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

A Numerical Method for General Relativistic Magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, and Wilson, and uses Evans and Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfv\'en wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and non-relativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-$l$ tori that are subject to the magnetorotational instability.Comment: 37 pages, 14 figures, submitted to ApJ. Animations can be viewed at http://www.astro.virginia.edu/~jd5v/grmhd/grmhd.htm

An efficient numerical method for shakedown analysis

The algorithm proposed in [9] for incremental elastoplasticity is extended and applied to shakedown analysis. Using the three field mixed finite element proposed in [22] a series of mathematical programming problems or steps, obtained from the application of the proximal point algorithm to the static shakedown theorem, are obtained. Each step is solved by an Equality Constrained Sequential Quadratic Programming (EC-SQP) tech- nique that allows a consistent linearization of the equations improving the computational efficiency

A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach

In this paper, a novel finite-element based method for finite-strain mechanochemistry with moving reaction fronts, which separate the chemically transformed and the untransformed phases, is proposed. The reaction front cuts through the finite elements and moves independently of the finite-element mesh, thereby removing the necessity for remeshing. The proposed method solves the coupled mechanics-diffusion–reaction problem. In the mechanical part of the problem, the force equilibrium and the displacement continuity conditions at the reaction front are enforced weakly using a Nitsche-like method. The formulation is applicable to the case of large deformations and arbitrary constitutive behaviour, and is also consistent with the minimisation of the total potential energy