60 research outputs found
A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems
We derive a posteriori error bounds for a quasilinear parabolic problem,
which is approximated by the -version interior penalty discontinuous
Galerkin method (IPDG). The error is measured in the energy norm. The theory is
developed for the semidiscrete case for simplicity, allowing to focus on the
challenges of a posteriori error control of IPDG space-discretizations of
strictly monotone quasilinear parabolic problems. The a posteriori bounds are
derived using the elliptic reconstruction framework, utilizing available a
posteriori error bounds for the corresponding steady-state elliptic problem.Comment: 8 pages, conference ENUMATH 200
Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions
In an intense laser field, an electron may decay by emitting a pair of
photons. The two photons emitted during the process, which can be interpreted
as a laser-dressed double Compton scattering, remain entangled in a
quantifiable way: namely, the so-called concurrence of the photon polarizations
gives a gauge-invariant measure of the correlation of the hard gamma rays. We
calculate the differential rate and concurrence for a backscattering setup of
the electron and photon beam, employing Volkov states and propagators for the
electron lines, thus accounting nonperturbatively for the electron-laser
interaction. The nonperturbative results are shown to differ significantly
compared to those obtained from the usual double Compton scattering.Comment: 32 pages, 12 figure
Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
Several stochastic simulation algorithms (SSAs) have been recently proposed
for modelling reaction-diffusion processes in cellular and molecular biology.
In this paper, two commonly used SSAs are studied. The first SSA is an
on-lattice model described by the reaction-diffusion master equation. The
second SSA is an off-lattice model based on the simulation of Brownian motion
of individual molecules and their reactive collisions. In both cases, it is
shown that the commonly used implementation of bimolecular reactions (i.e. the
reactions of the form A + B -> C, or A + A -> C) might lead to incorrect
results. Improvements of both SSAs are suggested which overcome the
difficulties highlighted. In particular, a formula is presented for the
smallest possible compartment size (lattice spacing) which can be correctly
implemented in the first model. This implementation uses a new formula for the
rate of bimolecular reactions per compartment (lattice site).Comment: 33 pages, submitted to Physical Biolog
Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3)
Ice flow forced by gravity is governed by the full Stokes (FS) equations,
which are computationally expensive to solve due to the nonlinearity
introduced by the rheology. Therefore, approximations to the FS equations are
commonly used, especially when modeling a marine ice sheet (ice sheet, ice
shelf, and/or ice stream) for 103 years or longer. The shallow ice
approximation (SIA) and shallow shelf approximation (SSA) are commonly used
but are accurate only for certain parts of an ice sheet. Here, we report a
novel way of iteratively coupling FS and SSA that has been implemented in
Elmer/Ice and applied to conceptual marine ice sheets. The FS–SSA coupling
appears to be very accurate; the relative error in velocity compared to FS is
below 0.5 % for diagnostic runs and below 5 % for prognostic runs.
Results for grounding line dynamics obtained with the FS–SSA coupling are
similar to those obtained from an FS model in an experiment with a periodical
temperature forcing over 3000 years that induces grounding line advance and
retreat. The rapid convergence of the FS–SSA coupling shows a large
potential for reducing computation time, such that modeling a marine ice
sheet for thousands of years should become feasible in the near future.
Despite inefficient matrix assembly in the current implementation,
computation time is reduced by 32 %, when the coupling is applied to a
3-D ice shelf.</p
Robustness analysis of spatiotemporal models in the presence of extrinsic fluctuations
© 2017 Society for Industrial and Applied Mathematics. We analyze the governing partial differential equations of a model of pole-to-pole oscillations of the MinD protein in a bacterial cell. The sensitivity to extrinsic noise in the parameters of the model is explored. Our analysis shows that overall, the oscillations are robust to extrinsic perturbations in the sense that small perturbations in reaction coefficients result in small differences in the frequency and in the amplitude. However, a combination of analysis and simulation also reveals that the oscillations are more sensitive to some extrinsic time scales than to others
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