26,475 research outputs found
Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures
The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly
transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit
parametrization of boundary surfaces to impose traction and displacement boundary conditions, which
constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing
traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model
generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as
initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer
all boundary terms in the variational formulation into volumetric terms. We show that in the context of the
voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions
defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field,
the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method
by analyzing stresses in a human femur and a vertebral body
The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries
We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body
Applying machine learning to improve simulations of a chaotic dynamical system using empirical error correction
Dynamical weather and climate prediction models underpin many studies of the
Earth system and hold the promise of being able to make robust projections of
future climate change based on physical laws. However, simulations from these
models still show many differences compared with observations. Machine learning
has been applied to solve certain prediction problems with great success, and
recently it's been proposed that this could replace the role of
physically-derived dynamical weather and climate models to give better quality
simulations. Here, instead, a framework using machine learning together with
physically-derived models is tested, in which it is learnt how to correct the
errors of the latter from timestep to timestep. This maintains the physical
understanding built into the models, whilst allowing performance improvements,
and also requires much simpler algorithms and less training data. This is
tested in the context of simulating the chaotic Lorenz '96 system, and it is
shown that the approach yields models that are stable and that give both
improved skill in initialised predictions and better long-term climate
statistics. Improvements in long-term statistics are smaller than for single
time-step tendencies, however, indicating that it would be valuable to develop
methods that target improvements on longer time scales. Future strategies for
the development of this approach and possible applications to making progress
on important scientific problems are discussed.Comment: 26p, 7 figures To be published in Journal of Advances in Modeling
Earth System
Fourier Optics approach to imaging with sub-wavelength resolution through metal-dielectric multilayers
Metal-dielectric layered stacks for imaging with sub-wavelength resolution
are regarded as linear isoplanatic systems - a concept popular in Fourier
Optics and in scalar diffraction theory. In this context, a layered flat lens
is a one-dimensional spatial filter characterised by the point spread function.
However, depending on the model of the source, the definition of the point
spread function for multilayers with sub-wavelength resolution may be
formulated in several ways. Here, a distinction is made between a soft source
and hard electric or magnetic sources. Each of these definitions leads to a
different meaning of perfect imaging. It is shown that some simple
interpretations of the PSF, such as the relation of its width to the resolution
of the imaging system are ambiguous for the multilayers with sub-wavelenth
resolution. These differences must be observed in point spread function
engineering of layered systems with sub-wavelength sized PSF
The dynamics of individual nucleosomes controls the chromatin condensation pathway: direct AFM visualization of variant chromatin
Chromatin organization and dynamics is studied in this work at scales ranging
from single nucleosome to nucleosomal array by using a unique combination of
biochemical assays, single molecule imaging technique and numerical modeling.
We demonstrate that a subtle modification in the nucleosome structure induced
by the histone variant H2A.Bbd drastically modifies the higher order
organization of the nucleosomal arrays. Importantly, as directly visualized by
AFM, conventional H2A nucleosomal arrays exhibit specific local organization,
in contrast to H2A.Bbd arrays, which show "beads on a string" structure. The
combination of systematic image analysis and theoretical modeling allows a
quantitative description relating the observed gross structural changes of the
arrays to their local organization. Our results strongly suggest that
higher-order organization of H1-free nucleosomal arrays is mainly determined by
the fluctuation properties of individual nucleosomes. Moreover, numerical
simulations suggest the existence of attractive interactions between
nucleosomes to provide the degree of compaction observed for conventional
chromatin fibers.Comment: Biophys J. in pres
High accuracy binary black hole simulations with an extended wave zone
We present results from a new code for binary black hole evolutions using the
moving-puncture approach, implementing finite differences in generalised
coordinates, and allowing the spacetime to be covered with multiple
communicating non-singular coordinate patches. Here we consider a regular
Cartesian near zone, with adapted spherical grids covering the wave zone. The
efficiencies resulting from the use of adapted coordinates allow us to maintain
sufficient grid resolution to an artificial outer boundary location which is
causally disconnected from the measurement. For the well-studied test-case of
the inspiral of an equal-mass non-spinning binary (evolved for more than 8
orbits before merger), we determine the phase and amplitude to numerical
accuracies better than 0.010% and 0.090% during inspiral, respectively, and
0.003% and 0.153% during merger. The waveforms, including the resolved higher
harmonics, are convergent and can be consistently extrapolated to
throughout the simulation, including the merger and ringdown. Ringdown
frequencies for these modes (to ) match perturbative
calculations to within 0.01%, providing a strong confirmation that the remnant
settles to a Kerr black hole with irreducible mass and spin $S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}
Plasmonic color filters as dual-state nanopixels for high-density microimage encoding
Plasmonic color filtering has provided a range of new techniques for âprintingâ images at resolutions beyond the diffraction-limit, significantly improving upon what can be achieved using traditional, dye-based filtering methods. Here, a new approach to high-density data encoding is demonstrated using full color, dual-state plasmonic nanopixels, doubling the amount of information that can be stored in a unit-area. This technique is used to encode two data sets into a single set of pixels for the first time, generating vivid, near-full sRGB (standard Red Green Blue color space)color images and codes with polarization-switchable information states. Using a standard optical microscope, the smallest âunitâ that can be read relates to 2 Ă 2 nanopixels (370 nm Ă 370 nm). As a result, dual-state nanopixels may prove significant for long-term, high-resolution optical image encoding, and counterfeit-prevention measures
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