27,856 research outputs found
Extending the reach of uncertainty quantification in nuclear theory
The theory of the strong interactionâquantum chromodynamics (QCD)âis unsuited to practical calculations of nuclear observables and approximate models for nuclear interaction potentials are required. In contrast to phenomenological models, chiral effective field theories (ÏEFTs) of QCD grant a handle on the theoretical uncertainty arising from the truncation of the chiral expansion. Uncertainties in ÏEFT are preferably quantified using Bayesian inference, but quantifying reliable posterior predictive distributions for nuclear observables presents several challenges. First, ÏEFT is parametrized by unknown low-energy constants (LECs) whose values must be inferred from low-energy data of nuclear structure and reaction observables. There are 31 LECs at fourth order in Weinberg power counting, leading to a high-dimensional inference problem which I approach by developing an advanced sampling protocol using Hamiltonian Monte Carlo (HMC). This allows me to quantify LEC posteriors up to and including fourth chiral order. Second, the ÏEFT truncation error is correlated across independent variables such as scattering energies and angles; I model correlations using a Gaussian process. Third, the computational cost of computing few- and many-nucleon observables typically precludes their direct use in Bayesian parameter estimation as each observable must be computed in excess of 100,000 times during HMC sampling. The one exception is nucleon-nucleon scattering observables, but even these incur a substantial computational cost in the present applications. I sidestep such issues using eigenvector-continuation emulators, which accurately mimic exact calculations while dramatically reducing the computational cost. Equipped with Bayesian posteriors for the LECs, and a model for the truncation error, I explore the predictive ability of ÏEFT, presenting the results as the probability distributions they always were
Numerical simulations of divergence-type theories for conformal dissipative fluids
We present the first numerical simulations of the symmetric--hyperbolic
theory for conformal dissipative relativistic fluids developed in [1]. In this
theory, the information of the fluid dynamics is encoded in a scalar generating
function which depends on three free parameters. By adapting the WENO-Z
high-resolution shock-capturing central scheme, we show numerical solutions
restricted to planar symmetry in Minkowski spacetime, from two qualitatively
different initial data: a smooth bump and a discontinuous step. We perform a
detailed exploration of the effect of the different parameters of the theory,
and numerically assess the constitutive relations associated with the shear
viscosity by analyzing the entropy production rate when shocks are produced.Comment: 22 pages, 14 figure
Is it possible to construct asymptotically flat initial data using the evolutionary forms of the constraints?
Near-Kerr black hole initial datasets are constructed by applying either the
parabolic-hyperbolic or the algebraic-hyperbolic form of the constraints. In
both cases, strongly and weakly asymptotically flat initial datasets with
desirable falloff rates are produced by controlling only the monopole part of
one of the freely specifiable variables. The viability of the applied method is
verified by numerically integrating the evolutionary forms of the constraint
equations in the case of various near-Kerr configurations.Comment: 43 pages, 6 figure
Lie-Poisson gauge theories and -Minkowski electrodynamics
We consider a Poisson gauge theory with a generic Poisson structure of Lie
algebraic type. We prove an important identity, which allows to obtain simple
and manifestly gauge-covariant expressions for the Euler-Lagrange equations of
motion, the Bianchi and the Noether identities. We discuss the non-Lagrangian
equations of motion, and apply our findings to the -Minkowski case. We
construct a family of exact solutions of the deformed Maxwell equations in the
vacuum. In the classical limit, these solutions recover plane waves with
left-handed and right-handed circular polarization, being classical
counterparts of photons. The deformed dispersion relation appears to be
nontrivial.Comment: 20 page
A first-principles method to calculate fourth-order elastic constants of solid materials
A first-principles method is presented to calculate elastic constants up to
the fourth order of crystals with the cubic and hexagonal symmetries. The
method relies on the numerical differentiation of the second Piola-Kirchhoff
stress tensor and a density functional theory approach to compute the Cauchy
stress tensors for a minimal list of strained configurations of a reference
state. The number of strained configurations required to calculate the
independent elastic constants of the second, third, and fourth order is 24 and
37 for crystals with the cubic and hexagonal symmetries, respectively. Here,
this method is applied to five crystalline materials with the cubic symmetry
(diamond, silicon, aluminum, silver, and gold) and two metals with the
hexagonal close packing structure (beryllium and magnesium). Our results are
compared to available experimental data and previous computational studies.
Calculated linear and nonlinear elastic constants are also used, within a
nonlinear elasticity treatment of a material, to predict values of volume and
bulk modulus at zero temperature over an interval of pressures. To further
validate our method, these predictions are compared to results obtained from
explicit density functional theory calculations
Multimodal spatio-temporal deep learning framework for 3D object detection in instrumented vehicles
This thesis presents the utilization of multiple modalities, such as image and lidar, to incorporate spatio-temporal information from sequence data into deep learning architectures for 3Dobject detection in instrumented vehicles. The race to autonomy in instrumented vehicles or self-driving cars has stimulated significant research in developing autonomous driver assistance systems (ADAS) technologies related explicitly to perception systems. Object detection plays a crucial role in perception systems by providing spatial information to its subsequent modules; hence, accurate detection is a significant task supporting autonomous driving. The advent of deep learning in computer vision applications and the availability of multiple sensing modalities such as 360° imaging, lidar, and radar have led to state-of-the-art 2D and 3Dobject detection architectures. Most current state-of-the-art 3D object detection frameworks consider single-frame reference. However, these methods do not utilize temporal information associated with the objects or scenes from the sequence data. Thus, the present research hypothesizes that multimodal temporal information can contribute to bridging the gap between 2D and 3D metric space by improving the accuracy of deep learning frameworks for 3D object estimations. The thesis presents understanding multimodal data representations and selecting hyper-parameters using public datasets such as KITTI and nuScenes with Frustum-ConvNet as a baseline architecture. Secondly, an attention mechanism was employed along with convolutional-LSTM to extract spatial-temporal information from sequence data to improve 3D estimations and to aid the architecture in focusing on salient lidar point cloud features. Finally, various fusion strategies are applied to fuse the modalities and temporal information into the architecture to assess its efficacy on performance and computational complexity. Overall, this thesis has established the importance and utility of multimodal systems for refined 3D object detection and proposed a complex pipeline incorporating spatial, temporal and attention mechanisms to improve specific, and general class accuracy demonstrated on key autonomous driving data sets
Nonlinear realisation approach to topologically massive supergravity
We develop a nonlinear realisation approach to topologically massive
supergravity in three dimensions, with and without a cosmological term. It is a
natural generalisation of a similar construction for supergravity
in four dimensions, which was recently proposed by one of us. At the heart of
both formulations is the nonlinear realisation approach to gravity which was
given by Volkov and Soroka fifty years ago in the context of spontaneously
broken local supersymmetry. In our setting, the action for cosmological
topologically massive supergravity is invariant under two different local
supersymmetries. One of them acts on the Goldstino, while the other
supersymmetry leaves the Goldstino invariant. The former can be used to gauge
away the Goldstino, and then the resulting action coincides with that given in
the literature.Comment: 29 page
- âŠ