scholarly journals Lectures on the asymptotic expansion of a Hermitian matrix integral

2007 ◽  
pp. 91-134 ◽  
Author(s):  
Motohico Mulase
Keyword(s):  
Asymptotic Expansion ◽  
Hermitian Matrix ◽  
Matrix Integral

scholarly journals ASYMPTOTIC ANALYSIS OF A HERMITIAN MATRIX INTEGRAL

1995 ◽  
Vol 06 (06) ◽  
pp. 881-892 ◽  
Author(s):  
MOTOHICO MULASE
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Hermitian Matrix ◽  
Matrix Integral

The asymptotic expansion of a Hermitian matrix integral known as the Penner model is rigorously calculated.

scholarly journals THE TOPOLOGICAL CP1 MODEL AND THE LARGE-N MATRIX INTEGRAL

1994 ◽  
Vol 09 (31) ◽  
pp. 2893-2902 ◽  
Author(s):  
TOHRU EGUCHI ◽  
SUNG-KIL YANG
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Riemann Surfaces ◽  
Hermitian Matrix ◽  
Coupling Constants ◽  
Holomorphic Maps ◽  
Matrix Integral ◽  
Large N

We discuss the topological CP 1 model which consists of the holomorphic maps from Riemann surfaces onto CP 1. We construct a large-N matrix model which reproduces precisely the partition function of the CP 1 model at all genera of Riemann surfaces. The action of our matrix model has the form [Formula: see text] where M is an N × N Hermitian matrix and tn,P(tn,Q), (n = 0, 1, 2, …) are the coupling constants of the nth descendant of the puncture (Kähler) operator.

Influence of free convection on the diffusion current to a sphere in a laminar forced flow regime

1985 ◽  
Vol 50 (12) ◽  
pp. 2697-2714
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Asymptotic Expansion ◽  
Free Convection ◽  
Boundary Value Problem ◽  
Concentration Gradient ◽  
Empirical Formula ◽  
Convective Diffusion ◽  
Forced Flow ◽  
Diffusion Current ◽  
Wide Range ◽  
Free And Forced Convection

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

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