987 research outputs found
Model Reduction for the Kuramoto-Sakaguchi Model: analyzing the effect of non-entrained rogue oscillators
The Kuramoto-Sakaguchi model is a paradigmatic model of coupled oscillator
system which displays collective behaviour. This thesis is concerned
with better understanding of the model through construction of lowerdimensional
reduced models that are more tractable for analysis. The
role of non-entrained rogue oscillators on the synchronized oscillators is
highlighted. After reviewing traditional analysis via mean-field theory
in the thermodynamic limit of infinitely many oscillators, we proceed to
construct reduced models for finite-size systems, where we investigate on how the effects of rogue oscillators should be incorporated. We first
describe the rogue oscillatorsâ effect via averaging, leading to a closed
deterministic system that involves the synchronized oscillators only. We
perform model reduction analysis on the system via the collective coordinate
framework. It is demonstrated that inclusion of the effect of
rogue oscillators is crucial for obtaining an accurate description of the
system. A new non-linear ansatz is introduced which significantly improves
the accuracy of the reduced system, both for finite-size systems
and in the thermodynamic limit. We then analyze the fluctuation of
rogue oscillatorâs effect around their mean, by constructing stochastic
process approximations. It is demonstrated that utilizing an Ornstein-
Uhlenbeck process leads to stochastic reduced model that can capture
the fluctuations exhibited in the full model. This thesis also adds to the
mean-field theory analysis for Kuramoto-like model by performing meanfield
analysis on the Kuramoto-Sakaguchi model with uniform intrinsic
frequency distribution, which reviews that for a non-zero phase-offset
parameter, the system exhibits an intricate transition to synchronization,
with first-order transition to partial synchronization followed by a
second-order transition to global synchronization
Non-Equilibrium Quantum Dynamics in a Disordered Ising Magnet
The quantum two-level system, or âqubit,â is a simple platform that nonetheless displays fundamentally non-trivial quantum behavior. The rare-earth magnet LiHoFâ is a natural physical representation of a system of coupled qubits. With its uncommonly high crystal anisotropy, LiHoFâ can be mapped to the problem of the Ising model in a transverse field. However, while this Ising approximation can quantitatively predict much of the equilibrium behavior, quantum corrections, originating from off-diagonal terms in the dipolar interaction that generate quantum fluctuations, are crucial in driving non-equilibrium dynamics when subject to an external drive. Furthermore, quenched disorder can be introduced through chemical substitution, which, through the dipolar interaction, generates spatially random pinning fields, as well as internal transverse fields, which drive quantum fluctuations. Noise measurements on the disordered ferromagnet LiHo0.65Y0.35F4 show critical behavior, whose statistics are driven from the underlying pinning distribution, while measurements on LiHo0.40Y0.60F4 display non-critical behavior that can only be attributed to quantum co-tunneling processes. This is the first demonstration of crackling noise in a ferromagnet in the purely quantum regime. Furthermore, pump-probe susceptibility measurements on the decoupled cluster glass show the system being driven out of equilibrium with astonishingly weak drives, due to resonant transitions arising from off-diagonal dipolar terms Ďiz Ďjx. Non-linear sample response is observable in inelastic Raman scattering measurements, and these spin clusters also exhibit asymmetric Fano resonances with high Q-factors of ~10âľ. Quantum interference effects can be tuned to fully decouple one of the dressed states from the others, rendering the sample transparent to the drive. This is analogous to optical systems that display electromagnetically-induced transparency, but at 100 Hz frequencies
Proceedings of SIRM 2023 - The 15th European Conference on Rotordynamics
It was our great honor and pleasure to host the SIRM Conference after 2003 and 2011 for the third time in Darmstadt. Rotordynamics covers a huge variety of different applications and challenges which are all in the scope of this conference. The conference was opened with a keynote lecture given by Rainer Nordmann, one of the three founders of SIRM âSchwingungen in rotierenden Maschinenâ. In total 53 papers passed our strict review process and were presented. This impressively shows that rotordynamics is relevant as ever. These contributions cover a very wide spectrum of session topics: fluid bearings and seals; air foil bearings; magnetic bearings; rotor blade interaction; rotor fluid interactions; unbalance and balancing; vibrations in turbomachines; vibration control; instability; electrical machines; monitoring, identification and diagnosis; advanced numerical tools and nonlinearities as well as general rotordynamics. The international character of the conference has been significantly enhanced by the Scientific Board since the 14th SIRM resulting on one hand in an expanded Scientific Committee which meanwhile consists of 31 members from 13 different European countries and on the other hand in the new name âEuropean Conference on Rotordynamicsâ. This new international profile has also been
