scholarly journals A functional approach to the numerical conformal bootstrap

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Miguel F. Paulos ◽  
Bernardo Zan
Keyword(s):  
Functional Approach ◽  
Numerical Results ◽  
Extremal Solutions ◽  
Usual Approach ◽  
Functional Basis ◽  
Conformal Bootstrap ◽  
Higher Dimensional

Abstract We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in opposition to hundreds of components in the usual approach. We explain how this is a consequence of the functional basis correctly capturing the asymptotics of bound-saturating extremal solutions to crossing. We discuss how these methods can and should be implemented in higher dimensional applications.

scholarly journals Bootstrap experiments on higher dimensional CFTs

2018 ◽  
Vol 33 (07) ◽  
pp. 1850036 ◽  
Author(s):  
Yu Nakayama
Keyword(s):  
Empirical Relationship ◽  
Adjoint Representation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Time Dimension ◽  
Unitarity Bound ◽  
Conformal Field ◽  
Dimension Formula ◽  
Conformal Bootstrap ◽  
Higher Dimensional

Recent programs on conformal bootstrap suggest an empirical relationship between the existence of nontrivial conformal field theories and nontrivial features such as a kink in the unitarity bound of conformal dimensions in the conformal bootstrap equations. We report the existence of nontrivial kink-like behaviors in the unitarity bound of scalar operators in the adjoint representation of the [Formula: see text] symmetric conformal field theories. They have interesting properties: (1) the kink-like behaviors exist in [Formula: see text] dimensions; (2) the location of kink-like behaviors are when the unitarity bound hits the space–time dimension [Formula: see text]; (3) there exists a “conformal window” of [Formula: see text], where [Formula: see text] in [Formula: see text] and [Formula: see text] in [Formula: see text].

scholarly journals Stability analysis of swarming model with time delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adsadang Himakalasa ◽  
Suttida Wongkaew
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Long Range ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Short Range ◽  
Functional Approach ◽  
Numerical Results ◽  
The Social ◽  
Short Range Repulsion

AbstractA swarming model is a model that describes the behavior of the social aggregation of a large group of animals or the community of humans. In this work, the swarming model that includes the short-range repulsion and long-range attraction with the presence of time delay is investigated. Moreover, the convergence to a consensus representing dispersion and cohesion properties is proved by using the Lyapunov functional approach. Finally, numerical results are provided to demonstrate the effect of time delay on the motion of the group of agents.

Applying a functional approach to participation in online groups

2011 ◽  
Author(s):  
Paul T. Fuglestad ◽  
John S. Kim ◽  
Clelia Anna Mannino ◽  
Rich Davies ◽  
Patrick C. Dwyer ◽  
...  
Keyword(s):  
Functional Approach ◽  
Online Groups

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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