The Navier-Stokes equations consists of a time-dependent continuity equation for conservation of mass, three time-dependent conservation of momentum equations and a time-dependent conservation of energy equation. There are four independent variables in the problem, the x, y, and z spatial coordinates of some domain, and the time t. There are six dependent variables; the pressure p, density r, and temperature T (which is contained in the energy equation through the total energy Et) and three components of the velocity vector; the u component is in the x direction, the v component is in the y direction, and the w component is in the z direction, All of the dependent variables are functions of all four independent variables. The differential equations are therefore partial differential equations and not the ordinary differential equations that you study in a beginning calculus class.

You will notice that the differential symbol is different than the usual “d /dt” or “d /dx” that you see for ordinary differential equations. The symbol “” is is used to indicate partial derivatives. The symbol indicates that we are to hold all of the independent variables fixed, except the variable next to symbol, when computing a derivative. The set of equations are:

Continuity: r/t + (r * u)/x + (r * v)/y + (r * w)/z = 0

X – Momentum: (r * u)/t + (r * u^2)/x + (r * u * v)/y + (r * u * w)/z = – p/x

+ 1/Re * { tauxx/x + tauxy/y + tauxz/z}

Y – Momentum: (r * v)/t + (r * u * v)/x + (r * v^2)/y + (r * v * w)/z = – p/y

+ 1/Re * { tauxy/x + tauyy/y + tauyz/z}

Z – Momentum: (r * w)/t + (r * u * w)/x + (r * v * w)/y + (r * w^2)/z = – p/z

+ 1/Re * { tauxz/x + tauyz/y + tauzz/z}

Energy: Et/t + (u * Et)/x + (v * Et)/y + (w * Et)/z = – (r * u)/x – (r * v)/y – (r * w)/z

– 1/(Re*Pr) * { qx/x + qy/y + qz/z}

+ 1/Re * {(u * tauxx + v * tauxy + w * tauxz)/x + (u * tauxy + v * tauyy + w * tauyz)/y + (u * tauxz + v * tauyz + w * tauzz)/z}

where Re is the Reynolds number which is a similarity parameter that is the ratio of the scaling of the inertia of the flow to the viscous forces in the flow. The q variables are the heat flux components and Pr is the Prandtl number which is a similarity parameter that is the ratio of the viscous stresses to the thermal stresses. The tau variables are components of the stress tensor. A tensor is generated when you multiply two vectors in a certain way. Our velocity vector has three components; the stress tensor has nine components. Each component of the stress tensor is itself a second derivative of the velocity components.

The terms on the left hand side of the momentum equations are called the convection terms of the equations. Convection is a physical process that occurs in a flow of gas in which some property is transported by the ordered motion of the flow. The terms on the right hand side of the momentum equations that are multiplied by the inverse Reynolds number are called the diffusion terms. Diffusion is a physical process that occurs in a flow of gas in which some property is transported by the random motion of the molecules of the gas. Diffusion is related to the stress tensor and to the viscosity of the gas. Turbulence, and the generation of boundary layers, are the result of diffusion in the flow. The Euler equations contain only the convection terms of the Navier-Stokes equations and can not, therefore, model boundary layers. There is a special simplification of the Navier-Stokes equations that describe boundary layer flows.

Notice that all of the dependent variables appear in each equation. To solve a flow problem, you have to solve all five equations simultaneously; that is why we call this a coupled system of equations. There are actually some other equation that are required to solve this system. We only show five equations for six unknowns. An equation of state relates the pressure, temperature, and density of the gas. And we need to specify all of the terms of the stress tensor. In CFD the stress tensor terms are often approximated by a turbulence model.

Source: https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html

[learn_press_profile]

I wrote about 15 pages on Navier Stokes back in March of 2020 under one of my “states.” But I can’t, for the life of me, figure out what I said.

The solution is rather extensive.

I should go back a bit. Maybe I should explain why I went to study Navier Stokes in the first place.

A friend of mine told me that I wasn’t good at mathematics and that I didn’t deserve to have children with him because I’m a black. I get it. Whatever.

