Boundary conditions for the Cauchy potential for two-dimensional hyperbolic equations

2017 ◽  
Author(s):  
Tynysbek Sh. Kal’menov
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equations ◽  
Two Dimensional

Two alternatives for solving hyperbolic boundary value problems of geophysical fluid dynamics

2007 ◽  
Vol 588 ◽  
pp. 331-351 ◽  
Author(s):  
UWE HARLANDER ◽  
LEO R. M. MAAS
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Hyperbolic Equations ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Cauchy Data ◽  
Tricomi Problem ◽  
Two Dimensional ◽  
Collocation Points ◽  
Hyperbolic Boundary

Linear internal waves in inviscid bounded fluids generally give a mathematically ill-posed problem since hyperbolic equations are combined with elliptic boundary conditions. Such problems are difficult to solve. Two new approaches are added to the existing methods: the first solves the two-dimensional spatial wave equation by iteratively adjusting Cauchy data such that boundary conditions are satisfied along a predefined boundary. After specifying the data in this way, solutions can be computed using the d'Alembert formula.The second new approach can numerically solve a wider class of two dimensional linear hyperbolic boundary value problems by using a ‘boundary collocation’ technique. This method gives solutions in the form of a partial sum of analytic functions that are, from a practical point of view, more easy to handle than solutions obtained from characteristics. Collocation points have to be prescribed along certain segments of the boundary but also in the so-called fundamental intervals, regions along the boundary where Cauchy data can be given arbitrarily without over-or under-determining the problem. Three prototypical hyperbolic boundary value problems are solved with this method: the Poincaré, the Telegraph, and the Tricomi boundary value problem. All solutions show boundary-detached internal shear layers, typical for hyperbolic boundary value problems. For the Tricomi problem it is found that the matrix that has to be inverted to find solutions from the collocation approach is ill-conditioned; thus solutions depend on the distribution of the collocation points and need to be regularized.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

scholarly journals Phase transitions in GLSMs and defects

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilka Brunner ◽  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Phase Transitions ◽  
Boundary Conditions ◽  
Sigma Models ◽  
Domain Walls ◽  
Two Dimensional ◽  
Linear Sigma Models

Abstract In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.

Structure of the Flow Associated with a Two-Dimensional Supersonic Intake

1965 ◽  
Vol 16 (2) ◽  
pp. 122-138 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Boundary Conditions ◽  
Flow Structure ◽  
Analytical Procedure ◽  
Qualitative Description ◽  
Mapping Technique ◽  
Two Dimensional ◽  
Shock System

SummaryThe intake is conceived as a device that generates a shock system and a subsonic patch within a supersonic field. The object of the paper is to obtain a qualitative description of this flow structure. The analytical procedure is a simple but fairly powerful mapping technique. Several examples are discussed and these show how the flow on the intake alters under the influence of gradually changing boundary conditions.

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