181 research outputs found
Energy cascade in the Garrett-Munk spectrum of internal gravity waves
We study the spectral energy transfer due to wave-triad interactions in the
Garrett-Munk spectrum of internal gravity waves (IGWs) based on a numerical
evaluation of the collision integral in the wave kinetic equation. Our
numerical evaluation builds on the reduction of the collision integral on the
resonant manifold for a horizontally isotropic spectrum. We directly evaluate
the downscale energy flux available for ocean mixing, whose value is in close
agreement with the empirical finescale parameterization. We further decompose
the energy transfer into contributions from different mechanisms, including
local interactions and three types of nonlocal interactions, namely parametric
subharmonic instability (PSI), elastic scattering (ES) and induced diffusion
(ID). Through analysis on the role of each type of interaction, we resolve two
long-standing paradoxes regarding the mechanism for forward cascade in
frequency and zero ID flux for GM76 spectrum. In addition, our analysis
estimates the contribution of each mechanism to the energy transfer in each
spectral direction, and reveals new understanding of the importance of local
interactions and ES in the energy transfer
Breather Solutions to a Two-dimensional Nonlinear Schr\"odinger Equation with Non-local Derivatives
We consider the nonlinear Schr\"odinger equation with non-local derivatives
in a two-dimensional periodic domain. For certain orders of derivatives, we
find a new type of breather solution dominating the field evolution at low
nonlinearity levels. With the increase of nonlinearity, the breathers break
down, giving way to wave turbulence (or Rayleigh-Jeans) spectra. Phase-space
trajectories associated with the breather solutions are found to be close to
that of the linear system, revealing a connection between the breather solution
and Kolmogorov-Arnold-Moser (KAM) theory
A generalized likelihood-weighted optimal sampling algorithm for rare-event probability quantification
In this work, we introduce a new acquisition function for sequential sampling
to efficiently quantify rare-event statistics of an input-to-response (ItR)
system with given input probability and expensive function evaluations. Our
acquisition is a generalization of the likelihood-weighted (LW) acquisition
that was initially designed for the same purpose and then extended to many
other applications. The improvement in our acquisition comes from the
generalized form with two additional parameters, by varying which one can
target and address two weaknesses of the original LW acquisition: (1) that the
input space associated with rare-event responses is not sufficiently stressed
in sampling; (2) that the surrogate model (generated from samples) may have
significant deviation from the true ItR function, especially for cases with
complex ItR function and limited number of samples. In addition, we develop a
critical procedure in Monte-Carlo discrete optimization of the acquisition
function, which achieves orders of magnitude acceleration compared to existing
approaches for such type of problems. The superior performance of our new
acquisition to the original LW acquisition is demonstrated in a number of test
cases, including some cases that were designed to show the effectiveness of the
original LW acquisition. We finally apply our method to an engineering example
to quantify the rare-event roll-motion statistics of a ship in a random sea
An adaptive multi-fidelity sampling framework for safety analysis of connected and automated vehicles
Testing and evaluation are expensive but critical steps in the development of
connected and automated vehicles (CAVs). In this paper, we develop an adaptive
sampling framework to efficiently evaluate the accident rate of CAVs,
particularly for scenario-based tests where the probability distribution of
input parameters is known from the Naturalistic Driving Data. Our framework
relies on a surrogate model to approximate the CAV performance and a novel
acquisition function to maximize the benefit (information to accident rate) of
the next sample formulated through an information-theoretic consideration. In
addition to the standard application with only a single high-fidelity model of
CAV performance, we also extend our approach to the bi-fidelity context where
an additional low-fidelity model can be used at a lower computational cost to
approximate the CAV performance. Accordingly, for the second case, our approach
is formulated such that it allows the choice of the next sample in terms of
both fidelity level (i.e., which model to use) and sampling location to
maximize the benefit per cost. Our framework is tested in a widely-considered
two-dimensional cut-in problem for CAVs, where Intelligent Driving Model (IDM)
with different time resolutions are used to construct the high and low-fidelity
models. We show that our single-fidelity method outperforms the existing
approach for the same problem, and the bi-fidelity method can further save half
of the computational cost to reach a similar accuracy in estimating the
accident rate
“It is difficult to balance research and teaching time, let alone family”: An analysis of women’s experiences working as academics in contemporary Chinese universities
This thesis explores the experience of women academics in China, focusing on gender inequalities in their professional and domestic lives and the conflict between these two spheres. Three analysis chapters respectively address women's reasons for choosing an academic career and the wider social perception of academic work as ‘good’ work for women
On the time scales of spectral evolution of nonlinear waves
As presented in Annenkov & Shrira (2009), when a surface gravity wave field
is subjected to an abrupt perturbation of external forcing, its spectrum
evolves on a ``fast'' dynamic time scale of , with
a measure of wave steepness. This observation poses a challenge
to wave turbulence theory that predicts an evolution with a kinetic time scale
of . We revisit this unresolved problem by studying the
same situation in the context of a one-dimensional Majda-McLaughlin-Tabak (MMT)
equation with gravity wave dispersion relation. Our results show that the
kinetic and dynamic time scales can both be realised, with the former and
latter occurring for weaker and stronger forcing perturbations, respectively.
