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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
Gas Physics Introduction
Gas Physics Introduction Chapter 1:Energy Distribution Evolution Energy Diffusion from Mono-energetic of a Three Dimensional Gas Rotating Gas in a 3D Toroid Gas Velocity Equilibration 2D Gas Velocity Equilibration 3D Circulating Gas in a Wind Tunnel Density Modulated Rotating Gas in a 3D Toroid Position Diffusion (Mixing) of a Three Dimensional Gas Energy Distribution 3D with MathJax Equations and Embedded Canvases Gas Energy Distributions 2D Rigid Rotors Energy Distribution 2D 1D Gas Energy and Momentum Distribution Rotor Energies 2D Rotor Energies 3D H2O Energies 3D CO2 Energies 3D 2D Rigid Arrays with Rotation and Translation 3D Rigid Arrays with Rotation and Translation Gas Energy Distributions 1D, 2D, 3D Chapter 2:Particle Scattering Effects
Inelastic Collision Conversion to Internal Energy Brownian Motion Animation 2D Using Hard Sphere Scattering Large Disc Kinetics 2D Condensation of a Gas on a 2D Solid Maxwell's Demon Energy Seperator 2D Minimize Final Energy 2D and 3D Gas Diffusion 2D Gas Expansion 2D Linear Gas Expansion 2D Constant Pressure Gas Expansion 2D Circular Gas Explosion 2D Circular MagnetoCaloric Effect 2D Convection Loops in a Numerical Gas Chapter 3: Gas Energy Equipartition Energy Equipartition of a Two Dimensional Gas with Two Different Masses Energy Equipartition of a Three Dimensional Gas with Two Different Masses Gas Energy Equipartition 3D
Chapter 2.1
Chapter 2.2
Chapter 2.3
Chapter 3.1
Chapter 3.2
Chapter 3.3
Chapter 4.1
Chapter 4.2
Chapter 4.3
Photoelectric Effect Alpha Particle Emission from a Large Nucleus 2D Black Body Emission from Charged Harmonic Oscillators Quantum Animation of Energy Band Gap 1D Animation of Quantum Wave Packets in a pn Junction 1D Quantum Mirror Focusing by Iterating the Schrodinger Equation Quantum Lens Focusing by Iterating the Schrodinger Equation Quantum Two Mirror Resonator by Iterating the Schrodinger Equation Entangled Quantum Object Propagation in a Parabolic Potential Classic and Quantum Object Propagation in a Parabolic Potential Accurate Wave Packet Propagation in a Parabolic Potential Comparison of Quantum to Classical Physics 1D-Time Dependent Accurate Wave Packet Propagation in a Swaged Potential Series Solution of Wave Packet Propagation in a Infinite Square Potential Propagation of a Wave Packet in a Parabolic Potential Propagation of a 2D Wave Packet in a 2D Parabolic Potential Propagation of an Asymmetric Shaped Wave Packet in a 2D Parabolic Potential Two Slit Diffraction by Iterating the Schrodinger Equation Two Potential Slit Diffraction by Iterating the Schrodinger Equation Propagation of an Electron Wave Packet in an Infinite Square Well (Series Solution) Propagation of a Free Wave Packet (Series Solution) Series and Algebraic Solutions for Propagation of a Wave Packet in a Parabolic Potential Comparison of Quantum to Classical Physics 1D-Time Independent Mexican Hat Stationary Quantum States of a Finite Square Potential Well Various Wave Packet Motion in a Finite Square Potential Well Various Wave Packet Motion in a Swaged Potential Well Comparison of Quantum to Classical Physics 1D-Time Independent Cosine/Parabola Electromagnetic Modes of a 2D Cavity Black Body Radiation Experiment and Theory Emission of the Inner Walls of a Black Body Cavity Multiple Slit Diffraction Statistics of Indistinguishable Dice or Particles Quantum Field Collapse Visualization Matrix Operations and Eigenmodes
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Tumbling Block on Inclined Plane New Roller on Inclined Plane Sliding Block on Inclined Plane Classic Objects Motion 1D Generation of Curve for Fastest Time between Two Points Curve for Fastest Time between Two Points Bead Sliding On a Stiff Wire Sound Wave in Two Solid Media Mechanical Properties of a 2D Numerically Modeled Lattice Vibrating Reed Numerical Model 2D Laminar Flow of a Fluid in a 2D Bearing Animation of a Fountain 2D Gravity Leveling of a 2D Liquid Longitudinal and Shear Wave Sound Speed in a 2D Lattice Mechanical Properties of a 2D Numerically Modeled Lattice Vibration Frequencies of a 2D Numerically Modeled Lattice Damped Harmonic Oscillator Motion and Modes of a Particle in a Mexican Hat Potential Forced Oscillator Roller Bearing Cam and Roller Follower Simple Hybrid Gear Train Ratchet Animation Child's Swing Height Increase Mechanics Roller Chain Animation Elasticity of 3D Gas Driving a Piston Free to Forced Harmonic Oscillator Transition Physics of Mounting a Tire on a Rim Physics of a Pendulum Clock Escapement Physics of a Gas Pressure Gauge
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Physics of a Gas Pressure Gauge Ion Drift in Neutral Particle Sea Diffusion Equation Solved by Finite Difference Method Linear Particle Diffusion Heat Flow 1D with Time Dependent Boundary Solid Cube in Liquid Column Drag on a Large Sphere Due to a Digital Gas Animation of a Gas Centrifuge Laminar Flow of a Gas in an Annular Space Laminar Flow of a Fluid in a 2D Bearing Incompressible Fluid Flow through a Constriction Fluid Flow Due To Pressure Gradients
