Public Articles
The Inchanted Hallway. Ch.2
How to write a thesis proposal and analyse data
Chemistry, OZ Revision Notes
Extends 100km above Earth
Troposphere and Stratosphere most important
90% of all molecules in troposphere
\label{Atmospheric Gases}
Gas | Concentration |
Nitrogen | 78% |
Oxygen | 21% |
Argon | 1% |
Carbon Dioxide | 400ppm |
Chemistry, ES Revision Notes
Extremely high water density
Salt is 350gdm-1
Normal is 40gdm-1
400m below sea level
Huge evaporating basin
High proportion of bromide salts
Major source of minerals
Mainly group 7 ions
Halogens are group 7 elements
All have 7 electrons in outer shell
Most reactive group of non-metals
Not found naturally in elemental form
Abundance decreases down group
All occur as diatomic molecules
In compounds, there several ways by which a halogen can achieve stability:
Gaining an electron from a metal atom, forming a halide ion in an ionic compound
Sharing an electron with a non-metal atom in a covalently bonded compound
Chemistry, EL Revision Notes
Atoms can be considered to consist of 3 sub-atomic particles
Proton, Mr 1, Charge of +1
Neutron, Mr 1, Neutral
Electron, Mr $\frac{1}{2000}$, Charge of -1
Most of the atom is empty space
Atomic Number, Z
Number of protons
Lower number
Equal to charge on Nucleus
Mass Number, A
Number of protons and neutrons
Highest number
Atoms of same element with different mass numbers
Different number of neutrons
Average of relative Isotopic Masses relative to Carbon-12
Taking abundance into account
Mass Spectrometry used to find it
Measures atomic/molecular mass of different particles, and relative abundances
Ionised to cations
Separated by mass to charge ratios
In a nuclear fusion reaction, two light atomic nuclei fuse together to form a single, heavier nuclei, releasing huge amounts of energy in the process of doing so
Impossible at normal temperature and pressure
Positive nuclei repel too strongly
Possible in stars, repulsion overcome
\begin{equation*} {^{1}_{1}H}+{^{2}_{1}H}={^{3}_{2}He}+\gamma \end{equation*}
Physics, Motion and Forces, 9-12
Scalar quantities just have magnitude
Energy
Distance
Speed
Mass
Vectors have magnitude and direction
Velocity
Displacement
Acceleration
Force
Physics, Waves and WPD, 5-8
Progressive waves transfer energy without transferring any matter. There is no net movement of the medium, although each particle does oscillate around its equilibrium position.
In a transverse wave, particles oscillate at right angles to the direction of propagation.
In a longitudinal wave, particles oscillate parallel to the direction of propagation. These have compressions and rarefactions.
Mechanical waves transfer energy through a medium by the oscillation of particles, and can be transverse or longitudinal.
EM waves are not mechanical, and no not require a medium to propagate.
Linked electric and magnetic fields
Regions of space when an electric charge would experience a force
As an EM wave passes, the electric and magnetic fields oscillate
Electric field changes, inducing a magnetic filed perpendicularly
Magnetic field varies, changing electric field
Wave is self perpetuating
EM waves are always transverse
Displacement is measured from the equilibrium position, and can be positive or negative
Maximum displacement is equal to the amplitude
The amount of energy transferred by a wave is dependent on its amplitude
Wavelength sis the distance between two consecutive points with identical displacement and velocity
Two points exactly one wavelength apart are in phase - they oscillate in step with each other
Two points half a wavelength apart are in antiphase
Phase difference is dependent on the fraction of a wavelength between two points
One wavelength is represented by 360
Two points with a phase difference of 360are in phase
Two points with a phase difference of 180are in antiphase
One radian is equivalent to 180
360∘ = 2π
The time taken for one complete wave to pass a certain point is its period, T. The phase difference can then be described as the fraction of a period between two points. \begin{gather*} f=\frac{1}{T}\\ T=\frac{1}{f} \end{gather*}
The speed of a wave depends on the properties of the medium. For a mechanical wave, it depends on:
The size of the forces between oscillating particles - the elasticity of the medium
The intertia of the vibrating particles - how easy or difficult it is to accelerate each particle
Sound travels faster through solids because of the stronger forces between adjacent particles
v = fλ
Chemistry, CI Revision Notes
The low reactivity of nitrogen molecules arises from the strong triple bond between nitrogen atoms.
A2 Physics, Thermal Physics and Gravity, 3-4
Internal energy is the sum of the randomly distributed kinetic energy and the potential energy of all particles in a body.
Kinetic energy can be:
Translational
Rotational
Vibrational
The energy of a system can be increased by doing work on it or heating it.
Doing work is the energy transfer due to a force
Heating is a thermal energy transfer
A system can do work against an external force in some circumstances:
CO2 will expand rapidly if released from a high pressure container
Does work against the atmosphere, rapidly losing energy
Cools enough to solidify to dry ice
The change in the internal energy of a system is equal to the sum of the energy transferred from or to the system by heating, and the energy transferred from or to the system as a result of work being done against or by an external force.
