587 research outputs found
Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity
We preset a computational study of bending models for the curvature
elasticity of lipid bilayer membranes that are relevant for simulations of
vesicles and red blood cells. We compute bending energy and forces on
triangulated meshes and evaluate and extend four well established schemes for
their approximation: Kantor and Nelson 1987, Phys. Rev. A 36, 4020, J\"ulicher
1996, J. Phys. II France 6, 1797, Gompper and Kroll 1996, J. Phys. I France 6,
1305, and Meyer et. al. 2003 in Visualization and Mathematics III, Springer,
p35, termed A, B, C, D. We present a comparative study of these four schemes on
the minimal bending model and propose extensions for schemes B, C and D. These
extensions incorporate the reference state and non-local energy to account for
the spontaneous curvature, bilayer coupling, and area-difference elasticity
models. Our results indicate that the proposed extensions enhance the models to
account for shape transformation including budding/vesiculation as well as for
non-axisymmetric shapes. We find that the extended scheme B is superior to the
rest in terms of accuracy, and robustness as well as simplicity of
implementation. We demonstrate the capabilities of this scheme on several
benchmark problems including the budding-vesiculating process and the
reproduction of the phase diagram of vesicles
Flow reconstruction by multiresolution optimization of a discrete loss with automatic differentiation
We present a potent computational method for the solution of inverse problems
in fluid mechanics. We consider inverse problems formulated in terms of a
deterministic loss function that can accommodate data and regularization terms.
We introduce a multigrid decomposition technique that accelerates the
convergence of gradient-based methods for optimization problems with parameters
on a grid. We incorporate this multigrid technique to the ODIL (Optimizing a
DIscrete Loss) framework. The multiresolution ODIL (mODIL) accelerates by an
order of magnitude the original formalism and improves the avoidance of local
minima. Moreover, mODIL accommodates the use of automatic differentiation for
calculating the gradients of the loss function, thus facilitating the
implementation of the framework. We demonstrate the capabilities of mODIL on a
variety of inverse and flow reconstruction problems: solution reconstruction
for the Burgers equation, inferring conductivity from temperature measurements,
and inferring the body shape from wake velocity measurements in three
dimensions. We also provide a comparative study with the related, popular
Physics-Informed Neural Networks (PINNs) method. We demonstrate that mODIL has
three to five orders of magnitude lower computational cost than PINNs in
benchmark problems including simple PDEs and lid-driven cavity problems. Our
results suggest that mODIL is a very potent, fast and consistent method for
solving inverse problems in fluid mechanics.Comment: 16 pages, 9 figure
A hybrid particle volume-of-fluid method for curvature estimation in multiphase flows
We present a particle method for estimating the curvature of interfaces in
volume-of-fluid simulations of multiphase flows. The method is well suited for
under-resolved interfaces, and it is shown to be more accurate than the
parabolic fitting that is employed in such cases. The curvature is computed
from the equilibrium positions of particles constrained to circular arcs and
attracted to the interface. The proposed particle method is combined with the
method of height functions at higher resolutions, and it is shown to outperform
the current combinations of height functions and parabolic fitting. The
algorithm is conceptually simple and straightforward to implement on new and
existing software frameworks for multiphase flow simulations thus enhancing
their capabilities in challenging flow problems. We evaluate the proposed
hybrid method on a number of two- and three-dimensional benchmark flow problems
and illustrate its capabilities on simulations of flows involving bubble
coalescence and turbulent multiphase flows.Comment: 25 pages, 33 figure
Isochronous Mode of the Future Collector Ring At the Centre for Heavy Ion Research, Darmstadt, Germany
Short-lived exotic nuclei can be produced and separated with the high-energy nuclear beam facility called fragment separator at the Centre for Heavy Ion Research. These nuclides can be injected and stored in the storage ring called experimental storage ring. The lower lifetime limit of the presently existing methods for mass measurements on these nuclides at the experimental storage ring is about a few seconds. We have developed and investigated an isochronous operational mode of the future collector ring, that makes mass measurements feasible for nuclides with lifetimes down to a few microseconds. A mass resolving power of about 150 000 is expected
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