mathdom

[mathdom]

We need a physics fandom too. This is not a question.

there may not be an official physics fandom blog (you could start one), but there are plenty of physics-y blogs out there.

check out these lovely blogs:-anndyruyan-carl-sagan-themathsbitch-thephysicsbitch-procyonvulpecula-the-mighty-ribozyme -poemsandequations-mathematica-itsokaytobesmart-quantummaniac-isomorphismes-lfoster141

and many, many more!

[mathdom]

You're strongly attractive ;)

(Happy late Valentine's day and sorry for never posting anything.  We are terrible, terrible physics majors who are much to busy!)

<3 Strange

[mathdom]

Science Time

Okay, it's science time, kiddies.  These may be jokes, they may be serious, I don't care.  I care about you, my followers, being informed, rational, intelligent human beings.  I believe as Descartes did, that the mind and soul are one, so an educated, healthy, and whole mind is a whole soul.  

The first problem with this post is a lack of understanding of what even a star, like our Sun, is.  Anyone who knows what a star is would never think that there is any way that one could be between the Earth and our natural satellite, the Moon.  

A star is a huge nuclear fusion machine, made primarily of hydrogen and helium, the two most common elements in the universe.  Stars are hot.  The temperature on the surface of our sun alone is 5,778 K.  To put that in perspective, human bone will integrator at about 1300 K.  Stars are large.  The radius of our sun is about 700 million meters, or over a billion meters across.  The Earth's radius is 7 million meters, two orders of magnitude smaller.  The distance between the Earth and the moon is about a quarter of the diameter of sun.  Stars are massive.  Our sun, one of the smaller in the universe, is 2 nonillion kilograms, or 2000000000000000000000000000000 kg (that's 30 zeros!!).  The Earth's mass is about 6000000000000000000000 kg (24 zeros).  

To begin, there could not be a star between the Earth and the moon.  Even a little one.  First of all, a star couldn't fit.  Even if it could, its gravitational force due to its extreme mass.  And even if that didn't happen, the heat would kill us all.  

But we can understand this even better when we know more about what a star is.

A star begins as a nebula, a cloud of hydrogen and helium atoms in space.  These atoms condense into the main sequence star, which lives for a couple billion years.  If the main sequence star is of average size, when it reaches the end of its life, it will become a Red Giant, and die as either a white dwarf (a dense star) and a planetary nebula (a cloud of atoms, similar to stellar nebula, but which will form planets instead of stars.)  Our sun will become a white dwarf and planetary nebula, because it is very small.  If the main sequence is very large, at the end of its life, it will become a Red Supergiant, and explode as a supernova.  A supernova will leave behind either a black hole (a mass dense enough to bend light) or a neutron star (a remnant composed entirely of neutrons).

On Earth, hydrogen is very chemically reactive, while helium isn't.  In space, with extreme pressures and temperatures, however, "normal" chemical reactions don't take place.  When gravity condenses the nebula, hydrogen and helium begin fusion, which is the process by which two atoms smash together and combine into different atoms (as opposed to fission, during which one atoms breaks apart into two, plus some neutrons).  Your chemistry teacher may have told you that atoms of one kind cannot change into atoms of another kind.  This is true in chemical reactions, but when you get into cool stuff, like nuclear physics, this is false.  The diagram below shows two Helium atoms (He) fussing to form a Beryllium atom (Be), releasing a lot of energy.

The energy that is released during fusion is humongous, since it must overcome the strong nuclear forces holding atoms together.  But gravity pushing down on a star is also large, since stars are incredibly massive.  According to Newton's Law of Universal Gravitation, the more massive something is, the more it exerted a gravitational force, and the more force it feels.  When the fusion force holding the star up and the gravitational force pushing it in are equal, the star is stable.

But stars don't stay stable forever, which is what is responsible for a star's "death," as discussed earlier.  Hydrogens fuse to heliums, and heliums to beryliums, and so on, but this process can't go forever. Most stars can't fuse past Iron, element number 26, because there starts to be an imbalance of the forces.  First, the star expands (into either a red giant or a re supergiant) and then collapses into one of the star remnants.

