20,232 research outputs found
MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry
We have developed a new global eigenvalue code, Multiscale Analysis for
plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode
number n and frequency omega in a broad range of interest in general tokamak
geometry, based on a five-field Landau-fluid description of thermal plasmas.
Beyond keeping the necessary plasma fluid response, we further retain the
important kinetic effects including diamagnetic drift, ion finite Larmor
radius, finite parallel electric field, ion and electron Landau resonances in a
self-consistent and non-perturbative manner without sacrificing the attractive
efficiency in computation. The physical capabilities of the code are evaluated
and examined in the aspects of both theory and simulation. In theory, the
comprehensive Landau-fluid model implemented in MAS can be reduced to the
well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic
model in various limits, which clearly delineates the physics validity regime.
In simulation, MAS has been well benchmarked with theory and other gyrokinetic
and kinetic-MHD hybrid codes in a manner of adopting the unified physical and
numerical framework, which covers the kinetic Alfven wave, ion sound wave,
low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode.
Moreover, MAS is successfully applied to model the Alfven eigenmode (AE)
activities in DIII-D discharge #159243, which faithfully captures the frequency
sweeping of RSAE, the tunneling damping of TAE, as well as the polarization
characteristics of KBAE and BAAE being consistent with former gyrokinetic
theory and simulation. With respect to the key progress contributed to the
community, MAS has the advantage of combining rich physics ingredients,
realistic global geometry and high computation efficiency together for plasma
stability analysis in linear regime.Comment: 40 pages, 21 figure
Rank-based linkage I: triplet comparisons and oriented simplicial complexes
Rank-based linkage is a new tool for summarizing a collection of objects
according to their relationships. These objects are not mapped to vectors, and
``similarity'' between objects need be neither numerical nor symmetrical. All
an object needs to do is rank nearby objects by similarity to itself, using a
Comparator which is transitive, but need not be consistent with any metric on
the whole set. Call this a ranking system on . Rank-based linkage is applied
to the -nearest neighbor digraph derived from a ranking system. Computations
occur on a 2-dimensional abstract oriented simplicial complex whose faces are
among the points, edges, and triangles of the line graph of the undirected
-nearest neighbor graph on . In steps it builds an
edge-weighted linkage graph where
is called the in-sway between objects and . Take to be
the links whose in-sway is at least , and partition into components of
the graph , for varying . Rank-based linkage is a
functor from a category of out-ordered digraphs to a category of partitioned
sets, with the practical consequence that augmenting the set of objects in a
rank-respectful way gives a fresh clustering which does not ``rip apart`` the
previous one. The same holds for single linkage clustering in the metric space
context, but not for typical optimization-based methods. Open combinatorial
problems are presented in the last section.Comment: 37 pages, 12 figure
A hybrid quantum algorithm to detect conical intersections
Conical intersections are topologically protected crossings between the
potential energy surfaces of a molecular Hamiltonian, known to play an
important role in chemical processes such as photoisomerization and
non-radiative relaxation. They are characterized by a non-zero Berry phase,
which is a topological invariant defined on a closed path in atomic coordinate
space, taking the value when the path encircles the intersection
manifold. In this work, we show that for real molecular Hamiltonians, the Berry
phase can be obtained by tracing a local optimum of a variational ansatz along
the chosen path and estimating the overlap between the initial and final state
with a control-free Hadamard test. Moreover, by discretizing the path into
points, we can use single Newton-Raphson steps to update our state
non-variationally. Finally, since the Berry phase can only take two discrete
values (0 or ), our procedure succeeds even for a cumulative error bounded
by a constant; this allows us to bound the total sampling cost and to readily
verify the success of the procedure. We demonstrate numerically the application
of our algorithm on small toy models of the formaldimine molecule
(\ce{H2C=NH}).Comment: 15 + 10 pages, 4 figure
Tonelli Approach to Lebesgue Integration
Leonida Tonelli devised an interesting and efficient method to introduce the
Lebesgue integral. The details of this method can only be found in the original
Tonelli paper and in an old italian course and solely for the case of the
functions of one variable. We believe that it is woth knowing this method and
here we present a complete account for functions of every number of variables
Digital Image Correlation for Measuring Full-Field Residual Stresses in Wire and Arc Additive Manufactured Components
This study aims to demonstrate the capability of the digital image correlation (DIC) technique for evaluating full-field residual stresses in wire and arc-additive-manufactured (WAAM) components. Investigations were carried out on WAAM steel parts (wall deposited on a substrate) with two different wall heights: 24 mm and 48 mm. Mild steel solid wire AWS ER70S-6 was used to print WAAM walls on substrates that were rigidly clamped to H-profiles. DIC was used to monitor the bending deformation of WAAM parts during unclamping from the H-profiles, and residual stresses were calculated from the strain field captured during unclamping. Residual stresses determined from the proposed DIC-based method were verified with an analytical model and validated by the results from established residual stress measurement techniques, i.e., the contour method and X-ray diffraction.</jats:p
Offline and Online Models for Learning Pairwise Relations in Data