emphasized by participants of the 15th SIRM coming from 17 different countries out of three continents. We experienced a vital discussion and dialogue between industry and academia at the conference where roughly one third of the papers were presented by industry and two thirds by academia being an excellent basis to follow a bidirectional transfer what we call xchange at Technical University of Darmstadt. At this point we also want to give our special thanks to the eleven industry sponsors for their great support of the conference. On behalf of the Darmstadt Local Committee I welcome you to read the papers of the 15th SIRM giving you further insight into the topics and presentations
GNN-Assisted Phase Space Integration with Application to Atomistics
Overcoming the time scale limitations of atomistics can be achieved by
switching from the state-space representation of Molecular Dynamics (MD) to a
statistical-mechanics-based representation in phase space, where approximations
such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic
ensemble in a time-coarsened fashion. In practice, this requires the
computation of expensive high-dimensional integrals over all of phase space of
an atomistic ensemble. This, in turn, is commonly accomplished efficiently by
low-order numerical quadrature. We show that numerical quadrature in this
context, unfortunately, comes with a set of inherent problems, which corrupt
the accuracy of simulations -- especially when dealing with crystal lattices
with imperfections. As a remedy, we demonstrate that Graph Neural Networks,
trained on Monte-Carlo data, can serve as a replacement for commonly used
numerical quadrature rules, overcoming their deficiencies and significantly
improving the accuracy. This is showcased by three benchmarks: the thermal
expansion of copper, the martensitic phase transition of iron, and the energy
of grain boundaries. We illustrate the benefits of the proposed technique over
classically used third- and fifth-order Gaussian quadrature, we highlight the
impact on time-coarsened atomistic predictions, and we discuss the
computational efficiency. The latter is of general importance when performing
frequent evaluation of phase space or other high-dimensional integrals, which
is why the proposed framework promises applications beyond the scope of
atomistics
A performance portable, fully implicit Landau collision operator with batched linear solvers
Modern accelerators use hierarchically parallel programming models that
enable massive multithreading within a processing element (PE), with multiple
PEs per device driven by traditional processes. Batching is a technique for
exposing PE-level parallelism in algorithms that previously ran on entire
processes or multiple threads within a single MPI process. Kinetic
discretizations of magnetized plasmas, for example, advance the Vlasov-Maxwell
system, which is then followed by a fully implicit time advance of a collision
operator. These collision advances are independent at each spatial point and
are well suited to batch processing.
This paper builds on previous work on a high-performance, fully nonlinear
Landau collision operator by batching the linear solver, as well as batching
the spatial point problems and adding new support for multiple grids for highly
multiscale, multi-species problems. An anisotropic relaxation verification test
that agrees well with previous published results and analytical solutions is
presented. The performance of the NVIDIA A100 and AMD MI250X nodes is
evaluated, with a detailed hardware utilization analysis on the A100. For
portability, the entire Landau operator time advance is implemented in Kokkos
and is available in the PETSc numerical library
Turbulence closure with small, local neural networks: Forced two-dimensional and -plane flows
We parameterize sub-grid scale (SGS) fluxes in sinusoidally forced
two-dimensional turbulence on the -plane at high Reynolds numbers
(Re25000) using simple 2-layer Convolutional Neural Networks (CNN) having
only O(1000)parameters, two orders of magnitude smaller than recent studies
employing deeper CNNs with 8-10 layers; we obtain stable, accurate, and
long-term online or a posteriori solutions at 16X downscaling factors. Our
methodology significantly improves training efficiency and speed of online
Large Eddy Simulations (LES) runs, while offering insights into the physics of
closure in such turbulent flows. Our approach benefits from extensive
hyperparameter searching in learning rate and weight decay coefficient space,
as well as the use of cyclical learning rate annealing, which leads to more
robust and accurate online solutions compared to fixed learning rates. Our CNNs
use either the coarse velocity or the vorticity and strain fields as inputs,
and output the two components of the deviatoric stress tensor. We minimize a
loss between the SGS vorticity flux divergence (computed from the
high-resolution solver) and that obtained from the CNN-modeled deviatoric
stress tensor, without requiring energy or enstrophy preserving constraints.