To spite him, I flew to Princeton University and squatted in Fine Hall during Spring Break for two weeks. In the span of those two weeks, I managed to learn about Navier Stokes, or that’s what I thought at least.

I spent two days intensively answering the question, and eventually I found a counterexample.

I just don’t understand my own work. I can’t decipher it. See, I have this communication disorder called Aspergers. It makes me incredibly awesome at just about everything except for communicating. I’m getting better though. The meth helps me a lot. I don’t know how or why yet, but I figured that out too, when I wrote about topological data analysis on neuronal networks. I discovered holes in my brain. Topological holes.

Yeah, so anyway, about Navier Stokes.

Let’s just say I wasn’t too stoked to publish this paper.

Mental State: 60 hours without sleep, low carb ketogenic diet, methamphetamine dose

[learn_press_profile]

Knowing that it was now or never, I took all of the remaining money I had from student loans at UW, and left for Princeton. I had only planned on visiting the school during spring break and had these classes in mind to sit on for the first week:

However, it didn’t happen. Everything went virtual and my flight back to Seattle was canceled. For the next couple of months, I started building my business and learning the in-and-outs of starting a professional corporation. That’s when I came up with the name JAS THE PHYSICIST PC.

My company started off as a brain-child under the name BLUME and even DAILITE where I wrote about

Medical science failed me. I scarred me with incurable stretch marks, discolored skin and a weakened immune system because doctors couldn’t figure out what was wrong with me.

Medical science failed my family. My mother, grandmother, sister and uncle all suffering from type-2 diabetes and my grandfather dying by its hand.

Medical science failed my advisor Steve Mitchell, who died of cancer my second year of graduate school.

Diagnostic psychiatry failed me, while in graduate school I was misdiagnosed as ADHD, OCD, bipolar, and finally Asperger’s Syndrome, none of which fit. Why? How could I have went to so many specialists for so many years? Allergists, gastroenterologists, psychologists, neurologists, dermatologists… every diagnosis wrong, and every treatment making me worse, damaging my body in the process until eventually the drug treatments began to corrode my mind.

While in a psychotic state still a student at University of Washington, which I theorize was due to autoimmunity-based encephalitis, I created mAAd academy. Here is what I wrote:

I may not have any publications in any peer reviewed journals, but that didn’t stop me from writing extensive research articles, while still attending courses in commutative algebra, differential geometry and algebraic topology.

Yeah maybe I spent too much time watching House MD, Dr. Sang Suh, neurologist and psychiatrist told me that’s part of Asperger’s, and so I liked to pretend that I was Gregory House, escaping from the pain caused by the collective ignorance of current medical science.

[learn_press_profile]

According to Webster, a professor is the highest-ranking teacher. According to me, a professor is a lifelong student. According to academia, a professor is a person who attains a PhD, but who says certification is a linear process anyway? Time surely isn’t.

Hi, I’m Jas the Physicist, that’s my stage name at least. You could call me Jas, the Physician, that’s my life goal or you can call me Jasmine. In 2017, Reddit called me the mAAd Professor.

Just like the rest of us mathematicians, I was gifted in mathematics at an early age, and continued along that path. I stuck to mathematics because I love it, there’s no doubt about that, but I also had something to prove. Forgive me, I speak in puns pathologically, it’s part of the autism, or any class of schizoid disorders which I have discovered to be topologically equivalent in neuroscience, but I’m getting a head of myself.

Alongside mathematics, I wrote academically and causally online, and have a publication record that rivals professors in academia currently, save for my reluctance to publish them in any academic journals, but the drafts are archived.

So back to my mAAd Professorship, which stands for Music As Alternate Discourse, and was an online school of music philosophy that I built while in a Master’s program in Mathematics at the University of Washington. I would like to emphasize this point, because I don’t think I even appreciated the amount of work I was outputting at this time: I was publishing “papers” alongside taking core courses in graduate mathematics (algebraic topology, differential geometry, and commutative algebra), on top of teaching undergraduate integral calculus (I wanted to teach linear algebra but never got the assignment unfortunately), while researching algebraic topology as it applies to neuroscience, where I opened up a diagnostic psychiatric consulting firm JAS THE PHYSICIST PC. I formally established this in 2020 of this year.

