We explain the usage of MEX files to call Fortran routines from Matlab in a "quick and dirty" but... more We explain the usage of MEX files to call Fortran routines from Matlab in a "quick and dirty" but simple and efficient way. Our main examples are interfaces to the ODE solver SODEX and the PDE solver PDETWO. We apply the SODEX interface to the van der Pol oscillator and Chua's circuit, illustrating a significant speedup compared to Matlab integrators, and use the PDETWO interface to integrate a reaction diffusion system, the porous medium equation, a wave equation, some shallow water equations, and some more examples.
Traveling interface modulations in the catalytic NH3+ O2 reaction on a Rh (110) surface
Physical Chemistry …, 2012
... citable. References 1 M. Cross and P. Hohenberg, Rev. Mod. Phys., 1993, 65, 854. 2 Chemical W... more ... citable. References 1 M. Cross and P. Hohenberg, Rev. Mod. Phys., 1993, 65, 854. 2 Chemical Waves and Patterns, ed. R. Kapral and K. Showalter, Kluwer, Dordrecht, 1995. 3 R. Imbihl and G. Ertl, Chem. Rev, 1995, 95, 697. ...
Given a bounded domain G ⊂ Rd, d ≥ 3, we study smooth solutions of a linear parabolic equation wi... more Given a bounded domain G ⊂ Rd, d ≥ 3, we study smooth solutions of a linear parabolic equation with non-constant coefficients inG, which at the boundary have to C1-match with some harmonic function in Rd \ G vanishing at spatial infinity. This problem arises in the framework of magnetohydrodynamics if certain dynamo- generated magnetic fields are considered: For example,
Given a bounded domain G ⊂ R d , d ≥ 3, we study smooth solutions of a linear parabolic equation ... more Given a bounded domain G ⊂ R d , d ≥ 3, we study smooth solutions of a linear parabolic equation with non-constant coefficients in G, which at the boundary have to C 1 -match with some harmonic function in R d \ G vanishing at spatial infinity.
We provide and explain some simple self-contained matlab (octave) implementations of Fourier spec... more We provide and explain some simple self-contained matlab (octave) implementations of Fourier spectral solvers for nonlinear parabolic PDE and for the 2D Navier-Stokes equations in a periodic box, including a discussion of anti-aliasing and power spectra. We illustrate the solvers with various examples including some (weakly) turbulent flows.
We explain the usage of MEX files to call Fortran routines from Matlab in a "quick and dirty" but... more We explain the usage of MEX files to call Fortran routines from Matlab in a "quick and dirty" but simple and efficient way. Our main examples are interfaces to the ODE solver SODEX and the PDE solver PDETWO. We apply the SODEX interface to the van der Pol oscillator and Chua's circuit, illustrating a significant speedup compared to Matlab integrators, and use the PDETWO interface to integrate a reaction diffusion system, the porous medium equation, a wave equation, some shallow water equations, and some more examples.
p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the numerical solution ... more p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the numerical solution of optimal control (OC) problems with an infinite time horizon for parabolic systems of PDE over 1D or 2D spatial domains. The basic idea is to treat the OC problem via the associated canonical system in two steps. First we use pde2path to find branches of stationary solutions of the canonical system, also called canonical steady states (CSS). In a second step we use the results and the spatial discretization of the first step to calculate the objective values of time-dependent canonical paths ending at a CSS with the so called saddle point property. This is a (typically very high dimensional) boundary value problem (BVP) in time, which we solve by combining a modification of the BVP solver TOM with a continuation algorithm in the initial states. We explain the design and usage of the package via two example problems, namely the optimal management of a distributed shallow lake model, and...
Optimal control and spatial patterns in a semi arid grazing model
DESCRIPTION We consider an infinite time horizon spatially distributed optimal control problem fo... more DESCRIPTION We consider an infinite time horizon spatially distributed optimal control problem for a semi arid grazing model where vegetation and soil water as the state variables fulfill a two species reaction diffusion system, with rainfall as the main external parameter. We numerically analyze the associated four component canonical system and hence the optimal control problem in two steps. First we use the continuation and bifurcation package pde2path to find a rather rich bifurcation structure of Flat and Patterned Canonical Steady States (FCSS and PCSS, respectively), in 1D and 2D. Then we use the BVP solver TOM to calculate canonical paths to some of the FCSS and PCSS, i.e., time dependent solutions of the canonical system that connect to some FCSS or PCSS. It turns out that over wide parameter regimes the FCSS are never optimal. Instead, driving the system to a PCSS yields a higher profit. Moreover, an important benefit of the (social) optimal control is that compared to pri...
Amplitude equations–an invitation to multi-scale analysis
The Lombardo-Fink-Imbihl model of the NO+NH 3 reaction on a Pt(100) surface consists of 7 coupled... more The Lombardo-Fink-Imbihl model of the NO+NH 3 reaction on a Pt(100) surface consists of 7 coupled ODE and shows stable relaxation oscillations with sharp transitions in the relevant temperature range. Here we study numerically the effect of coupling of these oscillators by surface diffusion in 2D. We find different types of patterns, in particular phase clusters and standing waves. In models of related surface reactions such clustered solutions are known to exist only under a global coupling through the gas phase. This global coupling is replaced here by relatively fast diffusion of two variables which are kinetically slaved in the ODE. We also compare our simulations with experimental results and discuss some shortcomings of the model.
We provide and explain some simple self-contained matlab (octave) implementations of Fourier spec... more We provide and explain some simple self-contained matlab (octave) implementations of Fourier spectral solvers for nonlinear parabolic PDE and for the 2D Navier-Stokes equations in a periodic box, including a discussion of anti-aliasing and power spectra. We illustrate the solvers with various examples including some (weakly) turbulent flows.
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Papers by Hannes Uecker