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**Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Springer Series in Materials Science)**

Gauge/String Duality, Hot QCD and Heavy Ion Collisions

__Nonlinear Waves in Elastic Media__

The Wave Mechanics of Atoms, Molecules and Ions

__ION RATIO INSIDE BODY (Qi) HYPOTHESIS THEORY AND ACTUALITY [HT3]__

It has been shown above how the classical concept of a well defined particle location has been replaced by the quantum concept of a statistical expectation value , e.g. Research Topics in Electromagnetic Wave Theory *read pdf*. EVERYDAY COMMON SENSE leads us to expect a delayed knowledge lasting two weeks. During this time period the primary event (electron hitting wall) and quickly-occurring secondary events (cat killed or protected, and T or B typed on paper) already have occurred, even though we don't know what the outcome is until someone observes the results , source: Localization in Periodic Potentials: From Schrödinger Operators to the Gross-Pitaevskii Equation (London Mathematical Society Lecture Note Series) read pdf. The increased oscillation amplitudes and energy levels in the system can perform work in a variety of ways, depending on which element or oscillation amplitude is increased. For example, changes in motion, chemical, material, organizational, or behavioral states may all result from a resonant energy excitement in the system. Expressed at the microscale level, a complete energy dynamics formula for the total energy of an individual element in a system is formulated parallel to Helmholtz’s system formula: where “We”, is the total microscale work variable representing the total work performed on an individual element Quantum Coherence: From Quarks download epub download epub. All the rays arriving at O are in phase, as only the rays focused on this point have not been diffracted at all. This means that they all interfere constructively, and there is a brightness *epub*. No, a radio wave is not a mechanical wave ref.: Recent Developments in Nonperturbative Quantum Field Theory (High Energy Physics Conference Proceedin) download for free. Suppose the two clouds are initially separated by a distance $d$. Consider some point a distance $x_0$ away from one cloud (and hence a distance $d-x_0$ away from the other) Solitons (London Mathematical Society Lecture Note Series) *http://tedmcginley.com/lib/solitons-london-mathematical-society-lecture-note-series*. I then have a three-dimensional data set (because I have time). One approach is to extract one number from each density profile which characterizes it ref.: The Dawning of Gauge Theory http://tedmcginley.com/lib/the-dawning-of-gauge-theory.

*http://tedmcginley.com/lib/fundamentals-of-electromagnetic-field-theory-engineering-science-monographs*. Topics will vary and may include: phase transition and critical phenomena; many body quantum systems; quantum chromodynamics and the electroweak model ref.: String Theory: Volumes I & II (Cambridge Monographs on Mathematical Physics)

*read here*. The Heisenberg-Schrödinger model of the atom, in which each electron acts as a wave (sometimes referred to as a "cloud") around the nucleus of an atom replaced the Rutherford-Bohr model , e.g. Thermo Field Dynamics and read pdf

*http://tedmcginley.com/lib/thermo-field-dynamics-and-condensed-states*. Annihilation: process in which a particle and its antiparticle are converted into energy. Antenna: device used to receive or transmit electromagnetic waves ref.: The Field: The Quest for the read pdf ironrodleadership.org.

Elie Cartan and Albert Einstein: Letters on Absolute Parallelism, 1929-1932 (Princeton Legacy Library)

