scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

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.

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.

scholarly journals Inversion of Potential Vorticity Density

2017 ◽  
Vol 74 (3) ◽  
pp. 801-807 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka ◽  
Thomas Spengler
Keyword(s):  
Boundary Conditions ◽  
Potential Vorticity ◽  
Potential Temperature ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Absolute Vorticity ◽  
Vertical Vector ◽  
The North ◽  
And Function

Abstract Inversion of potential vorticity density with absolute vorticity and function η is explored in η coordinates. This density is shown to be the component of absolute vorticity associated with the vertical vector of the covariant basis of η coordinates. This implies that inversion of in η coordinates is a two-dimensional problem in hydrostatic flow. Examples of inversions are presented for (θ is potential temperature) and (p is pressure) with satisfactory results for domains covering the North Pole. The role of the boundary conditions is investigated and piecewise inversions are performed as well. The results shed new light on the interpretation of potential vorticity inversions.

CHIRAL ZEROMODES ON VORTEX-TYPE INTERSECTING FIVE-BRANE IN HETEROTIC STRING

2013 ◽  
Vol 21 ◽  
pp. 191-192
Author(s):  
MASAYA YATA
Keyword(s):  
Dirac Equation ◽  
String Theory ◽  
Boundary Conditions ◽  
Heterotic String ◽  
The Other ◽  
Two Dimensional ◽  
Complete Spectrum ◽  
Heterotic String Theory ◽  
Brane Solution ◽  
Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8 × E8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two.

Two point fractional boundary value problems with a fractional boundary condition

2018 ◽  
Vol 21 (2) ◽  
pp. 442-461 ◽  
Author(s):  
Jeffrey W. Lyons ◽  
Jeffrey T. Neugebauer
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

Abstract In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given.

Development of Welding Distortion Analysis Method Using Residual Strain as Boundary Condition

2008 ◽  
Vol 580-582 ◽  
pp. 649-654 ◽  
Author(s):  
Yun Sok Ha ◽  
Si Hoon Cho ◽  
Tae Won Jang
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Residual Strain ◽  
The Other ◽  
Welding Distortion ◽  
Thermal Distortion ◽  
Analysis Method ◽  
Distortion Analysis ◽  
Direct Input ◽  
Inherent Strain

There are two ways of conventional thermal distortion analysis. One is thermal elastoplastic analysis and the other is equivalent forces method based on inherent strain. The former needs exorbitant analysis time, while the latter cannot obtain stress results and requires more time with loads modeling on curved plates. To solve those time-consuming problems, a new kind of thermal distortion analysis method was developed. In this method, inherent strains are devised to be used as direct input factors as boundary conditions. Suggested analysis method was already adopted at welding distortion analysis of large hull block, which was considered as impossible.

scholarly journals VORTEX NUCLEATION IN ROTATING BOSE–EINSTEIN CONDENSATE: THE ROLE OF THE BOUNDARY CONDITION FOR THE ORDER PARAMETER

2006 ◽  
Vol 20 (15) ◽  
pp. 2147-2158
Author(s):  
W. V. POGOSOV ◽  
K. MACHIDA
Keyword(s):  
Boundary Condition ◽  
Order Parameter ◽  
Topological Defects ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Surface Modes ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Vortex Nucleation

We study the problem of vortex nucleation in rotating two-dimensional Bose–Einstein condensate confined in a harmonic trap. We show that, within the Gross–Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then vortices move toward the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes.

A Comparative Study of Artificial Boundary Conditions in ABAQUS

2013 ◽  
Vol 671-674 ◽  
pp. 1386-1389
Author(s):  
Yan Wei Wang ◽  
Shan You Li ◽  
Qiang Ma ◽  
Wei Li
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Element Model ◽  
The Other ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Dimensional Finite Element ◽  
Viscous Boundary ◽  
Better Than

Viscous boundary, viscous spring boundary, infinite boundary have been widely used during the last decades to solve the wave propagation in the infinite ground. In this paper we evaluate the performance of the three boundary conditions focusing on their solution precision. The comparison is performed on a two dimensional finite element model built by ABAQUS. The results show that viscous spring boundary outperforms the other boundary conditions, and viscous boundary is better than infinite element.

Study of the Effect of Boundary Conditions on Residual Stresses in Welding Using Element Birth and Element Movement Techniques

2003 ◽  
Vol 125 (4) ◽  
pp. 432-439 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
Maher Y. A. Younan ◽  
Abdalla S. Wifi
Keyword(s):  
Residual Stresses ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Welding Process ◽  
Computation Time ◽  
The Other ◽  
Two Dimensional ◽  
The Media ◽  
Three Dimensional Models ◽  
Element Movement

The structure in which the welding process is performed highly affects the residual stresses generated in the welding. This effect is simulated by choosing the appropriate boundary conditions in modeling the welding process. The major parameters of the boundary conditions are the method by which the base metal is being fixed and the amount of heat being applied through the torch. Other parameters may include the coefficients of thermal heat loss from the plate which may simulate the media in which the welding is taking place. In modeling the welding process, two-dimensional forms of approximation were developed in analyzing most of the models of such problem. Three-dimensional models analyzing the welding process were developed in limited applications due to its high computation time and cost. With the development of new finite element tools, namely the element movement technique developed by the authors, full three-dimensional analysis of the welding process is becoming in hand. In the present work, three different boundary conditions shall be modeled comparing their effect on the welding. These boundary conditions shall be applied to two models of the welding process: one using the element birth technique and the other using the element movement technique showing the similarity in their responses verifying the effectiveness of the latter being accomplished in a shorter time.

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