987 research outputs found

    Model Reduction for the Kuramoto-Sakaguchi Model: analyzing the effect of non-entrained rogue oscillators

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    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 oscillators’ 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 oscillator’s 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

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    The quantum two-level system, or “qubit,” is a simple platform that nonetheless displays fundamentally non-trivial quantum behavior. The rare-earth magnet LiHoF₄ is a natural physical representation of a system of coupled qubits. With its uncommonly high crystal anisotropy, LiHoF₄ 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 σiz σjx. 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 ~10⁵. 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

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    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 “Schwingungen in rotierenden Maschinen”. 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 “European Conference on Rotordynamics”. 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

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    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

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    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 β\beta-plane flows

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    We parameterize sub-grid scale (SGS) fluxes in sinusoidally forced two-dimensional turbulence on the β\beta-plane at high Reynolds numbers (Re∟\sim25000) 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

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    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

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    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

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    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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