Difference methods for the solution of the time-dependent semiconductor flow equations

1971 ◽  
Vol 7 (12) ◽  
pp. 353 ◽  
Author(s):  
M. Reiser
Keyword(s):  
Time Dependent ◽  
Flow Equations ◽  
Difference Methods

scholarly journals Examining instabilities due to driven scalars in AdS

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Brad Cownden
Keyword(s):  
Turbulent Energy ◽  
Time Dependent ◽  
Linear Solution ◽  
Driven Systems ◽  
Flow Equations ◽  
Energy Cascades ◽  
Analytic Expressions ◽  
Bulk Scalar Field ◽  
Dependent Sources ◽  
Secular Terms

Abstract We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdSd+1 to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations mass values $$ {m}_{BF}^2<{m}^2\le 0 $$ m BF 2 < m 2 ≤ 0 , and for various driving functions. Finally, we numerically evaluate these sources for d = 4 and discuss what role these driven solutions play in the perturbative stability of AdS.

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