Generalized Thermal Agents with Multiple Boundary Conditions and Three-Dimensional Thermal Agents

2006 ◽  
Author(s):  
S.P. Gent ◽  
D.A. Ashlock ◽  
A.R. Willms ◽  
K.M. Bryden
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Multiple Boundary Conditions

A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs

2015 ◽  
Vol 70 (8) ◽  
pp. 673-682 ◽  
Author(s):  
Elyas Shivanian
Keyword(s):  
Boundary Conditions ◽  
Meshless Method ◽  
Spline Interpolation ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Poisson Equations ◽  
Second Derivatives ◽  
Radial Basis ◽  
Collocation Scheme ◽  
Multiple Boundary Conditions

AbstractThis paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.

scholarly journals Charge algebra in Al(A)dSn spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adrien Fiorucci ◽  
Romain Ruzziconi
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Structure ◽  
Asymptotic Symmetry ◽  
Renormalization Procedure ◽  
Field Dependent ◽  
Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

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 Numerical Study of Three-Dimensional Surface Jets Emerging from a Fishway Entrance Slot

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1079
Author(s):  
Lena Mahl ◽  
Patrick Heneka ◽  
Martin Henning ◽  
Roman B. Weichert
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Free Water ◽  
Lateral Wall ◽  
Lateral Spreading ◽  
Propagation Length ◽  
Vertical Slot ◽  
Surface Jets

The efficiency of a fishway is determined by the ability of immigrating fish to follow its attraction flow (i.e., its jet) to locate and enter the fishway entrance. The hydraulic characteristics of fishway entrance jets can be simplified using findings from widely investigated surface jets produced by shaped nozzles. However, the effect of the different boundary conditions of fishway entrance jets (characterized by vertical entrance slots) compared to nozzle jets must be considered. We investigate the downstream propagation of attraction jets from the vertical slot of a fishway entrance into a quiescent tailrace, considering the following boundary conditions not considered for nozzle jets: (1) slot geometry, (2) turbulence characteristics of the approach flow to the slot, and (3) presence of a lateral wall downstream of the slot. We quantify the effect of these boundary conditions using three-dimensional hydrodynamic-numeric flow simulations with DES and RANS turbulence models and a volume-of-fluid method (VoF) to simulate the free water surface. In addition, we compare jet propagation with existing analytical methods for describing jet propagations from nozzles. We show that a turbulent and inhomogeneous approach flow towards a vertical slot reduces the propagation length of the slot jet in the tailrace due to increased lateral spreading compared to that of a jet produced by a shaped nozzle. An additional lateral wall in the tailrace reduces lateral spreading and significantly increases the propagation length. For highly turbulent flows at fishway entrances, the RANS model tends to overestimate the jet propagation compared to the transient DES model.

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