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Essentially, a Boundary Integral Method (BIM) reduces the degrees of freedom of a problem to those of the boundary. It also means that the problem becomes meshless, which means that there is no need for simple domains.

There is a technique called Smoothed Particle Hydrodynamics ( SPH) which deals with simulating the behaviour of continuous media such as fluids, deformable solids, and viscous materials. It is a type of phenomenological simulation, as it consists of heuristic arguments rather than physical principles.

We won! (second place). After a week of lectures and 48 hours of intense coding and learning, I’m proud to announce that our team was awarded the Best Team Project prize by Quantinuum and the International Centre for Theoretical Physics.

Fiber optics technology has revolutionized communication by enabling the efficient transmission of data over long distances. At the heart of this technology lies the Nonlinear Schrödinger Equation (NLSE), a mathematical model that describes the behavior of optical pulses in fiber optic communication systems.

Wave simulations are essential in optics and electrodynamics. Here are some of the simulations I’ve done for wave propagation using finite-difference schemes. The difference between using ABCs and not using these are highlighted in Figures 1 and 2.

Similar to the Ising Model, Simulated Annealing takes a step implements a similar cost function to that of the Ising Hamiltonian. Once again, the probability of accepting a less-efficient state follows the Maxwell-Boltzmann distribution.

The Metropolis-Hastings algorithm for simulating the Lenz-Ising model is an excellent example of a Markov chain, since the former is actually a version of a Markov chain Monte Carlo (MCMC) simulation.

The Mandelbrot set is a captivating and intricate mathematical object that has fascinated mathematicians and enthusiasts alike. It’s a set of complex numbers, often denoted by (M), that is defined through a relatively simple iterative process.