The transition between the two regimes corresponds to a critical forcing
perturbation, with which the spectral evolution time scale drops to the same
order as the linear wave period (of some representative mode). Such fast
spectral evolution is mainly induced by a far-from-stationary state after a
sufficiently strong forcing perturbation is applied. We further develop a
set-based interaction analysis to show that the inertial-range modal evolution
in the studied cases is dominated by their (mostly non-local) interactions with
the low-wavenumber ``condensate'' induced by the forcing perturbation. The
results obtained in this work should be considered to provide significant
insight into the original gravity wave problem
Energy transfer for solutions to the nonlinear Schr\"odinger equation on irrational tori
We analyze the energy transfer for solutions to the defocusing cubic
nonlinear Schr\"odinger (NLS) initial value problem on 2D irrational tori.
Moreover we complement the analytic study with numerical experimentation. As a
biproduct of our investigation we also prove that the quasi-resonant part of
the NLS initial value problem we consider, in both the focusing and defocusing
case, is globally well-posed for initial data of finite mass
Node-aware Bi-smoothing: Certified Robustness against Graph Injection Attacks
Deep Graph Learning (DGL) has emerged as a crucial technique across various
domains. However, recent studies have exposed vulnerabilities in DGL models,
such as susceptibility to evasion and poisoning attacks. While empirical and
provable robustness techniques have been developed to defend against graph
modification attacks (GMAs), the problem of certified robustness against graph
injection attacks (GIAs) remains largely unexplored. To bridge this gap, we
introduce the node-aware bi-smoothing framework, which is the first certifiably
robust approach for general node classification tasks against GIAs. Notably,
the proposed node-aware bi-smoothing scheme is model-agnostic and is applicable
for both evasion and poisoning attacks. Through rigorous theoretical analysis,
we establish the certifiable conditions of our smoothing scheme. We also
explore the practical implications of our node-aware bi-smoothing schemes in
two contexts: as an empirical defense approach against real-world GIAs and in
the context of recommendation systems. Furthermore, we extend two
state-of-the-art certified robustness frameworks to address node injection
attacks and compare our approach against them. Extensive evaluations
demonstrate the effectiveness of our proposed certificates
Direct Numerical Investigation of Turbulence of Capillary Waves
We consider the inertial range spectrum of capillary wave turbulence. Under the assumptions of weak turbulence, the theoretical surface elevation spectrum scales with wave number k as I[subscript η] ∼ k[superscript α], where α = α[subscript 0] = -19/4, energy (density) flux P as P[superscript 1/2]. The proportional factor C, known as the Kolmogorov constant, has a theoretical value of C = C[subscript 0] = 9.85 (we show that this value holds only after a formulation in the original derivation is corrected). The k[superscript -19/4] scaling has been extensively, but not conclusively, tested; the P[superscript 1/2] scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of C[subscript 0] remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical k[superscript -19/4] and P[superscript 1/2] scalings as well as value of C[subscript 0] are well recovered by our numerical results. For a given number of numerical modes N, as nonlinearity decreases, the long-time spectra deviate from theoretical predictions with respect to scaling with P, with calculated values of α C[subscript 0], all due to finite box effect
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