Nonlinear Oscillations: Exact Solutions and their Approximations

Toward accommodating realistic fuel chemistry in large-scale computations

A chemical explosive mode analysis (CEMA) was developed as a new diagnostic to identify flame and ignition structure in complex flows. CEMA was then used to analyse the near-field structure of the stabilization region of a turbulent lifted hydrogen–air slot jet flame in a heated air coflow computed with three-dimensional direct numerical simulation. The simulation was performed with a detailed hydrogen–air mechanism and mixture-averaged transport properties at a jet Reynolds number of 11000 with over 900 million grid points. Explosive chemical modes and their characteristic time scales, as well as the species involved, were identified from the Jacobian matrix of the chemical source terms for species and temperature. An explosion index was defined for explosive modes, indicating the contribution of species and temperature in the explosion process. Radical and thermal runaway can consequently be distinguished. CEMA of the lifted flame shows the existence of two premixed flame fronts, which are difficult to detect with conventional methods. The upstream fork preceding the two flame fronts thereby identifies the stabilization point. A Damkohler number was defined based on the time scale of the chemical explosive mode and the local instantaneous scalar dissipation rate to highlight the role of auto-ignition in affecting the stabilization points in the lifted jet flame.

Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis

Modeling dynamic geophysical phenomena is at the core of Earth and environmental studies. The geoscientific community relying mainly on physical representations may want to consider much deeper adoption of artificial intelligence (AI) instruments in the context of AI's global success and emergence of big Earth data. A new perspective of using hybrid physics-AI approaches is a grand vision, but actualizing such approaches remains an open question in geoscience. This study develops a general approach to improving AI geoscientific awareness, wherein physical approaches such as temporal dynamic geoscientific models are included as special recurrent neural layers in a deep learning architecture. The illustrative case of runoff modeling across the conterminous United States demonstrates that the physics-aware DL model has enhanced prediction accuracy, robust transferability, and good intelligence for inferring unobserved processes. This study represents a firm step toward realizing the vision of tackling Earth system challenges by physics-AI integration.

/pdf/improving-ai-system-awareness-of-geoscience-knowledge-1ss6gzx1l5.pdf

Improving AI System Awareness of Geoscience Knowledge: Symbiotic Integration of Physical Approaches and Deep Learning

1. Climate variability 2. Deterministic dynamical systems 3. Introduction to stochastic calculus 4. Stochastic dynamical systems 5. Analysing data from stochastic dynamical systems 6. The climate modeling hierarchy 7. The North Atlantic Oscillation 8. El Nino variability 9. Multidecadal variability 10. Dansgaard-Oeschger events 11. The Pleistocene ice ages 12. Predictability.

Nonlinear Climate Dynamics

The computational singular perturbation (CSP) method ofLam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary differential equations with multiple time scales. In [J. Nonlinear Sci., 14 (2004), pp. 59--91], the authors of this paper showed that each iteration of the CSP algorithm improves the approximation of the slow manifold by one order. In this paper, it is shown that the CSP method simultaneously approximates the tangent spaces to the fast fibers along which solutions relax to the slow manifold. Again, each iteration adds one order of accuracy. In some studies, the output of the CSP algorithm is postprocessed by linearly projecting initial data onto the slow manifold along these approximate tangent spaces. These projections, in turn, also become successively more accurate.

/pdf/fast-and-slow-dynamics-for-the-computational-singular-4o09mhn14v.pdf

Fast and Slow Dynamics for the Computational Singular Perturbation Method

Dynamical systems analysis of the Maasch–Saltzman model for glacial cycles

This chapter introduces British Columbia’s weather and climate. “Weather” refers to the specific condition of the atmosphere at a particular place and time. It is measured in terms of variables including wind speed and direction, air temperature, humidity, atmospheric pressure, cloudiness, and precipitation. Weather can change from hour to hour, day to day, and season to season. “Climate” is a statistical characterization of the weather, averaged over many years; it is usually represented in terms of means, variability, and extremes of the various weather elements. The following sections focus on (1) the large-scale context of British Columbia’s weather and its expression at the scale of synoptic atmospheric circulation; (2) a description of regional climatic variations resulting from the interaction of weather systems with the topography of British Columbia; (3) an overview of large-scale ocean–atmosphere interactions, including El Niño, and their influence on the province’s weather and climate; (4) an overview of the climatology and meteorology of extreme hydrogeomorphic events; and (5) a discussion of historic climatic variability and projected future climate change. Weather and Climate Chapter 3

/pdf/chapter-3-weather-and-climate-23frossbz0.pdf

Chapter 3: Weather and Climate

Chapter 9: Regression Analysis

Chapter 8: Energy

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