RNA matrix models with external interactions and their asymptotic behavior.
We study a matrix model of RNA in which an external perturbation on n nucleotides is introduced in the action of the partition function of the polymer chain. The effect of the perturbation appears in the exponential generating function of the partition function as a factor exp(1-nalpha/L) (where alpha is the ratio of strengths of the original to the perturbed term and L is the length of the chain). The asymptotic behavior of the genus distribution functions as a function of length for the matrix model with interaction is analyzed numerically for all n<or=L. It is found that as nalpha/L is increased from 0 to 1, the term 3L in the number of diagrams a'L,g,alpha at a fixed length L, genus g and alpha, goes to 2L [(3-nalpha/L)L for any nalpha/L] and the total number of diagrams Nalpha' at a fixed length L and alpha but independent of genus g, undergoes a change in the factor exp(sqrt[L]) to 1 (exp[(1-nalpha/L)sqrt[L]] for any nalpha/L). However the exponent L of the dominant length dependent term in a'L,g,alpha stays unchanged. Hence the universality is robust to changes in the interaction (alpha). The distribution functions also exhibit unusual behavior at small lengths.
Garg
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Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
Deo
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D001483:Base Sequence; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D008969:Molecular Sequence Data; D009690:Nucleic Acid Conformation; D012313:RNA / Q000737:chemistry* / Q000648:ultrastructure*
D012313:RNA