Combining Computational and Data Functionality: Expanding Mathematica’s Scientific Capabilities

Jason Martinez, Wolfram|Alpha LLC

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Specialized Data Domains

Combining the entity-property structure of the Wolfram Knowledgebase functions (WeatherData, ElementData, GenomeData) with freely specified input parameters.

ThermodynamicData["Water","Entropy",{"Pressure"->(Quantity[0.2, "MPa", megapascals, "Megapascals"]),"Temperature"->(Quantity[300, "K", kelvins, "Kelvins"])} ]

Features:

A wide range of entities and properties

Property values calculated based on input parameters rather than “standard values”

Incorporates both static information and dynamically calculated properties (magnetic field at a set of coordinates at a specific date in the past)

FormulaData["TimeDilationRelativistic"]

GeomagneticModelData[GeoPosition[{45, -120, 100}],DateObject[{2012,12,22}],"NorthComponent"]

Fully integrated with Quantity and QuantityVariable functionality

FormulaLookup["moment of inertia formula",RequiredPhysicalQuantities->{"Radius"},ExcludedPhysicalQuantities->{"Height"}]

FormulaData[%[[1]],{"m"->Quantity[1,"Kilogram"],"r"->Quantity[2,"Meters"]}]

Formulas

Direct programmatic access to an extensive and ever expanding selection of curated scientific and technical formulas.

FormulaData[]//Length

RandomChoice[FormulaData[],10]

LinguisticAssistant

Functions

DimensionalCombinations

FormulaData

FormulaLookup

PlanckRadiationLaw

QuantityVariable and related functions

The Earth Sciences

Combining geographic mapping and elevation data with models of the earth’s magnetic and gravitational fields. Examining the thermodynamic properties of the planet’s oceans and atmosphere.

disolvedgasdata=Transpose[Table[Normal[StandardOceanData[\[LeftAssociation]"PracticalSalinity"->35,"Pressure"->(Quantity[5, "dbar", decibars, "Decibars"]),"Temperature"->Quantity[t,"DegreesCelsius"]\[RightAssociation],"Concentration"]],{t,0,45,5}]];

ListPlot[Transpose[{Quantity[Range[0,45,5],"DegreesCelsius"],#}]&/@disolvedgasdata[[All,All,2]],Joined->True,PlotLegends->disolvedgasdata[[All,1,1]],AxesLabel->Automatic]

Functions

EarthquakeData

GeogravityModelData

GeomagneticModelData

PsychrometricPropertyData (coming soon)

StandardOceanData

StandardAtmosphereData

Physics & Chemistry

Calculating the size and composition of the universe, the properties of elements and chemicals across a wide range of temperature and pressures, and the interactions of matter and radiation.

StoppingPowerData[(Entity["lead", Entity["Element","Lead"], "Entity[\"Element\", \"Lead\"]", "element"]),{"Particle"->"Photon", "Energy"->Quantity[0.5,"Megaelectronvolts"]},"TenthValueLayer"]

lists=Quantity[10^{3.,3.5,4.,4.5,5.,5.5,6.,6.5,7.,7.5,8.,8.5,9.,9.2,9.4,9.6,9.8,10.,10.2,10.4,10.6,10.8,11.},"Years"];
data=Table[UniverseModelData[t,p],{p,{"DarkEnergyDensityRatio","MatterEnergyDensityRatio","RadiationEnergyDensityRatio"}},{t,lists}];
compositiondata={Transpose[{lists,data[[1]]+data[[2]]}],Transpose[{lists,data[[1]]}],Transpose[{lists,Table[(QuantityPostfix[100, "%", percent, "Percent"]),{Length[data[[1]]]}]}]};

ListLogLinearPlot[compositiondata,PlotRange->All,Joined->True,Filling->{1->{2},2->0,3->{1}},FrameLabel->Automatic,GridLines->{{13.8*10^9},None},PlotRangePadding->0,Frame->True,PlotLegends->{"MatterEnergyDensity","DarkEnergyDensity","RadiationEnergyDensity"}]

New Functions

StoppingPowerData

SpectralLineData (coming soon)

ThermodynamicData

UniverseModelData

Where is North?

What do we mean by North?

Particularly when it comes to the north pole there are several competing definitions which rarely point to the exact same place on the globe:

Local magnetic declination or the direction a compass needle points at your current location.

Graphics[CompassGauge[GeomagneticModelData["Declination"],0.15,0.1],ImageSize->Small]

The Geomagnetic North Pole treats the earth’s magnetic field as if were a giant magnet. This is a fairly accurate approximation for most of the planet which is why compasses work quite well for navigation. At higher latitudes though it deviates significantly from compass readings.

The Magnetic North Dip Pole or Magnetic North Pole where the magnetic field points straight down. This depends on local topography in addition to the local magnetic field.

GeomagneticModelData allows us to calculate both magnetic types of poles (incorporating elevation data in the latter case).

