Designing Models For River Drain Networks

Rivers almost always lead to the sea (they can also lead to evaporation planes, in fact, every river in Uzbekistan does this) and in doing so they follow a very distinct geometry which can be aptly described as a branching network. It is through these networks that water flows and carries with it sediment and debris and it through this action that rivers evolve and change the landscape around them.

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Examining The Result Of Eliminating Hydrogen Bonds In Methanol Models

Methanol is the simplest chemical with the alcohol functional group (unless you get really technical and count water) being written as H3C-OH. It is this OH which defines a chemical as an alcohol. It is also this OH which is responsible for providing methanol with hydrogen bonds in its liquid state. The oxygen atom, being very electronegative, pulls strongly on the electrons in the covalent bond between the oxygen and its adjacent hydrogen resulting in the hydrogen gaining a slight (but significant) positive charge. This then leads to the lone pairs (pairs of unbonded electrons in the outer shells of atoms) on the oxygen of other methanol molecules being attracted to these slightly positive hydrogens creating what is known as a hydrogen bond.

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Calculating Distance Over Which Charged Particles Pause

Stopping power is the ability of a material to slow down charged particles (stopping power is only used for charged particles) passing through it by removing their energy through interactions with the particles in the material. In the early 1930s a physicist named Hans Bethe developed the Bethe formula for calculating the average energy loss over a distance within a material:-{\frac {dE}{dx}}={\frac {4\pi nz^{2}}{m_{e}v^{2}}}\cdot \left({\frac {e^{2}}{4\pi \varepsilon _{0}}}\right)^{2}\cdot \left[\ln \left({\frac {2m_{e}v^{2}}{I}}\right)\right].

where me and e are the mass and charge of an electron; I is the average potential of the electrons in the material and is their number density; and and both refer to the particle being retarded, being velocity and charge respectively (it should also be noted that this is a simplification for a non relativistic particle. Electrons and fast moving particles require corrections to the above formula). Continue reading Calculating Distance Over Which Charged Particles Pause

Relating Temperature To Superconductor Resitivity

I have briefly written before about a physical theory called the electron gas where the electrons in a metal, having become separated from their ions, can be treated like an ideal gas. This involves the homogenising of the background positive charge caused by the metal ions and also ignoring the Coulomb repulsive force between the electrons. When this force is added the situation becomes known as the electron liquid model and it requires advanced computational methods to solve the many body problem that results (as all electrons modelled will exert some repulsion on each other).

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Producing More General Form Of Optic Predicting Equation

In optics the refractive index of a materiel is dependent on the wavelength of light passing through it. There is no perfect equation which can theoretically predict the refractive index as a result only very tedious and computer intensive calcuations can give a definite result; but there are empirical and experimentally derived expressions which are very accurate. An example is the Sellmeier equation which is most commonly written as:n^{2}(\lambda )=1+{\frac  {B_{1}\lambda ^{2}}{\lambda ^{2}-C_{1}}}+{\frac  {B_{2}\lambda ^{2}}{\lambda ^{2}-C_{2}}}+{\frac  {B_{3}\lambda ^{2}}{\lambda ^{2}-C_{3}}},

when applied to glass. The Bs and Cs are constants found for the particular material. Now when equation contains three terms it will give the refractive index to a value within 5×10−6 of the actual one. More terms can be added to improve the precision and the summation sign is used when required. For gasses the form of the Sellmeier equation is: Continue reading Producing More General Form Of Optic Predicting Equation

Modelling Many Thermostats Simultaneously

Thermostatically controlled loads are electrical devices which are only needed in certain temperature conditions. A radiator or cooling fan doesn’t need to operate when the surroundings are hot or cold respectively and in many cases continued operation will result in discomfort or damage. Often these devices are connected to a bang–bang controller, a device that switches them between completely on or completely off depending on ambient temperature. This is not ideal. Such a process, when the controlled operates quickly, often leads to oscillation around the critical temperature (technically a small range of temperate for which the device toggles at one of the boundaries) as the device rapidly switches on and off at the slightest temperature fluctuation. A slow controlled with a greater delay to avoid this effect loses functionality as the temperature is allowed to progress past the ideal point before being curbed.

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Collecting Information To Explain Ethnic Conflicts

In classical physics it is a simple fact that if you knew enough information nothing could be beyond prediction. If quantum physics was to be ignored someone could have calculated the entire universe provided they knew every detail of the big bang. When companies make predictions they are not of this kind. You will probably heard the practically vapid phrase that “correlation does not equal causation” but the simple fact is that correlation is the only thing required. If 90% of people who buy pens online also buy paper later, who cares if its causation. Advertisements will appear for various notepads because it is statically likely the pen buyer will soon be looking for one. In a similar way it is estimated that some life insurance companies have so much information that they can predict the date of someone’s death (based on neighbourhood, average income, previous family medical records, ect) to within a year.

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