Planck's Radiation Law | Quantum Physics

I was going through Max Planck's radiation law for a couple of days and the way that Planck had derived his beautiful equations just by assuming that the energy is not continuous rather it is an integral multiple of h (Planck constant) just amazed me. I couldn't resist my temptation after realizing that these formulas…

I was going through Max Planck's radiation law for a couple of days and the way that Planck had derived his beautiful equations just by assuming that the energy is not continuous rather it is an integral multiple of h (Planck constant) just amazed me. I couldn't resist my temptation after realizing that these formulas…

I am going to write a code in python for determining the minimum cushion pressure required to break the given thickness of ice by implementing the Newton-Raphson technique. I will also be running a setup to find the optimum relaxation factor for the thickness of 0.6 feet. Equations:The equation that was derived by Muller…

I am going to minimize a non-linear function by using Lagrange Multipliers. Problem statement:Minimize the function `5-(x-2)^2 -2(y-1)^2` subject to `x + 4y - 3 = 0`. Solution:    `L = f - lambdag`,    where ` f = 5-(x-2)^2 -2(y-1)^2` and `g = x + 4y - 3`  Thus, I solve `L = 5-(x-2)^2…

I am going to write a program in MATLAB for solving Quasi one dimensional nozzle flows using MacCormack's Technique implementing both of the conservative and non-conservative forms of governing equations and perform the grid dependence test. Note, I will use the set of initial conditions provided in Anderson's…

I am going to write a program in MATLAB for solving Quasi one dimensional nozzle flows using MacCormack's Technique. I will be using Initial and boundary conditions which are provided in Jhon D Anderson's textbook. I am posting the solutions of non-conservative form and working on the conservative part which I will be…

I am going to write a program in python to simulate a 2R Robotic Arm. I've used online GIF maker to stitch all of my figures and generate the GIF. Note that, I have just used it to stitch the figures, everything else is done by the program. All the figures (200) have been uploaded here. Program: # Simulating a 2R Robotic…

I am going to write a program in MATLAB for solving Quasi one dimensional nozzle flows using MacCormack's Technique implementing both of the conservative and non-conservative forms of governing equations and perform the grid dependence test. Note: I will use the set of initial conditions provided in Anderson's textbook…

I am going to write a program in python to parse information from the CONVERGE output file (IC engine simulation results) and use that data for basic performance calculations for engine and generating appropriate plots. Aim:1. Plot the data for any columns and save it by giving an appropriate name and labels. …

I am going to write a program in python to demonstrate the curve fit on the data set provided by increasing the degree of polynomials namely first degree, third degree and fourth degree. Program: # Program to demonstrate Curve Fit by increasing the degree of the polynomials import matplotlib.pyplot as plt import numpy…

I am going to write a program in python to simulate the Otto cycle. I will be calculating the thermal efficiency of the engine and be generating the P - V diagram.   Problem Setup and geometric parameters:1. Gamma is set to `1.4`.2. The pressure at state point `1` is set to `101325` bars.3. The temperature…

I am going to write a program in python which will calculate the drag force over a bicycle and plot it against velocity and drag coefficients.   Problem Setup:1. Velocities to be used are `2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12` and `13`2. Drag Coefficients to be used are `0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9`…

I am going to write a MATLAB program to simulate the Ideal Rankine Cycle. I will be using standard Xsteam library to get the steam table data for water.    Problem setup: 1. The Pressure at the Turbine Inlet is set to `44` bars. 2. The Temperature at the Turbine inlet is set to `538` °C.3.…

I am going to write down the expressions and units for the quantities below:1. Kinematic viscosity2. Dynamic viscosity3. Peclet number4. Nusselt number5. Momentum flux6. Fourier's law of heat conduction7. Fick's law of diffusion8. Wall shear stress9. Gradient of Temperature field10. Divergence of velocity field  …

I am going to explain the meaning of divergence, gradient, curl and rank of a matrix along with examples.   Vector differential operator:The vector differential operator `grad`, pronounced as 'del' or 'nabla', is defined in three dimensions to be`nabla = partial/(partialx)hati + partial/(partialy)hatj + partial/(partialz)hatk`…

Introduction Programming statements: %1st statement A=[1,2,3,4,5] %2nd statement B=[1;2;3;4;5] %3rd statement C = A*B' %4th statement C = B*A %5th statement A(1:end) %6th statement A(1:2) %7th statement B(1:2,3) %8th statement B(length(B)-2) Here I will be explaining what does each of the above programming statement mean…