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Parallel Resistors Gas Discharge Animation Oscilloscope Animation Permanent Magnet in Solenoid Cross Product of Two Vectors Magnetic Braking with Cylindrical Geometry Stopping a Falling Magnet by Eddy Currents Magnetic Brake Magnetic Field of a Long Solenoid Coil Light Propagation in a Transparent Dielectric Material Dipole Array Animations Angular Distribution of Emission of Arrays of Excited Dipoles Geometric Derivation of Snell's Refraction Angle Law Electromagnetic (EM) Wave Response to a Row of Dipoles Electromagnetic (EM) Wave Response to a Single Dipole Optics of a Transparent Plate by Iterating the Maxwell Wave Equation Diffraction by Iterating the Maxwell or Schrodinger Wave Equations Lens Focusing by Iterating the Maxwell or Schrodinger Wave Equations Optical Wave Packet Propagation by Finite Difference Matrix 1D Potential(x,y) Using Laplace's Equation Div(gradV)=0 with Variable Boundary Geometry Potential(x,y) Using Laplace's Equation Div(epsilon*gradV)=0 Laplace's Equation Div(gradV)=0 with Mixed BCs Potential(x,y) for Surface Electrodes with Dielectric Slab Dipolar Media Field Plots LCR Oscillator Animation Beam Trajectory of a Moving Laser Beam Trajectory in a Square Ring Laser Doppler Effect Converting Magnetic Forces to Electric Forces Converting Permanent Magnet Orbital Moments to Solenoid Currents Electron Beam Collimation by Axial Magnetic Field Electron Buncher for Klystron Charged Particle Spatial and Speed Bunching Electrical Conduction-Particle Picture Electromagnetic Bell Triode Vacuum Tube
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
E=mc^2 and Mexican Jumping Bean Radar Pulse Return Time Interval Experiment to Determine Gamma Current Loop with a Rotating Test Particle Moving Fabry-Perot Interferometer Space Time Invariant Intervals of a Moving Clock Relativity Transformations by Requiring Simulataneity Accelerated Space Trip Clock Times and Rates Minguzzi Invariant Inertial Frame Time Accelerated Space Trip with Light Pulse Signaling
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Solar Power Generation Planet Formation Illumination of Planets Change of Orbit due to Asteroid Impact Earth Time Zones Day Lengths Astronomical Aberration Kepler Planetary and Sun Orbits Model of Ocean Tides Gravity Course Iteration Spacecraft Speed Assistance by Gravity Hohmann Transfer from One Circcular Orbit to Another Star Distances Using the Parallax Method
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Semiconductor Electron Energies and Band Gap 1D Semiconductor Electron Energies and Band Gap 2D Simple Fermi Surface p-nJunctionDiode Depletion Width Temperature Dependence of 2D Fermi-Dirac Particles
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Assembly of 3D Parts Using Javascript Web Graphics Library 3D Compared to Javascript 3D Graphics 3D Graphics Tutorial Beginnings Proof of Pythagoras a^2+b^2=c^2
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Multiple Slider Animation Template for Plotting with HTML Enhanced Sliders or Ranges Collapsible Dropdown Menu Example Arrow Functions Fast Fourier Transform (FFT) Demonstration
Animation of a Progress Bar
Template for Scientific Plots
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Probability of Birthday Match Random Creation of Probability Function Profiles Two Dies Probability Distribution Three Dies Probability Distribution
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Light Rays in a Transparent Isosceles Prism Light Ray in a Series of Wedges of Various Index of Refraction Snells Law of Refraction Refraction Due to Dipoles in Two Media Refraction and Reflection Two Media Animation of Concave Mirror Reflection Animation of Convex Lens Refraction Prism Refraction-Wave Picture Thick Lens Ray Trace Monochromator (Czerny-Turner Type) Wavelets from Concave Mirror> Thick Lens Focusing
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Sagnac Effect Fiber Optical Gyro (FOG) Ring Laser Gyro (RLG)
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Paticle Motion in a Venturi: Wall Reflections Paticle Motion in a Venturi Potential Elliptical Ion Trap Using Boundary Potential Distribution Prediction of Hard Disc Collision Time and Position Rigid Rotor Collisions
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Acoustic Wave with Built-in Pressure Acoustic Waves in 2D Numerically Modeled Solid Wave 1D on a Linear Array Waves on Discrete Model of Vibrating String Linear Acoustic Wave in a 3D Gas Spherical Acoustic Wave in a 3D Gas Laterally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces Longitudinally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Bicep and Forearm Animation Blood Pressure Measurement Multiple Dose Residual Medicine Vs Time The Eye and its Resolution Breathing Animation Scoliosis Animation Muscle Animation
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Scattering from a Crystalline Target 2D Scattering from a Crystalline Target 3D
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Energy Conduction in a 2D Numerically Modeled Solid Lattice Unbalanced Gas Dynamics:Energy Flow in a Gas
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12

