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  1. matt_crouch

    Maple Step by step solution in Maple

    Is it possible to get Maple to show me step by step how to solve a complex contour integral? f := (x,y,z,v) -> (x+I*x*cos(v)+I*y*sin(v))^(-2) int(f(x,y,z,v),v=0..2*Pi) assuming(x,real,y,real,z,real,v,real) But I would like to know how Maple solves this step by step. I tried using the tutor...
  2. matt_crouch

    Complex contour integrals

    I am trying to teach myself complex analysis . There seems to be multiple ways of achieving the same thing and I am unsure on which approach to take, I am also struggling to visualise the problem...Would someone show me step by step how to solve for example...
  3. matt_crouch

    Whittaker's solution and separable variables

    So It is well known that the 2D solution to the Laplace equation can be obtained by changing to complex coordinates ##u=x+iy## and ##v=x-iy##. This can be extended to n dimensions as long as the complex coordinates chosen also solve the Laplace equation. For example in 3D...
  4. matt_crouch

    Integral inconsistency with variable change

    so ## \int wdw = \frac{1}{2}w^{2} ## now if w=x+y, ## \int (x+y)(dx+dw)= \int xdx + \int ydx + \int xdy + \int ydy ## which can be evaluated and gives ##\int(x+y)(dx+dy)=\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2}## but ##\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2} \neq \frac{1}{2}w^{2}## can...
  5. matt_crouch

    Analytical integral

    can someone suggest a method to solve an integral of the form analytically? ##\int \left[\frac{1}{(1+x^{2})}\right]^{-n}e^{-x^{2}}dx##
  6. matt_crouch

    First order partial differential equation

    How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...
  7. matt_crouch

    Lorentz Transform of a radial & longitudinal dependent magnetic field

    Basically I am trying to lorentz transform the magnetic field along θ of a bunch particles which have a gaussian distribution to the radial electric field. However the magnetic field in θ is dependent on the longitiudinal distribution. Now initially i thought we would just use the standard LT...
  8. matt_crouch

    Starting a Phd in particle physics any advice?

    Hi I wil be starting a PhD in particle/accelerator physics in September it's titled " beam dynamics and beam beam effects for Hilumi LHc and LHeC" Has anyone got any advice for me? It's a fully funded Phd at Manchester university Uk, but it's mainly based at the cockcroft institute. I'm...
  9. matt_crouch

    Calculate the spin wave dispersion relation for a ferromagnetic heisenberg model

    Homework Statement Calculate the spin wave dispersion relation Ek for the ferromagnetic heisenberg model with jtot = 1/2 Assume a 1d square lattice and interactions of strength J between nearest neighbours and zero elsewhere Homework Equations H|k> = [E0 +2jtot\sum J(r)(1-Exp(ik.r) ]...
  10. matt_crouch

    Calculate the Change in entropy of the universe

    Homework Statement Calculate the changes in the entropy of the universe for a) A copper block of mass 0.5kg is dropped into a lake of 10 degrees with the block having a thermal capicity of 2J/K and a temperature of 100 degrees Homework Equations dS=dQ/T The Attempt at a...
  11. matt_crouch

    Fermions that can access 10 distinct energy states; Statistical Physics

    Homework Statement Consider a system made of 4 quantum fermions that can access 10 distinct states respectively with energies: En=n/10 eV with n=1,2,3,4,5,6,7,8,9,10 1) Write the expression for the entropy when the particles can access all states with equal probability 2) Compute...
  12. matt_crouch

    Matlab code fitting a line to a histogram

    Im analyzing some data from a previous student im trying to plot a line of best fit over the histogram and hense find the value of the coefficiants the files had to be loaded as -ascii so this is the code i have typed so far x=load('filename.mat','-ascii'); mean(x); hist(x,300) this...
  13. matt_crouch

    Plotting a best fit curve over a histogram

    Im analyzing some data from a previous student im trying to plot a line of best fit over the histogram and hense find the value of the coefficiants the files had to be loaded as -ascii so this is the code i have typed so far x=load('filename.mat','-ascii'); mean(x); hist(x,300) this then...
  14. matt_crouch

    The Physics of Crumpled paper

    I am currently a 3rd year university student and the project i have been assigned is the the above title, and basically involves looking at statistal physics and its applications. My interests are all in astrophysics and cosmology i was wondering if there was any place for my interests in this...
  15. matt_crouch

    Calculate the electric field strength inside and outside a wire

    Homework Statement An infinitly long conducting cylinder of Radius R carries a unifom surface charge of (lambda per unit length) determine the electric field strength inside and outside the cylinder Homework Equations integral (E.ds)= q/e0 The Attempt at a Solution im not really sure what...
  16. matt_crouch