Magnetic North Pole(s) and their movement

Track the location of the dip pole over time compared to the geomagnetic north pole:

Ndips=Table[GeomagneticModelData["NorthModelDipPole",DateObject[{i,1,1}]],{i,1650,2010,10}];

NGeo=Table[GeomagneticModelData["NorthGeomagneticPole",DateObject[{i,1,1}]],{i,1650,2010,10}];

Animate[GeoGraphics[{{Red,Point[Ndips[[i]]],Line[Ndips[[;;i]]]},{Blue,NGeo[[i]],Line[NGeo[[;;i]]]}},GeoRange->{{60,90},{-180,180}}],{i,1,Length[Ndips],1},SaveDefinitions->True]

Navigating the Northwest Passage

Charting the Northwest Passage

Code

course=GeoPosition[{{60.7,-56},{67.7,-58.5},{70.5,-62.5},{72,-66.5},{73.5,-74.4},{74.4,-91.8},{74.3,-95.9},{74.2,-98.5},{73.7,-113.5},{73.08,-116.86},{72.57,-118.9},{71.29,-119.9},{70.7,-124.3},{70.83,-128.4},{69.85,-139.6},{70.44,-143.1},{71.6,-156.5},{70.4,-163.2},{68.9,-167.3},{65.7,-168.5},{62.3,-167.9}}];
samplepoints=course[[All,{2,5,6,9,13,15,17,19,21}]];
geomagneticNorthLocation=Table[GeomagneticModelData["NorthGeomagneticPole",DateObject[{y,9,1}]],{y,1700,2000,20}];
bearings[point_,date_]:=Module[{d1,d2,distance=(QuantityUnit[400]),h1,geomagneticNorthLocation=GeomagneticModelData["NorthGeomagneticPole",date],h2=GeomagneticModelData[point,date,"Declination"]},
h1=GeoDirection[point,geomagneticNorthLocation];d1=GeoDestination[point,GeoDisplacement[{distance,h1}]];d2=GeoDestination[point,GeoDisplacement[{distance,h2}]];
{Red,Arrow[{GeoPosition@point,d1}],Blue,Arrow[{GeoPosition@point,d2}]}
]

Observe the difference between compass readings to Geomagnetic north pole in red and local north in blue:

bearingvalues=Table[Map[bearings[#,DateObject[{y,9,1}]]&,samplepoints[[1]]],{y,1700,2000,20}];

Manipulate[GeoGraphics[{{Red,PointSize[Large],Text[DateObject[{1700+(i-1)*20}],GeoPosition[{90,0}]],Point[geomagneticNorthLocation[[i]]]},Line[course],
bearingvalues[[i]]},GeoRange->{{60,90},All},ImageSize->Large],{i,1,16,1},SaveDefinitions->True]

Thunder and Lightning (and Rain)

The Speed of Thunder

Calculate the height of the base of a thunderstorm:

baseheight=FormulaData["CloudBaseHeight",{(QuantityVariable[(Subscript["T", "db"]), "Temperature"])->UnitConvert[(Quantity[60, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"Kelvins"],(QuantityVariable[(Subscript["T", "dew"]), "Temperature"])->UnitConvert[(Quantity[50, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"Kelvins"]}]

Typical temperatures and pressures at that altitude:

{baseTemperature,basePressure}={StandardAtmosphereData[Last[baseheight],"Temperature"],StandardAtmosphereData[Last[baseheight],"Pressure"]}

Calculate the speed of sound at ground level and base:

{StandardAtmosphereData[(Quantity[0, "m", meters, "Meters"]),"SoundSpeed"],StandardAtmosphereData[Last[baseheight],"SoundSpeed"]}

ThermodynamicData["Air","SoundSpeed",{"T"->(Quantity[50, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"P"->(Quantity[1019, "mbar", millibars, "Millibars"])}]

PsychrometricPropertyData[Association["DryBulbTemperature"->(Quantity[90, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"DewPointTemperature"->(Quantity[80, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"Pressure"->(Quantity[1019, "mbar", millibars, "Millibars"])],"SoundSpeed"]

PsychrometricPropertyData[Association["DryBulbTemperature"->(Quantity[90, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"DewPointTemperature"->(Quantity[80, "°F", degrees Fahrenheit, "DegreesFahrenheit"]),"Pressure"->(Quantity[1019, "mbar", millibars, "Millibars"])],"RelativeHumidity"]

The Color of Lightning

Blackbody wavelength distribution

Examine the distribution of light emitted by a lightning bolt if it were a black body:

PlanckRadiationLaw[Quantity[30000,"Kelvins"],"SpectralPlot"]

{PlanckRadiationLaw[Quantity[30000,"Kelvins"],"MaxWavelength"],PlanckRadiationLaw[Quantity[30000,"Kelvins"],"MeanWavelength"]}

Spectral lines

Explore how nitrogen and oxygen lines might contribute to the visible spectrum:

nitrogenwavelengths=Flatten[SpectralLineData[#,"Wavelength"]&/@{(EntityClass["nitrogen I", EntityClass["AtomicLine",{"Nitrogen",1}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 1}]", "spectral lines"]),(EntityClass["nitrogen II", EntityClass["AtomicLine",{"Nitrogen",2}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 2}]", "spectral lines"]),(EntityClass["nitrogen III", EntityClass["AtomicLine",{"Nitrogen",3}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 3}]", "spectral lines"]),(EntityClass["nitrogen IV", EntityClass["AtomicLine",{"Nitrogen",4}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 4}]", "spectral lines"]),(EntityClass["nitrogen V", EntityClass["AtomicLine",{"Nitrogen",5}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 5}]", "spectral lines"])}];
oxygenwavelengths=Flatten[SpectralLineData[#,"Wavelength"]&/@{(EntityClass["oxygen I", EntityClass["AtomicLine",{"Oxygen",1}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 1}]", "spectral lines"]),(EntityClass["oxygen II", EntityClass["AtomicLine",{"Oxygen",2}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 2}]", "spectral lines"]),(EntityClass["oxygen III", EntityClass["AtomicLine",{"Oxygen",3}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 3}]", "spectral lines"]),(EntityClass["oxygen IV", EntityClass["AtomicLine",{"Oxygen",4}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 4}]", "spectral lines"]),(EntityClass["oxygen V", EntityClass["AtomicLine",{"Oxygen",5}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 5}]", "spectral lines"])}];

nvalues=QuantityMagnitude[nitrogenwavelengths,"Angstroms"];
ovalues=QuantityMagnitude[oxygenwavelengths,"Angstroms"];
GraphicsRow[Function[{x},Graphics[{ColorData["VisibleSpectrum"][#/10],Line[{{#,0},{#,1}}]}&/@x[[2]],Frame->True,FrameTicks->{True,False},AspectRatio->1/3,Background->Black,PlotLabel->x[[1]],FrameLabel->Quantity[None,"Angstroms"],PlotRange->{{4000,7000},{0,1}}]]/@{{"Nitrogen lines",nvalues},{"Oxygen lines",ovalues}},ImageSize->1000]

