arXiv subjects

Thomas Wolf

Publications and source records attributed to Thomas Wolf.

149 records · Page 9Linked to original sources

arXiv2003

The integration of systems of linear PDEs using conservation laws of syzygies

A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Groebner Basis computation. Compared with the more obvious way of integrating a single equation and substituting the result in other equations the new technique integrates more than one equation at once and therefore introduces temporarily fewer new functions of integration that in addition depend on fewer variables. Especially for high order PDE systems in many variables the conventional integration technique may lead to an explosion of the number of functions of integration which is avoided with the new method. A further benefit is that redundant free functions in the solution are either prevented or that their number is at least reduced.

cs.SC↗

arXiv2003

Size reduction and partial decoupling of systems of equations

A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely to be factorizable or integrable. A variation of this method is applicable to non-linear systems. Modifications to improve efficiency are given and examples are shown. This procedure can be used in connection with the computation of the radical of a differential ideal (differential Groebner basis).

cs.SC↗

arXiv2003

Applications of CRACK in the Classification of Integrable Systems

Work on different classification problems is described as: the classification of integrable vector evolution equations, NLS systems with two vector unknowns, systems with one scalar and one vector unknown, classification of integrable Hamiltonians and non-local 2+1 dimensional equations. All these problems lead to large bi-linear algebraic systems to be solved. In an extended appendix an overview of the computer algebra package is given that was used to solve these systems.

nlin.SI↗

arXiv2002

G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The three-dimensional conformal group is restricted to the case when the two-dimensional abelian isometry subalgebra is an ideal and it is also assumed to act on non-null hypersurfaces (both, spacelike and timelike cases are studied). We consider both, diagonal and non-diagonal metrics and find all the perfect-fluid solutions under these assumptions (except those already known). We find four families of solutions, each one containing arbitrary parameters for which no differential equations remain to be integrated. We write the line-elements in a simplified form and perform a detailed study for each of these solutions, giving the kinematical quantities of the fluid velocity vector, the energy-density and pressure, values of the parameters for which the energy conditions are fulfilled everywhere, the Petrov type, the singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker metrics contained in each family.

gr-qc↗

arXiv1999

Structure and Tc of Y0.8Ca0.2Ba2Cu3O6.92 under High Pressure

The lattice parameters and Tc of Y1-yCayBa2Cu3Ox have been determined under pressure up to 10 GPa using a diamond anvil cell. The results are used to test the extended charge transfer model that connects the pressure effect on Tc to an intrinsic dTc,max/dp and a pressure induced hole doping dnh/dp, the latter being caused by charge transfer from the CuO chains to the CuO2 planes. dnh/dp and dTc,max/dp are usually assumed to be constant with respect to pressure p. However, our experiments show that the usage of this model gives a poor description of the experimental Tc(p) values. We connected the extended charge transfer model to the pressure induced changes of the compressibilities. With this ansatz the calculated Tc(p) values show an excellent agreement with the experimentally determined values.

cond-mat.supr-con↗