The success of shallow CNNs in accurately parameterizing this class of
turbulent flows implies that the SGS stresses have a weak non-local dependence
on coarse fields; it also aligns with our physical conception that small-scales
are locally controlled by larger scales such as vortices and their strained
filaments. Furthermore, 2-layer CNN-parameterizations are more likely to be
interpretable and generalizable because of their intrinsic low dimensionality.Comment: 27 pages, 13 figure
Generative data-driven approaches for stochastic subgrid parameterizations in an idealized ocean model
Subgrid parameterizations of mesoscale eddies continue to be in demand for
climate simulations. These subgrid parameterizations can be powerfully designed
using physics and/or data-driven methods, with uncertainty quantification. For
example, Guillaumin and Zanna (2021) proposed a Machine Learning (ML) model
that predicts subgrid forcing and its local uncertainty. The major assumption
and potential drawback of this model is the statistical independence of
stochastic residuals between grid points. Here, we aim to improve the
simulation of stochastic forcing with generative models of ML, such as
Generative adversarial network (GAN) and Variational autoencoder (VAE).
Generative models learn the distribution of subgrid forcing conditioned on the
resolved flow directly from data and they can produce new samples from this
distribution. Generative models can potentially capture not only the spatial
correlation but any statistically significant property of subgrid forcing. We
test the proposed stochastic parameterizations offline and online in an
idealized ocean model. We show that generative models are able to predict
subgrid forcing and its uncertainty with spatially correlated stochastic
forcing. Online simulations for a range of resolutions demonstrated that
generative models are superior to the baseline ML model at the coarsest
resolution
Multiscale modelling of mesoscopic behaviour in soft matter systems
Soft matter modelling has a wide range of applications, such as polymer additive manufacturing, organics electronics, and biomolecular engineering. Many physical properties and phenomena of soft matter are determined by interactions and processes at a wide range of length and time scales. Therefore, it is challenging for theoretical models to simulate processes involving features from multiple scales. To reach the mesoscopic scales for soft matter behaviour, coarse-grained models have been developed to accelerate the atomistic models by projecting out the relevant degrees of freedom, allowing coverage of a wider range of scales. However, due to the lack of a formalism to capture the dynamics and anisotropy of the system, conventional coarse-grained model shows significant errors in dynamical properties and inconsistent soft matter behaviour.
In this thesis, a generalised systematic formalism for coarse-graining is presented. The Mori-Zwanzig formalism provides a dynamically-guided projection to construct a mesoscopic system directly from the underlying microscopic system. Moreover, the Gay-Berne functional is introduced to describe the anisotropic effect of the pairwise interactions at mesoscopic level. The performance of the model is demonstrated by comparing it to other coarse-grained models using benzene as an example, which shows significant improvement in both static and dynamical properties. For application, crystallization of pentacene is studied by treating pentacene molecule as ellipsoidal particle. Furthermore, a modified atomistic model and a modified continuum model are employed to simulate mesosopic behaviour of polymers in electrospinning and electro-optical poling, demonstrating mesoscopic modelling from the atomistic and continuum limits
Particle-Continuum Multiscale Modeling of Sea Ice Floes
Sea ice profoundly influences the polar environment and the global climate.
Traditionally, Sea ice has been modeled as a continuum under Eulerian
coordinates to describe its large-scale features, using, for instance,
viscous-plastic rheology. Recently, Lagrangian particle models, also known as
the discrete element method (DEM) models, have been utilized for characterizing
the motion of individual sea ice fragments (called floes) at scales of 10 km
and smaller, especially in marginal ice zones. This paper develops a multiscale
model that couples the particle and the continuum systems to facilitate an
effective representation of the dynamical and statistical features of sea ice
across different scales. The multiscale model exploits a Boltzmann-type system
that links the particle movement with the continuum equations. For the
small-scale dynamics, it describes the motion of each sea ice floe. Then, as
the large-scale continuum component, it treats the statistical moments of mass
density and linear and angular velocities. The evolution of these statistics
affects the motion of individual floes, which in turn provides bulk feedback
that adjusts the large-scale dynamics. Notably, the particle model
characterizing the sea ice floes is localized and fully parallelized, in a
framework that is sometimes called superparameterization, which significantly
improves computation efficiency. Numerical examples demonstrate the effective
performance of the multiscale model. Additionally, the study demonstrates that
the multiscale model has a linear-order approximation to the truth model
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