GraphicsRow[Function[{x},Histogram[x[[2]],{1000},AxesLabel->{Quantity[None,"Angstroms"],Automatic},PlotLabel->x[[1]]]]/@{{"Nitrogen lines",nvalues},{"Oxygen lines",ovalues}},ImageSize->1000]

Water Content of Clouds

The liquid water content of cumulonimbus clouds varies but typically ranges from 1 to 3 g/m^3. The water vapor content however is much higher.

hratio=PsychrometricPropertyData[Association["DryBulbTemperature"->baseTemperature,"DewPointTemperature"->baseTemperature,"Pressure"->basePressure],"HumidityRatio"]

density=PsychrometricPropertyData[Association["DryBulbTemperature"->baseTemperature,"DewPointTemperature"->baseTemperature,"Pressure"->basePressure],"Density"]

UnitConvert[hratio*density,"Grams"/"Meters"^3]

Calculate the total water content in a column of cloud:

{topTemperature,topPressure}={StandardAtmosphereData[(Quantity[12, "km", kilometers, "Kilometers"]),"Temperature"],StandardAtmosphereData[(Quantity[12, "km", kilometers, "Kilometers"]),"Pressure"]}

watervaporDensity[h_?NumericQ]:=Module[{t=StandardAtmosphereData[Quantity[h,"Kilometers"],"Temperature"],
p=StandardAtmosphereData[Quantity[h,"Kilometers"],"Pressure"],hr,d},
hr=PsychrometricPropertyData[Association["DryBulbTemperature"->t,"DewPointTemperature"->t,"Pressure"->p],"HumidityRatio"];
d=PsychrometricPropertyData[Association["DryBulbTemperature"->t,"DewPointTemperature"->t,"Pressure"->p],"Density"];
UnitConvert[hr*d,"Grams"/"Meters"^3]]

densities=Table[{h,watervaporDensity[h]},{h,QuantityMagnitude[Last[baseheight],"Kilometers"],12,0.5}];
ListPlot[densities,Joined->True,AxesLabel->{Quantity[None,"Kilometers"],Quantity[None,"Grams"/"Meters"^3]}]

f[x_?NumericQ]=Interpolation[QuantityMagnitude[densities]][x];
vapor=Quantity[NIntegrate[1000f[h],{h,QuantityMagnitude[Last[baseheight],"Kilometers"],12}],"Grams"/"Meters"^2]

Include the liquid water content for a thunderstorm:

totalmass=vapor+Quantity[2,"Grams"/"Meters"^3]*(Quantity[12,"Kilometers"]-Last[baseheight]);
UnitConvert[totalmass,"Kilograms"/"Meters"^2]

Compared to the mass of the air itself within the cloud:

air=StandardAtmosphereData["SymbolicApproximation","Density"];
NIntegrate[air[Quantity[x,"Meters"]],{x,QuantityMagnitude[Last[baseheight],"Meters"],12000}]

Cherenkov Radiation

Cherenkov radiation is electromagnetic radiation emitted by charged particle passing through a dielectric medium while moving faster than the local phase velocity of light. The intensity of this radiation varies in proportion to frequency and thus is strongest in the blue edge of the visible spectrum.

FormulaData["CerenkovRadiation"]

FormulaData["CerenkovRadiation","QuantityVariableNames"]

Nuclear Decay

Examine the distribution of energies of emitted electrons:

Quiet[Histogram[Uranium235decayElectronEnergies,AxesLabel->Automatic]]

Mean[Uranium235decayElectronEnergies]

Cherenkov radiation

Calculate the parameters of the Cherenkov radiation released by a typical electron decay particle:

mass=(Entity["e-", Entity["Particle","Electron"], "Entity[\"Particle\", \"Electron\"]", "particle"])[(EntityProperty["mass", EntityProperty["Particle","Mass"], "EntityProperty[\"Particle\", \"Mass\"]"])];
n=(Entity["water", Entity["Chemical","Water"], "Entity[\"Chemical\", \"Water\"]", "chemical"])[(EntityProperty["refractive index", EntityProperty["Chemical","RefractiveIndex"], "EntityProperty[\"Chemical\", \"RefractiveIndex\"]"])];

initialenergy=(Quantity[1116, "keV", kiloelectronvolts, "Kiloelectronvolts"]);

FormulaData["CerenkovRadiation",{(QuantityVariable["n", "Unitless"])->n,(QuantityVariable["K", "Energy"])->initialenergy,(QuantityVariable["m", "Mass"])->mass}]

The Interaction of Water and Radiation

Let us take a step back and examine how high energy electrons and water interact. Discover how the components of the total stopping power for water varies with impact energy:

stoppingpowerdata=Table[{Quantity[10^t,"Megaelectronvolts"],StoppingPowerData["Water",{"Particle"->"Electron","Energy"->Quantity[10^t,"Megaelectronvolts"]},"LinearStoppingPower"],StoppingPowerData["Water",{"Particle"->"Electron","Energy"->Quantity[10^t,"Megaelectronvolts"]},"CollisionLinearStoppingPower"],StoppingPowerData["Water",{"Particle"->"Electron","Energy"->Quantity[10^t,"Megaelectronvolts"]},"RadiativeLinearStoppingPower"]},{t,-2,2.9,0.2}];

