scholarly journals Large-charge limit of AdS boson stars with mixed boundary conditions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shi-Fa Guo ◽  
Hai-Shan Liu ◽  
H. Lü ◽  
Yi Pang
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Numerical Data ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Boson Stars ◽  
Universal Structure ◽  
Close Form ◽  
Large Charge

Abstract It was recently shown that charged AdS boson stars can reproduce the universal structure of the lowest scaling dimension in the subsector of a CFT with fixed large global U(1) charge Q. Using the model consisting of Einstein-Maxwell gravity with a negative cosmological constant, coupled to a U(1)-charged conformally massless scalar with the fourth-order self interaction, we construct a class of charged AdS boson star solutions in the large Q limit, where the scalar field obeys a mixed boundary condition, parameterized by k that interpolates between the Neumann and Dirichlet boundary conditions corresponding to k = 0 and ∞ respectively. By varying k, we numerically read off the k dependence of the leading coefficient c3/2(k) ≡ limQ→∞M/Q3/2. We find that c3/2(k) is a monotonously increasing function which grows linearly when k is sufficiently small. When k → ∞, c3/2(k) approaches the maximal value at a decreasing rate given by k−3/2. We also obtain a close form expression that fits the numerical data for the entire range of k within 10−4 accuracy.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Stability of Optimal Controls for the Stationary Boussinesq Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Gennady Alekseev ◽  
Dmitry Tereshko
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Boussinesq Equations ◽  
Mixed Boundary Conditions ◽  
State Equation ◽  
Dirichlet Boundary Conditions ◽  
Heat Conducting ◽  
Optimal Controls ◽  
Viscous Heat ◽  
Cost Functionals

The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect to some disturbances of both cost functionals and state equation is proved.

scholarly journals Casimir Effect in Domain Wall Formation

2003 ◽  
Vol 18 (23) ◽  
pp. 4285-4293 ◽  
Author(s):  
M. R. Setare
Keyword(s):  
Domain Wall ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces

The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.

scholarly journals $T\bar T$ and the mirage of a bulk cutoff

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Monica Guica ◽  
Ruben Monten
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Stress Tensor ◽  
Deformation Parameter ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Gravitational Theory ◽  
Dirichlet Boundary Conditions ◽  
Bulk Solution ◽  
Matter Fields

We use the variational principle approach to derive the large NN holographic dictionary for two-dimen-sional T\bar TTT‾-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial ``bulk cutoff’’ is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.

scholarly journals Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term

2021 ◽  
Author(s):  
Jon Asier Bárcena-Petisco
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Space Variable ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Mixed Boundary Conditions ◽  
Null Controllability ◽  
Dirichlet Boundary Conditions ◽  
The Cost ◽  
Transport Term

In this paper we consider the heat equation with Neumann, Robin and mixed boundary conditions (with coefficients on the boundary which depend on the space variable). The main results concern the behaviour of the cost of the null controllability with respect to the diffusivity when the control acts in the interior. First, we prove that if we almost have Dirichlet boundary conditions in the part of the boundary in which the flux of the transport enters, the cost of the controllability decays for a time $T$ sufficiently large. Next, we show some examples of Neumann and mixed boundary conditions in which for any time $T>0$ the cost explodes exponentially as the diffusivity vanishes. Finally, we study the cost of the problem with Neumann boundary conditions when the control is localized in the whole domain.

scholarly journals The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions

2019 ◽  
Vol 19 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Sergio Fernández-Rincón ◽  
Julián López-Gómez
Keyword(s):  
Singular Perturbation ◽  
Boundary Conditions ◽  
Distance Function ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Logistic Equations ◽  
Perturbation Problem ◽  
Second Order Elliptic Operators

Abstract This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, {d\mathcal{L}u=uh(u,x)} , under non-classical mixed boundary conditions, {\mathcal{B}u=0} on {\partial\Omega} . Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To overcome the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of {\partial\Omega} through the regularity of the associated conormal projections and conormal distances. This seems to be a new result of a huge relevance on its own. It actually complements some classical findings of Serrin, [39], Gilbarg and Trudinger, [21], Krantz and Parks, [27], Foote, [18] and Li and Nirenberg [28] concerning the regularity of the inner distance function to the boundary.

scholarly journals The condition number of the BEM-matrix arising from Laplace's equation

2007 ◽  
Vol 4 (2) ◽  
Author(s):  
W. Dijkstra ◽  
R.M.M. Mattheij
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Condition Number ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Circular Domain ◽  
Block Matrix ◽  
Dirichlet Boundary Conditions ◽  
System Matrix

We investigate the condition number of the matrices that appear in the boundary element method. In particular we consider the Laplace equation with mixed boundary conditions. For Dirichlet boundary conditions, the condition number of the system matrix increases linearly with the number of boundary elements. We extend the research and search for a relation between the condition number and the number of elements in the case of mixed boundary conditions. In the case of a circular domain, we derive an estimate for the condition number of the system matrix. This matrix consists of two blocks, each block originating from a well-conditioned matrix. We show that the block matrix is also well-conditioned.

On the Boundary Conditions for Heat Transfer Using Immersed Boundary Methods

2006 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Tamara Rodic ◽  
Arturo Pacheco-Vega
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Numerical Data ◽  
Mixed Boundary Conditions ◽  
Heat Diffusion ◽  
Special Treatment ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
Transfer Problems

We describe the implementation of a general interpolation technique which allows the accurate imposition of the Dirichlet, Neumann and mixed boundary conditions on complex geometries when using the immersed boundary technique on Cartesian grids. The scheme is general in that it does not involve any special treatment to handle either one of the three types of boundary conditions. The accuracy of the interpolation algorithm on the boundary is assessed using three heat transfer problems: (1) forced convection over a cylinder placed in an unbounded flow, (2) natural convection on a cylinder placed inside a cavity, and (3) heat diffusion inside an annulus. The results show that the accuracy of the scheme is second order and are in agreement with analytical and/or numerical data.

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