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Blog articles in progress (Rev #84, changes)

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Contents

Tim van Beek

Your model is verified, but not valid! Huh?

Summary: Critics of climate science in general, and sceptics of the statement that anthropogenic (man-made) global warming is real, often claim that climate models are wrong and cannot be trusted. But what does “wrong” mean here and what can and should be done to make models more trustworthy, from a software engineering viewpoint? In a first step, we’ll introduce some relevant technobabble.

Putting the Earth in a box

Summary: An introduction to energy balance models.

A quantum of warmth

Summary: A closer look at the heat balance of the Earth and its atmosphere. An explanation of downward longwave radiation (DLR), generated by the atmosphere of the earth and why it does not violate the second law of thermodynamics.

Eddy who?

Summary: A short introduction to turbulence: It is all about eddies.

Fluid flows and infinite dimensional manifolds (part 1)

Summary: Fluid flows can be modelled by one parameter subgroups of diffeomorphism groups. How diffeomorphism groups can be seen as infinite dimensional Riemannian manifolds, and how certain nonlinear partial differential arise as geodesic equations.

Fluid flows and infinite dimensional manifolds (part 2)

Summary: Explaining Euler’s equation as a geodesic equation of ideal incompressible fluids.

Fluid flows and infinite dimensional manifolds, manifolds interlude (part 3)

Summary: Comparing the Euler equation with the Navier-Stokes equation for incompressible fluids.

Fluid flows and infinite dimensional manifolds (part 4)

Summary: Explaining the Jacobi equation and how this can be used to put a bound on weather predictions.

Fluid flows and infinite dimensional manifolds (part 5)

Summary: Revisiting the Burgers equation as the simplest example of a nonlinear partial differential equation

Good vibrations

Summary: Recapitulation of previous blog posts and short tour to molecular quantum mechanics necessary to understand that radiation equations of the atmosphere of the earth.

The color of night

Summary: How big is the effect of downward longwave radiation (DLR) really? What do measurements say? What instruments are used? Are there alternative explanations of the 33 Kelvin gap of the zero dimensional energy balance model?

Increasing the signal-to-noise ratio with more noise

Summary: An introduction to stochastic resonance.

Staffan Liljgeren

Carbon cycle box models (part 1)

Carbon cycle box models (part 2)

Curtis Faith

Curtis Faith on the Azimuth Project

Summary: Curtis Faith introduces himself and talks about why he decided to help out on the Azimuth Project.

Making decisions under uncertainty

Summary: Groups often want to make the right decisions. So they spend a lot of time in the decision process itself. A better approach is to acknowledge when perfect decisions don’t exist and to incorporate the uncertainty itself into your plans.

Cameron Smith

Hierarchical organization and biological evolution (part 1)

Summary: An introduction to hierarchical systems, which asks why evolution favors the development of such systems. See also the old Wiki page: [[Blog - evolution and categories]. This is part of a larger attempt to review some of the literature on major transitions in evolution and multi-level selection, sketch a few connections to concepts in category theory, and discuss the potential for using experimental evolution to investigate and strengthen those connections.

Hierarchical organization and biological evolution (part 2)

Summary: An attempt to review some of the literature on major transitions in evolution and multi-level selection, sketch a few connections to concepts in category theory, and discuss the potential for using experimental evolution to investigate and strengthen those connections.

Hierarchical organization and biological evolution (part 3)

Summary: An attempt to review some of the literature on major transitions in evolution and multi-level selection, sketch a few connections to concepts in category theory, and discuss the potential for using experimental evolution to investigate and strengthen those connections.

This Week’s Finds

Week 309

Summary: Another application of Hopf bifurcations with noise, this time to predator-prey systems.

Week 314

Summary: The first part of an interview with Thomas Fischbacher.

Week 317

Summary: A sketchy introduction to glacial cycles and Milankovich cycles.

Week 318

Summary: A bit more detail on Milankovitch cycles.

Interview with Didier Paillard

Summary: John Baez interviewing Didier Paillard about his work on the glacial cycles.

Other

Azimuth Project news

Summary: What’s new on the Azimuth Project?

Stabilization wedges (part 5)

Summary: Pacala’s 2008 followup on the original Pacala-Socolow Stabilization wedges paper.

Worried about the environment? You’re seeing things!

Summary: Thoughts about the disproportionate impact of pictures on human psychology.

Invasion fitness in moment-closure treatments

Summary: Moment closures are a way of forgetting information about a system in a controlled fashion, in the hope that an incomplete, fairly heavily “coarse-grained” picture of the system will still be useful in figuring out what will happen to it. Sometimes, this is a justifiable hope, but in other cases, we are right to wonder whether all the algebra it generates actually leads us to any insights. Here, we’ll be concerned with a particular application of this technology: studying the vulnerability of an ecosystem to invasion. We shall find expressions for invasion fitness, the expected relative growth rate of an initially-rare species or variety.

Network theory

Network theory (part 1)

Summary: Networks, and diagrams of networks, show up in many branches of science. It would be nice to find a unified framework for these ideas.

Network theory (part 2)

Summary: One can adapt ideas from quantum field theory to describe the theory of stochastic Petri nets. The master equation versus the rate equation.

Network theory (part 3)

Summary: The rate equation of a stochastic Petri net, and applications to chemistry and infectious disease.

Network theory (part 4)

Summary: The master equation of a stochastic Petri net, and analogies to quantum field theory.

Network theory (part 5)

Summary: Analogies between quantum theory and probability theory.

Network theory (part 6)

Summary: Writing the master equation using annihilation and creation operators.

Network theory (part 7)

Summary: An example: the stochastic version of the logistic equation in terms of annihilation and creation operators, and how to obtain an equilibrium Poisson distribution.

Network theory (part 8)

Summary: A review of our work so far: how to get the rate equation and the master equation from a stochastic Petri net. A bit about Feynman diagrams.

Network theory (part 9)

Summary: A quantum field theory proof of the most exciting theorem in D. F. Anderson, G. Craciun and T. G. Kurtz’s paper Product-form stationary distributions for deficiency zero chemical reaction networks.

Network theory (part 10)

Summary: An example of a simple reversible reaction.

Network theory (part 11)

Summary: Brendan Fong proves a version of Noether’s theorem for Markov processes.

Network theory (part 12)

Summary: A comparison of quantum mechanics and stochastic mechanics.

Network theory (part 13)

Summary: A comparison of the quantum and stochastic versions of Noether’s theorem.

Network theory (part 14)

Summary: The Desargues graph and its role in chemistry.

Network theory (part 15)

Summary: More on the Desargues graph; graph Laplacians and how they generate Markov processes and also quantum processes.

Network theory (part 16)

Network theory (part 17)

Network theory (part 18)

Summary: Example of many of the concepts to date.

Network theory (Biamonte guest posts)

Summary: Jacob Biamonte on stochastic Petri nets and chemical reaction networks: material that might go into posts on the Azimuth blog.

Network theory (Fong guest posts)

Summary: Brendan Fong on stochastic Petri nets and chemical reaction networks: material that might go into posts on the Azimuth blog.

category: blog, meta