ◽  
System Transformation ◽  
Third Order ◽  
The Third ◽  
Symmetrical Form ◽  
Uniform Grids ◽  
Slope Limiters ◽  
Eno Scheme

In the present paper the third order finite-difference shock-capturing essentially non-oscillatory (ENO) scheme for a non-uniform grid has been developed. The design of the ENO scheme is based on the methodology for uniform grids. To construct the essentially non-oscillatory piecewise polynomial, the Newtoninterpolant of the third order degree is adapted for the non-uniform grid. Also, the implementation of the symmetrical form of the slope limiters on non-uniform meshes is examined. The efficiency of the developed algorithm is demonstrated by the numerical experiments on the simulation of the three-dimensional turbulent steady flowfield generated by the transverse hydrogen injection into the supersonic air cross-flow. The comparison with results on the uniform grid using the coordinate system transformation is done.

Algebraic Geodesics on Three-Dimensional Quadrics

2015 ◽  
Vol 70 (12) ◽  
pp. 1049-1054
Author(s):  
Yue Kai
Keyword(s):  
Implicit Function Theorem ◽  
Three Dimensional ◽  
Algebraic Surfaces ◽  
Jacobi Method ◽  
Implicit Function ◽  
Third Order ◽  
Numerical Examples ◽  
The Real ◽  
The Third ◽  
Order Surface

AbstractBy Hamilton-Jacobi method, we study the problem of algebraic geodesics on the third-order surface. By the implicit function theorem, we proved the existences of the real geodesics which are the intersections of two algebraic surfaces, and we also give some numerical examples.

The Generation Of Lump Solitons By A Bottom Topography In A Surface-Tension Dominated Flow

2005 ◽  
Vol 60 (5) ◽  
pp. 328-334 ◽  
Author(s):  
Zhiming Lu ◽  
Yulu Liu
Keyword(s):  
Surface Tension ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Kutta Method ◽  
Third Order ◽  
The Third ◽  
Runge Kutta Method ◽  
The One ◽  
Nicolson Scheme ◽  
The Waves

The generation of lump solitons by a three-dimensional bottom topography is numerically investigated by use of a forced Kadomtsev-Petviashvili-I (KP-I) equation. The numerical method is based on the third order Runge-Kutta method and the Crank-Nicolson scheme. The main result is the pairwise periodic generation of two pairs of lump-type solitons downstream of the obstacle. The pair with the smaller amplitude is generated with a longer period and moves in a larger angle with respect to the positive x-axis than the one with the larger amplitude. Furthermore, the effects of the detuning parameter on the generation and evolution of lumps are studied. Finally the waves propagating upstream of the obstacle are also briefly investigated.

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