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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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Blood Pressure Measurement

The heart pumps blood with fairly short strokes and then rests approximately 3/4 second between strokes. Blood pressure measurement procedure is to first close the arteries and then slowly allow them to open. This is done by applying external pressure to an extremity like the upper arm as shown in Canvas 0. The external pressure that just closes the artery, even when the heart-induced pressure is maximum, is called the systolic pressure-this pressure is the same as the minimum pressure needed for a tourniquet. The pressures are measured by pumping air into a cuff that surrounds the cross section of the extremity. As the pressure in the cuff is increased it will reach a value where the pressure monitor will show short, slight surges. These are due to the arteries expanding and contracting during the heart's pump strokes. The pressure in the cuff is increased until the pressure monitor no longer shows these small surges in pressure. After that, the pressure in the cuff is slowly bled off while the pressure is monitored for the small surges. The pressure reading during the bleed off, where the small surges are again first detected is the systolic pressure. This is where the heart's peak pressure is just enough to start to open the artery. These pressure surges are monitored as the bleed off continues and the arteries open farther. When the surges are no longer detected, that pressure is called the diastolic pressure. The reason the surges stop is that the cuff pressure is to longer sufficient to even partially close the arteries at peak heart pressure. The diastolic pressure is greater than zero because, between heart pulses, the blood never has time to flow into the smaller arteries and capillaries during the filling phase of the heart. The flow into these smaller vessels continues driven by the elastic contraction of the larger arteries (see link 1) 1. The walls of the artery are made up of several layers and are actually pretty thick compared to the lumen which is the inner diameter which carries the blood. The walls get even thicker and the artery has less capacity to carry blood when they build up a layer called plaque, often due to high blood sugar content.Reference 2

Pulse Pressure and the Effect of Exercise

The difference between the systolic and distolic pressure is called the pulse pressure. The pulse pressure is proportional to the heart's stroke volume. When the person is at rest and not emotionally agitated, the product of the stroke volume times the heart rate (beats per minute) should be constant because that is the volume per minute of oxygenated blood that the person needs to keep him alive. When the person performs mechanical work (exercises), this flow rate (volume per minute) has to increase to support the muscle cells. Since the heart volume can't increase much, the heart beats per minute (bpm) has to increase. Also, since the arteries and the capillaries still offer the same resistance to blood flow, the pulse pressure has to increase to support the increased blood volume per minute so that higher bpm causes increased pulse pressure. Reference 3 There is an equation that shows the relation between pulse pressure and stroke volume: Reference 4

`"Pulse Pressure"=(Stroke Volume)/(Arterial Compliance)`

The artery compliance is a measure of how easily the large arteries stretch (comply, usually radially) so as to accommodate a larger volume of blood when the heart places pressure on them. The typical values for younger adults are artery compliance of 2 milliliters per mm Hg while stroke volume is typically 80 milliliters which results in a pulse pressure of 40 mm Hg which is also the average. As discussed in Reference 3, during exercise, the stroke volume increases slightly while the arterial compliance also increases which might increase pulse pressure a bit but the main increase in the pulse pressure is due to the large increase in heart rate:

"During exercise, the cardiac output increases more than the total resistance decreases, so the mean arterial pressure usually increases by a small amount. Pulse pressure, in contrast, markedly increases because of an increase in both stroke volume and the speed at which the stroke volume is ejected. The cardiac output increase is due to a large increase in heart rate and a small increase in stroke volume."

Canvas 0:Cross Sectional View of the
extremity where Blood Pressure is measured

Explanation of the Graphics

Canvas 0 shows a cross section of the extremity (in this case the arm) where the measurement cuff is centered. The cuff, arm, artery wall and the artery are clearly labeled. When the button "Start Inflation" is pressed, as one would expect, the cuff becomes thicker radially by the inner radius getting smaller and the outer radius getting larger. The radius of the artery gets smaller and smaller until the systolic cuff pressure is reached, where even at the maximum heart muscle contraction, its radius stays zero. A cuff pressure meter scaled in millimeters of mercury (mm Hg) is shown just to the right.
The pressure meter shows gradual pressure increase when the button "Start Inflation" is pressed. It also shows fluctuations during the increase up to a pressure that represents the systolic pressure. After the systolic pressure is reached, the meter fluctuations stop. They stop because the artery remains closed even when the heart's highest pressure is incident on the artery.
When the "Start Deflation" button is pressed, the cuff pressure is reduced and the meter fluctuations re-occur down to what is the diastolic pressure. At this pressure the artery is fully open to blood flow.

The next graphic is a horizontal top view of the extremity (e.g. arm) where blood pressure is being measured. In this view it is convenient to show the Blood flow. This flow is depicted by white chevrons pointing to the right. These chevrons move when two conditions are met:

1. The heart muscle is contracting

2. The cuff pressure is lower than the systolic pressure.

Just as in Canvas 0, when the button "Start Inflation" is pressed. the cuff inflates and, at the systolic pressure, moves inward enough to choke off the artery. As might be expected, the blood flow speed decreases when the cuff pressure increases and becomes zero at the systolic pressure.

Canvas 1: Arm Showing Cuff, Artery and Blood Flow:Top View

Explanation of the Plots Vs Time

The remainder of the graphics (you might have to scroll down) are moving plots of the heart's electrical signals, and the heart muscle and blood flow responses to those electrical signals. To see these plots, the Animation has to be running. Animation is started by pressing either "Start" button.

First is the very familiar EKG that is obtained by measuring the voltage differences between probes strategically placed on the chest. The EKG is some measure of the electrical signal that the heart will see. The EKG has 5 components, P, Q, R, S, T. The R peak is by far the largest. Medical doctors critically examine the size and placement of the EKG components. Sometimes, the frequency of the EKG is sporadic and that can be a serious condition called fibrillation.

Next is a plot of the electrical signal that the heart itself sees. Reference 5.   Typically this signal is much wider time wise than the signal that the skeletal muscles use. The reason for the wider width is that the heart muscle has to remain contracted for roughly 1/4 of its period in order for it to refill.

Next is a plot of the heart muscle's response to the previous plot. As might be expected, there is a slight lag to the response and the muscle pulse width is approximately the same as the width of the heart's electrical signal.

Last is a plot of the blood flow (e.g. milliliters per second) rate versus time. It is scaled to the value when the artery is fully open and the heart muscle contraction is maximum. Of course it goes to zero and stays there when the cuff pressure is above the systolic pressure.