**When and where**: 12:00noon, Chase319

Everybody is welcome!

Department of Mathematics and Statistics at Dalhousie University blog

Starting with the discrete aggregation model with attraction-repulsion force inside the single-species swarm and repulsion against the alien particle in 2D, we derive the continuum system of the model. We show that interesting equilibrium patterns occur for certain interaction functions and use perturbation theory to analyze the stability of the annulus-like steady state solution with uniform density. Some numerical simulations for different potential functions and parameters will be presented. This is an honours thesis study supervised by Prof. Theodore Kolokolnikov.

This week's **Friday challenge** is the following problem aimed at high school students. A solution to this problem will be posted next week.

Let there be several numbers written on a blackboard. It is allowed to erase any two of them, which are not simultaneously equal to 0, say $a$ and $b$ and replace them with $a - b/2$ and $b+a/2$. Is it possible after several of such steps to arrive at the original numbers?

Source: www.nature.ru

**Hint**: Check what happens to the sum of squares of these numbers.

**Solution**

Let there be several numbers written on a blackboard. It is allowed to erase any two of them, which are not simultaneously equal to 0, say $a$ and $b$ and replace them with $a - b/2$ and $b+a/2$. Is it possible after several of such steps to arrive at the original numbers?

Source: www.nature.ru

Vortex dynamics, a classical field in mathematical physics, features a problem very similar to the $N$-body problem of celestial mechanics. This $N$-vortex problem is concerned with the motion of $N$ vortices in an ideal fluid, modeled as points on a plane or other manifold. Like the $N$-body problem, chaos will develop in most such systems for high enough values of $N$. However, there are certain initial conditions which allow for stable, large $N$ solutions. We will discuss a small selection of these cases, called ring or regular N-gon solutions, where precisely such stability may arise.

<b>When and where</b>: 2:30pm-3:30pm, Chase319<br />

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<b>Speaker</b>: Dorette Pronk<br />

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<b>Title</b>: Weakly Globular Double Categories - the final frontier

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