I would also like to point out that a master’s student and phd candidate at UW are no different save for the amount of funding they are guaranteed and whether they want to take preliminary exams first or second year. The workload, courseload and interactions are indistinguishable and I say that to say I was essentially a phd candidate, but again these labels are sometimes overly confining.

I’m not going to say that I did all of these things well, because among my prolific output (and I’m not tooting my own horn here, I am being objective about my capabilities), I was also psychotically depressed, in and out of hospitals and battling homelessness on top of income insecurity. That was one of the downfalls of living on a graduate student’s salary with a professor’s level work ethic, and I will not make that mistake again, because it was inefficient and worst of all it left me exhausted and ill.

In April of 2020, I decided I was finally going to leave the UW mathematics department in search for a more flexible and interdisciplinary position, but it was necessary the four years of graduate courses I studied because I need to understand both algebraic and differential geometry enough to be a conversational geometer in a research and professional setting, so that any conference I attend on these subjects I can follow and contribute to meaningfully. UW is particularly strong in algebraic geometry and I am glad to have learned from wonderful geometers and category theorists but it wasn’t enough.

Okay, are you still following along? In 2019, I began studying partial differential equations as an extension of my research in differential geometry, that is when I started reading the work of professor Yu Yuan and Gunther , two of the only PDE and analysis professors in the department,

THE SECOND LAW OF THERMODYNAMICS IS WRONG.

I CAN PROVE IT.

Now, please accept me as Professor of Mathematics so that I may have access to the resources, scientists, labs and technology to prove this.

I have been studying independently for years, many subjects across various disciplines. I am a polymath, and so when I was forced to spend 16+ hours a day on abstract mathematics, I rebelled. I could not dedicate all of my time to one subject, THAT IS NOT HOW DIAGNOSTICS WORKS

I don’t just want this job. This is my life. This is what I do. I love and enjoy it so much, I enjoy researching and teaching and reading and lecturing that even when I’m unemployed, even when I’m homeless, even when I’m suicidal, I still do these things. I have been teaching for over 20 years. Don’t believe me?

Every class that I’ve been in as a child until adulthood moved too slow and so I would always host extracurricular activities so that I may teach my classmates and reinforce the information for myself. I just loved learning that much. Now I was young when I wrote this little sentence but imagine having a child write that they are teaching the other children to read? That’s impressive, right? This pattern of teaching while learning and doing independent study is precisely what a professor is, and I am one. I just need a school that will allow me the freedom to pursue my research and hunches with reckless abandon, without poverty constantly holding me back.

I found out about the Institute for Advanced Study some time in 2019 when I was perusing one of Jacob Lurie’s recent papers in category theory. After reading its mission statement, and learning the extensive history of the Institute and the minds who attended and professed there, I knew that was where I was supposed to be. It’s exactly the intellectual refuge I had only dreamed about, and I had no idea a place like this existed.

I belong here, and I won’t let external circumstances dictate my exclusion. You say you want exceptional professors, well I’m here to say that I am an exception and all I ask is that you make one for me.

And don’t even get me started on Navier Stokes… my goodness.

However there is much research that needs to be done. I’ve begun recording online lectures on YouTube for the MCAT (Medical College Admissions Test) where I detail subjects including biochemistry, organic and inorganic chemistry, mathematics and physics, both as a means of exposing myself to this material for my own research and because I know the demand for these subjects are high, where medical researchers are needed now more than ever. It is something I do in my spare time, when I’m not searching for jobs. My business (JTP PC) is currently receiving unemployment benefits and I live paycheck to paycheck. Again, this is another unnecessary stressor and impediment to my research. I never stop researching, however, I really want to emphasize that I never stop researching no matter the circumstances. It’s a drive that I have, that I can’t necessarily explain, but moves me beyond words. Okay, I’m getting a bit corny here, but I know there are passionate researchers around, that’s one of the reasons I chose this location. I anticipate nothing but fun and engagement.

