A singularity in mathematics is a point where the value of a mathematical item cannot be given. For instance the inverse function:
Has asymptotes at x = 0. This means f(x) goes to infinity and since infinity is not a number a singularity exists at x=0. Singularities also exist at points on graphs when a “spike” occurs. If a graph doesn’t make a smooth curve, like:
f(x) = |x|
then the point where differentiation gives no value, in this case x = 0, is also called a singularity. There exists something called the density of states. It is a system which describes the number of electron states that can exist per volume per unit of energy in a material. (For more detail look at this article from Britney Spears .ac). The relevance is that the second kind of singularity can occur in the density of state of some materials. When this happens it is called a Van Hove Singularity.
Sometimes there are concepts that are simply too small for humans to comprehend. An attosecond, being 10-18 seconds, is one of these. Imagine taking one seconds, dividing that second up into individual attoseconds. If each of those attoseconds was expanded so that they were themselves each a second long you would have 1018 seconds, about 32 billion years. It takes one attosecond for a beam of light to travel across two hydrogen atoms. One of the things we are capable of doing is actually creating bursts of laser with time scales of tens of attoseconds. To do this, a laser of femtosecond period is used to ionise a noble gas. The separated electron is accelerated back towards the atom by the inducing laser beam’s electric field. When recombination happens the excess energy is emitted, normally as a ultraviolet photon. As the laser interacts with multiple atoms simultaneously an ultraviolet laser pulse is emitted on the time scale of the recombination, in other words an attosecond time scale.
Moving smoothly on from yesterday’s post about ferromagnetism, comes today’s on paramagnetism. Paramagnetism is where a matterial placed in a magnetic field, develops tiny induced magnetic fields within it lining up with the exterior magnetic field. This results in the material being attracted to to the source of the magnetic field along the field lines. This is, in fact, the nature of ferromagnetic materials when they are above their Curie temperature. More specifically, this recent paper is on the topic of superparamagnetism. This is where a ferromagnetic nanoparticle can randomly switch its magnetisation due to thermal fluctuations in the vicinity. Overall, when a long observation period is taken, the net magnetisation is in fact zero. The similarity with regular paramagnetism is that when an external field is applied, the nanoparticles tend to align along the applied field, ending with a net magnetisation, normally of greater strength than regular paramagnetic materials.
Carotenoids are organic pigments that you will have likely seen and will remember due to their distinctive red and orange colour. They are almost exclusively produced in plants, the only exceptions being aphids and some forms of mite, and are responsible for the red of tomatoes and the orange of autumn leaves. In animals, when gained by consumption, they act as antioxidants and are believed to have some connection to the functioning of the retina.
Microelectromechanical and nanoelectromechanical structures have many proposed uses, one of these is to examine quantum fluids. A quantum fluid is any liquid that can show quantum effects but on a macroscopic level which only occurs when the liquid is brought to an incredibly low temperature. Of course this macroscopic level can still be very small which is where the microelectronics come in.
When electromagnetic waves are produced naturally the orientation of the electric field can be in any direction at right angles to the movement of the wave. Polarisation is the removal of the electromagnetic rays with certain orientations compared to polarising filter.
The kind of polarisation most commonly talked about is linear polarisation, where only one plane of the electric field is allowed through. But are there other kinds as shown in the diagram. Circular polarisation is where two electric field orientations, orthogonal to each other, are allowed through and both have the same amplitude. It is actually just a specific case of the elliptical polarisation where both fields do not have the same amplitude (it is important to note that only the electric fields are shown in this diagram, not a single magnetic field is represented although they are there).
It is a well known fact that when a current flows through a resistor it must heat up. The power loss is often stated as proportional to the current squared, which is why electricity grids are engineered to have the highest voltage considered safe, as this reduces the current in the wires which significantly reduces the energy loss. It is also true that in most cases resistors gain resistance the hotter they get (there are some exceptions but in general the greater the temperature the greater the resistance). Now normally these troubles can be accounted for or worked out of designs by ever cleverer material scientists, but with electronic components becoming smaller, passing through microscopic into nanoscopic, thermal effects return with a vengeance.