Gauge Field Theories

*Backlund and Darboux Transformations:*. Dutch physicist Willem Gravesande (1688 –1742) performed meticulous experiments and concluded that energy of motion, “follow[s] the Ratio compounded of the Masses, and the Squares of the Velocities” (underline added). ( Gravesande, 1747 ) The noted French Newtonian scholar, Emilie du Châtelet (1706 – 1749) in her 1740 book, “Institutions Physiques” asserted that vis viva energy is proportional to the product of mass and velocity squared, based on Gravesand’s painstaking experiments ref.: High Temperature Phenomena in read epub High Temperature Phenomena in Shock. PI; var bouncingBall1IsBigPoints = true; var bouncingBall1BigPointsAreaColor = 'yellow'; var bouncingBall1BigPointsLineColor = 'black'; var bouncingBall1BigPointsRadius = 5; // Pixels; var bouncingBall1AxisThickness = 3; var bouncingBall1XAxisColor = 'rgb(255, 0, 0)'; var bouncingBall1YAxisColor = 'rgb( 0, 255, 0)'; var bouncingBall1OriginColor = 'rgb(255, 255, 255)'; var bouncingBall1GridColor = 'rgb(200, 200, 200)'; var bouncingBall1GridThickness = 1; var bouncingBall1GridDeltaX = 1.0; var bouncingBall1GridDeltaY = 1.0; var bouncingBall1TurtleX = 0.0; var bouncingBall1TurtleY = 0.0; var bouncingBall1TurtleHeading = 0.0; var bouncingBall1TurtleIsPenDown = true; bouncingBall1SetupGraph = function() { bouncingBall1ClearGraph(); bouncingBall1DrawGrid(); bouncingBall1DrawAxes(); bouncingBall1DrawOrigin(); bouncingBall1SetAreaColor('yellow'); bouncingBall1SetLineThickness(2); bouncingBall1SetLineColor('black'); }; bouncingBall1ClearGraph = function() { bouncingBall1GC.clearRect(0, 0, bouncingBall1DeviceWidthPlus1, bouncingBall1DeviceHeightPlus1); }; bouncingBall1WorldToDeviceX = function(worldX) { return Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)); }; bouncingBall1WorldToDeviceY = function(worldY) { return Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin))); }; bouncingBall1SetLineThickness = function(thickness) { bouncingBall1GC.lineWidth = thickness; }; bouncingBall1SetLineCap = function(capStyle) // 'butt', 'round', or 'square' { bouncingBall1GC.lineCap = capStyle; }; bouncingBall1SetLineJoin = function(joinStyle) // 'round', 'bevel', or 'miter'' { bouncingBall1GC.lineJoin = joinStyle; }; bouncingBall1SetLineColor = function(color) { bouncingBall1GC.strokeStyle = color; }; bouncingBall1SetAreaColor = function(color) { bouncingBall1GC.fillStyle = color; }; bouncingBall1DrawPoint = function(worldX, worldY) { if(bouncingBall1IsBigPoints) { bouncingBall1GC.beginPath(); bouncingBall1GC.arc(Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin))), bouncingBall1BigPointsRadius, 0.0, bouncingBall1TwoPi, true); bouncingBall1GC.fill(); bouncingBall1GC.stroke(); } else { bouncingBall1GC.beginPath(); bouncingBall1GC.moveTo(Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin)))); bouncingBall1GC.lineTo(Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin)))); bouncingBall1GC.stroke(); } }; bouncingBall1DrawLineSegment = function(worldX1, worldY1, worldX2, worldY2) { bouncingBall1GC.beginPath(); bouncingBall1GC.moveTo(Math.round(bouncingBall1DevicePerWorldX * (worldX1 - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY1 - bouncingBall1WorldYMin)))); bouncingBall1GC.lineTo(Math.round(bouncingBall1DevicePerWorldX * (worldX2 - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY2 - bouncingBall1WorldYMin)))); bouncingBall1GC.stroke(); }; bouncingBall1DrawArcLine = function(x, y, r, angle1, angle2) // World. { r = Math.round(bouncingBall1DevicePerWorldX * r); // x- and y-axes must be scaled the same. x = bouncingBall1WorldToDeviceX(x); y = bouncingBall1WorldToDeviceY(y); if(bouncingBall1IsAngleMeasurementInDegrees) { angle1 *= bouncingBall1RadiansPerDegree; } while(angle1 < 0.0) { angle1 += bouncingBall1TwoPi; } while(angle1 > bouncingBall1TwoPi) { angle1 -= bouncingBall1TwoPi; } if(bouncingBall1IsAngleMeasurementInDegrees) { angle2 *= bouncingBall1RadiansPerDegree; } while(angle2 < 0.0) { angle2 += bouncingBall1TwoPi; } while(angle2 > bouncingBall1TwoPi) { angle2 -= bouncingBall1TwoPi; } bouncingBall1GC.beginPath(); bouncingBall1GC.arc(x, y, r, angle1, -angle2, true); bouncingBall1GC.stroke(); }; bouncingBall1RectangleArea = function(x, y, width, height) // World. { bouncingBall1GC.fillRect(Math.round(bouncingBall1DevicePerWorldX * (x - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (y - bouncingBall1WorldYMin))), Math.round(bouncingBall1DevicePerWorldX * (width)), Math.round(bouncingBall1DevicePerWorldY * (height))); }; bouncingBall1RectangleLine = function(x, y, width, height) // World. { bouncingBall1GC.strokeRect(Math.round(bouncingBall1DevicePerWorldX * (x - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (y - bouncingBall1WorldYMin))), Math.round(bouncingBall1DevicePerWorldX * (width)), Math.round(bouncingBall1DevicePerWorldY * (height))); }; bouncingBall1RectangleClear = function(x, y, width, height) // World. { bouncingBall1GC.clearRect(Math.round(bouncingBall1DevicePerWorldX * (x - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (y - bouncingBall1WorldYMin))), Math.round(bouncingBall1DevicePerWorldX * (width)), Math.round(bouncingBall1DevicePerWorldY * (height))); }; bouncingBall1DrawAxes = function() { bouncingBall1SetLineThickness(bouncingBall1AxisThickness); bouncingBall1SetLineColor(bouncingBall1XAxisColor); bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, 0.0, bouncingBall1WorldXMax, 0.0); bouncingBall1SetLineColor(bouncingBall1YAxisColor); bouncingBall1DrawLineSegment(0.0, bouncingBall1WorldYMin, 0.0, bouncingBall1WorldYMax); bouncingBall1SetLineColor(bouncingBall1OriginColor); bouncingBall1DrawPoint(0.0, 0.0); }; bouncingBall1DrawOrigin = function() { bouncingBall1SetLineThickness(bouncingBall1OriginLineThickness); bouncingBall1SetLineColor(bouncingBall1OriginLineColor); bouncingBall1SetAreaColor(bouncingBall1OriginAreaColor); var x = bouncingBall1WorldToDeviceX(0) - 2; var y = bouncingBall1WorldToDeviceY(0) - 2; bouncingBall1GC.fillRect(x, y, 4, 4); bouncingBall1GC.strokeRect(x, y, 4, 4); }; bouncingBall1DrawGrid = function() { bouncingBall1SetLineThickness(bouncingBall1GridThickness); bouncingBall1SetLineColor(bouncingBall1GridColor); var x, y; for(x = 0.0; x <= bouncingBall1WorldXMax; x += bouncingBall1GridDeltaX) { bouncingBall1DrawLineSegment(x, bouncingBall1WorldYMin, x, bouncingBall1WorldYMax); } for(x = 0.0; x >= bouncingBall1WorldXMin; x -= bouncingBall1GridDeltaX) { bouncingBall1DrawLineSegment(x, bouncingBall1WorldYMin, x, bouncingBall1WorldYMax); } for(y = 0.0; y <= bouncingBall1WorldYMax; y += bouncingBall1GridDeltaY) { bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, y, bouncingBall1WorldXMax, y); } for(y = 0.0; y >= bouncingBall1WorldYMin; y -= bouncingBall1GridDeltaY) { bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, y, bouncingBall1WorldXMax, y); } }; bouncingBall1SetBounds = function(worldXMin, worldXMax, worldYMin, worldYMax) { bouncingBall1WorldXMin = worldXMin; bouncingBall1WorldXMax = worldXMax; bouncingBall1WorldYMin = worldYMin; bouncingBall1WorldYMax = worldYMax; bouncingBall1WorldPerDeviceX = (bouncingBall1WorldXMax - bouncingBall1WorldXMin) / (bouncingBall1DeviceWidth); bouncingBall1WorldPerDeviceY = (bouncingBall1WorldYMax - bouncingBall1WorldYMin) / (bouncingBall1DeviceHeight); bouncingBall1DevicePerWorldX = (bouncingBall1DeviceWidth) / (bouncingBall1WorldXMax - bouncingBall1WorldXMin); bouncingBall1DevicePerWorldY = (bouncingBall1DeviceHeight) / (bouncingBall1WorldYMax - bouncingBall1WorldYMin); }; bouncingBall1ShowBounds = function() { // TODO: Present graph bounds. }; bouncingBall1InitializeTurtle = function() { bouncingBall1TurtleX = 0.0; bouncingBall1TurtleY = 0.0; bouncingBall1TurtleHeading = 0.0; bouncingBall1TurtleIsPenDown = true; }; bouncingBall1PenUp = function() { bouncingBall1TurtleIsPenDown = false; }; bouncingBall1PenDown = function() { bouncingBall1TurtleIsPenDown = true; }; bouncingBall1SetH = function(a) { if(bouncingBall1IsAngleMeasurementInDegrees) { a *= bouncingBall1RadiansPerDegree; } while(a < 0.0) { a += bouncingBall1TwoPi; } while(a > bouncingBall1TwoPi) { a -= bouncingBall1TwoPi; } bouncingBall1TurtleHeading = a; }; bouncingBall1Home = function() { bouncingBall1TurtleX = 0.0; bouncingBall1TurtleY = 0.0; bouncingBall1TurtleHeading = 0.0; }; bouncingBall1Forward = function(d) { var turtleNewX; var turtleNewY; turtleNewX = bouncingBall1TurtleX + d * Math.cos(bouncingBall1TurtleHeading); turtleNewY = bouncingBall1TurtleY + d * Math.sin(bouncingBall1TurtleHeading); if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, turtleNewX, turtleNewY); } bouncingBall1TurtleX = turtleNewX; bouncingBall1TurtleY = turtleNewY; }; bouncingBall1Back = function(d) { bouncingBall1Forward(-d); }; bouncingBall1Right = function(a) { var turtleNewHeading; if(bouncingBall1IsAngleMeasurementInDegrees) { a *= bouncingBall1RadiansPerDegree; } turtleNewHeading = bouncingBall1TurtleHeading - a; while(turtleNewHeading < 0.0) { turtleNewHeading += bouncingBall1TwoPi; } while(turtleNewHeading > bouncingBall1TwoPi) { turtleNewHeading -= bouncingBall1TwoPi; } bouncingBall1TurtleHeading = turtleNewHeading; }; bouncingBall1Left = function(a) { bouncingBall1Right(-a); }; bouncingBall1SetX = function(x) { if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, x, bouncingBall1TurtleY); } bouncingBall1TurtleX = x; }; bouncingBall1SetY = function(y) { if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, bouncingBall1TurtleX, y); } bouncingBall1TurtleY = y; }; bouncingBall1SetXY = function(x, y) { if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, x, y); } bouncingBall1TurtleX = x; bouncingBall1TurtleY = y; }; bouncingBall1SetDegrees = function() { bouncingBall1IsAngleMeasurementInDegrees = true; }; bouncingBall1SetRadians = function() { bouncingBall1IsAngleMeasurementInDegrees = false; }; bouncingBall1Sine = function(a) { return Math.sin((bouncingBall1IsAngleMeasurementInDegrees)? (a * bouncingBall1RadiansPerDegree): a); }; bouncingBall1Cosine = function(a) { return Math.cos((bouncingBall1IsAngleMeasurementInDegrees)? (a * bouncingBall1RadiansPerDegree): a); }; bouncingBall1Tangent = function(a) { return Math.tan((bouncingBall1IsAngleMeasurementInDegrees)? (a * bouncingBall1RadiansPerDegree): a); }; bouncingBall1RandomX = function() { return bouncingBall1WorldXMin + (Math.random() * (bouncingBall1WorldXMax - bouncingBall1WorldXMin)); }; bouncingBall1RandomY = function() { return bouncingBall1WorldYMin + (Math.random() * (bouncingBall1WorldYMax - bouncingBall1WorldYMin)); }; ////////// // End: bouncingBall1 (x, y) graph canvas ////////// ////////// // Start: bouncingBall1 animation timeline ////////// var bouncingBall1Fps = 6; var bouncingBall1FrameIndex = 0; var bouncingBall1UserEventHandler = null; var bouncingBall1SystemEventHandler = null; var bouncingBall1Done = false; var bouncingBall1Timeout = null; var bouncingBall1TimeoutPeriod = 1000 / bouncingBall1Fps; bouncingBall1TimelineInitialize = function() { }; bouncingBall1Start = function() { clearTimeout(bouncingBall1Timeout); bouncingBall1Timeout = null; bouncingBall1UserEventHandler = null; bouncingBall1SystemEventHandler = null; bouncingBall1Done = false; bouncingBall1FrameIndex = 0; bouncingBall1SetUp(); bouncingBall1NextFrame(); }; bouncingBall1Resume = function() { bouncingBall1Done = false; bouncingBall1NextFrame(); }; bouncingBall1Pause = function() { clearTimeout(bouncingBall1Timeout); bouncingBall1Timeout = null; bouncingBall1Done = true; }; bouncingBall1Stop = function() { clearTimeout(bouncingBall1Timeout); bouncingBall1Timeout = null; bouncingBall1UserEventHandler = null; bouncingBall1SystemEventHandler = null; bouncingBall1Done = true; bouncingBall1SetDown(); }; bouncingBall1GotoFrame = function(frameIndex) { bouncingBall1FrameIndex = frameIndex; }; bouncingBall1SetUp = function() { }; bouncingBall1SetDown = function() { }; bouncingBall1NextFrame = function() { /* if(bouncingBall1UserEventHandler) { bouncingBall1UserEventHandler(); bouncingBall1UserEventHandler = null; } if(bouncingBall1SystemEventHandler) { bouncingBall1SystemEventHandler(); bouncingBall1SystemEventHandler = null; } */ bouncingBall1EveryFrameHandler(); //bouncingBall1SpecificFrameHandler(); if(!bouncingBall1Done) { bouncingBall1FrameIndex++; bouncingBall1Timeout = setTimeout(bouncingBall1NextFrame, bouncingBall1TimeoutPeriod); } }; bouncingBall1EveryFrameHandler = function() { // Every frame code goes here. }; bouncingBall1SpecificFrameHandler = function() { return; // Remove for use. //switch(bouncingBall1FrameIndex) //{ // case 0: // // // Specific frame code goes here. // // break; //} }; ////////// // End: bouncingBall1 animation timeline ////////// ////////// // Start: bouncingBall1 particle motion ////////// // Mass. var bouncingBall1M = 1.0; // X-axis. var bouncingBall1Xo = 0.0; var bouncingBall1Vxo = 0.0; var bouncingBall1Axo = 0.0; var bouncingBall1X1 = 0.0; var