This report covers a theoretical and experimental investigation on magnetic fields caused by eddy currents of spherically conducting objects. These eddy currents are caused by a time-varying...Show moreThis report covers a theoretical and experimental investigation on magnetic fields caused by eddy currents of spherically conducting objects. These eddy currents are caused by a time-varying magnetic field. First, the magnetic field is determined analytically from the Maxwell’s equations. Then an experiment is done to measure this magnetic field. By comparing the theoretical and experimental results, one can determine the material properties such as the conductivity σ and relative permeability μ_r. For a solid aluminum sphere the experiment gave σ = 4.75 · 10^7 S/m while the theoretical value is 3.767 · 10^7 S/m, thus differing by 26%. For the spherical steel shell, we found σ = 5 · 10^6 S/m and μ_r = 200. This is approximately the same as the estimated theoretical values for hull steel which has σ = 5 · 10^6 S/m and μ_r = 250.Show less
In recent years, deep neural networks have attracted the attention of both the academic community and the general public. An effort to theoretically understand the intricacies of these systems is...Show moreIn recent years, deep neural networks have attracted the attention of both the academic community and the general public. An effort to theoretically understand the intricacies of these systems is ongoing and physics-inspired approaches may have a part to play. In this thesis, we will discuss recent results in the theoretical study of deep linear neural networks. This class of neural networks has very limited real-world applications, but it could provide a good training ground for developing theoretical techniques that could prove useful beyond the simple linear case. We will also argue that Fisher information, and in particular “sloppy model” logic, can be a useful tool for future research on deep neural networks, in particular for network architecture optimization.Show less
We present a method to link phenomenological parameterizations of dark energy on cosmological scales with theory. We will use the phenomenological parameterization adopted by the Planck...Show moreWe present a method to link phenomenological parameterizations of dark energy on cosmological scales with theory. We will use the phenomenological parameterization adopted by the Planck collaboration [], parameterizing the phenomenological functions $\mu$ and $\eta$ as functions of scale $k$, and time using the scale factor $a$. When linking the phenomenological functions with theory, we restrict ourselves to the Horndeski class of theories [] and neglect time derivatives, i.e. we work with the general and model independent quasi static approximation (QSA), to be able to find analytical expressions for our phenomenological parameterizations. Despite its generality, the QSA forces the phenomenological parameterization adopted by the Planck collaboration into a scale-independent one; which motivated us to propose an alternative phenomenological parameterization using a parameterization of the phenomenological functions $\mu(a,k)$ and $\Sigma(a,k)$. This phenomenological parameterization does allow for scale dependence in $\mu$ under our conditions. The effect of imposing extra conditions on our models, e.g. imposing the speed of gravitational waves to equal the speed of sound, is investigated by searching the parameter space of the phenomenological parameterizations for points that yield physically viable models. The viability here is evaluated by means of ghost and gradient stability conditions.Show less
We will show the weak lensing effects from filaments connecting galaxy pairs for two separate galaxy subsets. The lensing galaxies are selected from the Galaxy And Mass Assembly (GAMA) survey,...Show moreWe will show the weak lensing effects from filaments connecting galaxy pairs for two separate galaxy subsets. The lensing galaxies are selected from the Galaxy And Mass Assembly (GAMA) survey, where we use version 7 of the GAMA galaxy group catalogue in our galaxy selection. We select the background galaxies from the ’KiDS-450’ weak lensing data set. Two galaxies are considered to form a pair when they are within an angular separation of 6h^-1 Mpc and 10h^-1 Mpc and are within a line of sight separation of 10h^-1 Mpc. In addition, we select galaxies with an angular separation between 6h^-1 Mpc and 10h^-1 Mpc, with a line of sight separation between 100h^-1 Mpc and 120h^-1 Mpc, to be ’unphysical pairs’. They appear to be galaxy pairs projected on the sky but are physically to far separated to form a pair. The subtraction of the signal of the unphysical pairs from the physical pairs will then result in the isolation of the filament. We use two subsets of galaxies in our pair selection; galaxies isolated in space, and the central galaxies of galaxy groups with at least 4 group members and consider the lensing effects of both subsets. Using 25 000 and 8 279 galaxy pairs from the isolated galaxy pairs subset and group central galaxy pair subset respectively, we will show the detection of filaments with a significance of 2.3\sigma and 2.9\sigma for these subsets.Show less
