Rational approximations to Tricomi's psi function Interim report, 20 Mar. - 19 Jun. 1968

Closed form rational approximations to Tricomi psi functio

Numerical integration of nonlinear differential equations by use of rational approximation Final report, 15 Jan. 1965 - 14 Jul. 1967

Numerical integration of nonlinear differential equations by use of rational approximatio

Differential-difference properties of generalized Jacobi polynomials Interim report

Differential-difference properties of generalized Jacobi polynomial

Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

Random walk weakly attracted to a wall

We consider a random walk X_n in Z_+, starting at X_0=x>= 0, with transition probabilities P(X_{n+1}=X_n+1|X_n=y>=1)=1/2-\delta/(4y+2\delta) P(X_{n+1}=X_n+1|X_n=y>=1)=1/2+\delta/(4y+2\delta) and X_{n+1}=1 whenever X_n=0. We prove that the expectation value of X_n behaves like n^{1-(\delta/2)} as n goes to infinity when \delta is in the range (1,2). The proof is based upon the Karlin-McGregor spectral representation, which is made explicit for this random walk.Comment: Replacement with minor changes and additions in bibliography. Same abstract, in plain text rather than Te

Single polymer dynamics in elongational flow and the confluent Heun equation

We investigate the non-equilibrium dynamics of an isolated polymer in a stationary elongational flow. We compute the relaxation time to the steady-state configuration as a function of the Weissenberg number. A strong increase of the relaxation time is found around the coil-stretch transition, which is attributed to the large number of polymer configurations. The relaxation dynamics of the polymer is solved analytically in terms of a central two-point connection problem for the singly confluent Heun equation.Comment: 9 pages, 6 figure

Improved Nearside-Farside Decomposition of Elastic Scattering Amplitudes

A simple technique is described, that provides improved nearside-farside (NF) decompositions of elastic scattering amplitudes. The technique, involving the resummation of a Legendre partial wave series, reduces the importance of unphysical contributions to NF subamplitudes, which can arise in more conventional NF decompositions. Applications are made to a strong absorption model and to a $^{16}$O + $^{12}$C optical potential at $E_{\text{lab}} = 132$ MeV.Comment: 5 pages, 2 figure