I have seen some texts mention axial heat dispersion as being different to axial heat conduction, in that dispersion is typically 'undesirable' heat transfer. What is the difference between the two?

For example, here is an energy balance to a fluid:

https://imgur.com/gallery/N0LinL9

I guess the first term on the right is the axial heat dispersion term? Why is there a need to define heat dispersion as being different from heat conduction?

Hey, I had a set of questions pretty much all regarding dispersion relations and deriving them for particles on my homework, and I'm pretty stuck. Any help would be greatly appreciated!

(a) What is the dispersion relation of a non-relativistic particle in free space? Derive its group velocity and phase velocity in terms of the velocity of the particle.

(b) What is the dispersion relation of a relativistic particle in free space? Derive its group velocity and phase velocity in terms of the velocity of the particle.

(c) What is the dispersion relation of a massless particle in free space? Derive its group velocity and phase velocity in terms of the particle’s velocity, the speed of light.

(d) If an electron and a proton have the same non-relativistic kinetic energy, which particle has the larger de Broglie wavelength?

Starting with D, my approach was that since it's non-relativistic, we can apply E = p^2/2m -> p = sqrt(2Em), and then the wavelength is h/sqrt(2Em). Since the mass of a proton is greater than an electron, the electron has a greater De Broglie wavelength. Is my line of reasoning correct?

As for deriving the dispersion relation of each of the listed particles, I really have no idea where to start -- any tips would be greatly appreciated. From what I know, I should be trying to find the angular frequency as a function of the wavenumber, so I would be finding w(k), and then to get the group/phase velocity I would compute dw/dk and w/k, respectfully. But I have no idea what equations I should start out with for each. Does anyone have an idea? Thanks!

Let’s say I’ve 9 complex scalar fields governed by coupled nonlinear PDEs. And Hamiltonian density contains contributions from all of these 9 fields. How do I get the dispersion relation(s) for such a system?

Edit: forgot to mention that these scalar fields don’t evolve unitarily i.e. their norm isn’t a conserved charge of the system. So I think i*dphi/dt is not equal to omega * phi

So I’m doing an question looking at the dispersion relation for a 1d chain with 2 different ‘spring constants’ as to model single and double bonds.

Finding the relationship isn’t too bad and one may graph it as following

https://i.imgur.com/3R00hPt.jpg

Now a final part of the question asks how would changing the relative lengths of the bonds affect my result. My thinking tells me that it would be unchanged as firsts one may see the intersections don’t depend on the distance between atoms. And moreover the brilliouin zone is pi/a to -pi/a, but if one alters the relative length then surely a would be the same and thus the brillouin zone would be the same.

I feel like I may be missing something though so any help is much appreciated

I get the distinction between phase- and group velocity, but I don't understand how we find the group velocity of a wave packet from the dispersion relation.

Let's say we're given a wave packet with a Gaussian envelope and we know the dispersion relation of the medium the wave travels through. Then the group velocity is the derivative of the dispersion relation, with respect to the wave number.

But the group velocity is then a function of the wave number, is it not? So when we represent the wave packet as a Fourier series, each of the harmonic waves that make up the wave packet has its own group velocity, right? (I realize upon writing this that it kinda makes sense if each harmonic wave has a group velocity, because the entirety of a harmonic wave moves with a certain speed, and this is the group (and phase) velocity of the wave)

But we can talk about the group velocity of the whole wave packet, which is the velocity with which the envelope moves. How does this make sense when each of the waves that make up the wave packet has its own distinct group velocity?

I know this post was a mess, but to try to clear up what I'm confused about: I don't understand how the whole wave packet can have one group velocity when the group velocity is a function of the wavelength, and the whole wave packet doesn't have one wavelength. Is it just the average of all the group velocities of the harmonic waves in the wave packet?

I am having trouble understanding this concept.

The frequency ω is plotted against the wave vector k, but how do I actually read it? Do I search for a frequency and look which modes are "(co)existing" at that frequency? Or do I pick a wave vector (a direction) and look which frequencies are allowed for these values of k? I can probably read it both ways, but where is cause and effect exactly?

Here's what I know: Let's assume a 2D case with a simple Brillouin Zone Γ-X-Y-Γ. The sections of the dispersion relation correspond to values of k, where Γ denotes the point where k is very small and the wavelength λ is very large. Traveling along the x-axis is basically like traversing the edges of the Brillouin Zone, covering all possible directions of the wave vector.

1. Suppose, a dispersion branch for Γ-X has two possible frequencies. What is the "real world meaning" of that? Do both these modes exist at a certain excitation frequency?
2. Now assume there are two different branches that occur at the same frequency inside Γ-X. Does that make it any different than case 1 where the same branch has one frequency twice?
3. So for example, does Γ-X tell me the size of the wavelength propagating in that direction?

Hi everyone,

I'm a first year physics PHD student, and in my QM class I had a problem where I had to show that graphene has a linear dispersion relation close to the Dirac Points, where the positive energy bands and negative energy bands touch. This linear dispersion is analogous to the linear dispersion that massless particles have. So, I was wondering is there a deep connection here? Or is this just a coincidence?