ListLogLinearPlot[{stoppingpowerdata[[All,;;2]],stoppingpowerdata[[All,{1,3}]],stoppingpowerdata[[All,{1,4}]]},AxesLabel->Automatic,Joined->True,PlotLegends->{"total stopping power","collision stopping power","radiative stopping power" }]

Find the maximum depth a typical electron from the radioactive decay can reach into water:

StoppingPowerData["Water",{"Particle"->"Electron", "Energy"->initialenergy},"CSDARangeLinearStoppingPower"]

Evolution of Cherenkov radiation over the path of an emitted particle

Minimum Energy

First we need to determine the minimum energy necessary to generate the radiation.

sol=FormulaData["KineticEnergyRelativistic", {"m"->mass,"v"->(Quantity[, "c", speed of light in vacuum, "SpeedOfLight"])/n}]

min=UnitConvert[sol[[1,2]],"Electronvolts"]

minimumenergy=QuantityMagnitude[min,"Megaelectronvolts"]

Duration of Radiation Emission

e0=QuantityMagnitude[initialenergy,"Megaelectronvolts"];

Calculate the slowdown rate -(dE/dt) for a beta particle in water.

slowdownrate[e_Real?Positive]:=Module[{mass=Quantity["ElectronMass"]},QuantityMagnitude@UnitConvert[Quantity["SpeedOfLight"]*Sqrt[1-mass^2*Quantity["SpeedOfLight"]^4/(Quantity[e,"Megaelectronvolts"]+mass*Quantity["SpeedOfLight"]^2)^2]*StoppingPowerData["Water",{"Particle"->"Electron", "Energy"->Quantity[e,"Megaelectronvolts"]},"LinearStoppingPower"],"Megaelectronvolts"/"Nanoseconds"]
]
slowdownrate[s_,p_,e_Real]:=0

Examine how the slowdown rate and energy vary with time:

sol=NDSolveValue[{KiM'[t] == -QuantityMagnitude[slowdownrate[KiM[t]]], KiM[0] == e0,
  WhenEvent[KiM[t] <= minimumenergy,(tfinal=t; "StopIntegration")]}, KiM, {t, 0, 0.09},
 PrecisionGoal -> 3];

Determine how long the particle emits Cherenkov radiation:

Quantity[tfinal,"Nanoseconds"]

Evolution of Cherenkov Radiation

Examine how energy changes over time:

Plot[sol[x],{x,0,tfinal},Frame->True,GridLines->Automatic,FrameLabel->{Row[{"time traveled",Quantity[None,"Nanoseconds"]},"  "],Row[{"KE",Quantity[None,"Megaelectronvolts"]},"  "]}]

Explore how the Cerenkov angle changes over that period

Plot[FormulaData["CerenkovRadiation",{(QuantityVariable["n", "Unitless"])->n,(QuantityVariable["K", "Energy"])->Quantity[sol[x],"Megaelectronvolts"],(QuantityVariable["m", "Mass"])->mass}][[2,2]],{x,0,tfinal},Frame->True,GridLines->Automatic,FrameLabel->{Row[{"time traveled",Quantity[None,"Nanoseconds"]},"  "],Row[{"Cerenkov Angle",Quantity[None,"Radians"]},"  "]}]

Initialization

New Functions

Get["/Users/jmartinez/Desktop/Tech Conference/PsychrometricPropertyData.m"]
Get["/Users/jmartinez/Desktop/Tech Conference/SpectralLineData.m"]