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Solar Power Calculation

Introduction

Obviously, it would be best to have the solar panel's normal vector pointing toward the sun at all times. But here we will assume that the solar panels lie flat on the roof of our building. That is the simplest from the design and construction standpoint. In the northern hemisphere it is obvious that having the panels on a south facing roof slope gets the panel normal closer to the sun direction at midday and conversely for the southern hemisphere. If the roof slope faces east or west then the improvement in the solar power due to the roof slope is zero. If the roof is horizontal, then the solar power is the same as if the panels were laid on the ground. If the roof slope faces north in the northern hemisphere then it actually detracts from the what the solar power would be on a flat roof.

This is an animation that shows the variation with season and planet hour of solar power as it applies to a panel on the roof of a house at any latitude and longitude on a planet. The planet tilt with respect to its orbital plane is a variable. Both the house roof orientation relative to a meridian and the house roof slope are variable by the learner. The graphics include a depiction of the roof panel as it rotates with the planet and a color plot of the intensity of the solar light Vs position on the planet. Since the tilt of the planet's rotational axis is constant with respect to its spin and orbit angle, we can invoke seasons by changing the direction of the sun with respect to the planet. The sun direction vector can cause seasons to vary from summer to fall to winter to spring with house situated in either the northern or southern hemisphere. However, with our present depiction of the planet sphere, we can only show Northern Hemisphere summer and Southern Hemisphere winter. In order to depict Northern Winter and Southern Summer we can negate the planet axis tilt angle. This facility is provided by radio buttons "Northern Summer" and "Northern Winter" Of course, to see results for Southern Summer, one has to move the solar Roof to the southern hemisphere.

Graphics Descriptions

In Canvas 1 we compute and plot the power Vs planet axis rotation angle for a full rotation. When the Start button is pressed, we compute and plot the Power Vs time or (equivalently) angle as the planet rotates about its axis. Both of these plots depend strongly on the present slider settings.

On Canvas 2 we show the 3D planet with the 3D solar roof panel applied to its surface. It appearance also depends strongly on the present slider settings.

Northern Summer
Northern Winter

Learner Control Descriptions

First we have Start and Pause buttons to initiate and pause the rotation of the planet about its axis.

Radio Buttons

After these we have radio buttons that select between Northern summer and Northern winter by changing the planet tilt angle relative to the plane in which the sun apparently rotates. Note that for purposes of power calculation, it is perfectly equivalent for the sun to rotate about the planet or to have the planet rotate about the sun which we all know is what it actually does. The advantage of this choice is that we can have a much larger planet in order to show a solar roof at a reasonable scale.

Sliders

First we have manual control of the sun angle in the orbital plane. Note that the planet illumination changes when this is adjusted.

Next we include a slider to adjust the orientation of the roof relative to south which is the optimum orientation in the northern hemisphere.

Also we have a slider to adjust the roof slope relative to horizontal at the particular latitude chosen.

We include a slider to adjust the longitude of the solar panel roof. This just affects the hours at which power starts, peaks, and stops being produced.

Of course we have a slider to adjust the latitude at which the solar panels are placed

Finally we include a slider with which to ajust the planet axis tilt angle with repect to its orbital plane

Minimum and Maximum Solar Power and Plots Vs Time of Day

We can clearly state what will be the summer maximum and winter maximum irradiance that an area `bb A` on a roof panel will see by using the equation:

`P_"summer max"=P_"normal"cos(|l|-t-s_r)`
`P_"winter max"=P_"normal"cos(|l|+t-s_r)`

d where `P_"normal"` is the solar power that would be provided if the sun direction is normal to the solar panel , `P_"summer max"` is the power at solar noon at the date of the summer solstice and `P_"winter max"` is the power at solar noon at the date of the winter solstice. The arguments of the cosines are angles in radians: `l` is the home latitude angle, `t` is the planet axis tilt angle, and `s_r` is the roof slope angle.

Canvas 3 shows the expected winter and summer power Vs hour. Note, with starting slider settings, that the sunrise time for winter is about 1.5 hours later than for summer. Also note that the sunset time for winter is about 1.5 hours earlier than for summer. This difference in day length is often just as important as the difference in peak power in determining the total energy collected.