In the case of a regular main sequence star, like our sun, the remnant is a planetary nebula containing all the elements up to iron.  These can be brought together by gravity to form planets made with iron, calcium, oxygen, etc.  But, if stars can only fuse up to Iron, how can we have elements like gold?  Well, our star is not the first to be in its spot, but the third, or fourth.  The first star there exploded and left elements up to iron.  The next exploded and its atoms and the atoms of the last planetary nebula were able to form higher elements, like gold, which can be found on Earth.

Science is a very important thing to know.  For years, humans thought that the sun went around the Earth and ignored things like the back track of the planets because it didn't fit with their world view.  When Copernicus first tried to suggest otherwise, he was exiled by the Church.  Science illiteracy is a major problem.  It's bad for the soul, it's bad for the mind, and it's bad for humanity.  It is out natural sate to progress: morally, technologically, and intellectually.  

I hope I have been successful in imparting some knowledge of the cosmos on you, so that you can be an informed, successful person.  There are no stars between the Earth and the Moon.

-Strange 

Idk if this counts as a peeve more of an art-astronomy pet peeve

but when people draw the cresent moon and where the dark, shaddowed part of the moon is they put in stars

like studdenly that part of the moon is invisible instead of just being in the shadow

like wtf

[mathdom]

Look, guys!  Charm made a drawing, too!  Isn't it perfect?

[mathdom]

In which Tumblr is used for Math/Physics homework

Methods HW #12, Question 2, Part b Use Mathematica code to explore the normal nodes!

In the case of this problem, there wasn't much to explore in the way of changing the code to reflect a change in the graph.  So, exploration came in different forms.

To start, adjusted the time such that every point was at a zero, when it was at equilibrium,

the increased the time until the wave reached its peak, and compared different modes.

Mode 1

Mode 6

Mode 46

I then looked at the graphs from above, to admire the radial symmetry.

Mode 1

Mode 6

Mode 21

After Mode 21, it stops looking so pretty.

Question 3: Examine the rate of convergence of the series.  

This was a little difficult to see at first, because the differences are very small.  Take for example, the following graphs with

n[1]

n[1,10]

n[1,100]

n[1,1000]

From this angle, it might appear that there is no difference between the graphs, suggesting a very quick convergence rate.  This is supported by the cn terms, which have in the denominator an n^3 term, which converges very quickly.

Seen from another angle, with graphs of

n[1]

n[1,10]

n[1,100]

n[1,1000]

we can confirm that the only difference between the graphs is the time it takes Mathematica to load the code.  This is significantly more efficient than most other series we have looked at this year, especially the Fourier series, which must be summed to infinity to get a completely accurate graph.

Question 4, Part b: The Electron in a Box!

The graphs below show the wave function of the electron in a box for various nx and ny.  The peaks and valleys represent the probability of finding the electron at that place.  This seems a little odd at first, since probability ranges from 0 to 1 and can never be negative, but probability is actually the square of the wave function, which results in all positive peaks between 0 and 1.

nx-ny=1

nx=ny=2

nx=ny=3

nx=ny=4

Of course, since there is no orthogonality between nx and ny, they don't have to have the same value.  Here's the graph for when nx=1 and ny=2

and for when nx=2 and ny=1

Interestingly enough, these look an awful lot like ... (drum roll please) ...

VIBRATIONS OF A RECTANGULAR MEMBRANE!  (A square drum.  It's PUNny). Which of course makes sense, seeing as their equations follow the same form.

[mathdom]

The difference between Physics and Chemistry: one is cool.

[mathdom]

Did you know that the top and bottom quarks used to be called truth and beauty?  But scientists thought such frivolity wouldn't appeal to the general population.  They kept strange and charm, though...

[mathdom]

I dated a capacitor once.  She kept charging and discharging, I could never figure out what she wanted.

[mathdom]

Thank you to all of you amazing followers!  We're so happy you're here and hope that you enjoy the ride.  Feel free to message us at any time, with questions, comments, math problems, anything!  We love you!!

