32,850 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
Quantum Mechanics Lecture Notes. Selected Chapters
These are extended lecture notes of the quantum mechanics course which I am
teaching in the Weizmann Institute of Science graduate physics program. They
cover the topics listed below. The first four chapter are posted here. Their
content is detailed on the next page. The other chapters are planned to be
added in the coming months.
1. Motion in External Electromagnetic Field. Gauge Fields in Quantum
Mechanics.
2. Quantum Mechanics of Electromagnetic Field
3. Photon-Matter Interactions
4. Quantization of the Schr\"odinger Field (The Second Quantization)
5. Open Systems. Density Matrix
6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation
7. Mean Field Approaches for Many Body Systems -- Fermions and Boson
Graph Convex Hull Bounds as generalized Jensen Inequalities
Jensen's inequality is ubiquitous in measure and probability theory,
statistics, machine learning, information theory and many other areas of
mathematics and data science. It states that, for any convex function on a convex domain and any
random variable taking values in , . In this paper, sharp upper and lower bounds on
, termed "graph convex hull bounds", are derived for
arbitrary functions on arbitrary domains , thereby strongly generalizing
Jensen's inequality. Establishing these bounds requires the investigation of
the convex hull of the graph of , which can be difficult for complicated
. On the other hand, once these inequalities are established, they hold,
just like Jensen's inequality, for any random variable . Hence, these bounds
are of particular interest in cases where is fairly simple and is
complicated or unknown. Both finite- and infinite-dimensional domains and
codomains of are covered, as well as analogous bounds for conditional
expectations and Markov operators.Comment: 12 pages, 1 figur
Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio
This paper reviews the most common situations where one or more regularity
conditions which underlie classical likelihood-based parametric inference fail.
We identify three main classes of problems: boundary problems, indeterminate
parameter problems -- which include non-identifiable parameters and singular
information matrices -- and change-point problems. The review focuses on the
large-sample properties of the likelihood ratio statistic. We emphasize
analytical solutions and acknowledge software implementations where available.
We furthermore give summary insight about the possible tools to derivate the
key results. Other approaches to hypothesis testing and connections to
estimation are listed in the annotated bibliography of the Supplementary
Material
Interpolating Discriminant Functions in High-Dimensional Gaussian Latent Mixtures
This paper considers binary classification of high-dimensional features under
a postulated model with a low-dimensional latent Gaussian mixture structure and
non-vanishing noise. A generalized least squares estimator is used to estimate
the direction of the optimal separating hyperplane. The estimated hyperplane is
shown to interpolate on the training data. While the direction vector can be
consistently estimated as could be expected from recent results in linear
regression, a naive plug-in estimate fails to consistently estimate the
intercept. A simple correction, that requires an independent hold-out sample,
renders the procedure minimax optimal in many scenarios. The interpolation
property of the latter procedure can be retained, but surprisingly depends on
the way the labels are encoded
Path integrals and stochastic calculus
Path integrals are a ubiquitous tool in theoretical physics. However, their
use is sometimes hindered by the lack of control on various manipulations --
such as performing a change of the integration path -- one would like to carry
out in the light-hearted fashion that physicists enjoy. Similar issues arise in
the field of stochastic calculus, which we review to prepare the ground for a
proper construction of path integrals. At the level of path integration, and in
arbitrary space dimension, we not only report on existing Riemannian
geometry-based approaches that render path integrals amenable to the standard
rules of calculus, but also bring forth new routes, based on a fully
time-discretized approach, that achieve the same goal. We illustrate these
various definitions of path integration on simple examples such as the
diffusion of a particle on a sphere.Comment: 96 pages, 4 figures. New title, expanded introduction and additional
references. Version accepted in Advandes in Physic
Nonlocal error bounds for piecewise affine functions
The paper is devoted to a detailed analysis of nonlocal error bounds for
nonconvex piecewise affine functions. We both improve some existing results on
error bounds for such functions and present completely new necessary and/or
sufficient conditions for a piecewise affine function to have an error bound on
various types of bounded and unbounded sets. In particular, we show that any
piecewise affine function has an error bound on an arbitrary bounded set and
provide several types of easily verifiable sufficient conditions for such
functions to have an error bound on unbounded sets. We also present general
necessary and sufficient conditions for a piecewise affine function to have an
error bound on a finite union of polyhedral sets (in particular, to have a
global error bound), whose derivation reveals a structure of sublevel sets and
recession functions of piecewise affine functions
Worst-Case Control and Learning Using Partial Observations Over an Infinite Time-Horizon
Safety-critical cyber-physical systems require control strategies whose
worst-case performance is robust against adversarial disturbances and modeling
uncertainties. In this paper, we present a framework for approximate control
and learning in partially observed systems to minimize the worst-case
discounted cost over an infinite time-horizon. We model disturbances to the
system as finite-valued uncertain variables with unknown probability
distributions. For problems with known system dynamics, we construct a dynamic
programming (DP) decomposition to compute the optimal control strategy. Our
first contribution is to define information states that improve the
computational tractability of this DP without loss of optimality. Then, we
describe a simplification for a class of problems where the incurred cost is
observable at each time-instance. Our second contribution is a definition of
approximate information states that can be constructed or learned directly from
observed data for problems with observable costs. We derive bounds on the
performance loss of the resulting approximate control strategy
Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps
In this paper, we study the random dynamical system generated by
a family of maps $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\
(\mathrm{mod }\ 1),\xi: \mathbb S^1 \to \mathbb Ra\in \mathbb S^1\alpha,\varepsilon>0c\in (0,1)\alpha\varepsilon > \alpha^{-1+c},f_\omega^n$
presents a random Young tower structure and quenched decay of correlations.Comment: 38 pages, 0 figure
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