Basic Examples

compositiondata=
{{{(Quantity[1000.`, "yr", years, "Years"]),(QuantityPostfix[12.015041206115276`, "%", percent, "Percent"])},{(Quantity[3162.2776601683795`, "yr", years, "Years"]),(QuantityPostfix[19.791371574355374`, "%", percent, "Percent"])},{(Quantity[10000.`, "yr", years, "Years"]),(QuantityPostfix[31.067517546751098`, "%", percent, "Percent"])},{(Quantity[31622.776601683792`, "yr", years, "Years"]),(QuantityPostfix[45.558527952453694`, "%", percent, "Percent"])},{(Quantity[100000.`, "yr", years, "Years"]),(QuantityPostfix[61.38250660088481`, "%", percent, "Percent"])},{(Quantity[316227.7660168379`, "yr", years, "Years"]),(QuantityPostfix[75.6312611603137`, "%", percent, "Percent"])},{(Quantity[1.`*^6, "yr", years, "Years"]),(QuantityPostfix[86.17996933203959`, "%", percent, "Percent"])},{(Quantity[3.1622776601683795`*^6, "yr", years, "Years"]),(QuantityPostfix[92.77759562375253`, "%", percent, "Percent"])},{(Quantity[1.`*^7, "yr", years, "Years"]),(QuantityPostfix[96.42299942938709`, "%", percent, "Percent"])},{(Quantity[3.162277660168379`*^7, "yr", years, "Years"]),(QuantityPostfix[98.28338978113837`, "%", percent, "Percent"])},{(Quantity[1.`*^8, "yr", years, "Years"]),(QuantityPostfix[99.19057783676449`, "%", percent, "Percent"])},{(Quantity[3.1622776601683795`*^8, "yr", years, "Years"]),(QuantityPostfix[99.62307247235275`, "%", percent, "Percent"])},{(Quantity[1.`*^9, "yr", years, "Years"]),(QuantityPostfix[99.82905650228423`, "%", percent, "Percent"])},{(Quantity[1.5848931924611108`*^9, "yr", years, "Years"]),(QuantityPostfix[99.87229956286508`, "%", percent, "Percent"])},{(Quantity[2.511886431509582`*^9, "yr", years, "Years"]),(QuantityPostfix[99.91211714133527`, "%", percent, "Percent"])},{(Quantity[3.9810717055349693`*^9, "yr", years, "Years"]),(QuantityPostfix[99.9443204300785`, "%", percent, "Percent"])},{(Quantity[6.309573444801943`*^9, "yr", years, "Years"]),(QuantityPostfix[99.97115260427532`, "%", percent, "Percent"])},{(Quantity[1.`*^10, "yr", years, "Years"]),(QuantityPostfix[99.99168318775588`, "%", percent, "Percent"])},{(Quantity[1.5848931924611109`*^10, "yr", years, "Years"]),(QuantityPostfix[100.00174379583679`, "%", percent, "Percent"])},{(Quantity[2.511886431509582`*^10, "yr", years, "Years"]),(QuantityPostfix[100.00205645651624`, "%", percent, "Percent"])},{(Quantity[3.981071705534969`*^10, "yr", years, "Years"]),(QuantityPostfix[100.00045192839956`, "%", percent, "Percent"])},{(Quantity[6.3095734448019424`*^10, "yr", years, "Years"]),(QuantityPostfix[100.00002842480491`, "%", percent, "Percent"])},{(Quantity[1.`*^11, "yr", years, "Years"]),(QuantityPostfix[100.00000033370715`, "%", percent, "Percent"])}},{{(Quantity[1000.`, "yr", years, "Years"]),(QuantityPostfix[1.3930408511214107`*^-12, "%", percent, "Percent"])},{(Quantity[3162.2776601683795`, "yr", years, "Years"]),(QuantityPostfix[1.3537185976397553`*^-11, "%", percent, "Percent"])},{(Quantity[10000.`, "yr", years, "Years"]),(QuantityPostfix[1.2949187920674688`*^-10, "%", percent, "Percent"])},{(Quantity[31622.776601683792`, "yr", years, "Years"]),(QuantityPostfix[1.215562199889132`*^-9, "%", percent, "Percent"])},{(Quantity[100000.`, "yr", years, "Years"]),(QuantityPostfix[1.1223132485543263`*^-8, "%", percent, "Percent"])},{(Quantity[316227.7660168379`, "yr", years, "Years"]),(QuantityPostfix[1.0294218311677269`*^-7, "%", percent, "Percent"])},{(Quantity[1.`*^6, "yr", years, "Years"]),(QuantityPostfix[9.51442695654812`*^-7, "%", percent, "Percent"])},{(Quantity[3.1622776601683795`*^6, "yr", years, "Years"]),(QuantityPostfix[8.953627143517514`*^-6, "%", percent, "Percent"])},{(Quantity[1.`*^7, "yr", years, "Years"]),(QuantityPostfix[0.00008597688528921297`, "%", percent, "Percent"])},{(Quantity[3.162277660168379`*^7, "yr", years, "Years"]),(QuantityPostfix[0.0008391920565012223`, "%", percent, "Percent"])},{(Quantity[1.`*^8, "yr", years, "Years"]),(QuantityPostfix[0.008280334130894344`, "%", percent, "Percent"])},{(Quantity[3.1622776601683795`*^8, "yr", years, "Years"]),(QuantityPostfix[0.0821899284475752`, "%", percent, "Percent"])},{(Quantity[1.`*^9, "yr", years, "Years"]),(QuantityPostfix[0.8150404736874446`, "%", percent, "Percent"])},{(Quantity[1.5848931924611108`*^9, "yr", years, "Years"]),(QuantityPostfix[1.7881506237175553`, "%", percent, "Percent"])},{(Quantity[2.511886431509582`*^9, "yr", years, "Years"]),(QuantityPostfix[4.414267721555165`, "%", percent, "Percent"])},{(Quantity[3.9810717055349693`*^9, "yr", years, "Years"]),(QuantityPostfix[10.63340173973201`, "%", percent, "Percent"])},{(Quantity[6.309573444801943`*^9, "yr", years, "Years"]),(QuantityPostfix[24.1639490865149`, "%", percent, "Percent"])},{(Quantity[1.`*^10, "yr", years, "Years"]),(QuantityPostfix[48.37967159890955`, "%", percent, "Percent"])},{(Quantity[1.5848931924611109`*^10, "yr", years, "Years"]),(QuantityPostfix[77.441805524613`, "%", percent, "Percent"])},{(Quantity[2.511886431509582`*^10, "yr", years, "Years"]),(QuantityPostfix[95.2808231687351`, "%", percent, "Percent"])},{(Quantity[3.981071705534969`*^10, "yr", years, "Years"]),(QuantityPostfix[99.6603653816626`, "%", percent, "Percent"])},{(Quantity[6.3095734448019424`*^10, "yr", years, "Years"]),(QuantityPostfix[99.9949643518251`, "%", percent, "Percent"])},{(Quantity[1.`*^11, "yr", years, "Years"]),(QuantityPostfix[99.99999391455746`, "%", percent, "Percent"])}},{{(Quantity[1000.`, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[3162.2776601683795`, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[10000.`, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[31622.776601683792`, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[100000.`, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[316227.7660168379`, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.`*^6, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[3.1622776601683795`*^6, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.`*^7, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[3.162277660168379`*^7, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.`*^8, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[3.1622776601683795`*^8, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.`*^9, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.5848931924611108`*^9, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[2.511886431509582`*^9, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[3.9810717055349693`*^9, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[6.309573444801943`*^9, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.`*^10, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.5848931924611109`*^10, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[2.511886431509582`*^10, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[3.981071705534969`*^10, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[6.3095734448019424`*^10, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])},{(Quantity[1.`*^11, "yr", years, "Years"]),(QuantityPostfix[100, "%", percent, "Percent"])}}};

