Preprints

Filtering by Subject: Non-linear Dynamics

Diapycnal motion, diffusion, and stretching of tracers in the ocean

Henri Francois Drake, Xiaozhou Ruan, Raffaele Ferrari

Published: 2022-01-07
Subjects: Applied Mathematics, Fluid Dynamics, Non-linear Dynamics, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Small-scale mixing drives the diabatic upwelling that closes the abyssal ocean overturning circulation. Measurements of in-situ turbulence reveal that mixing is bottom-enhanced over rough topography, implying downwelling in the interior and stronger upwelling in a sloping bottom boundary layer. However, in-situ mixing estimates are indirect and the inferred vertical velocities have not yet been [...]

Nonlinear time series analysis of palaeoclimate proxy records

Norbert Marwan, Jonathan F. Donges, Reik V. Donner, et al.

Published: 2021-11-08
Subjects: Applied Statistics, Climate, Dynamic Systems, Earth Sciences, Geology, Longitudinal Data Analysis and Time Series, Multivariate Analysis, Non-linear Dynamics, Physical Sciences and Mathematics, Sedimentology, Statistical, Nonlinear, and Soft Matter Physics

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, [...]

Goal-Oriented Error Estimation and Mesh Adaptation for Shallow Water Modelling

Joseph Gregory Wallwork, Nicolas Barral, Stephan C. Kramer, et al.

Published: 2019-12-31
Subjects: Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics

Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this [...]

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

Ashesh Kumar Chattopadhyay, Pedram Hassanzadeh, Devika Subramanian

Published: 2019-06-20
Subjects: Applied Mathematics, Artificial Intelligence and Robotics, Atmospheric Sciences, Climate, Computer Sciences, Dynamic Systems, Earth Sciences, Fluid Dynamics, Non-linear Dynamics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics, Physics

In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural network (ANN), and recurrent neural network with long short-term memory [...]

River deltas as Multiplex networks: A framework for studying multi-process multi-scale connectivity via coupled-network theory

Alejandro Tejedor, Anthony Longjas, Paola Passalacqua, et al.

Published: 2018-04-13
Subjects: Applied Mathematics, Dynamic Systems, Earth Sciences, Environmental Sciences, Geomorphology, Hydrology, Mathematics, Non-linear Dynamics, Physical Sciences and Mathematics, Physics, Statistical, Nonlinear, and Soft Matter Physics

Transport of water, nutrients or energy fluxes in many natural or coupled human-natural systems occurs along different pathways that often have a wide range of transport timescales and might exchange fluxes with each other dynamically (e.g., surface-subsurface). Understanding this type of transport is key to predicting how landscapes will change under changing forcing. Here, we present a general [...]

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