bouncingBall1X2 = 0.0; var bouncingBall1Vx1 = 0.0; var bouncingBall1Vx2 = 0.0; var bouncingBall1Ax1 = 0.0; var bouncingBall1Ax2 = 0.0; var bouncingBall1Fx = 0.0; var bouncingBall1XMin = -10.0; var bouncingBall1XMax = 10.0; // Y-axis. var bouncingBall1Yo = 0.0; var bouncingBall1Vyo = 0.0; var bouncingBall1Ayo = 0.0; var bouncingBall1Y1 = 0.0; var bouncingBall1Y2 = 0.0; var bouncingBall1Vy1 = 0.0; var bouncingBall1Vy2 = 0.0; var bouncingBall1Ay1 = 0.0; var bouncingBall1Ay2 = 0.0; var bouncingBall1Fy = 0.0; var bouncingBall1YMin = -10.0; var bouncingBall1YMax = 10.0; // Z-axis. //var bouncingBall1Zo = 0.0; //var bouncingBall1Vzo = 0.0; //var bouncingBall1Azo = 0.0; //var bouncingBall1Z1 = 0.0; //var bouncingBall1Z2 = 0.0; //var bouncingBall1Vz1 = 0.0; //var bouncingBall1Vz2 = 0.0; //var bouncingBall1Az1 = 0.0; //var bouncingBall1Az2 = 0.0; //var bouncingBall1Fz = 0.0; //var bouncingBall1ZMin = -10.0; //var bouncingBall1ZMax = 10.0; // Time interval per advance. var bouncingBall1Dt = 0.1; // Current time. var bouncingBall1T = 0.0; bouncingBall1ParticleMotionInitialize = function() { }; bouncingBall1SetOriginals = function() { bouncingBall1X1 = bouncingBall1X2 = bouncingBall1Xo; bouncingBall1Vx1 = bouncingBall1Vx2 = bouncingBall1Vxo; bouncingBall1Ax1 = bouncingBall1Ax2 = bouncingBall1Axo; bouncingBall1Y1 = bouncingBall1Y2 = bouncingBall1Yo; bouncingBall1Vy1 = bouncingBall1Vy2 = bouncingBall1Vyo; bouncingBall1Ay1 = bouncingBall1Ay2 = bouncingBall1Ayo; //bouncingBall1Z1 = bouncingBall1Z2 = bouncingBall1Zo; //bouncingBall1Vz1 = bouncingBall1Vz2 = bouncingBall1Vzo; //bouncingBall1Az1 = bouncingBall1Az2 = bouncingBall1Azo; bouncingBall1T = 0.0; }; bouncingBall1Advance = function() { // New position. bouncingBall1X2 = bouncingBall1X1 + (bouncingBall1Vx1 * bouncingBall1Dt) + (0.5 * bouncingBall1Ax1 * bouncingBall1Dt * bouncingBall1Dt); bouncingBall1Y2 = bouncingBall1Y1 + (bouncingBall1Vy1 * bouncingBall1Dt) + (0.5 * bouncingBall1Ay1 * bouncingBall1Dt * bouncingBall1Dt); //bouncingBall1Z2 = bouncingBall1Z1 + (bouncingBall1Vz1 * bouncingBall1Dt) + (0.5 * bouncingBall1Az1 * bouncingBall1Dt * bouncingBall1Dt); // New force. //bouncingBall1Fx = 1.0; //bouncingBall1Fy = 1.0; //bouncingBall1Fz = 1.0; // New acceleration. bouncingBall1Ax2 = bouncingBall1Ax1; bouncingBall1Ay2 = bouncingBall1Ay1; //bouncingBall1Az2 = bouncingBall1Az1; //bouncingBall1Ax2 = bouncingBall1Fx / bouncingBall1M; //bouncingBall1Ay2 = bouncingBall1Fy / bouncingBall1M; //bouncingBall1Az2 = bouncingBall1Fy / bouncingBall1M; // New Velocity. bouncingBall1Vx2 = bouncingBall1Vx1 + (((bouncingBall1Ax1 + bouncingBall1Ax2) / 2.0) * bouncingBall1Dt); bouncingBall1Vy2 = bouncingBall1Vy1 + (((bouncingBall1Ay1 + bouncingBall1Ay2) / 2.0) * bouncingBall1Dt); //bouncingBall1Vz2 = bouncingBall1Vz1 + (((bouncingBall1Az1 + bouncingBall1Az2) / 2.0) * bouncingBall1Dt); // X Bounce if(bouncingBall1X2 > bouncingBall1XMax) { //bouncingBall1X2 = (2 * bouncingBall1XMax) - bouncingBall1X2; bouncingBall1Vx2 = -bouncingBall1Vx2; } else if(bouncingBall1X2 < bouncingBall1XMin) { //bouncingBall1X2 = (2 * bouncingBall1XMin) - bouncingBall1X2; bouncingBall1Vx2 = -bouncingBall1Vx2; } // Y Bounce if(bouncingBall1Y2 > bouncingBall1YMax) { bouncingBall1Vy2 = -bouncingBall1Vy2; } else if(bouncingBall1Y2 < bouncingBall1YMin) { bouncingBall1Vy2 = -bouncingBall1Vy2; } // Z Bounce //if(bouncingBall1Z2 > bouncingBall1ZMax) //{ // bouncingBall1Vz2 = -bouncingBall1Vz2; //} //else if(bouncingBall1Z2 < bouncingBall1ZMin) //{ // bouncingBall1Vz2 = -bouncingBall1Vz2; //} // Tic-toc. bouncingBall1T += bouncingBall1Dt; }; bouncingBall1NewToOld = function() { // Position. bouncingBall1X1 = bouncingBall1X2; bouncingBall1Y1 = bouncingBall1Y2; //bouncingBall1Z1 = bouncingBall1Z2; // Velocity. bouncingBall1Vx1 = bouncingBall1Vx2; bouncingBall1Vy1 = bouncingBall1Vy2; //bouncingBall1Vz1 = bouncingBall1Vz2; // Acceleration. bouncingBall1Ax1 = bouncingBall1Ax2; bouncingBall1Ay1 = bouncingBall1Ay2; //bouncingBall1Az1 = bouncingBall1Az2; }; ////////// // End: bouncingBall1 particle motion ////////// // bouncingBall1_ main animation file var bouncingBall1TrailsX = new Array(); var bouncingBall1TrailsY = new Array(); var bouncingBall1TrailsColor = new Array(); var bouncingBall1NumTrails = 7; bouncingBall1TrailsColor[0] = '#222222'; bouncingBall1TrailsColor[1] = '#444444'; bouncingBall1TrailsColor[2] = '#666666'; bouncingBall1TrailsColor[3] = '#888888'; bouncingBall1TrailsColor[4] = '#aaaaaa'; bouncingBall1TrailsColor[5] = '#cccccc'; bouncingBall1TrailsColor[6] = '#eeeeee'; bouncingBall1Initialize = function() { bouncingBall1Xo = bouncingBall1RandomX(); bouncingBall1Vxo = 5.0 + Math.random() * 5.0; bouncingBall1Vxo = Math.random() < 0.5? bouncingBall1Vxo: -bouncingBall1Vxo; bouncingBall1Axo = 0.0; bouncingBall1Yo = bouncingBall1WorldYMin; bouncingBall1Vyo = 10.0 + Math.random() * 10.0; //bouncingBall1Vyo = Math.random() < 0.5? bouncingBall1Vyo: -bouncingBall1Vyo; bouncingBall1Ayo = -9.8; }; bouncingBall1SetUp = function() { bouncingBall1SetOriginals(); for(var i = 0; i < bouncingBall1NumTrails; i++) { bouncingBall1TrailsX[i] = bouncingBall1X1; bouncingBall1TrailsY[i] = bouncingBall1Y1; } }; bouncingBall1SetDown = function() { }; bouncingBall1EveryFrameHandler = function() { bouncingBall1ClearGraph(); bouncingBall1Advance(); bouncingBall1NewToOld(); bouncingBall1TrailsX.pop(); bouncingBall1TrailsX.unshift(bouncingBall1X1); bouncingBall1TrailsY.pop(); bouncingBall1TrailsY.unshift(bouncingBall1Y1); for(var i = 0; i < bouncingBall1NumTrails; i++) { bouncingBall1SetLineColor(bouncingBall1TrailsColor[i]); bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, bouncingBall1TrailsY[i], bouncingBall1WorldXMax, bouncingBall1TrailsY[i]); bouncingBall1DrawLineSegment(bouncingBall1TrailsX[i], bouncingBall1WorldYMin, bouncingBall1TrailsX[i], bouncingBall1WorldYMax); } for(var i = 0; i < bouncingBall1NumTrails - 1; i++) { bouncingBall1SetLineColor(bouncingBall1TrailsColor[i]); bouncingBall1DrawLineSegment(bouncingBall1TrailsX[i], bouncingBall1TrailsY[i], bouncingBall1TrailsX[i+1], bouncingBall1TrailsY[i+1]); } bouncingBall1SetLineColor('black'); bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, bouncingBall1Y1, bouncingBall1WorldXMax, bouncingBall1Y1); bouncingBall1DrawLineSegment(bouncingBall1X1, bouncingBall1WorldYMin, bouncingBall1X1, bouncingBall1WorldYMax); bouncingBall1DrawPoint(bouncingBall1X1, bouncingBall1Y1); }; Welcome to the Physics Department of Zona Land Education