North

Earth Field Lines

fieldlines=Show[Table[ParametricPlot3D[{(2 Sin[u]+2),0,2 Cos[u]}.{{Cos[t],Sin[t],0},{-Sin[t],Cos[t],0},{0,0,1}},{u,0,2 π},PlotStyle->{RGBColor[1,0,0],Thickness[.005]},MaxRecursion->0],{t,0,2 π,2 π/10}]];

a=(90-80)2 Pi/180.;
Graphics3D[{{RGBColor[1,1,0],Thickness[.007],GeometricTransformation[Line[{{0,0,-3},{0,0,3}}],RotationTransform[π-a,{1,0,0},{0,0,0}]]},RGBColor[0,1,0],Thickness[.007],Line[{{0,0,-2.5},{0,0,2.5}}],Specularity[White,20],RGBColor[.5,.5,.5],Opacity[1],RGBColor[.5,.5,1],Specularity[GrayLevel[1],20],Sphere[{0,0,0},1.5],RGBColor[1,.1,.8],GeometricTransformation[fieldlines[[1]],RotationTransform[π-a,{1,0,0},{0,0,0}]]},SphericalRegion->True,Lighting->{{"Ambient",GrayLevel[.7]},{"Directional",RGBColor[.4,.4,1],{0,0,1}.{{1,0,0},{0,Cos[π-a],Sin[π-a]},{0,-Sin[π-a],Cos[π-a]}}},{"Directional",RGBColor[.4,.4,1],{0,0,-1}.{{1,0,0},{0,Cos[π-a],Sin[π-a]},{0,-Sin[π-a],Cos[π-a]}}}},PlotRange->{{-4,4},{-4,4},{-3,3}},Boxed->False,Background->Black,ImageSize->{391,430}]

Compass

needle[t_,w_,l_]:={Thickness[t],CapForm["Butt"],{Red,Circle[{0,0},w,{Pi/2,Pi}],Polygon[{{0,w},{0,l},{-w ,w}/Sqrt[2]}]},{Darker[Red],Circle[{0,0},w,{Pi/2,0}],Polygon[{{0,w},{0,l},{w ,w}/Sqrt[2]}]},{Blue,Circle[{0,0},w,{Pi,3Pi/2}],Polygon[{{0,-w},{0,-l},{-w ,-w}/Sqrt[2]}]},{Darker[Blue],Circle[{0,0},w,{3Pi/2,2Pi}],Polygon[{{0,-w},{0,-l},{w ,-w}/Sqrt[2]}]}};
Clear[CompassGauge];
CompassGauge[angle_,scale_,border_]:=Module[{t=0.2*border,w=0.1*scale,l=0.8*scale,
	labels={"N","NE","E","SE","S","SW","W","NW"}},
{{Thickness[0.3*border],White,Disk[{0,0},scale],Darker[Gray],Circle[{0,0},scale]},
Translate[{Rotate[needle[t,w,l],-angle],
Table[Rotate[Line[{{0,scale},{0,0.85*scale}}],Pi/4 i,{0,0}],{i,8}],Table[Rotate[Line[{{0,scale},{0,0.9*scale}}],Pi/8 +Pi/4(i-1),{0,0}],{i,8}],
Table[Rotate[Text[Style[labels[[i]],100*scale],{0,0.75*scale}],Pi/4 (-i+1),{0,0}],{i,8}]},{0,0}]}]