I have an small archive on Reddit of articles that I want to read for my research but have been paywalled out of. I know Princeton has access to all of the cutting edge research articles, research databases, computer technology so that my online lectures can be better formatted, chalkboards galore, it really is a research paradise.

Mental state: low carb, raw dairy, raw milk

[learn_press_profile]

What is Artificial Intelligence?

Hi, I’m Jasmine (Blaise), a poly-mathematic graduate student and research scientist. My research interests vary but my first project is in computational psychiatry and neuroscience. More specifically, I’m interested in the topology of the brain (and by extension, the mind). Every disorder can be categorized and not only categorized, but given a topological structure. Using mathematics as the map, computational neuroscience as the compass, and Hippocrates as my guide, I connect neurobiological disorders to their psychological manifestations. The mind and the body are not independent, and it was a grave mistake when psychology decided to separate the two: neuroscience is here to fix that.

Have you heard of Computer Vision?

My *current* interests are flows. Flowing along a manifold. Flowing on a beat. Being a flower. I am the founder of BLOOM and Maad Academy. If the link doesn’t work it’s because I don’t. We’re broke.

You’re going to have a hard time flow-o-o-o-wing along. I suggest you try immersion.

Mental state: vegan diet, high inflammation

[learn_press_profile]

Hi, I’m Jas.

I’m a mathematician and research scientist who likes to experimentally study mathematical physics.

I have aspirations of getting a Nobel Prize in Physics and in Medicine. I know it’s a stupid goal, or worse it’s pretty delusional, but I enjoy solving puzzles that help humanity. I’m also going for the Millenium Prize in Mathematics, so you’ll see me talk about the Hodge Conjecture a lot.

I’ve always liked topological manifolds, so I hope one day I can show you how cool they are too.

Feel free to chat with me on a livestream or join us at BLUME LABS.

Enjoy your stay.

[learn_press_profile]

I’m starting to feel better, my stomach isn’t cleared out completely but I am starting to feel that coldness that happens. I lost two pounds since yesterday, which is encouraging. Actually, if you think about it the rate at which the body loses fat when in an energy deficit is kind of a lot. 2 pounds of fat a day? Until when?

Maybe some people lose 2 pounds of fat a day depends on their energy requirements. Someone like me can lose that much a day because I’m very large, just like people who are obese can lose like 10 pounds a day or something.

Hm, I know I’m fat for my height. I may land within the BMI range, but I’m overweight. It’s not really a concern of vanity (though it is) as much as it is, I can see what’s happening to my body because my weight is too high.

For one thing, my knees are shot. There was fat depositing around my knees that shouldn’t take long to clear once the body taps into it. Stretch marks of course, but I get them from just having dry skin in general. Discoloration from enhanced blood flow to fat areas, and something I’d like to call the butt flap. Some may find this to be aesthetically pleasing but I think it’s symptom of too much fat on my ass. The cellulite obviously doesn’t help it, and also the hyperpigmentation from the heat and friction. My legs feel hot, that’s another indicator that I’ve put on too much weight in some area.

Yes, there is objective beauty just like there is objective health. The problem people have is that they confuse objective with standard. People are trying to standardize beauty, not objectify it. Everyone has an objectively beautiful version of themselves, literally everyone. What’s happening in society right now is that people are attempting to find it, but are inappropriately inferring with biochemical processes. For example, fat transfers in theory should reject. I’d put them on the level of organ transplants, and while there isn’t an immediate immune system failure, there is something to be said about various types of fat in various areas.

As a kid I always wanted to transfer the fat from my thighs to my breasts, and I thought about this for years. But I believe we can use viral structures (probably some sort of puzzle fit topologically) to recode how a person grows in various parts. Yeah, I’m actually sure of this.

That’s one benefit of all this budding virology research, is that we will have the biochemical tools to augment without invasive surgeries. This is going to say money on equipment, healing, and a hell of a lot of other things.

