Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userModel dynamics on a multigrid across multiple length and time scales
142
0
0.0
(
0
)
Authors
A. J. Roberts
Ask ChatGPT about the research
No Arabic abstract
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time scales. I discuss an approach to modelling the discretised dynamics of advection and diffusion with rigorous support for changing the resolved spatial grid scale by just a factor of two. The mapping of dynamics from a finer grid to a coarser grid is then iterated to generate a hierarchy of models across a wide range of space-time scales, all with rigorous support across the whole hierarchy. This approach empowers us with great flexibility in modelling complex dynamics over multiple scales.
rate research
Read More
This paper presents a novel spatio-temporal LSTM (SPATIAL) architecture for time series forecasting applied to environmental datasets. The framework was evaluated across multiple sensors and for three different oceanic variables: current speed, temperature, and dissolved oxygen. Network implementation proceeded in two directions that are nominally separated but connected as part of a natural environmental system -- across the spatial (between individual sensors) and temporal components of the sensor data. Data from four sensors sampling current speed, and eight measuring both temperature and dissolved oxygen evaluated the framework. Results were compared against RF and XGB baseline models that learned on the temporal signal of each sensor independently by extracting the date-time features together with the past history of data using sliding window matrix. Results demonstrated ability to accurately replicate complex signals and provide comparable performance to state-of-the-art benchmarks. Notably, the novel framework provided a simpler pre-processing and training pipeline that handles missing values via a simple masking layer. Enabling learning across the spatial and temporal directions, this paper addresses two fundamental challenges of ML applications to environmental science: 1) data sparsity and the challenges and costs of collecting measurements of environmental conditions such as ocean dynamics, and 2) environmental datasets are inherently connected in the spatial and temporal directions while classical ML approaches only consider one of these directions. Furthermore, sharing of parameters across all input steps makes SPATIAL a fast, scalable, and easily-parameterized forecasting framework.
The dynamics of membrane undulations inside a viscous solvent is governed by distinctive, anomalous, power laws. Inside a viscoelastic continuous medium these universal behaviors are modified by the specific bulk viscoelastic spectrum. Yet, in structured fluids the continuum limit is reached only beyond a characteristic correlation length. We study the crossover to this asymptotic bulk dynamics. The analysis relies on a recent generalization of the hydrodynamic interaction in structured fluids, which shows a slow spatial decay of the interaction toward the bulk limit. For membranes which are weakly coupled to the structured medium we find a wide crossover regime characterized by different, universal, dynamic power laws. We discuss various systems for which this behavior is relevant, and delineate the time regime over which it may be observed.
Using small-angle neutron scattering, we demonstrate that the complex magnetic domain patterns at the surface of Nd2Fe14B, revealed by quantitative Kerr and Faraday microscopy, propagate into the bulk and exhibit structural features with dimensions down to 6 nm, the domain wall thickness. The observed fractal nature of the domain structures provides an explanation for the anomalous increase in the bulk magnetization of Nd2Fe14B below the spin-reorientation transition. These measurements open up a rich playground for studies of fractal structures in highly anisotropic magnetic systems.
We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and feedforward loops, we found that feedforward loops can provide higher temporal order (coherence) with lower entropy (randomness) in a temporal program of gene expression. In addition, complexity of the state space that increases with longer length of attractors and greater number of attractors is also reduced for networks with more feedforward loops. Feedback loops show opposite effects on dynamics of the networks. These results suggest that feedforward loops are one of the favorable local structures in biomolecular and neuronal networks.
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We then show how to simulate the canonical real computation model, BSS machines, with infinite time cellular automata in exactly omega steps.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
