58,056 research outputs found
Multi-scale space-variant FRep cellular structures
Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures
on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular
structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic
space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due
to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or
along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel
representations
Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids
With the eventual aim of describing flowing elasto-plastic materials, we
focus on the elementary brick of such a flow, a plastic event, and compute the
long-range perturbation it elastically induces in a medium submitted to a
global shear strain. We characterize the effect of a nearby wall on this
perturbation, and quantify the importance of finite size effects. Although for
the sake of simplicity most of our explicit formulae deal with a 2D situation,
our statements hold for 3D situations as well.Comment: submitted to EPJ
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
We present a novel kernel regression framework for smoothing scalar surface
data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel
constructed from the eigenfunctions, we formulate a new bivariate kernel
regression framework as a weighted eigenfunction expansion with the heat kernel
as the weights. The new kernel regression is mathematically equivalent to
isotropic heat diffusion, kernel smoothing and recently popular diffusion
wavelets. Unlike many previous partial differential equation based approaches
involving diffusion, our approach represents the solution of diffusion
analytically, reducing numerical inaccuracy and slow convergence. The numerical
implementation is validated on a unit sphere using spherical harmonics. As an
illustration, we have applied the method in characterizing the localized growth
pattern of mandible surfaces obtained in CT images from subjects between ages 0
and 20 years by regressing the length of displacement vectors with respect to
the template surface.Comment: Accepted in Medical Image Analysi
Quantum circuits based on coded qubits encoded in chirality of electron spin complexes in triple quantum dots
We present a theory of quantum circuits based on logical qubits encoded in
chirality of electron spin complexes in lateral gated semiconductor triple
quantum dot molecules with one electron spin in each dot. Using microscopic
Hamiltonian we show how to initialize, coherently control and measure the
quantum state of a chirality based coded qubit using static in-plane magnetic
field and voltage tuning of individual dots. The microscopic model of two
interacting coded qubits is established and mapped to an Ising Hamiltonian,
resulting in conditional two-qubit phase gate
Atomistic simulations of adiabatic coherent electron transport in triple donor systems
A solid-state analogue of Stimulated Raman Adiabatic Passage can be
implemented in a triple well solid-state system to coherently transport an
electron across the wells with exponentially suppressed occupation in the
central well at any point of time. Termed coherent tunneling adiabatic passage
(CTAP), this method provides a robust way to transfer quantum information
encoded in the electronic spin across a chain of quantum dots or donors. Using
large scale atomistic tight-binding simulations involving over 3.5 million
atoms, we verify the existence of a CTAP pathway in a realistic solid-state
system: gated triple donors in silicon. Realistic gate profiles from commercial
tools were combined with tight-binding methods to simulate gate control of the
donor to donor tunnel barriers in the presence of cross-talk. As CTAP is an
adiabatic protocol, it can be analyzed by solving the time independent problem
at various stages of the pulse - justifying the use of time-independent
tight-binding methods to this problem. Our results show that a three donor CTAP
transfer, with inter-donor spacing of 15 nm can occur on timescales greater
than 23 ps, well within experimentally accessible regimes. The method not only
provides a tool to guide future CTAP experiments, but also illuminates the
possibility of system engineering to enhance control and transfer times.Comment: 8 pages, 5 figure
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