North Poles Over Time

NGeo=
{GeoPosition[{82.95375207205372`,-41.00325919682992`}],GeoPosition[{82.63044344105136`,-42.13319691224573`}],GeoPosition[{82.31300097836629`,-42.855579853555604`}],GeoPosition[{81.96029415285462`,-43.301706696146645`}],GeoPosition[{81.71538765250213`,-43.66838688634085`}],GeoPosition[{81.59623273371724`,-45.16008378729296`}],GeoPosition[{81.4124353995865`,-47.481485643782065`}],GeoPosition[{80.96425728949383`,-50.57713605778447`}],GeoPosition[{80.70054133703069`,-53.07659293085675`}],GeoPosition[{80.58573488224711`,-54.46986488025021`}],GeoPosition[{80.4410141801932`,-55.92332972870759`}],GeoPosition[{80.18314289980582`,-56.358962333477535`}],GeoPosition[{79.76747708983919`,-56.63679038102745`}],GeoPosition[{79.47606175774864`,-57.475377916263724`}],GeoPosition[{79.06921871141294`,-59.5520107272708`}],GeoPosition[{78.83836016670023`,-60.97210197911371`}],GeoPosition[{78.68178346693021`,-61.51534162928232`}],GeoPosition[{78.65893538414775`,-61.96445266449632`}],GeoPosition[{78.71556445972844`,-63.06754667424079`}],GeoPosition[{78.69817181604282`,-64.24953823435538`}],GeoPosition[{78.69837554786957`,-65.20737153684532`}],GeoPosition[{78.60530224094404`,-65.97752592709436`}],GeoPosition[{78.57611606283773`,-67.02335802357`}],GeoPosition[{78.55982415826449`,-68.19383745257014`}],GeoPosition[{78.56782889380884`,-68.38919149965812`}],GeoPosition[{78.61387641067635`,-68.79152689559189`}],GeoPosition[{78.58695709194696`,-68.72137225687189`}],GeoPosition[{78.556233669648`,-68.3762696407318`}],GeoPosition[{78.52609813400898`,-68.25984756035064`}],GeoPosition[{78.4652659949124`,-68.50811974948587`}],GeoPosition[{78.46608129571213`,-68.8470333024798`}],GeoPosition[{78.50968141043899`,-69.46672777760429`}],GeoPosition[{78.59103187653359`,-70.17743265509263`}],GeoPosition[{78.80556291915228`,-70.75915346489435`}],GeoPosition[{79.13827197746043`,-71.12739681014787`}],GeoPosition[{79.54331897040599`,-71.57002289888715`}],GeoPosition[{80.01602250926406`,-72.2105924149161`}]};
Ndips=
{GeoPosition[{76.70898341175163`,-110.4450498706939`}],GeoPosition[{76.27932823896187`,-110.70310356369204`}],GeoPosition[{75.83101073873755`,-111.08089249800234`}],GeoPosition[{75.38223718370982`,-111.46122935369873`}],GeoPosition[{75.01195530157703`,-112.1806383673077`}],GeoPosition[{74.58280443570558`,-113.35001940533114`}],GeoPosition[{74.12909301773472`,-114.48151666493001`}],GeoPosition[{73.49883259221937`,-114.58899783767617`}],GeoPosition[{73.14743586408657`,-114.56025897462148`}],GeoPosition[{73.4136757213169`,-114.63542422116257`}],GeoPosition[{73.84352566727813`,-114.20341134656276`}],GeoPosition[{74.15009657974933`,-112.58973818752233`}],GeoPosition[{73.82822136678784`,-109.34364851592024`}],GeoPosition[{73.1210820467055`,-106.28061705083555`}],GeoPosition[{72.12732934398139`,-103.74862484095114`}],GeoPosition[{71.5337279241508`,-101.82103850535836`}],GeoPosition[{71.08230094175717`,-100.02354450505`}],GeoPosition[{70.7215020412781`,-98.72483199882207`}],GeoPosition[{70.46403058616166`,-98.12746660938016`}],GeoPosition[{69.68132987679101`,-96.85983277303109`}],GeoPosition[{69.27117597290764`,-96.78516413672247`}],GeoPosition[{69.17818044027295`,-96.76343151622886`}],GeoPosition[{69.53642984296984`,-96.95580994748389`}],GeoPosition[{70.01243757651542`,-97.31381900220003`}],GeoPosition[{70.54583516037694`,-97.42549071488246`}],GeoPosition[{70.45976609032977`,-96.18545278157734`}],GeoPosition[{70.78510406778226`,-96.71983745908348`}],GeoPosition[{71.33711315283915`,-97.38474401647211`}],GeoPosition[{72.2678356050576`,-98.68326766198993`}],GeoPosition[{73.29849312101423`,-99.87046433725975`}],GeoPosition[{74.63792625232561`,-100.85873398436632`}],GeoPosition[{75.30090801463732`,-101.03272847115399`}],GeoPosition[{75.87835271251907`,-100.97422340213937`}],GeoPosition[{76.90632609488935`,-101.67719603349062`}],GeoPosition[{78.09528129157168`,-103.6885902272651`}],GeoPosition[{80.97161165578382`,-109.63957050762963`}],GeoPosition[{85.01985091354697`,-132.83676678186546`}]};

Timeline

TimelinePlot[{Labeled[DateObject[{1776}],"Captain Cook searches"],Labeled[DateObject[{1845}],"Franklin Expedition"],Labeled[DateObject[{1850}],"Robert McClure"],
Labeled[DateObject[{1853}],"John Rae"],
Labeled[Interval[{DateObject[{1903}],DateObject[{1906}]}],"1st successful navigation:\nRoald Amundsen"],Labeled[Interval[{DateObject[{1940}],DateObject[{1943}]}],"Henry Larsen twice traverses the passage"],Labeled[DateObject[{1969}],"1st trip by oil tanker: the SS Manhatten"],Labeled[DateObject[{1984}],"1st trip by cruise ship:\nMS Explorer"],Labeled[DateObject[{2009}],"9 small vessels and 2 cruise ships complete the transit"],Labeled[DateObject[{2013}],"1st commercial bulk carrier: MS Nordic Orion"]}]

Bearings

course=GeoPosition[{{60.7,-56},{67.7,-58.5},{70.5,-62.5},{72,-66.5},{73.5,-74.4},{74.4,-91.8},{74.3,-95.9},{74.2,-98.5},{73.7,-113.5},{73.08,-116.86},{72.57,-118.9},{71.29,-119.9},{70.7,-124.3},{70.83,-128.4},{69.85,-139.6},{70.44,-143.1},{71.6,-156.5},{70.4,-163.2},{68.9,-167.3},{65.7,-168.5},{62.3,-167.9}}];
samplepoints=course[[All,{2,5,6,9,13,15,17,19,21}]];
geomagneticNorthLocation=Table[GeomagneticModelData["NorthGeomagneticPole",DateObject[{y,9,1}]],{y,1700,2000,20}];
bearings[point_,date_]:=Module[{d1,d2,distance=(QuantityUnit[400]),h1,geomagneticNorthLocation=GeomagneticModelData["NorthGeomagneticPole",date],h2=GeomagneticModelData[point,date,"Declination"]},
h1=GeoDirection[point,geomagneticNorthLocation];d1=GeoDestination[point,GeoDisplacement[{distance,h1}]];d2=GeoDestination[point,GeoDisplacement[{distance,h2}]];
{Red,Arrow[{GeoPosition@point,d1}],Blue,Arrow[{GeoPosition@point,d2}]}
]