Pairwise relations between data points are essential for numerous machine learning algorithms. Many representation learning methods consider pairwise relations to identify the latent features and patterns in the data. This thesis, investigates learning of pairwise relations from two different perspectives: offline learning and online learning.The first part of the thesis focuses on offline learning by starting with an investigation of the performance modeling of a synchronization method in concurrent programming using a Markov chain whose state transition matrix models pairwise relations between involved cores in a computer process.Then the thesis focuses on a particular pairwise distance measure, the minimax distance, and explores memory-efficient approaches to computing this distance by proposing a hierarchical representation of the data with a linear memory requirement with respect to the number of data points, from which the exact pairwise minimax distances can be derived in a memory-efficient manner. Then, a memory-efficient sampling method is proposed that follows the aforementioned hierarchical representation of the data and samples the data points in a way that the minimax distances between all data points are maximally preserved. Finally, the thesis proposes a practical non-parametric clustering of vehicle motion trajectories to annotate traffic scenarios based on transitive relations between trajectories in an embedded space.The second part of the thesis takes an online learning perspective, and starts by presenting an online learning method for identifying bottlenecks in a road network by extracting the minimax path, where bottlenecks are considered as road segments with the highest cost, e.g., in the sense of travel time. Inspired by real-world road networks, the thesis assumes a stochastic traffic environment in which the road-specific probability distribution of travel time is unknown. Therefore, it needs to learn the parameters of the probability distribution through observations by modeling the bottleneck identification task as a combinatorial semi-bandit problem. The proposed approach takes into account the prior knowledge and follows a Bayesian approach to update the parameters. Moreover, it develops a combinatorial variant of Thompson Sampling and derives an upper bound for the corresponding Bayesian regret. Furthermore, the thesis proposes an approximate algorithm to address the respective computational intractability issue.Finally, the thesis considers contextual information of road network segments by extending the proposed model to a contextual combinatorial semi-bandit framework and investigates and develops various algorithms for this contextual combinatorial setting
Corporate Social Responsibility: the institutionalization of ESG
Understanding the impact of Corporate Social Responsibility (CSR) on firm performance as it relates to industries reliant on technological innovation is a complex and perpetually evolving challenge. To thoroughly investigate this topic, this dissertation will adopt an economics-based structure to address three primary hypotheses. This structure allows for each hypothesis to essentially be a standalone empirical paper, unified by an overall analysis of the nature of impact that ESG has on firm performance. The first hypothesis explores the evolution of CSR to the modern quantified iteration of ESG has led to the institutionalization and standardization of the CSR concept. The second hypothesis fills gaps in existing literature testing the relationship between firm performance and ESG by finding that the relationship is significantly positive in long-term, strategic metrics (ROA and ROIC) and that there is no correlation in short-term metrics (ROE and ROS). Finally, the third hypothesis states that if a firm has a long-term strategic ESG plan, as proxied by the publication of CSR reports, then it is more resilience to damage from controversies. This is supported by the finding that pro-ESG firms consistently fared better than their counterparts in both financial and ESG performance, even in the event of a controversy. However, firms with consistent reporting are also held to a higher standard than their nonreporting peers, suggesting a higher risk and higher reward dynamic. These findings support the theory of good management, in that long-term strategic planning is both immediately economically beneficial and serves as a means of risk management and social impact mitigation. Overall, this contributes to the literature by fillings gaps in the nature of impact that ESG has on firm performance, particularly from a management perspective
Richness of dynamics and global bifurcations in systems with a homoclinic figure-eight
We consider 2D flows with a homoclinic figure-eight to a dissipative saddle. We study the rich dynamics that such a system exhibits under a periodic forcing. First, we derive the bifurcation diagram using topological techniques. In particular, there is a homoclinic zone in the parameter space with a non-smooth boundary. We provide a complete explanation of this phenomenon relating it to primary quadratic homoclinic tangency curves which end up at some cubic tangency (cusp) points. We also describe the possible attractors that exist (and may coexist) in the system. A main goal of this work is to show how the previous qualitative description can be complemented with quantitative global information. To this end, we introduce a return map model which can be seen as the simplest one which is 'universal' in some sense. We carry out several numerical experiments on the model, to check that all the objects predicted to exist by the theory are found in the model, and also to investigate new properties of the system
Isotopic piecewise affine approximation of algebraic or varieties
We propose a novel sufficient condition establishing that a piecewise affine
variety has the same topology as a variety of the sphere defined
by positively homogeneous functions. This covers the case of
varieties in the projective space . We prove that this condition
is sufficient in the case of codimension one and arbitrary dimension. We
describe an implementation working for homogeneous polynomials in arbitrary
dimension and codimension and give experimental evidences that our condition
might still be sufficient in codimension greater than one
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