*epub*.

Advanced Physics Project for Independent Learning: Forces and Motion Unit FM (Advanced Physics Project for Independent Learning (APPIL))

__Elements of Engineering Electromagnetics__

__Elements of Photonics Volume 1__

Supersymmetry: Lectures and Reprints

Spectral and scattering theory for wave propagation in perturbed stratified media (Applied mathematical sciences)

CDMA: Access and Switching: For Terrestrial and Satellite Networks

Optical Semiconductor Devices (Wiley Series in Microwave and Optical Engineering)

An Introduction to Twistor Theory (London Mathematical Society Student Texts)

*Renormalization: From Lorentz to Landau (and Beyond)*

Theory and Computation of Electromagnetic Fields

__Fields and Waves in Communication Electronics__

__Probabilistic Treatment of Gauge Theories (Contemporary Fundamental Physics)__

__Yang-Baxter Equation in Integrable Systems (Advanced Series in Mathematical Physics)__

__Introduction to Hydrodynamic Stability (Cambridge Texts in Applied Mathematics)__

__Space-Time Symmetry and Quantum Yang Mills Gravity : How Space-Time Translational Gauge Symmetry Enables the Unification of Gravity with Other Forces (Advanced Series on Theoretical Physical Science)__

Quantum Mechanics in Curved Space-Time (NATO Science Series B: Physics)

**The Historical Development of Quantum Theory : Vol. 5, Part 2**

Nonlinear Diffusive Waves

*read for free*. An obvious example of this is light curving past the sun. So let us now explain and solve the many problems and paradoxes of Quantum Theory using the Two Principles of the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter , source: Satellite Communications read for free http://tedmcginley.com/lib/satellite-communications-systems-systems-techniques-and-technology. Absorption of resonant EM waves initially results in increased population of an upper energy level. As the energy is converted to work in the system, the energy state devolves and relaxes. When all of the work energy has been spent, a thermal distribution is once again exhibited , source: Electronic Noise and Low Noise read online

__http://simplyfreshdesigns.com/books/electronic-noise-and-low-noise-design__. Eliminating X between the above two equations results in a relationship between T and T ′: T ′ = T (1 − V 2 /c2 )1/2 ≡ T /γ, (4.9) Figure 4.7: Two views of the relationship between three events, A, B, and C Nonclassical Light from read for free

__http://votersforsanity.org/books/nonclassical-light-from-semiconductor-laser-and-led__. Now a purely particle theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of light, to introduce the idea of a particle and that of frequency simultaneously. On the other hand, determination of the stable motion of electrons in the atom introduces integers, and up to this point the only phenomena involving integers in physics were those of interference and of normal modes of vibration ref.: Adaptive Array Systems: Fundamentals and Applications

**http://shop.pajjamaparty.com/books/adaptive-array-systems-fundamentals-and-applications**. Unlike light waves, which are very small, the wavelengths of audible sound are comparable to the sizes of ordinary objects. This creates an interesting contrast between the behaviors of sound and light when confronted with an obstacle to their transmission. It is fairly easy to block out light by simply holding up a hand in front of one's eyes ref.: Real-Time Communication Systems: Design, Analysis and Implementation jasperarmstrong.com. The opposite is the case with rarefactions, where, consequently, density is lesser. At a particular instant of time, an element / particle in the compressional phase and another one in the rarefactional phase are exactly out of phase with each other. Phase – it refers to the position and velocity of a particle oscillating in a wave. Same phase refers to the particles of the oscillating medium which are in the same displacement from their respective mean positions, moving in the same direction Wave Optics and Its read for free

**read for free**. And any linear combination of them will have the same energy. The proof that I did here doesn't assume non-degeneracy, it's even true with degenerate things Hyperspace : a Scientific read here

__http://fsquaremedia.com/library/hyperspace-a-scientific-oddysey-through-parallel-universes-time-warps-and-the-10-th-dimension__.

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