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Cherenkov

Shock Diagram

Line[{{-i*mach,0},{-i  Sqrt[mach^2-1]/mach ,i/mach}}]

Simplify[1/m/(Sqrt[m^2-1]/m-m)]

mach=4/3;
Show[Graphics[{Antialiasing->True,{Dashed,Arrow[{{-0.1*mach,0},{0,0}}],Line[{{-4 mach,0},{0,0}},VertexColors->{GrayLevel[0.8],GrayLevel[0]}]},Table[{Opacity[1-0.2 i],GrayLevel[0],Circle[{-i*mach,0},i],Blue,Opacity[0.4],Line[{{-i*mach,0},{-i  Sqrt[mach^2-1]/mach ,i/mach}}],Line[{{-i*mach,0},{-i  Sqrt[mach^2-1]/mach ,-i /mach}}],Opacity[1],Arrow[{{-i  Sqrt[mach^2-1]/mach ,i/mach},{-i  Sqrt[mach^2-1]/mach +0.5,i/mach-(0.5/(-(mach^2)+(Sqrt[-1+(mach^2)])))}}],Arrow[{{-i  Sqrt[mach^2-1]/mach ,-i/mach},{-i  Sqrt[mach^2-1]/mach +0.5,-i/mach+(0.5/(-(mach^2)+(Sqrt[-1+(mach^2)])))}}]},{i,0,4,1}],{Red,Line[{{-4 mach,4 mach/Sqrt[mach^2-1]},{0,0},{-4 mach,-4 mach/Sqrt[mach^2-1]}}]}}],PlotRange->{{Automatic,Automatic},{-4.2,4.2}}]

Uranium Decay

betaenergyList={};
betaenergies[isotope_]:=Module[{decaymode={}(*entries of the form: {original -> final, mode}*),newnuclides,modes,qvalues,p},
modes=extractmodes[isotope];
AppendTo[decaymode,modes];
{Flatten[decaymode],betaenergyList}
]
Clear[extractmodes]
extractmodes[_Missing]:={}
extractmodes[isotope_]:=Module[{newnuclides,modes,p,qvalues={},submodes},newnuclides=isotope[EntityProperty["Isotope", "DaughterNuclides"]];
If[newnuclides==={},Return[{}]];
modes=isotope[(EntityProperty["decay modes", EntityProperty["Isotope","DecayModeSymbols"], "EntityProperty[\"Isotope\", \"DecayModeSymbols\"]"])];
p=Flatten@Position[modes,"beta emission"|"positron emission"|"electron emission"|(Superscript["β", "-"])];
If[p=!={},qvalues=isotope[EntityProperty["Isotope", "DecayEnergies"]];
qvalues=qvalues[[p]];
];
betaenergyList=Join[betaenergyList,qvalues];
modes=MapThread[type[isotope->#1,#2]&,{newnuclides,modes/.{"electron emission"->"(SuperMinus[β])","alpha emission"->"α"}}];
submodes=Flatten[extractmodes/@newnuclides];
modes=DeleteCases[Append[modes,submodes],type[Rule[_,_Missing],_]];
modes]

data=betaenergies[(Entity["uranium-235", Entity["Isotope","Uranium235"], "Entity[\"Isotope\", \"Uranium235\"]", "isotope"])];
Uranium235decayElectronEnergies=data[[2]];

Uranium235decayModes=DeleteDuplicates[data[[1]]/.{type->List}];

EntityValue["Isotope","Properties"]

GraphPlot[Uranium235decayModes,VertexRenderingFunction->({Text[#2[(EntityProperty["brief symbol", EntityProperty["Isotope","Symbol"], "EntityProperty[\"Isotope\", \"Symbol\"]"])],#1,Background->White]}&),Method->"SpringEmbedding",ImageSize->800, EdgeRenderingFunction->({Darker[Red],Arrowheads[Small],Arrow[#],Black,Inset[#3,Mean[#1],Automatic,Automatic,Background->White]}&)]

Storms

Color of Lightning

nitrogenwavelengths=Flatten[SpectralLineData[#,"Wavelength"]&/@{(EntityClass["nitrogen I", EntityClass["AtomicLine",{"Nitrogen",1}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 1}]", "spectral lines"]),(EntityClass["nitrogen II", EntityClass["AtomicLine",{"Nitrogen",2}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 2}]", "spectral lines"]),(EntityClass["nitrogen III", EntityClass["AtomicLine",{"Nitrogen",3}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 3}]", "spectral lines"]),(EntityClass["nitrogen IV", EntityClass["AtomicLine",{"Nitrogen",4}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 4}]", "spectral lines"]),(EntityClass["nitrogen V", EntityClass["AtomicLine",{"Nitrogen",5}], "EntityClass[\"AtomicLine\", {\"Nitrogen\", 5}]", "spectral lines"])}];
oxygenwavelengths=Flatten[SpectralLineData[#,"Wavelength"]&/@{(EntityClass["oxygen I", EntityClass["AtomicLine",{"Oxygen",1}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 1}]", "spectral lines"]),(EntityClass["oxygen II", EntityClass["AtomicLine",{"Oxygen",2}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 2}]", "spectral lines"]),(EntityClass["oxygen III", EntityClass["AtomicLine",{"Oxygen",3}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 3}]", "spectral lines"]),(EntityClass["oxygen IV", EntityClass["AtomicLine",{"Oxygen",4}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 4}]", "spectral lines"]),(EntityClass["oxygen V", EntityClass["AtomicLine",{"Oxygen",5}], "EntityClass[\"AtomicLine\", {\"Oxygen\", 5}]", "spectral lines"])}];