Kinetic energy is directly related to temperature
Specific heat capacity, c, is the energy required to raise the temperature of 1kg of a material by 1K without any change of state, measured in Jkg−1K−1 \begin{equation*} Q=mc\Delta\theta \end{equation*} cwater = 4190Jkg−1K−1; a fairly large value. Hence, a large body of water will take alot of energy to heat.
Immersion heater in a block of a metal
Time and temperature change recorded
Q calculated as the energy transferred by the heater, using its current, voltage and power
Water boiled to 100∘C with object
Object placed in cool water
Temperature changes equated
If an object is dropped, and hits the ground without rebounding, all GPE will have been transferred to KE, and then to internal energy. This leads on to:
Lead shot in a tube
Length of tube and temperature of lead recorded
Tube repeatedly turned over, moving lead through length
Total GPE changes calculated, and equated to new temperature of lead
Gives a very rough estimate
Water is good for storing energy because of its high c, so it is used as a heat transfer liquid. With flow calculations, it is often used to use: \begin{gather*} \text{rate}=\frac{\Delta v}{\Delta t}=\frac{\mathrm{d} v}{\mathrm{d} t}\\ E=pt\\ \rho=\frac{m}{v}\\ \end{gather*}
When a substance changes state, work has to be done to break the intermolecular bonds. Whilst this is happening, potential energy will increase whilst kinetic energy remaincs constant. Work often has to be done against the surroundings if an object is expanding.
The energy required to change 1kg of a liquid into 1kg of a gas with no change in temperature.
The energy required to change 1kg of a liquid into 1kg of a solid with no change in temperature. For a substance of mass m, and specific latent heat of fusion l, the energy transferred is given by \begin{align*} Q=ml, \therefore l=\frac{Q}{m}. \end{align*}
Energy is supplied at a constant rate
Temperature will rise till melting point
Substance will melt at constant temperature
Temperature of liquid will rise once all melted
Liquid will boil at constant temperature
Temperature of gas will rise once all melted
Process can be recorded with a data logger
Cooling will not take place at a constant rate, as it is dependent on the temperature of the surroundings. Thermal energy will be dissipated from a substance that is cooling.
A2 Physics, Radioactivity and Nuclear Energy, 9-10
Alpha particles fired at gold foil
Foil thin so alpha particle only scattered once
Evacuated tube used
Zinc Sulfide screen showed scintillations
Alpha source produced a narrow beam to allow precise measurements
Also monoenergetic
Most passed through
Some were scattered
Very few were reflected
Showed that the alpha particle was colliding with a dense, positively charged object, much more massive than 24He
Allowed theoretical upper limit on size of gold nuclei to be calculated
A2 Physics, Electrical and Magnetic Fields, Capacitance, Electromagnetic Induction and Alternating Current, 5-8
The electrostatic effect is a result of static electricity.
Rubbing two materials together can move electrons by friction
Leaves a build up of charge
Eg. A Van der Graaf generator will remove belts from the metal dome via the belt
Approach a material of polarised molecules will cause the to realign
Eg. Comb and paper or water
Measured in coulombs
An electron has a charge of −1.6 × 10−19C
Materials can be charged by induction.
A negatively charged object is brought close to the object
The object is momentarily earthed
The electrons are repelled, and flow through the earth
This will leave a net positive charge
Coulomb’s Law states that the force between two point charges separated by a distance r in a vacuum is directly to the product of the two charges and inversely proportionate to the square of their separation. \begin{equation*} F=\frac{Qq}{4\pi\epsilon_0r^2}, \end{equation*} where ϵ0 is the permittivity of free space, 8.85 × 10−12Fm−1.
This assumes a vacuum
Negligible difference in air
Also assumes uniform point charges
Over microscopic distances, this force is much more important than the gravitational force, due to the small masses in comparison to charges. However, over macroscopic distances, the larger masses become more important as gravity is only attractive, whereas electrostatic forces can be attractive or repulsive.