    Doppler effect wavelength from car

    Homework Statement A car is travelling at 30m/s in still air. the frequency of the siren on the car is 600hz. The velocity of sound in still air is 330 m/s. what is the wavelength of the sound waves a)directly in front of the car b)directly behind the car What is the frequency of the...
  17. matt_crouch

    Describe geometrically the level surfaces of the functions

    So the question is as titled i) f=(x^2 +y^2 +z^2) ^1/2 if I can figure out the method I can solve the other equations but I'm not really sure where to start I know that a function f(x,y,z) of a level surface well be constant so do I just find del f ?
  18. matt_crouch

    Eigenvalues homework problem

    Homework Statement Show that lambda = 1 is an eigenvalue of the matrix 2,-1, 6 3,-3, 27 1,-1, 7 and find the eigenvalues and the corresponding eigenvectors Homework Equations The Attempt at a Solution I dont understand how to actually get eigenvalues and...
  19. matt_crouch

    Calculating the average speed of molecules in a gas

    Homework Statement Given that the integral [between infinity and 0] v3e-av2dv = 1/2a2 calculate the average speed vav of molecules in the gas using the maxwell-boltzmann distribution function Homework Equations The Attempt at a Solution i dont really know what to do some...
  20. matt_crouch

    Approximatly 5% of each exhaled breath is carbon dioxide

    Homework Statement In normal breathing conditions approximatly 5% of each exhaled breath is carbon dioxide. Given this informartion and neglecting any difference in water-vapor content estimate the typical difference in mass between an inhaled breath and an exhaled breath. assume one lungs...
  21. matt_crouch

    Weather balloon problem

    Homework Statement assume the balloon is a spherical shape whose radius is 2.5m and total mass of 15 kg a) what is the initial upward acceleration of the ballon when it is released from sea level Homework Equations The Attempt at a Solution i know the volume of a sphere is...
  22. matt_crouch

    Special relativity of a light source moving downstream

    Homework Statement Let Cw be the speed of light through water at rest. Water is now flowing at speed v parallel to the x axis according to one observer, and there is also a light source moving with the water at speed v 1) what is the speed at which the light source sends light signals in...
  23. matt_crouch

    Thermistor's temperature problem

    Homework Statement A thermistor's temperature dependence is given by R=R0eb/t where R is in ohms T is in Kelvins R0 and B are constants to be found. a) If R =7360 at the ice point and 153 at steam point find R0 and B Homework Equations The Attempt at a Solution I took...
  24. matt_crouch

    Virtual Photon

    In my lecture this morning i was told that charged particles interact by the exchange of virtual photons and that they serve as carriers of momentum and force. But it says that a photon is a boson with spin number 1, massless and zero charge. The question is basically how can a massless...
  25. matt_crouch

    Fx= -du/dx does the e2=-du

    im unsure about if two equations are mathematically similar whether they equal the same. ill give an example Fx=e2/ 4\pi\epsilon0x2 is similar to Fx= -du/dx does the e2=-du ? btw the pi and E are not raised to the power its just my inability to use latex =]
  26. matt_crouch

    Find the magnitude of the gravitational field

    Homework Statement Find the magnitude of the gravitational field a distance r from an infinitly long uniform thin rod whose mass per unit length is (lamda) Homework Equations The Attempt at a Solution Need some clarification really i know dgx=-Gdm/r2 r=r2-r1 lamda=m/L...
  27. matt_crouch

    Meteor impacts

    Has anyone got any good break down on what happens during and impact. Im using my example of Chicxulub ive seen the wikipedia and there is a good animation on there has anyone know where i can find some still diagrams ?
  28. matt_crouch

    Potential energy

    Homework Statement i wasnt really sure where to put this question. its kind of a maths question i suppose the potential energy funtion u along the x-axis is given as U=-U0x2 the question is really why do i not use the product rule on this equation as it is two variable multiplied...
  29. matt_crouch

    Differentiation problem

    Homework Statement i have been told to calculate DI/Dx i calculated I as being = m(L^2)/16 how do i differentiate this? im confussed with what happens to the m is it a constant an just removed? same with the 1/16 i assume that is removed as a constant? just need some clarification...
  30. matt_crouch

    Calculating the proper mean lifetime of pions

    Calculating the "proper mean lifetime" of pions Homework Statement The mean lifetime of pions at rest is to=2.6x10^-8. if a beam of pions has a speed v=0.85c a)what would their lifetime be in the laboratory? b)how far would they travel before they decay? c)what would your answer to b)...