-Strange and Charm, Mathdom Admins

[mathdom]

The cosmologist Carl Sagan once speculated that if aliens were observing Earth from orbit, they would come to the conclusion that the dominant life-form had wheels.  Human beings are their lesser symbionts who do everything for their wheeled masters; cleaning them, feeding them, maintaining them, and at great time and labour, constructing their massive migration pathways to render their going smooth.

[mathdom]

It's rather damped out today.

[mathdom]

Headcanon #4

The fundamental forces are the matchmakers of the universe.

[mathdom]

Headcanon # ln(0)

Niels Bohr could kick Albert Einstein's butt in ping pong.

[mathdom]

Newton's Third Law of Shipping

Gravity, pale and dark-haired, somehow managed to draw people in without trying.  There was a magnetic force to him; something hypnotizing, attractive.  Most elements said “he’s an enigma,” but that, of course, was only an excuse.  Nobody knew what drew them to him.  Metals like Gold and Iron and Bismuth were closer to him than elements like Hydrogen or Helium – of course, Helium was distant because that was just what his family was like. (That, however, seemed to be changing; he’d accompany Iron along to Gravity’s place, and might put in a word or two.)

Normal Force, on the other hand, was energetic, wild.  With a bright smile and an acute sense of humor, he made friends with the freer elements; Carbon and Oxygen were two of his closest ones.  Sometimes, he even palled around with Hydrogen, and Hydrogen would convince him to – for one night, or one week – separate some of Gravity’s friends from him for parties.  But he always had to try to make friends.  He always had to make an effort.

Gravity was jealous of Normal Force’s ability to do or say anything; Normal Force envied Gravity’s unconscious attraction to people.  Gravity resented Normal Force, because of how often he took his friends; Normal Force disliked Gravity because of how easily he drew them back.

Some say hate is the counterpart to love.

Of course, others say hate is just that – hate.

[mathdom]

CERN's official website will show you that the pictorial representation of a charm quark is a heart in a circle, and a strange quark is an upside down heart in a circle.  Physicists are all romantics.

[mathdom]

Functions and their Fourier transforms are totally bffs 5eva.  

[mathdom]

A Whole New Meaning To Chemical Bonding

{Here at the Mathdom, we like to ship everything, even the elements.  Please enjoy some Fe/He}

Every element was there: the metals, the gases, even Bromine and Mercury. Some mingled easily, like Oxygen, the life of every party, who moved through every guest with pose and grace. Oxygen caught everyone’s attention right away and never dulled. Everyone loved Oxygen, and Oxygen liked everyone, but Silicone had a particular attraction to Oxygen, always making sure to sit closest to him.

Calcium and Chlorine talked for a while, but it was Sodium who took the gas home that night. Copper and Sulfur made a night of it while Gold and Silver made their way to each other. The night was ending, the reactions were cooling down, and most of the guests had gone home. Iron began to clean up when he noticed the little wallflower, Helium, still skidding around, listening to Magnesium and Nitrogen talk.

Helium was a Nobel gas, though no where near as snooty as some of his siblings, like Neon. He was quiet and shy, but he tried his best to fit in and be sociable; he just failed. He wasn’t good with men or making friends, flirting or idle chit-chat. Iron wasn’t sure why exactly he was still getting invited to these parties, or why he still went: he didn’t seem to enjoy himself.

“Hey,” Iron said, approaching dusty-haired young man, “wanna hear a joke about Nitrous Oxide?”

Helium started for a moment, at first wondering if Iron was even talking to him and then shocked that he was. He coughed, smiled, and threw him the punchline, quietly, politely, “NO.”

Iron laughed, more at Helium’s nervousness than the terrible pun (lies, puns are always awesome no matter what). “You need a lift home?” he asked. “Or, maybe, not home?”

Slowly, as not to frighten him any more, Iron reached a hand out to Helium, who reluctantly took it. Iron took Helium back to his place. The sex was awful, at least the first time around. Helium was so skittish and kept asking questions: am I doing this right? Should I do this? Or that? Iron sighed. “Looks like I have a lot to teach you.”