Chemistry, DM Revision Notes
Chemistry of d-block is different to that of other elements
Results from electronic configurations
4s fills and empties before the 3d orbital
As the 4s orbital is filled, the transition metals in a period have the same valence electrons; except from Copper and Chromium
Lower energy to remove an electron from the 4s orbital
Chemistry, CD Revision Notes
Colourless substances absorb no light in the visible region
White light is reflected or passes through substance
Absorb particular wavelengths of visible light
Absorbing a colour will make a substance appear to be its complementary colour
Two complementary colours combined will produce white light
Enzymatic Degradation of Chlorella sp. using Protease and Celulase Fungal Broth
Leaf litter density and decomposition in small man-made ponds
and 1 collaborator
The input of terrestrial leaf litter into freshwater ecosystems supports aquatic food webs and fuels microbial metabolism. Although the role of leaf litter subsidies to streams have been studied extensively the effect of leaf litter on ecosystem function in lentic systems has received less attention. In particular the impact of leaf litter on trophic dynamics and biogeochemistry of small man-made ponds is virtually unknown, despite the fact that these systems are extremely common and likely represent a substantial modification to watersheds in the North America. We measured the areal density of leaf litter and the rate of leaf litter decomposition in small man–made ponds in central Virginia to determine the size of the leaf litter pool in these systems, the rate at which leaf litter is decomposed, and the extent to which pond characteristics alter leaf litter abundance or processing. We found that the areal density of leaf litter in the ponds ranged between 3.4 and 1179.0 g AFDM m-2. The areal density of leaf litter was significantly greater in the littoral zones, however leaf litter was present in the sediments throughout the pond. There was no relationship between the areal density of leaf litter in the sediments and the percent organic matter of the fine sediments, suggesting that leaf litter input is decoupled from bulk sediment organic matter. The decomposition rate of Liriodendron tulipifera leaves in coarse mesh leaf bags ranged between 0.0025 and 0.0035 d-1, which is among the slowest litter decomposition rates recorded in the literature for ponds and was unrelated to pond characteristics. Our results indicate that leaf litter is an abundant and persistent pool of organic matter in the sediments of small man–made ponds and it is likely to have a substantial effect on the trophic dynamics and biogeochemistry of these systems.
old version
and 2 collaborators
FPGA on musical contexts: a faster way to understand musicians movements
Laguerre Series: Functions in a Basis of Laguerre Polynomials
I show how to express functions with a known series expansion in terms of Laguerre polynomials.
We have the integral representation of the Laguerre polynomials, \begin{equation} L_n(z)= \frac{e^z}{n!}\int_0^\infty e^{-t}t^n J_0(2\sqrt{ t z})\;dt, \end{equation} where J0(x) is a modified Bessel function, as given on the Wolfram Functions website. If we have a function f(x) that admits a series representation \begin{equation} f(x)=\sum_{k=0}^\infty a_k x^k, \end{equation} with some coefficients ak, then we can define a transform on L[f] \begin{equation} F(s)=L[f(x)]=\int_0^\infty K(x,s)f(x)\;dx. \end{equation} If we pick the kernel function to be \begin{equation} K(x,s)= e^{-x}J_0(2\sqrt{xs}), \end{equation} then we have \begin{equation} F(s) = \sum_{k=0}^\infty a_k\int_0^\infty e^{-x}J_0(2\sqrt{xs})x^k \; dx = \sum_{k=0}^\infty \frac{a_k k!}{e^s}L_k(s), \end{equation} which is an expansion of the transformed function F(s) in terms of Laguerre polynomials. As an example, if f(x)=1, then ak = [k = 0], this gives \begin{equation} \int_0^\infty e^{-x}J_0(2\sqrt{xs})\;dx = \sum_{k=0}^\infty \frac{[k=0]k!}{e^s}L_k(s) = \frac{L_0(s)}{e^s} = e^{-s} \end{equation} this leads to an infinitely recursive integral \begin{equation} e^{-s} = \int_0^\infty \int_0^\infty \int_0^\infty \cdots \int_0^\infty e^{-x_n}J_0(2\sqrt{x_n x_{n-1}})\;dx_n \cdots J_0(2\sqrt{x_3x_2})\;dx_3J_0(2\sqrt{x_2x_1})\;dx_2J_0(2\sqrt{x_1s})\;dx_1 \end{equation} this should also lead to the set of results \begin{equation} e^{-s} = \int_0^\infty e^{x_1}J_0(2\sqrt{x_1 s})\;dx_1 \end{equation} \begin{equation} e^{-s} = \int_0^\infty\int_0^\infty e^{x_2}J_0(2\sqrt{x_2x_1})J_0(2\sqrt{x_1 s})\;dx_1dx_2 \end{equation} \begin{equation} e^{-s} = \int_0^\infty\int_0^\infty\int_0^\infty e^{x_3}J_0(2\sqrt{x_3x_2})J_0(2\sqrt{x_2x_1})J_0(2\sqrt{x_1 s})\;dx_1dx_2dx_3 \end{equation} and so on.
If we formally define a function \begin{equation} f(x) = \sum_{k=0}^\infty \frac{x^k}{e k!k!} = \frac{1}{e} I_0(2\sqrt{x}) \end{equation} we end up with a series expansion for F(s), starting \begin{equation} F(s) = 1 - 2s + \frac{7}{4}s^2 - \frac{17}{18}s^3 + \frac{209}{576}s^4 - \frac{773}{7200}s^5 + \cdots \end{equation}
It seems the inverse kernel is given by \begin{equation} K^{-1}(x,s) = \sum_{i=0}^\infty \sum_{j=0}^i \frac{(-1)^j s^j x^i}{(i-j)!j!j!} = \sum_{i=0}^\infty \frac{x^i}{i!}L_i(s) \end{equation} such that \begin{equation} f(x) = \int_0^\infty K^{-1}(x,s)F(s)\;ds \end{equation}
Notes
Создание системы ледовой разведки на основе роя БПЛА.