The nearly free electron model of a lattice gives a dispersion relation for a 1D chain of equally spaced atoms that looks like this. But what would happen to that dispersion relation if every other atom was displaced by a small amount in the same direction?

So far I've tried to think of this through comparison with the 2D case. Where the Brillouin zone boundary is further away in the (1,1) direction. The logic being that, considering any one atom, there will now be an atom to one side that's closer than the atom to the other side, meaning the Brillouin zone is not symmetrical.

What I can't work out is how this change affects the wavefunction. The electron bands arise as a result of the periodic boundary conditions which give two possible standing waves: one with electron distributions centred on the ionic potential minima, and one with electron distributions centred between the atoms, on the ionic potential maxima (thus two energy bands). Will an uneven spacing change this wavefunction?

As far as I can tell - no, since the spacing of the atoms plays no role in deriving the wavefunction (we just consider a box with the dimension of the lattice). So we end up with one set of atoms for which the electron distributions look the same, and a second set of atoms (the displaced ones) for which the electron distributions are now slightly off-center from the periodic potential minima and maxima. The result is then that the dispersion relation is no longer symmetrical, in one direction (say +k) we have a narrower band gap (due to the displacement of the periodic potential), and in the other direction (-k) we have the original band gap.

Recently a group reported a negative effective mass in the paper Negative mass hydrodynamics in a spin-orbit–coupled Bose-Einstein condensate.

As I understand it, this negative mass comes from the equation, derived from the dispersion relation, m = 1/k_ex * 1/(∂²ω/∂k²).

They showed that this negative mass exhibits many unusual phenomena, including accelerating in the opposite direction of applied force and "the breaking of parity and of Galilean covariance."

My question is: does this negative mass appear or count as negative mass in the stress-energy tensor of general relativity?

(And of particular interest, as it relates to the creating an energy-density lower than the vacuum for a hypothetical Alcubierre drive?)

I'm working through a problem set and I'm stumped on this question.

Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width?

How do I even go about this. I know how to find Ψ(x, t) using fourier theorem. However is there any easier way to find the function and width from the dispersion relation?

So I've been working on this lab and I'm not sure how to derive the error for this particular equation. The equation is:

n = cos(Dmin/2) + cot(A/2)sin(Dmin/2)

where n is the refractive index, A is the apex angle of the prism, and Dmin is the minimum deviation angle for each wavelength.

Hi everyone, first time poster, but I was wondering whether everyone else have noticed an increased media presence over the subject of UFO’s and such. My point and theory is that with the release of the mandated UFO report by the 2020 Corona Care Package passed last December, the Fed has had their hand forced on the release of this info. In order to counter that, a rapid, steady release of carefully tailored media has been introduced into the public.

Again, first time poster here. If there are holes in this theory, let me know and I’d be happy to discuss it with you.

Book 2

Book 3

I want to start this with a brief message about myself for those of you that don't follow me.

There is a lot of FUD about me that I would like to dismiss.

I think this is an important step so that my work and the work of many others who have helped me along the way. Is not judged on my personality or profession, but by it's quality and adherence to supporting evidence.

Many of you were likely unaware of my existence or never gave me a glance due to the fact that I did Technical Analysis on a "highly manipulated" stock.

So here is my GME story,

Exactly one year ago, to the day, I entered my first position on GME. It was November 17^(th),2020 and GME opened at $11.5, after following DFV's posts for a few weeks I decided that his analysis was solid (far better than anything else I had read on that sub in my couple years lurking there), Bought in Feb.19th 20c and 500 shares. I will never forget inputting those orders, it changed my life and many of you probably have that same memory.

I began at first to comment and then get more involved with community as a whole I liked watching the streams but found them to be disingenuous, I never felt that AMC was the play and I still don't. So I settled on warden, he was obviously inexperienced at TA and didn't have a lot of market knowledge, but it was cool to have a place to hang out and talk my favorite stock.

When warden announced he was leaving to handle personal matters I decided that I didn't want the daily posts to end. I thought they helped people hodl and provided a calm grounded narrative of what the stock was doing everyday. With a lot of people returning to work I considered this valuable and tried my hand at it. As it grew keeping up with the barrage of questions became daunting so as per many daily followers request I started a YT stream.

It was fun and small I got to answer questions and help apes better understand the markets, we had fun. many of the people that were with me those first few weeks are still around today.

I never did it to make money, GME had already assured that wouldn't be an issue. But, I had to eventually face the fact that there was a real cost to the time I took away from my job trading, and with most of my holdings still in GME I decided to monetize my stream. The support from the people that c

Preface

Over the past year I’ve spent countless hours outside my career and familial responsibilities independently researching and writing as part of ongoing effort to debunk the portrayal of Retail Investors by news outlets as bad-faith, reckless market participants through a fact-based understanding of how the collapse of Greensill and then Archegos Capital groups were related events triggered by a short squeeze in the bond market that left Credit Suisse holding a €1.5 billion bag - a narrative that remains unreported by financial reporters to this day.

