Andrew Krause

VisualPDE VisualPDE brings interactive science and mathematics to the web. Explore topics including waves, viruses and reaction—diffusion patterns, or create your own simulation.

This was the motivation for the "reverse-order" from how I learned the topic.

You may also be interested in VisualPDE.com as a way to build intuition, especially about nonlinear PDE. This is rather a different, but complementary, approach to the analysis-focused way of approaching PDE.

Partial Differential Equations: Second Edition

My personal recommendations might be (roughly in reverse order of how advanced they are):

bookstore.ams.org/gsm-19-r

www.amazon.co.uk/Introductory...

www.amazon.co.uk/Principles-M...

(As a student I studied them in the reverse order; the last Chapter of the 3rd book is measure theory).

Metals, Microbes, and Mathematics: Understanding Coexistence with Toxic Nutrients at Newcastle University on FindAPhD.com PhD Project - Metals, Microbes, and Mathematics: Understanding Coexistence with Toxic Nutrients at Newcastle University, listed on FindAPhD.com

Next, a glorious combo of maths, metals, and microbial ecology. This one is supervised by Denis Patterson and @blindmath.bsky.social, also at Durham.

www.findaphd.com/phds/project...

Nutrient uptake in commensal bacteria: exploring uncharacterised TonB-dependent transporters. at Newcastle University on FindAPhD.com PhD Project - Nutrient uptake in commensal bacteria: exploring uncharacterised TonB-dependent transporters. at Newcastle University, listed on FindAPhD.com

Lots of PhD opportunities for UK + international students involving my lab. Topics relate to metals & microbiology.

First up: TonB-dependent receptors in commensal Neisseria in my lab at Durham, with @kjosts.bsky.social and @mattbashton.bsky.social.

www.findaphd.com/phds/project...

I've found Feyerabend to be very good at these pithy quotes that make you think. AFAIK his whole schtick was to say controversial things that made people think, and then to claim that this is what science is — a big dialogue requiring constant thinking and refinement of arguments.

Among other difficulties is that most biological things are nonequilibrium, where there is not (AFAIK) a universal definition of phases etc. Though there are lots of areas/subfields where people do use precise definitions of course; just not with the same generality as in equilibrium stat mech.

Possibly useful for @joshuabull.bsky.social @josh-moore.bsky.social. Josh will also give a seminar in February @darrenjw.bsky.social; it'd be good for you two to chat I think!

Some lecture notes on spatial and temporal modelling, illustrated using R - darrenjw.github.io/spatio-tempo... - #rstats #rspatial #quarto

We are recruiting several PhD students. If you are interested in conservation conflicts, population ecology, quantitative ecology, or biodiversity, check these projects out (links in the thread, feel free to reach out):

So it begins again here, like the germ of a continuous function...

OK, that thread was worth unraveling!

YouTube video by Stanzi JK Rowling for some reason #shorts

You may enjoy this:

youtube.com/shorts/nQm1f...

Some festive vortices to spin you into the new year!

visualpde.com/fluids/vorti...

My vision is such that I can almost always make out images that "normal sighted" people can see, as long as I bring my device close to my face. But many people with low vision like me either use screen readers or prefer text which is easier to understand than many images.

This is obviously disgusting and racist shows utter contempt towards vulnerable people. But as one of the high earners (for now) who is supposedly (still) welcome here: I'm not actually here to "give" to a country that would kick me out if they could. I'm here cause I got a job, a fiance and friends

Mean-field models are often equivalent to asymptotics. Let epsilon = 1/N. Then the mean-field is like taking a variable u = u_0 + epsilon*u_1 + ... and truncating.

For even moderate values of epsilon, this approximation works well truncated to u_1 (or even u_0). Lots of caveats ofc.

Lots of mean-field models are "unreasonably effective" (a phrase Wigner famously popularized). In some recent work, N=40 (or even 10!) has been well-approximated by mean-field dynamics assuming N=infinity. Those examples are in ecology, but I anticipate neural fields to work similarly.

I can't take notes due to my eyesight, and didn't know you could *have someone take notes for you* until after my undergrad. This had some advantages, but means that I often now lecture in a way that isn't especially conducive to note-taking...

Development's Pathway to Independence Programme Our grants support and encourage the sharing of knowledge throughout the community by facilitating international collaboration, event attendance and the organisation of scientific meetings, conference...

Applications are open for @dev-journal.bsky.social 2026 Pathway to Independence (PI) programme, supporting postdocs applying for group leader positions:

Mentoring
Profile raising
Leadership training
Network building

Spread the word...

www.biologists.com/grants/devel...

I hope you're as OK as you can be. I can't even imagine the challenges you've faced, especially with what happened, but I do know that you have been such a force for good on this corner of the internet, at the very least.

I would argue that anyone with control over human life (doctors, police, soldiers) should be expected to make determinations about lawful orders. Of course we should allow some human ambiguity, but users of tools of death *should* be held to high standards!

I thought we all abandoned X back when it was Twitter?

...I'll see myself out.

A major physiological constraint is that the extreme plasticity of our brains means that we change rapidly over our early years; we have extroardinarily limited capacity to remember anything before the ages of 3-5 for example: en.wikipedia.org/wiki/Childho...

I am somewhat sympathetic to many of these ideas in theory. A good friend of mine subscribes to a version of this, and is currently raising their children as independently as possible. However...

en.wikipedia.org/wiki/Childre...

There are a few related movements related to anarchist principles of making children as agentic/independent as possible. These variously go by "childism" or "child liberation" though there are lots of differences between various instances of these ideas. See also opposing "adult supremacy."

I think the Joint Maths Meeting is ~6,000 mathematicians, and the APS meeting is around ~15,000 physicists just to give some context.

Yeah. I've never been involved in it, but they have whole cultures around preparing for them etc.

Part of the reason is that flying someone is expensive and necessary for most in-person interviews, and these meetings are often large enough that there is high probability of people being co-located.

Job papers AFAIK do not exist in these fields at least!

I think many US fields do this. Mathematics and Physics both have huge annual meetings where many job interviews occur. Hiring is more temporally-synchronized than in the UK.

Partly the conferences are just a venue, and alternative arrangements do usually exist. But the conferences are huge.