PDE2D: Easy-to-use software for general two-dimensional partial differential equations

Sewell, Granville

doi:10.1016/0965-9978(93)90047-w

Cited by 49 publications

(25 citation statements)

References 2 publications

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“…Again the density and the loss rate at the ends of the flux tube are equal. Again the source profile is assumed to be of the form (22), but now we allow either S 1 or S 2 to be negative. Because of the negative source term it is possible to obtain density profiles where the ratio max(n 1 , n 2 )/min(n 1 , n 2 ) of the densities at the midpoints of the two cells can take any value.…”

Section: Case 2: Field Lines With Two Poloidal Turnsmentioning

confidence: 99%

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Two dimensional modelling approach to transport properties of the TEXTOR-DED laminar zone

2000

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Abstract. An important operational range for TEXTOR-DED is the case of a high ergodization at the plasma edge. Under these conditions, the edge magnetic field forms a proper ergodic layer and a laminar zone. The laminar zone is established by magnetic field lines which intersect wall elements after only a few toroidal turns (open ergodic system). For this, both the heat and particle transport in the plasma edge are dominated by the laminar zone which shows a well defined structure compared with that of the ergodic layer. For the present analysis the regions containing field lines with connection lengths corresponding to one or to two poloidal turns are of particular interest; the radial width of these regions is of the same order as the width of the unperturbed SOL of a 'classical' limiter or divertor configuration. Field lines running poloidally twice around the torus introduce a particular new feature, they impose a connection between radially separated areas and thus enhance the radial temperature and particle transport. A new 2-D modelling approach code for the laminar zone of an ergodic divertor has been developed which is strongly oriented on the topology of the magnetic field lines in the plasma edge. A 2-D finite element method is used in order to model the perpendicular transport of particles and energy. For obtaining a solution of the parallel transport, an analytical model is discussed providing expressions for averaged particle and energy sources. By considering the topological properties of the magnetic field and corresponding assumptions in the code, the transport calculation in the perturbed plasma edge gives a first insight into the generic transport properties of the TEXTOR-DED laminar zone. As an important application for later experiments the power fluxes to the wall elements are estimated. They show a strong variation perpendicular to the perturbation coils and a medium variation over the helical divertor footprints.

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Section: Case 2: Field Lines With Two Poloidal Turnsmentioning

confidence: 99%

“…To solve the 2-D perpendicular transport equations, we use the commercially available partial differential equation solver PDE2-D [22], which is based on a finite element method (FEM). The parallel fluxes along field lines enter the differential equations for perpendicular transport as sources and sinks.…”

Section: Strategy For Modelling Of the Laminar Zonementioning

confidence: 99%

Two dimensional modelling approach to transport properties of the TEXTOR-DED laminar zone

2000

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“…This is a widely used tool and has been shown fairly effective in dealing with nonlinear boundary value problems for two-dimensional equations. PDE2D is a general-purpose two-dimensional time-dependent partial differential equation solver [33], using a finite element program. The main program is complied by a LF90 FORTRAN compiler.…”

Section: Numerical Resultsmentioning

confidence: 99%

Dirichlet inhomogeneous boundary value problem for the n+1 complex Ginzburg–Landau equation

Gao

2004

Journal of Differential Equations

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We study the following complex Ginzburg-Landau equation with cubic nonlinearity on OCR n for t40 : u t ¼ ða þ iaÞDu À ðb þ ibÞjuj 2 u ða; b40Þ under initial and Dirichlet boundary conditions uðx; 0Þ ¼ hðxÞ for xAO; uðx; tÞ ¼ Qðx; tÞ on @O where h; Q are given smooth functions. Under suitable conditions, we prove the existence of a global solution in H 1 : Further, this solution approaches to the solution of the NLS limit under identical initial and boundary data as a; b-0 þ : r

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“…9.3) [16] with an adaptive triangular grid. To minimize finite-size effects, we use a linear patch size L = 10, 000h and to minimize discretization effects we use N = 100, 000 triangles.…”

Section: Modelmentioning

confidence: 99%

Circumferential gap propagation in an anisotropic elastic bacterial sacculus

Taneja

Levitan²,

Rutenberg³

2014

Phys. Rev. E

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We have modelled stress concentration around small gaps in anisotropic elastic sheets, corresponding to the peptidoglycan sacculus of bacterial cells, under loading corresponding to the effects of turgor pressure in rod-shaped bacteria. We find that under normal conditions the stress concentration is insufficient to mechanically rupture bacteria, even for gaps up to a micron in length. We then explored the effects of stress-dependent smart-autolysins, as hypothesised by Arthur L Koch [Advances in Microbial Physiology 24, 301 (1983); Research in Microbiology 141, 529 (1990)]. We show that the measured anisotropic elasticity of the PG sacculus can lead to stable circumferential propagation of small gaps in the sacculus. This is consistent with the recent observation of circumferential propagation of PG-associated MreB patches in rod-shaped bacteria. We also find a bistable regime of both circumferential and axial gap propagation, which agrees with behavior reported in cytoskeletal mutants of B. subtilis. We conclude that the elastic anisotropies of a bacterial sacculus, as characterised experimentally, may be relevant for maintaining rod-shaped bacterial growth.

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PDE2D: Easy-to-use software for general two-dimensional partial differential equations

Cited by 49 publications

References 2 publications

Two dimensional modelling approach to transport properties of the TEXTOR-DED laminar zone

Two dimensional modelling approach to transport properties of the TEXTOR-DED laminar zone

Dirichlet inhomogeneous boundary value problem for the n+1 complex Ginzburg–Landau equation

Circumferential gap propagation in an anisotropic elastic bacterial sacculus

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