Fellow Comrade

This paper serves as a brief analysis of a number of computational experiments examining the running time and complexity of a brute force median selection algorithm.  C++ was used to implement and test the algorithm, while Python’s matplotlib.pyplot library was used to graphically visualise results. The main focus of the report was to test whether the theoretical prediction for the algorithms average-case time-complexity is consistent with observations. 1. Description of the Algorithm The algorithm, called BruteForceMedian (see Appendix A), is a median search algorithm which takes an array of ordered or unordered integers as input, and returns the median value of that list.  Unlike other algorithms used for finding a median, BruteForceMedian does not reshuffle or sort the input array, but rather compares every element of the array against every other element iteratively, including itself, until it determines the kth value in the list if it were sorted. It is important to ...

The aim of this experiment is to make an estimation of the Rydberg constant based on measurements of the wavelengths of visible lines on the atomic spectrum of hydrogen, also known as the Balmer series. In Part A of the experiment, a linear model is derived that represents the change in measured wavelength given expected wavelength values of the atomic spectra of mercury. This is just used as an initial comparison to ensure the spectrometer is calibrated. Part B of the experiment is intended to obtain a linear function that represents the change in 1/wavelength given 1/n2. The slope of this linear model is taken to determine an estimation of the Rydberg constant. The variables being used in the experiment are as follows: λ1 = A single column data table containing the measured wavelengths of each visible line on the mercury spectrum. λ2 = A single column data table containing the measured wavelengths of each visible line on the balmer series of the hydrogen spectrum. λa1 = A s...

The aim of this experiment is to find the magnitude of the magnetic field produced by a current carrying circular coil. Using the experimental values obtained from the following experiments, it is possible to estimate the horizontal component of the earth’s magnetic field. In Part A of the experiment, a function is derived that represents the tangent of the change in the angle shown on a compass positioned in the center of a circular coil in terms of the number of turns in the coil. Part B of the experiment is intended to derive a function that represents the tangent of the change in angle of a compass needle positioned in the center of a circular coil in terms of the input current. The variables being used in each experiment are as follows: Θ = The number of degrees the compass needle is displaced when the coil is charged. i = current in Amperes. N = the number of turns of the coil. Bh = estimation of the horizontal component of the earth’s magnetic field Be1 = An estimati...

Many services such as facebook require users to sign up with a valid mobile number and can choose to receive messages via SMS at their convenience. Facebook includes this option, and many users take advantage of this system. If a mobile number has been disconnected, after a period of time, the disconnected mobile number is recirculated in the available number pool and can be distributed to buyers of new sim cards. Failure to update your facebook mobile number may leave your account vulnerable to third parties. I personally experienced this vulnerability myself when purchasing a new sim card. I was given a choice of one from about twenty different available numbers in the number pool. I arbitrarily picked one of the numbers which seemed easy to remember. After setting up my new sim card I began receiving sms messages from facebook with links to updates from apparent friends and family. After checking that the sms messages were legitimately from facebook, I opened one of the links, o...

The aim of this experiment is to determine the Velocity of sound in air by measuring the resonant frequency of air columns of variable length. The variables being used in the experiment are as follows: L = Length of air column (meters) f = resonant frequency (Hertz) c = Velocity of sound (meters/second) t = air temperature (Celsius) x = 1/f, the reciprocal of the measured resonant frequency (period) (seconds) y = Length of the air column (meters) m = slope of the linear regression (meters/second) e = y intercept Experimental Method A speaker and oscillator was used to produce and record standing waves within a plastic cylinder, closed at one end, in order to determine the velocity of sound in air. The oscillator was first adjusted to a reasonable volume at 250 Hz so that the experimenters could hear the tone produced by the speaker. The cylinder was also emptied of any liquid that may have been inside. Given the accepted value of the velocity of sound in air at 0֯...

Predator-prey reversal: "In marine benthic communities, rock lobsters, Jasus lalandii, usually represent a keystone predator in diverse ecosystems. However, if its common prey, the whelk (Burnupena sp.), greatly outnumbers the rock lobster, it may result in an alternative stable ecosystem where rock lobsters are killed by whelks, which dominate in the alternated ecosystem." What if this system were bistable and looped indefinitely? The basic schematics of this system remind me of the alternation between left and right political dominance over time due to changes in a political landscape which shifts between two stable political paradigms, with the intermediate stance being centrism. The point at which the left-right political paradigm reversal is initiated might be explained by some kind of population threshold which, when reached, causes the 'predator' entity to become complacent and decline, or the 'prey' entity to adapt to the new paradigm and com...

The following is a MATLAB script which produces the projectile paths of a spherical object, such as a cannonball, given  radius (r), mass (m), initial velocity (v), and angle above the horizontal (theta) . By changing the experimental variables mentioned above, and others attributed to the environment, such as the  density of air (rho) ,  gravity (g)  and the  drag coefficient (C)  the various effects can be visualised in the graph this script outputs.  ifr=1; C=0; C1 = 0.5; theta=35;    v = 50;        g= 9.80;     dt = 0.0001;  i = 1; max_iters = 1000000; x(1) = 0; y(1) = 0; x1(1) = 0; y1(1) = 0; t0 = 0; while ifr<=2     r=0.036*ifr;     m=0.145*ifr^3;     rho=1.2;          A=pi*r^2; A1=pi*r^2;     D=rho*C*A/2; D1=rho*C1*A1/2;          vx =v*cosd(theta); vx1 =v*c...