A numerical method for NNLO calculations

A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.Comment: 5 pages, Talk presented at Radcor/Loops and Legs 2002, to appear in the proceeding

A Numerical Method for Conformal Mappings

A numerical technique is presented for calculating the Taylor coefficients of the analytic function which maps the unit circle onto a region bounded by any smooth simply connected curve. The method involves a quadratically convergent outer iteration and a super-linearly convergent inner iteration. If N complex points are distributed equidistantly around the periphery of the unit circle, their images on the edge of the mapped region, together with approximations for the N/2 first Taylor coefficients, are obtained in O(Nlog N) operations. A calculation of time-dependent waves on deep water is discussed as an example of the potential applications of the method

The Application of a Numerical Method for Taxonomy From Isoenzymatical Results : Coefficient of Parental Correlation Between Schistosoma Species

Using enzyme characters by starch gel electrophoresis, we have applied the method of Numerical Taxonomy to the Schistosomes isolate/stocks. Seven isoenzymes (Phosphoglucomutase = PGM; Phospho glucose isomerase = PGI; Hexokinase = HK; Mannose phosphate isomerase = MPI; Alcaline phosphatase = ALP; Malic enzyme = ME and Malate deshydrogenase = MDH) of 15 isolats/stocks are examined. Twenty six electromorphs, corresponding to equivalent number of isoenzymes, are identified by this method, and then grouped into 8 zymodemes. These zymodemes were used as Operational Taxonomy Unit (OTU) and compared pairwise, using these indice and it forms the basis for the taxonomic scheme elaborated. The final relationships are exhibited in the agglomerative dendrogram, constructed using complete linkage. The separation into phenons is confirmed by correspondence analysis. It is concluded that the original lines fall into four groups correspondings to the complexes Schistosoma mansoni, S. bovis, S. curasonni and S. haematobium. The phenons are recognised by Numerical Taxonomy, can be equated with the taxa of traditional systematics

Numerical Method for Shock Front Hugoniot States

We describe a Continuous Hugoniot Method for the efficient simulation of shock wave fronts. This approach achieves significantly improved efficiency when the generation of a tightly spaced collection of individual steady-state shock front states is desired, and allows for the study of shocks as a function of a continuous shock strength parameter, $v_p$. This is, to our knowledge, the first attempt to map the Hugoniot continuously. We apply the method to shock waves in Lennard-Jonesium along the $$ direction. We obtain very good agreement with prior simulations, as well as our own benchmark comparison runs.Comment: 4 pages, 3 figures, from Shock Compression of Condensed Matter 200

New Numerical Method for Fermion Field Theory

A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using Grassmann polynomial expansions for the generating functional $Z$, we calculate propagators for systems of interacting fermions. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. Because it is not based on a statistical technique, it does not have many of the difficulties often encountered when simulating fermions. Since no determinant is ever calculated, solutions to problems with dynamical fermions are handled more easily. This approach is very flexible, and can be taylored to specific problems based on convenience and computational constraints. We present simple examples to illustrate the method; more general schemes are desirable for more complicated systems.Comment: 24 pages, latex, figures separat

Improved transfer matrix method without numerical instability

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has no extra cost of computing time as the length of homogeneous scattering region becomes large. The comparison between the scattering matrix method(SMM) and our new TMM is given. It clearly shows that our new method is much faster than SMM.Comment: 5 pages,3 figure

Conjugate Function Method for Numerical Conformal Mappings

We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions and properties of quadrilaterals. Several numerical examples are given.Comment: 23 pages, 15 figures, 5 table