Relaxation Methods for Differential Equations

Physics/Research 2012. 7. 26. 21:25

In relaxation methods ODEs are replaced by approximate finite difference equations (FDEs) on a grid or mesh of points that spans the domain of interest.

 

알고리즘 및 사용 예제 관련문서들:

NumericalRecipiesInC/c17-3.pdf

NumericalRecipiesInC/c17-4.pdf

 

Numerical Recipes 에서 얻을 수 있는 필요한 코드들:

1) solvde() : main routine; 

2) bksub ()  : supplementary routine

3) pinvs ()  : supplementary routine

4) red ()  : supplementary routine

5) difeq ()  : user supplied  routine in which differential equations, boundary conditions, and their jacobians are defined. called by solvde().

 

주의점: 경계조건 설정에서 주의해야 한다;

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Wald’s Entropy, Area & Entanglement

Physics/Research 2012. 2. 25. 20:55

별로 도움은 안되지만,
http://www.phys.huji.ac.il/~barak_kol/HDGR/proceedings/Brustein.pps   

f(R) gravity에서 Wald entropy 계산:
D.N. Vollick, Phys. Rev. D76 (2007) 124001, "Noether charge and black hole entropy in modified theories of gravity". http://arxiv.org/abs/0710.1859
 ==> based on the Palatini formalism. connection이 일반적으로 metric compatible 하지 않음. 따라서 covariant derivative에 compatible인 새로운 metric을 이용해서 connection을 표현해야 한다. 이 새로운 metric을 이용하면 metric formalism을 그대로 적용 가능함.


R. Brustein, D. Gorbonos, M. Hadad and A.J.M. Medved, Phys.Rev. D84 (2011) 064011, "Evaluating the Wald entropy from two-derivative terms in quadratic actions". http://arxiv.org/abs/1106.4394   

horizon에서 벗어난 영역에서의 Wald entropy 계산: 
R. Brustein, and A.J.M. Medved, "Gravitational entropy and thermodynamics away from the horizon", http://arxiv.org/abs/1201.5754

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Physics/Research 2012. 2. 24. 18:08
http://www.ihes.fr/~vanhove/Slides/deruelle-ihes-apr2010.pdf
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