How do we perform row and column vector operations: Code for the above operations: %Row vector operation x = [1 2 3 4 5] %Column vector operation y = [6;7;8;9;10]

Crank Nicolson method implementation `(delT)/(dt) = alpha((del^2T)/(delx^2) + (del^2T)/(dely^2))` `(T_(i,j)^(n+1) - T_(i,j)^n)/(Deltat) = alpha(1/2(T_(i+1,j)^(n+1) - 2T_(i,j)^(n+1) + T_(i-1,j)^(n+1) + T_(i,j+1)^n - 2T_(i,j)^n + T_(i,j-1)^n))/(Deltax^2) + alpha(1/2(T_(i+1,j)^(n+1) - 2T_(i,j)^(n+1) + T_(i-1,j)^(n+1) + T_(i,j+1)^n…

I am going to calculate drag force and plot it vs velocity and drag coefficient using MATLAB   Coding for drag force vs Velocity: As `F prop v^2` where `F` is drag force and `v` is velocity, the plot will have a quadratic curve. Code: %Calculating the drag force over the bicycle and plotting drag force vs velocity…

I am going to code in MATLAB for solving linear system `Ax = b` using iterative methods namely, Jacobi, Gauss-Seidel, and Successive over-relaxation. I will be calculating the eigenvalues and spectral radius of iteration matrix. The aim of this project is to notice the behavior of spectral radius as the diagonal…

I am going to solve a second order ODE for the simple pendulum and created a simulation of that pendulum in MATLAB.   How does the function program to solve the pendulum ODE look like? Code for calling the function: %Calling a function - pendulum ode solver function [dtheta_dt] = pendulum_ode_solver(t, theta) g =…

I am going to write a MATLAB program to parse the NASA's thermodynamic data file namely 'therm.txt'. I will then calculate the thermodynamic properties of all the 53 species and plot them against the temperature.   Function filesThe series of functions used in the driver script is as follows:1. 'extract_data.m': %…

I am going to write a program in Matlab to solve a two-dimensional steady-state equation using point iterative techniques namely, Jacobi, Gauss-Seidel, and Successive Over-relaxation methods.    Problem Setup:1. The domain is a unit square.2. The number of points along the x-direction is equal to the number…

I am going to write a function in MATLAB that accepts time step as an argument and solves the same problem as mentioned here and compare the effect of time step on the numerical solution.   Problem Setup - Addition of assumptions to the problem setup discussed above:1. Grid points set to `80`.2. Time…

I am going to write a program in MATLAB which will compare initial and final velocity profile for 1D Linear convection for different value of grid points. 1D linear convection is described as follows:                                  …

I am going to derive fourth order accurate approximations of second order derivative using three differencing schemes namely, central differencing, skewed right sided differencing, and skewed left sided differencing. I will then be writing a program in MATLAB which will compare these schemes.   DERIVING SCHEMES:  …

I am going to write a program which will save the plot generated using MATLAB for comparing the effect of a number of moles of carbon on stoichiometric coefficient (ar). I will also describe how does this trend change with the fuel type (alkanes, alkenes, alkynes) by looking at the plot generated.   Below…

In this project, I have written a program in MATLAB which calculates the efficiency of the Otto cycle and creates a PV diagram for it.    How does the function code look like? Calling a function code which will solve the piston kinematics equation to calculate the volume trace: %Calling a function [V] function…

In this program, I have used MATLAB to code for getting an optimum solution (maximum value in this case) of stalagmite function using the genetic algorithm. The genetic algorithm is an optimization technique based on the evolution theory which was proposed by Charles Darwin and it is used for solving optimization…

I am going to write a program in MATLAB which will plot a bar graph showing the global truncation error for the 1st, 2nd and 4th order approximation of the first derivative at a step size of 0.1.   Analytical function and its derivative:Analytical function: `f(x) = sin(x)/x^3`, Analytical derivative: `f'(x) = (x^3cos(x)…

I am going to write a program in MATLAB which will show the trend of how global truncation error for 1st, 2nd and 4th order approximations of the first derivative changes when we change the step size.   Analytical function and its analytical derivative: Analytical function: `f(x) = sin(x)/x^3`, Analytical derivative:…