I’ll admit it to myself here, that I’ve slipped back into a period of non productivity so my research and theories have been lacking. It’s also a bit of mental exhaustion, as I’ve been trying to push virology research since 2017, and constructed a theoretical lab and all of that, and really am tired of fighting for my right to practice in this lab. Eh, forgive me, I tend to be more dramatic on extended fasts.

– Blume, MD, PhD

Mental state: at least 5 days extended fast, autophagy increase

[learn_press_profile]

In 2017 I was so concerned for my mental health, believing what I was seeing was wrong or that I was psychotic, that I dropped out of a math phd program because I became depressed and isolated feeling like I saw a level of reality that no one else did.

I started selling my things, and slowly making it so that I would move out of Seattle because I had kept saying a virus was going to hit Seattle. A Chinese virus, I kid you not.

I went to several doctors but never told them of my theories because when I wrote them on Reddit, I was called schizophrenic. Someone even said “It’s like I’m watching A Beautiful Mind but in real life” and that sat with me… for a while.

A friend of mine who was an undergrad at Princeton actually listened to my theories when I felt I had no one else to talk to, and then a guy I was dating said Princeton was a good school, so I left Seattle for Princeton before the virus shut everything down.

While in graduate school, I started studying biochem and microbiology, because I wanted to understand what viruses are and then I discovered that medical science knows nothing about bacteria or viruses, that germ theory was wrong, and that we collectively needed to go back to Botany to understand how viruses work, particularly neuroviruses.

I was still fucked up mentally, and couldn’t communicate to my graduate program what was happening, but in 2019, I told my boyfriend at the time that everything was going to be moved online and that’s when I bought a Surface Pro on craigslist, to prepare for indefinite online instruction. I attempted to show students at the UW the benefits of the technology and I even talked to my real analysis prof about how cool it is (I miss him he’s awesome).

But the graduate program eventually didn’t know what to do with me. I was seemingly insane, depressed and antisocial. I felt like there were more important things to study besides pure mathematics (I was studying differential geometry, algebraic geometry and category theory) and felt that my classmates were simply using mathematics to escape from the world.

…So I left. And I came to Princeton to study Physics, so that I can apply my out-of-this-crazy-world pattern recognition to Medicine. I knew that Princeton has a strong analysis and fluid modeling program, and I have researched many of the professors in the mathematics department and their work on Navier Stokes solely for this purpose of diagnostic medical technology.

I created mAAd Academy first to study schizophrenia, and then eventually psychopathy, where I created a theory of psychopathic autoimmunity.
Now here I am, after experimenting with drugs, diet and pharmacology, I have put myself into remission, despite the collective ignorance of doctors around me.

See, Descartes was a fine mathematician, great even. But his duality of body and mind has so insidiously poisoned medicine that people believe their psychology malady to be disconnected from the physical vessel they inhabit. I have theories of medicine and psychiatry that I feel need to be tested, so that diagnostic medicine can improve for everyone involved.

Princeton has state-of-the-art labs and technology and is a sort of center to many other great institutions on the east coast. I like that type of connectedness, and felt Seattle was a bit too isolated for my liking. I want to collaborate with more scholars in various fields, for my work is highly interdisciplinary.

Mental State: zero-carb ketogenic diet for approximately two weeks

[learn_press_profile]

okay, facebook looks more like twitter so now i can speak properly.
so here’s the thing. i don’t remember who i used to be so anyone who knows me from high school especially i don’t know who that person is, but i’m not her. i’m someone else. whatever, i’ll explain that another time.
anyway, so you know i study mathematics right. well, it got to a point in my phd program where i was really wondering WHY mathematicians were doing anything at all.
some time ago, at least 2013 where i have it documented, i wanted to understand why i got everything i wanted in life. i mean really, if it wanted it, i got. no ariana.
so i started studying eastern philosophy and discovered the tao of physics. great book.
i deliberately focused on mathematical physics, because it so easily intersected with what i was interested in, so i took a manifold theory course over and over and over. i still wasn’t fluent in manifold theory, but i knew enough to interpolate/extrapolate to make conjectures about how things are governed in physics.
the first thing i did was solve navier stokes. part of this was to get back and my boyfriend for dumping me. i wanted to prove to him that i’m more intelligent than him but was pretending to be stupid so that he could like me. if i’m from african, then why aren’t i white? type shit.
okay, so i found the solution to navier stokes one night while staying in Fine Hall. Fine Hall looks like a dick, i’m not even kidding you. and i’m a hypersapiosexual.
so anyway…
i want my goddamn Fields Medal. that’s the first demand.

