341,287 research outputs found
A multiscale-multiphysics strategy for numerical modeling of thin piezoelectric sheets
Flexible piezoelectric devices made of polymeric materials are widely used
for micro- and nano-electro-mechanical systems. In particular, numerous recent
applications concern energy harvesting. Due to the importance of computational
modeling to understand the influence that microscale geometry and constitutive
variables exert on the macroscopic behavior, a numerical approach is developed
here for multiscale and multiphysics modeling of piezoelectric materials made
of aligned arrays of polymeric nanofibers. At the microscale, the
representative volume element consists in piezoelectric polymeric nanofibers,
assumed to feature a linear piezoelastic constitutive behavior and subjected to
electromechanical contact constraints using the penalty method. To avoid the
drawbacks associated with the non-smooth discretization of the master surface,
a contact smoothing approach based on B\'ezier patches is extended to the
multiphysics framework providing an improved continuity of the
parameterization. The contact element contributions to the virtual work
equations are included through suitable electric, mechanical and coupling
potentials. From the solution of the micro-scale boundary value problem, a
suitable scale transition procedure leads to the formulation of a macroscopic
thin piezoelectric shell element.Comment: 11 pages, 6 pages, 21 reference
Two-step percolation in aggregating systems
The two-step percolation behavior in aggregating systems was studied both
experimentally and by means of Monte Carlo (MC) simulations. In experimental
studies, the electrical conductivity, , of colloidal suspension of
multiwalled carbon nanotubes (CNTs) in decane was measured. The suspension was
submitted to mechanical de-liquoring in a planar filtration-compression
conductometric cell. During de-liquoring, the distance between the measuring
electrodes continuously decreased and the CNT volume fraction
continuously increased (from up to % v/v). The two
percolation thresholds at and can reflect the interpenetration of loose CNT aggregates and
percolation across the compact conducting aggregates, respectively. The MC
computational model accounted for the core-shell structure of conducting
particles or their aggregates, the tendency of a particle for aggregation, the
formation of solvation shells, and the elongated geometry of the conductometric
cell. The MC studies revealed two smoothed percolation transitions in
dependencies that correspond to the percolation through the
shells and cores, respectively. The data demonstrated a noticeable impact of
particle aggregation on anisotropy in electrical conductivity
measured along different directions in the conductometric cell.Comment: 10 pages, 6 figure
A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting
An explicit moving boundary method for the numerical solution of
time-dependent hyperbolic conservation laws on grids produced by the
intersection of complex geometries with a regular Cartesian grid is presented.
As it employs directional operator splitting, implementation of the scheme is
rather straightforward. Extending the method for static walls from Klein et
al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme
calculates fluxes needed for a conservative update of the near-wall cut-cells
as linear combinations of standard fluxes from a one-dimensional extended
stencil. Here the standard fluxes are those obtained without regard to the
small sub-cell problem, and the linear combination weights involve detailed
information regarding the cut-cell geometry. This linear combination of
standard fluxes stabilizes the updates such that the time-step yielding
marginal stability for arbitrarily small cut-cells is of the same order as that
for regular cells. Moreover, it renders the approach compatible with a wide
range of existing numerical flux-approximation methods. The scheme is extended
here to time dependent rigid boundaries by reformulating the linear combination
weights of the stabilizing flux stencil to account for the time dependence of
cut-cell volume and interface area fractions. The two-dimensional tests
discussed include advection in a channel oriented at an oblique angle to the
Cartesian computational mesh, cylinders with circular and triangular
cross-section passing through a stationary shock wave, a piston moving through
an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil
profile.Comment: 30 pages, 27 figures, 3 table
Mechanistic and pathological study of the genesis, growth, and rupture of abdominal aortic aneurysms
Postprint (published version
Faster Algorithms for Largest Empty Rectangles and Boxes
We revisit a classical problem in computational geometry: finding the
largest-volume axis-aligned empty box (inside a given bounding box) amidst
given points in dimensions. Previously, the best algorithms known have
running time for (by Aggarwal and Suri [SoCG'87]) and near
for . We describe faster algorithms with running time (i)
for , (ii) time for ,
and (iii) time for any constant .
To obtain the higher-dimensional result, we adapt and extend previous
techniques for Klee's measure problem to optimize certain objective functions
over the complement of a union of orthants.Comment: full version of a SoCG 2021 pape
Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
We present a new family of high order accurate fully discrete one-step
Discontinuous Galerkin (DG) finite element schemes on moving unstructured
meshes for the solution of nonlinear hyperbolic PDE in multiple space
dimensions, which may also include parabolic terms in order to model
dissipative transport processes. High order piecewise polynomials are adopted
to represent the discrete solution at each time level and within each spatial
control volume of the computational grid, while high order of accuracy in time
is achieved by the ADER approach. In our algorithm the spatial mesh
configuration can be defined in two different ways: either by an isoparametric
approach that generates curved control volumes, or by a piecewise linear
decomposition of each spatial control volume into simplex sub-elements. Our
numerical method belongs to the category of direct
Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation
formulation of the governing PDE system is considered and which already takes
into account the new grid geometry directly during the computation of the
numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a
posteriori sub-cell finite volume limiter method, in which the validity of the
candidate solution produced in each cell by an unlimited ADER-DG scheme is
verified against a set of physical and numerical detection criteria. Those
cells which do not satisfy all of the above criteria are flagged as troubled
cells and are recomputed with a second order TVD finite volume scheme. The
numerical convergence rates of the new ALE ADER-DG schemes are studied up to
fourth order in space and time and several test problems are simulated.
Finally, an application inspired by Inertial Confinement Fusion (ICF) type
flows is considered by solving the Euler equations and the PDE of viscous and
resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure
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