scholarly journals On Galerkin Approximations of the Surface Active Quasigeostrophic Equations

2016 ◽  
Vol 46 (1) ◽  
pp. 125-139 ◽  
Author(s):  
Cesar B. Rocha ◽  
William R. Young ◽  
Ian Grooms
Keyword(s):  
Galerkin Approximation ◽  
Three Dimensional ◽  
Active Surface ◽  
Inversion Problem ◽  
Conservation Of Energy ◽  
Galerkin Approximations ◽  
Representation Of Solutions ◽  
Surface Active ◽  
Surface Buoyancy ◽  
Quasigeostrophic Equations

AbstractThis study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A, B, and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.

scholarly journals INDOOR AIR TEMPERATURE DISTRIBUTION – AN ALTERNATIVE APPROACH TO BUILDING SIMULATION

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
A. T. Franco ◽  
C. O. R. Negrão
Keyword(s):  
Temperature Distribution ◽  
Air Temperature ◽  
Indoor Air ◽  
Linear Equations ◽  
Three Dimensional ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Algebraic Equations ◽  
Conservation Of Energy ◽  
Energy Conservation Equation

The current paper presents a model to predict indoor air temperature distribution. The approach is based on the energy conservation equation which is written for a certain number of finite volumes within the flow domain. The magnitude of the flow is estimated from a scale analysis of the momentum conservation equation. Discretized two or three-dimensional domains provide a set of algebraic equations. The resulting set of non-linear equations is iteratively solved using the line-by-line Thomas Algorithm. As long as the only equation to be solved is the conservation of energy and its coefficients are not strongly dependent on the temperature field, the solution is considerably fast. Therefore, the application of such model to a whole building system is quite reasonable. Two case studies involving buoyancy driven flows were carried out and comparisons with CFD solutions were performed. The results are quite promising for cases involving relatively strong couplings between heat and airflow.

scholarly journals Active Surface with Dynamic Microstructures and Hierarchical Gradient Enabled by in situ Pneumatic Control

Micromachines ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 992
Author(s):  
Jian-Nan Wang ◽  
Benfeng Bai ◽  
Qi-Dai Chen ◽  
Hong-Bo Sun
Keyword(s):  
Large Amplitude ◽  
Three Dimensional ◽  
Active Surface ◽  
Bonding Process ◽  
Dynamic Topography ◽  
Large Area ◽  
Pneumatic Control ◽  
Design Flexibility ◽  
Surface Microstructures

An active surface with an on-demand tunable topography holds great potential for various applications, such as reconfigurable metasurfaces, adaptive microlenses, soft robots and four-dimensional (4D) printing. Despite extensive progress, to achieve refined control of microscale surface structures with large-amplitude deformation remains a challenge. Moreover, driven by the demand of constructing a large area of microstructures with increased complexity—for instance, biomimetic functional textures bearing a three-dimensional (3D) gradient—novel strategies are highly desired. Here, we develop an active surface with a dynamic topography and three-tier height gradient via a strain-tunable mismatching-bonding process. Pneumatic actuation allows for rapid, reversible and uniform regulation of surface microstructures at the centimeter scale. The in-situ modulation facilitates large-amplitude deformation with a maximum tuning range of 185 μm. Moreover, the structural gradient can be modulated by programming the strain value of the bonding process. With our strategy, another two types of surfaces with a four-tier gradient and without gradient were also prepared. By providing active modulation and design flexibility of complicated microstructures, the proposed strategy would unlock more opportunities for a wealth of novel utilizations.

scholarly journals Eclipse mapping at X-ray wavelengths

1996 ◽  
Vol 176 ◽  
pp. 85-94 ◽  
Author(s):  
J.H.M.M. Schmitt
Keyword(s):  
Solar Corona ◽  
Binary Systems ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Similar Amount ◽  
Inversion Problem ◽  
X Ray ◽  
Three Dimensional Structure ◽  
Spatially Resolved ◽  
Rotational Modulation

Stellar coronae cannot be spatially resolved, and yet stellar coronae are likely to exhibit a similar amount of structure as the solar corona. Currently, the only way to infer structure from spatially unresolved data is to look for rotational modulation of the X-ray emission or eclipses in the case of binary systems. I will discuss some of the observations obtained and critically review the methods used to infer structure from these data. Particular emphasis will be placed on the ill-conditioned nature of the inversion problem, that makes it next to impossible to infer the possibly three-dimensional structure of stellar coronae.

scholarly journals The periodic quasigeostrophic equations: existence and uniqueness of strong solutions

1982 ◽  
Vol 91 (3-4) ◽  
pp. 185-203 ◽  
Author(s):  
A. F. Bennett ◽  
P. E. Kloeden
Keyword(s):  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupled System ◽  
Classical Solutions ◽  
Schauder Estimates ◽  
Initial Vorticity ◽  
Relative Potential ◽  
Quasigeostrophic Equations

SynopsisThe periodic quasigeostrophic equations are a coupled system of a second order elliptic equation for a streamfunction and first order hyperbolic equations for the relative potential vorticity and surface potential temperatures, on a three-dimensional domain which is periodic in both horizontal spatial co-ordinates. Such equations are used in both numerical and theoretical studies in meteorology and oceanography. In this paper Schauder estimates and a Schauder fixed point theorem are used to prove the existence and uniqueness of strong, that is classical, solutions of the periodic quasigeostrophic equations for a finite interval of time, which is inversely proportional to the sum of the norms of the initial vorticity and surface temperatures.

Segmentation of cortical surface and interior brain structures using active-surface/active-volume templates

1997 ◽  
Author(s):  
David J. Schlesinger ◽  
John W. Snell ◽  
Lois E. Mansfield ◽  
James R. Brookeman ◽  
J. H. Downs III ◽  
...  
Keyword(s):  
Active Surface ◽  
Brain Structures ◽  
Cortical Surface ◽  
Active Volume ◽  
Surface Active

scholarly journals Световые пули с бесселевым поперечным сечением в среде углеродных нанотрубок

2022 ◽  
Vol 130 (3) ◽  
pp. 407
Author(s):  
А.М. Белоненко ◽  
И.С. Двужилов ◽  
Ю.В. Двужилова ◽  
М.Б. Белоненко
Keyword(s):  
Carbon Nanotubes ◽  
Key Words ◽  
Cross Section ◽  
Nonlinear Medium ◽  
Three Dimensional ◽  
Optical Pulses ◽  
Limited Region ◽  
Conservation Of Energy ◽  
Light Bullets ◽  
Extremely Short Optical Pulses

The propagation of three-dimensional extremely short optical pulses (light bullets) with a Bessel cross section in a medium of carbon nanotubes placed in an optical resonator is considered. As a result of numerical calculations, it was found that such pulses propagate stably with conservation of energy in a limited region of space, including at large times of the order of 100 ps. Key words: extremely short optical pulses, nonlinear medium, light bullets, carbon nanotubes.

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