Mental State: vegan diet with heavy cannabis usage

[learn_press_profile]

“What kind of Physics are you studying? Are you studying now that school is out? You better be! How did you start auditing classes? Nice to meet you, I’m Jasmine.”

“Hello Jasmine. Wow ur studying Mathematical Physics, that’s soo cool. Are you a grad student at Princeton? I am interested in gravitational physics. Well I wont be able to to attend virtual classes cause I am NOT an official student. So I have to figure out something soon.”

“I’m a grad student at UW, but I just moved to Princeton yesterday. I want to attend classes here just like you, but with the spring semester being virtual, I just decided to continue studying on my own, but right now I need to study Physics and it seems you and I both want to be in the Physics PhD program (I’m in a Math program now, that has a weak math/physics department). I’ve been looking for someone to study with for some time now, but I must admit I’m hardcore when it comes to this stuff, as I have aspirations to win a Nobel Prize.”

“Well, I am pretty confident that I can get one before you do. I travelled all the way from Texas to NJ solely because Princeton University had the Auditing program. For the last 2 years I had been sneaking into classes and listening to lectures, most of the Professors think I am an actual student cause they have seen attend all their classes without missing any. Yeah, we both have one goal as of now, study for GRE physics and get into PhD program..”

“Yeah, exactly.”

“May I ask you where you live? Would you like to meet at the campus now?How about this?, give me a puzzle to solve, and if I solve it soon then you will know that I am an intellectual and you should feel safe to meet.”

>”The fact that you even requested a puzzle is enough for me.”

“Lol hahaha”

“I’m at Fine Hall.”

“How did u get in?”

“I walked up to the door, said to myself ‘someone will be here soon’ and then waited. 5 minutes later, a student came and I walked in with him.”

“Haha, I cant believe u r as crazy as I am…. See you in 30mins.”

“Alright.”

The guy who opened the door for me, coincidentally, is named Dor. He is a probability grad student at Princeton. The guy who I met in Fine Hall… well let’s just say our relationship didn’t work out so well.

See alongside this desire to be great, is the desire to express myself in every dimension of my existence, and that includes sexuality. So when I met this guy, I wanted to study with him, but of course he wanted something else.

I meet this guy online within a day of moving to Princeton who also came to Princeton to study physics and was seemingly interesting. The first night he said, “You seem pretty smart, not Princeton smart, but…” I should have took that as a red flag. Listen here: any man who insults or belittles my intelligence is threatened by it. I don’t care what they tell you, I’ve talked to enough insecure men to see the pattern. Eventually he revealed himself to be my intellectual inferior, as I would literally see him go crossed-eyed anytime I talked about Gauge theory or even something as simply as the homotopy group for S1. That’s not to say he wasn’t trying, yeah he tried me a couple of times.

Over time he started getting pushy, and I obliged, but eventually saw that he wasn’t serious about physics and I don’t do well with milquetoast, I’m lactose and gluten intolerant. I blocked him on and off when he pissed me off, until the day I wanted to buy his keyboard from him to write my mixtape. We fucked once, okay? I regret it, he asked me again months later and when I said no, he started to see more of what I was about.

I had been so obsessed with fluid dynamics that all I attracted were thirsty or wishy-washy men. Let’s just say I wasn’t so Stoked about it.

We’ll revisit this relationship more later.

Mental State: high carb diet, adderall dose

[learn_press_profile]