4,043 research outputs found
Magnetism and topological phases in an interacting decorated honeycomb lattice with spin-orbit coupling
We study the interplay between spin-orbit coupling (SOC) and Coulomb
repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a
plethora of phases. While a quantum spin hall insulator is stable at weak
Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC
in a broad range of Coulomb repulsion. This semimetallic phase has topological
properties not observed in conventional metals such as a finite, non-quantized
spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit
coupling, electronic correlations stabilize a resonance valence bond (RVB) spin
liquid state in contrast to the classical antiferromagnetic state predicted by
mean-field theory. Under sufficiently strong SOC, such RVB state is transformed
into a magnetic insulator consisting on S~3/2 localized moments on a honeycomb
lattice with antiferromagnetic order and topological features.Comment: 13 pages, 10 figure
Multiple path prediction for traffic scenes using LSTMs and mixture density models
This work presents an analysis of predicting multiple future paths of moving objects in traffic scenes by leveraging Long Short-Term Memory architectures (LSTMs) and Mixture Density Networks (MDNs) in a single-shot manner. Path prediction allows estimating the future positions of objects. This is useful in important applications such as security monitoring systems, Autonomous Driver Assistance Systems and assistive technologies. Normal approaches use observed positions (tracklets) of objects in video frames to predict their future paths as a sequence of position values. This can be treated as a time series. LSTMs have achieved good performance when dealing with time series. However, LSTMs have the limitation of only predicting a single path per tracklet. Path prediction is not a deterministic task and requires predicting with a level of uncertainty. Predicting multiple paths instead of a single one is therefore a more realistic manner of approaching this task. In this work, predicting a set of future paths with associated uncertainty was archived by combining LSTMs and MDNs. The evaluation was made on the KITTI and the CityFlow datasets on three type of objects, four prediction horizons and two different points of view (image coordinates and birds-eye vie
Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations
We introduce a \textit{non-modal} analysis technique that characterizes the
diffusion properties of spectral element methods for linear
convection-diffusion systems. While strictly speaking only valid for linear
problems, the analysis is devised so that it can give critical insights on two
questions: (i) Why do spectral element methods suffer from stability issues in
under-resolved computations of nonlinear problems? And, (ii) why do they
successfully predict under-resolved turbulent flows even without a
subgrid-scale model? The answer to these two questions can in turn provide
crucial guidelines to construct more robust and accurate schemes for complex
under-resolved flows, commonly found in industrial applications. For
illustration purposes, this analysis technique is applied to the hybridized
discontinuous Galerkin methods as representatives of spectral element methods.
The effect of the polynomial order, the upwinding parameter and the P\'eclet
number on the so-called \textit{short-term diffusion} of the scheme are
investigated. From a purely non-modal analysis point of view, polynomial orders
between and with standard upwinding are well suited for under-resolved
turbulence simulations. For lower polynomial orders, diffusion is introduced in
scales that are much larger than the grid resolution. For higher polynomial
orders, as well as for strong under/over-upwinding, robustness issues can be
expected. The non-modal analysis results are then tested against under-resolved
turbulence simulations of the Burgers, Euler and Navier-Stokes equations. While
devised in the linear setting, our non-modal analysis succeeds to predict the
behavior of the scheme in the nonlinear problems considered
Implicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method
We present a high-order implicit large-eddy simulation (ILES) approach for
simulating transitional turbulent flows. The approach consists of an Interior
Embedded Discontinuous Galerkin (IEDG) method for the discretization of the
compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES
solver for the resulting nonlinear system of equations. The IEDG method arises
from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the
Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method
inherits the advantages of both the EDG method and the HDG method to make
itself well-suited for turbulence simulations. We propose a minimal residual
Newton algorithm for solving the nonlinear system arising from the IEDG
discretization of the Navier-Stokes equations. The preconditioned GMRES
algorithm is based on a restricted additive Schwarz (RAS) preconditioner in
conjunction with a block incomplete LU factorization at the subdomain level.
The proposed approach is applied to the ILES of transitional turbulent flows
over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both
design and off-design conditions. The high-order ILES results show good
agreement with a subgrid-scale LES model discretized with a second-order finite
volume code while using significantly less degrees of freedom. This work shows
that high-order accuracy is key for predicting transitional turbulent flows
without a SGS model.Comment: 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201
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Game-Theoretic Safety Assurance for Human-Centered Robotic Systems
In order for autonomous systems like robots, drones, and self-driving cars to be reliably introduced into our society, they must have the ability to actively account for safety during their operation. While safety analysis has traditionally been conducted offline for controlled environments like cages on factory floors, the much higher complexity of open, human-populated spaces like our homes, cities, and roads makes it unviable to rely on common design-time assumptions, since these may be violated once the system is deployed. Instead, the next generation of robotic technologies will need to reason about safety online, constructing high-confidence assurances informed by ongoing observations of the environment and other agents, in spite of models of them being necessarily fallible.This dissertation aims to lay down the necessary foundations to enable autonomous systems to ensure their own safety in complex, changing, and uncertain environments, by explicitly reasoning about the gap between their models and the real world. It first introduces a suite of novel robust optimal control formulations and algorithmic tools that permit tractable safety analysis in time-varying, multi-agent systems, as well as safe real-time robotic navigation in partially unknown environments; these approaches are demonstrated on large-scale unmanned air traffic simulation and physical quadrotor platforms. After this, it draws on Bayesian machine learning methods to translate model-based guarantees into high-confidence assurances, monitoring the reliability of predictive models in light of changing evidence about the physical system and surrounding agents. This principle is first applied to a general safety framework allowing the use of learning-based control (e.g. reinforcement learning) for safety-critical robotic systems such as drones, and then combined with insights from cognitive science and dynamic game theory to enable safe human-centered navigation and interaction; these techniques are showcased on physical quadrotorsâflying in unmodeled wind and among human pedestriansâand simulated highway driving. The dissertation ends with a discussion of challenges and opportunities ahead, including the bridging of safety analysis and reinforcement learning and the need to ``close the loop'' around learning and adaptation in order to deploy increasingly advanced autonomous systems with confidence
On-site approximation for spin-orbit coupling in LCAO density functional methods
We propose a computational method that simplifies drastically the inclusion
of spin-orbit interaction in density functional theory implemented on localised
atomic orbital basis sets. Our method is based on a well-known procedure for
obtaining pseudopotentials from atomic relativistic 'ab initio' calculations
and on an on-site approximation for the spin-orbit matrix elements. We have
implemented the technique in the SIESTA code, and we show that it provides
accurate results for the overall band structure and splittings of group IV and
III-IV semiconductors as well as for 5d metals.Comment: 8 pages, 4 figures. Published in J. Phys.: Condens. Matter 18
7999-8013, 2006. Some errata correcte
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