The effect of small viscous dissipation on Lagrangian transport in two-dimensional vorticityconserving fluid flows motivates this work. If the inviscid equation admits a base flow in which different fluid regions are divided by separatrices, then transport between these regions is afforded by the splitting of separatrices caused by viscous dissipation. Finite-time Melnikov theory allows us to m...

A non-traditional operator split (OS) scheme for the solution of the advection-diffusion-reaction (ADR) equation is proposed. The scheme is implemented with the recently published central scheme [A. Kurganov, E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000) 241–282] to accurately simulate advection-re...

In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and solving the remaining partial differential equation. First we give a short introduction to free boundary problems and the problems occurring in optimisation. Then...

We apply the point form of relativistic quantum mechanics to develop a Poincaré invariant coupled-channel formalism for two-particle systems interacting via one-particle exchange. This approach takes the exchange particle explicitly into account and leads to a generalized eigenvalue equation for the Bakamjian-Thomas type mass operator of the system. The coupling of the exchange particle is deri...

In this paper we compare any vector bundle (or, more generally, torsion free sheaf) F on P N and the free vector bundle ⊕ n i=1 O P N (b i) having the same rank and splitting type. We show that the first one has always " less " global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequen...

The Peaceman–Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman– Rachford scheme in the...

We present an integral equation formulation for the unsteady Stokes equations in two dimensions. This problem is of interest in its own right, as a model for slow viscous flow, but perhaps more importantly, as an ingredient in the solution of the full, incompressible Navier-Stokes equations. Using the unsteady Green’s function, the velocity evolves analytically as a divergence-free vector field...

1 This report is available by anonymous ftp from ftp.esat.kuleuven.ac.be in the directory pub/SISTA/moreau/reports/. The missing gures, which have been excluded because they are diicult to print, are available separately in the le chua gures.ps. Abstract Composition methods are methods for the integration of ordinary differential equations arising from diierential geometry, or more precisely, L...

Classical relativistic field theory is used as a basis for a general discussion of the problem of splitting up the total energy-momentum tensor ofa system into contributions from its component subsystems. Both the Minkowski and Abraham forms (including electrostriction) arise naturally in alternative split-up procedures applied to a nondispersive dielectric fluid. The case of an electromagnetic...

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. O...