Waves that are reflected and refracted by material bodies also transfer momentum to these bodies. This means that the wave field induces a force on the bodies, and multiple reflections between bodies induce forces between them. Light is an electromagnetic wave phenomenon, and the waves carry energy and momentum. Hence, any object that is scattering and refracting light is also acted upon by a ...

In this thesis we use mathematical models to study the mechanisms by which diseases spread. Transmission dynamics is modelled by the class of SIR models, where the abbreviation stands for susceptible (S), infected (I) and recovered (R). These models are also called compartmental models, and they serve as the basic mathematical framework for understanding the complex dynamics of infectious diseases. ...

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 Swift-Hohenberg equation is an evolution equation which can produce a Pattern, or a pattern-like picture, to be more precise. For example, it could be used to model some simple natural patterns, like stripes and rolls that one may observe in a Rayleigh-Benard convection experiment. But for any pattern formation obtained by an evolution equation to look ideal, we have to consider this equation ...

Character values are not the easiest to calculate, so it is important to find good algorithms that can help ease these calculations. In the 20th century, the two mathematicians Murnaghan and Nakayama developed a rule that calculates character values for partitions on some computations. This rule has later been given the name The Murnaghan-Nakayama rule, after these two authors. The Murnaghan-Nakayama ...

This thesis is concerned with the definition of elementary particles as irreducible projective unitary representations of the Poincaré group. During the contents of this work, we will introduce the relevant prerequisites and results. Concerning differential geometry, we will discuss smooth manifolds, Lie groups and Lie algebras. About quantum mechanics, we will introduce Hilbert spaces and the basic ...

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. ...

For high accuracy applications of integral operators in higher dimensions the complexity of operation and storage usually grows exponentially with dimensions. One method that has proven successful for handling these difficulties are the separation of the integral kernels as linear combinations of products of one-dimensional kernels, commonly referred to as separation of variables. In this ...

Polynomials appear in many different fields such as statistics, physics and optimization. However, when the degrees or the number of variables are high, it generally becomes quite difficult to solve polynomials or to optimize polynomial functions. An approach that can often be helpful to reduce the complexity of such problems is to study symmetries in the problems. A relatively new field, that has ...

Electricity spot markets and other financial markets are complex systems, and it is difficult to forecast their behaviour, especially uncontrolled and unmanageable situations, such as power crises and deflation of financial bubbles. An energy crisis is any price rise in the supply of energy resources to an economy. It has undesirable consequences, occasionally irreversible. The most known of these ...