The Monte Carlo method is an interesting example in physics where something was given a very good name. Normally the names that academics select fall into the categories of incomprehensibly dense jargon or being mundanely blunt. The Monte Carlo method however gets quite a creative name linked well into the theory behind it.
Superconductivity is one of the most interesting effects in modern physics. When a material undergoes the transition to a superconducting state then the Bardeen, Cooper and Schrieffer (BCS) theory tells us that the vibrations within the metal have resulted in the forming of cooper pairs, turning electrons from fermions into quasi-bosons which can now move through the metal with no resistance. This theory works very well to explain the observed qualities of superconductivity and even has had the particle pairing principle be reapplied to areas such as nuclear physics to explain phenomena there. It has been hypothesised that pretty much all crystalline materials have the potential to become superconductors at low enough temperatures provided cooper pair formation occurs.
The Kerr effect is the change of refractive index of a material when an electric field is applied to it. All materials demonstrate the Kerr effect to some degree but it most cases the change is so small as to be unnoticeable. In liquids the Kerr effect allows for existence of filament propagation. This is where a laser beam is able to travel through a medium without diffraction as the Kerr effect changes the refraction index along the laser beam as to constantly refocus it. Multiple filamentation can occur when a laser beam has an uneven beam pattern, an avoidable defect, which results in each hot zone across the beam individually focussing into their own mini filament.
Fluid dynamics is an interesting area of physics to study. In many ways where it shines is the seemingly disparate connections that it can form to other areas of physics. For instance in a 2D plane, the interaction of vortices in the liquid is very similar to the interaction of electric charges. The swirling fluid centres actually attract one another when they have counter-rotating motion and repel when they share co-rotating motion. Some people actually choose to imagine the electromagnetic field spreading out like a spiral from the charged particle (a combination of radial electric field and concentric magnetic field) which makes the vortex interaction the more fundamental system. Another would be the example of vortices (sometimes called maelstroms) in the ocean. These massive swirls move across the Atlantic and models seem to show that the process of water becoming trapped in the vortex for transport can be seen as analogous to that of the trapping of matter by a black hole.
The Hamiltonian is a concept in (unsurprisingly) Hamiltonian mechanics which represents an operator in a system. In many cases it corresponds to the total energy of a system and so I’ll continue to use it as analogous for the total energy although this is not always true. Just picture it as an equation with each term representing one of the kinds of energy a system contains. Now often you want to find the ground state, the lowest possible energy, for the system as this will provide useful information to solve it. But what if this Hamiltonian’s ground state is very complicated, if not impossible, to find algebraically? Well, this is the basis of an adapted form of quantum computing called adiabatic quantum computing.
The precise measurement of Earth’s gravitational field is very important. By timing the period of a simple pendulum it might be possible to get a measurement for the field with accuracies to three significant figures but not much more than that. A key part of geophysics is to use variations in gravitational field strength at different points around the surface of the Earth to estimate subterranean densities. These variations can be found to such resolution that they can be used to study tectonic plates, volcanoes and even the decrease in mass of melting glaciers.
The human eye is quite incredible. When it comes to resolving two images it is practically at the physical limit imposed by diffraction, it can identify over one million separate colour hues which is a whole lot more than anyone could ever need and it has intensity detection of about 5nW so maybe 150 visible photons. It’s these properties we use when we observe images as our eyes are able to detect the gradients of colour and of intensity. If we are dealing with greyscale images, in just black and white, then there is no colour and each pixel responds just to the intensity of light falling upon it. To simplify these are the kind of images that we’re discussing today.