Stoßbestimmte Grenzschicht in einem schwach ionisierten Plasma

1970 ◽  
Vol 25 (4) ◽  
pp. 525-541
Author(s):  
Karl Gerhard Müller ◽  
Peter Wahle
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Specular Reflection ◽  
Correction Term ◽  
Charge Carriers ◽  
Macroscopic Models ◽  
Basic Set ◽  
Transfer Equations ◽  
Set Up

Abstract In this work we develop a collision-dominated sheath model which includes the well known macroscopic models as extreme cases. We set up a description of the charge carriers with the help of the velocity distribution. In order to fulfil the microscopic boundary conditions at the wall we split up the velocity distributions into two parts. A basic set of new transport equations arises which differ from the usual equations by a correction term in the momentum transfer equations. Because of this splitting up of the velocity distribution we are able to take into account exactly specular reflection of the electrons at the wall. In a good approximation our results can also be obtained from the usual equations, if a suitably fitted factor is introduced into the electron boundary condition. at the wall.

A Note on Film Rupture in Hydrodynamic Lubrication

1987 ◽  
Vol 109 (3) ◽  
pp. 562-566 ◽  
Author(s):  
Terukazu Ota
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Experimental Study ◽  
Boundary Conditions ◽  
Present Model ◽  
Hydrodynamic Lubrication ◽  
Correction Term ◽  
Plane Geometry ◽  
Separation Boundary ◽  
Film Rupture

A theoretical and experimental study has been made for a film repture in hydrodynamic lubrication. A model is proposed on boundary conditions at the film rupture point. It contains a pressure correction term as a parameter, which simplifies that derived by Coyne and Elrod, and the so-called separation boundary condition. Some experiments have been conducted for a flow in a cylinder-plane geometry. It is found that numerical results using the present model agree reasonably well with the present and previous experimental data.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

MODELING THE SOUTH ATLANTIC OCEAN FROM MEDIUM TO HIGH RESOLUTION

2014 ◽  
Vol 31 (2) ◽  
Author(s):  
Mariela Gabioux ◽  
Vladimir Santos da Costa ◽  
Joao Marcos Azevedo Correia de Souza ◽  
Bruna Faria de Oliveira ◽  
Afonso De Moraes Paiva
Keyword(s):  
High Resolution ◽  
Atlantic Ocean ◽  
Large Scale ◽  
South Atlantic ◽  
Surface Relaxation ◽  
The South ◽  
Small Surface ◽  
Basic Model ◽  
Basic Set ◽  
Set Up

Results of the basic model configuration of the REMO project, a Brazilian approach towards operational oceanography, are discussed. This configuration consists basically of a high-resolution eddy-resolving, 1/12 degree model for the Metarea V, nested in a medium-resolution eddy-permitting, 1/4 degree model of the Atlantic Ocean. These simulations performed with HYCOM model, aim for: a) creating a basic set-up for implementation of assimilation techniques leading to ocean prediction; b) the development of hydrodynamics bases for environmental studies; c) providing boundary conditions for regional domains with increased resolution. The 1/4 degree simulation was able to simulate realistic equatorial and south Atlantic large scale circulation, both the wind-driven and the thermohaline components. The high resolution simulation was able to generate mesoscale and represent well the variability pattern within the Metarea V domain. The BC mean transport values were well represented in the southwestern region (between Vitória-Trinidade sea mount and 29S), in contrast to higher latitudes (higher than 30S) where it was slightly underestimated. Important issues for the simulation of the South Atlantic with high resolution are discussed, like the ideal place for boundaries, improvements in the bathymetric representation and the control of bias SST, by the introducing of a small surface relaxation. In order to make a preliminary assessment of the model behavior when submitted to data assimilation, the Cooper & Haines (1996) method was used to extrapolate SSH anomalies fields to deeper layers every 7 days, with encouraging results.

scholarly journals Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models

2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Conditions ◽  
Model Updating ◽  
Element Model ◽  
Computational Time ◽  
Stiffness Coefficients ◽  
First Case ◽  
Numerical Approaches

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.

scholarly journals Correction to: The Landau Equation with the Specular Reflection Boundary Condition

2021 ◽  
Vol 240 (1) ◽  
pp. 605-626
Author(s):  
Yan Guo ◽  
Hyung Ju Hwang ◽  
Jin Woo Jang ◽  
Zhimeng Ouyang
Keyword(s):  
Boundary Condition ◽  
Specular Reflection ◽  
Landau Equation ◽  
Reflection Boundary

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

scholarly journals An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

2020 ◽  
Vol 54 (4) ◽  
pp. 1373-1413 ◽  
Author(s):  
Huaiqian You ◽  
XinYang Lu ◽  
Nathaniel Task ◽  
Yue Yu
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Diffusion ◽  
Order Convergence ◽  
Flux Boundary Condition ◽  
Nonlocal Interactions ◽  
Local Case ◽  
Neumann Type ◽  
Type Boundary

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ2) in the L∞ (Ω) norm, which is optimal considering the O(δ2) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ2) convergence.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

An inverse problem for the Vlasov–Poisson system

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Fikret Gölgeleyen ◽  
Masahiro Yamamoto
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Specular Reflection ◽  
Nauk Sssr ◽  
Poisson System ◽  
Local Uniqueness ◽  
Electrical Field ◽  
Stability Theorems ◽  
Akad Nauk Sssr ◽  
Reflection Boundary

AbstractIn this paper, we discuss an inverse problem for the Vlasov–Poisson system. We prove local uniqueness and stability theorems by using the method in Anikonov and Amirov [Dokl. Akad. Nauk SSSR 272 (1983), 1292–1293] under the specular reflection boundary condition and with a prescribed outward electrical field at the boundary.

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