Studying how light interacts with materials has become important for many technological applications from optical communication to developing of new materials. Therefore scientists have always tried to improve their understanding of these effects. The primary goal has always been to microscopically describe the pertinent processes. This paper provides a brief introduction into the interactions of ...

In 2012, a new method for calculating the Casimir force between compact objects was developed, expressing the force in terms of a boundary integral equation. The case of perfectly conducting objects with Dirichlet boundary conditions in two dimensions was treated by Isak Kilen. The method was later extended to three dimensions by Karl Øyvind Mikalsen. The contribution of this thesis will be to ...

The observable universe consists of several non equilibrium systems that generate spatiotemporal behaviour in the form of various patterns. As the elementary laws of physics and chemistry are unable to explain the pattern forming behaviour of such systems, scientists have turned to desktop experiments and model equations to gain further insight. The model equations that generate numerical solutions ...

In this thesis work we develop and apply EOS formulation to three scattering problems: two of them are 1D problems and one is 2D. The first chapter comprises EOS formulations and numerical implementation for 1D scattering problems. Also in this chapter we use different numerical methods to solve test problem and choose the most stable and accurate method for solving of the given 1D problems. ...

Ultrafast laser pulse experiments and applications are entering a phase that challenges the validity of mathematical models utilised to model longer pulses in nonlinear optics. This thesis aims to propose a possible mathematical model for high intensity laser pulse propagation in air through a multiple scales expansion of Maxwell’s equations and discuss a method on how to solve the corresponding ...

The goal of this thesis is to classify all extensions where the kernel has order p^s and the cokernel has order p^t, p is a prime, and 1 ≤ s,t ≤ 2. We determine (up to weak congruence) the different combinations of kernel, cokernel and operators, and for each case, calculate the second cohomology group. By comparing resolutions, we get an explicit correspondence between the second cohomology group ...

With growing capabilities of high-intensity laser beams to generate ultra-short pulses of light, the simulation of pulse propagation in nonlinear media is expected to catch up with the front-line experimental setups. Among the challenges of nonlinear material response modeling is the ability to capture the back-scatter effect - a phenomenon inherently elusive for the well-established methods of ...

By restricting generating functions of infinitesimal symmetries of symplectic and contact vector spaces to quadratic forms, we obtain a finite-dimensional Lie subalgebra, consisting of vector fields isomorphic to the linear symplectic or conformal symplectic algebra. This allows us to look for joint invariants of the diagonal action of g on product manifolds. We find an explicit recipe for creating ...

The ice-albedo feedback is associated with the nonlinearity in the climate system, due to the sudden change in albedo between ice-free and ice-covered surfaces. This nonlinearity can potentially cause abrupt and dramatic shifts in the climate, referred to as tipping points. It is also believed that this mechanism has contributed significantly to the precipitous losses of Arctic sea ice, which have ...

COVID-19 is a respiratory disease with influenza-like symptoms originating from Wuhan, China, towards the end of 2019. There has been developed multiple vaccines to contain the virus and to protect the most vulnerable people in society. In this thesis we look at two different vaccination strategies to prevent most deaths and years of life lost. We conclude that the safest and most consistent strategy ...