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· 15 min read
Kiril Panayotov Blagoev

In two previous posts we got to know two main things:

  1. We can analyse the behaviour of groups of animals using statistical tools like correlation functions
  2. We can simulate this behaviour using for example the Vicsek model, and by analysing it the same way as natural groups we can measure the accurateness of the model in replicating natural phenomena.

We also learned that the standard Vicsek model suffers from one weakness: it lacks an inertial term, which seems to be important in imitating the behaviour of biological systems. So the goal of this post will be to figure out a way to simulate the Vicsek model with time delay. Let's start by

Analysing the equations of motion​

vi⃗(t+1)=v0RηΘ[vi⃗(t)+∑j≠inijvj⃗(t)],\vec{v_i}(t+1) = v_{0}\mathscr{R}_{\eta}\Theta \left[ \vec{v_i}(t) + \sum_{ j \neq i }{ n_{ij} \vec{v_j}(t) } \right] ,
ri⃗(t+1)=ri⃗(t)+vi⃗(t+1).\vec{r_i}(t+1) = \vec{r_i}(t) + \vec{v_i}(t+1) .

· 5 min read
Kiril Panayotov Blagoev

if you haven't seen the first part of this introduction, absolutely go check it out for context.

In this post we'll unravel how does the delay in a group of animals affect the group, and what should we understand under said delay (keyword: slowpoke). To get there, let's analyse the last two paragraphs of the introduction to my thesis, where we'll see what problems can be spotted in previous research, and motivate ourselves to look for solutions.

· 7 min read
Kiril Panayotov Blagoev

Posts on the subject so far:

  1. How do birds flock and insects swarm: the Introduction
  2. How do birds flock and insects swarm: the Problem with current models
  3. Simulating the Vicsek Model (with time delay) - How do birds flock and insects swarm

It's been my recent pleasure to work on a project (my thesis to be exact) which utilised Statistical Physics, to explore the emergent phenomena of flocking and swarming in natural systems. As past me had a stroke of creativity, I will let you enjoy his introduction to the subject - as seen in the finished thesis, interrupted by explanatory commentary:

· 6 min read
Kiril Panayotov Blagoev

Интродукция​

Наскоро се заинтересувах от един интересен закон за разпределението на думите използвани в даден език, наречен законът на Зиф. Според него честотата на употреба на думите в дадено произведение или просто смислена колекция следва експоненциален закон, т.е. броят на употреба на всяка следваща дума в списъка от използвани такива намаля експоненциално спрямо предишната. Последствие от това е, че горе долу във всяка такава колекция 80% от обема се състои от 20% от думите, принцип известен като Принципът на Парето.