25,183 research outputs found
A Detailed Comparison of Multi-Dimensional Boltzmann Neutrino Transport Methods in Core-Collapse Supernovae
The mechanism driving core-collapse supernovae is sensitive to the interplay
between matter and neutrino radiation. However, neutrino radiation transport is
very difficult to simulate, and several radiation transport methods of varying
levels of approximation are available. We carefully compare for the first time
in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura,
Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the
assumptions of a static fluid background, flat spacetime, elastic scattering,
and full special relativity. We find remarkably good agreement in all spectral,
angular, and fluid interaction quantities, lending confidence to both methods.
The DO method excels in determining the heating and cooling rates in the
optically thick region. The MC method predicts sharper angular features due to
the effectively infinite angular resolution, but struggles to drive down noise
in quantities where subtractive cancellation is prevalent, such as the net gain
in the protoneutron star and off-diagonal components of the Eddington tensor.
We also find that errors in the angular moments of the distribution functions
induced by neglecting velocity dependence are sub-dominant to those from
limited momentum-space resolution. We briefly compare directly computed second
angular moments to those predicted by popular algebraic two-moment closures,
and find that the errors from the approximate closures are comparable to the
difference between the DO and MC methods. Included in this work is an improved
Sedonu code, which now implements a fully special relativistic,
time-independent version of the grid-agnostic Monte Carlo random walk
approximation.Comment: Accepted to ApJS. 24 pages, 19 figures. Key simulation results and
codes are available at https://stellarcollapse.org/MCvsD
Cascade and Damping of Alfv\'{e}n-Cyclotron Fluctuations: Application to Solar Wind Turbulence Spectrum
With the diffusion approximation, we study the cascade and damping of
Alfv\'{e}n-cyclotron fluctuations in solar plasmas numerically. Motivated by
wave-wave couplings and nonlinear effects, we test several forms of the
diffusion tensor. For a general locally anisotropic and inhomogeneous diffusion
tensor in the wave vector space, the turbulence spectrum in the inertial range
can be fitted with power-laws with the power-law index varying with the wave
propagation direction. For several locally isotropic but inhomogeneous
diffusion coefficients, the steady-state turbulence spectra are nearly
isotropic in the absence of damping and can be fitted by a single power-law
function. However, the energy flux is strongly polarized due to the
inhomogeneity that leads to an anisotropic cascade. Including the anisotropic
thermal damping, the turbulence spectrum cuts off at the wave numbers, where
the damping rates become comparable to the cascade rates. The combined
anisotropic effects of cascade and damping make this cutoff wave number
dependent on the wave propagation direction, and the propagation direction
integrated turbulence spectrum resembles a broken power-law, which cuts off at
the maximum of the cutoff wave numbers or the He cyclotron frequency.
Taking into account the Doppler effects, the model can naturally reproduce the
broken power-law wave spectra observed in the solar wind and predicts that a
higher break frequency is aways accompanied with a greater spectral index
change that may be caused by the increase of the Alfv\'{e}n Mach number, the
reciprocal of the plasma beta, and/or the angle between the solar wind velocity
and the mean magnetic field. These predictions can be tested by future
observations
Scaling in Plasticity-Induced Cell-Boundary Microstructure: Fragmentation and Rotational Diffusion
We develop a simple computational model for cell boundary evolution in
plastic deformation. We study the cell boundary size distribution and cell
boundary misorientation distribution that experimentally have been found to
have scaling forms that are largely material independent. The cell division
acts as a source term in the misorientation distribution which significantly
alters the scaling form, giving it a linear slope at small misorientation
angles as observed in the experiments. We compare the results of our simulation
to two closely related exactly solvable models which exhibit scaling behavior
at late times: (i) fragmentation theory and (ii) a random walk in rotation
space with a source term. We find that the scaling exponents in our simulation
agree with those of the theories, and that the scaling collapses obey the same
equations, but that the shape of the scaling functions depend upon the methods
used to measure sizes and to weight averages and histograms
Semiparametric Bayesian models for human brain mapping
Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility
Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI
Purpose: Biophysical tissue models are increasingly used in the
interpretation of diffusion MRI (dMRI) data, with the potential to provide
specific biomarkers of brain microstructural changes. However, the general
Standard Model has recently shown that model parameter estimation from dMRI
data is ill-posed unless very strong magnetic gradients are used. We analyse
this issue for the Neurite Orientation Dispersion and Density Imaging with
Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from
Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the
ill-posedness and increases the accuracy of the parameter estimation. Methods:
We analyse theoretically the cumulant expansion up to fourth order in b of SDE
and DDE signals. Additionally, we perform in silico experiments to compare SDE
and DDE capabilities under similar noise conditions. Results: We prove
analytically that DDE provides invariant information non-accessible from SDE,
which makes the NODDIDA parameter estimation injective. The in silico
experiments show that DDE reduces the bias and mean square error of the
estimation along the whole feasible region of 5D model parameter space.
Conclusions: DDE adds additional information for estimating the model
parameters, unexplored by SDE, which is enough to solve the degeneracy in the
NODDIDA model parameter estimation.Comment: 22 pages, 7 figure
Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data
Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observation regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability. We provide two strategies for this critical choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, and a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using simulation studies, and real applications to estimation of fractional anisotropy profiles based on diffusion tensor imaging measurements, growth velocity functions and bone mineral density curves.No embarg
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