Until recently part of my overarching theory involved Archegos utilizing a Convertible Bond Arbitrage strategy referred to as Chinese Hedging by investing in tranches of Greensill-issued, Credit Suisse-syndicated loans with the goal of profiting off the demise of companies during bankruptcy auctions. The financial instruments employed by Archegos allowed them to avoid cross-broker margining, obtain obscene leverage and led me to believe Credit Suisse silently cultivated a Credit Insurance Bubble through the operation of a “shadow CLO market” that only became visible once the Archegos assets were liquidated and publicly repriced via SOFR.

Then I decided to read Structured Credit Products: Credit Derivatives and Synthetic Securitisation, 2nd Edition | Wiley during a few vacation days last week and some important realizations dawned on me:

1. It was Capital Structure Arbitrage, not Convertible Bond Arbitrage, that Bill Hwang practiced through the use of Total Return Swaps (as suggested by earlier reports and the Credit Suisse legal review of Archegos)
2. A

Hi all. I’m from Ohio and staying in Denver for the week. I’ve been researching dispersed camping in the area. I understand there’s lots of great places all over but I’m primarily concerned about driving to them and leaving safely. I’m in a compact Nissan rental car and I don’t trust it at all going up and down steep or treacherous forest service roads, especially considering I’m doing this completely alone.

Are there any well known spots I could check out that are easily accessible? I’m willing to drive up to 3 hours from Denver. I’d love to find a somewhat well travelled area that is known for being easy access. Worst case scenario is that I reserve a site at a state park and have to pay for it.

Also, what are the odds that the fire ban is lifted by 10/8? I’ve read mixed things on this. Not being able to build a fire kills some of the fun.

Thanks for any help you can provide.

DISCLAIMER: Don’t think of this post as a theory. It’s purely based on a head-canon and speculation and as such shouldn’t be considered as anything more. It's simply here as a (hopefully) fun read.

I don’t think this will turn out to be case but there is a rather large amount of hints pointing towards the fact that Luffy’s Devil Fruit is actually not the Gomu Gomu no Mi fruit but rather something else. There have always been theories surrounding Luffy’s Devil Fruit not actually being the Rubber Fruit, I’ve never paid much attention to it but in the light of multiple recent reveals I changed my tune a bit.

The Game Changer

https://preview.redd.it/r84tkxts5wb81.png?width=854&format=png&auto=webp&s=f781f0936d5bd74b1f78b2fa653421d02a765699

So, in Chapter 1037 we get the Gorosei hyping up the existence of a Devil Fruit that hasn’t “Awakened” for centuries and seemingly it did now. Clearly, this Devil Fruit is supposed to be something special and something of utmost importance. Besides the obvious pick for the fruit being Zunisha, which I don’t think it’s the case considering we don’t know about any Devil Fruit that it ate, I decided to have some fun with this notion.

So, in my mind there could only be a handful of people in possession of this fruit, the two main suspects being Blackbeard (Yami Yami no Mi) and Luffy (Gomu Gomu no Mi). I would expect nothing less from this fruit other than it being either Main Protagonist’s or Main Villain’s devil fruit judging by how much it’s importance has been played up.

https://preview.redd.it/iq3bu9cu5wb81.png?width=787&format=png&auto=webp&s=cee083d3e6c190ddbb85bfbace191e51cf73bddd

Another big thing revealed by these five is that they hid the real name (identity) of the fruit by calling it something else. This is a rather interesting notion because this has been debated in the fandom but always dismissed as hearsay or nonsense. Well now this seems like a possibility.

Note*: The Devil Fruit that Gorosei are talking about doesn’t necessarily have to be Gomu Gomu no Mi, but the notion that there exist a Devil Fruit that had its real name hidden opens up the possibility for other Devil Fruits to have the same done to them.*

Why Gomu Gomu no M

This post is an in depth analysis of a massive trade I made this year.

It will teach you how to evaluate trading opportunities like a professional.

This post is going to go through the trade from start to finish, with the hopes that it gives you some insight as to what it takes to find a really great edge in the market.

Now, full disclosure. This is a trade that was brought to my attention by a fried of mine. In late august he shared a really interesting idea with a ton of alpha and in this post I will be taking you through how he found it, the thesis he came up with and how he priced it out.

And to give you an idea of how big this trade was, between those I personally knew who were in the trade, we had a combined -30,000 vega exposure.

Note: If you want to read all the parts of my options guide, click here for a list of my posts.

The Opportunity:

In July and August of 2021 was when tensions with China really started to grow. The Evergrande crisis was in full swing, companies were under pressure from the Chinese government, and foreign relations with China seemed a bit more uncertain than usual.

KWEB down 35% when we began looking into this trade

We saw Chinese stocks take a massive hit, down about 35% in just a few weeks.

The trade involved selling volatility on KWEB, which is the China Internet Index.

It consists of China based companies whose primary business is focused on internet products/services (Similar companies to Google, FB, Twitter, Amazon, etc).

At first glance, a high level of volatility seems pretty justified. But remember, high volatility and expensive volatility are not the same thing. For example, implied volatility could be too high.

Most traders would't go near a situation like this...

But it is precisely these types of situations that can create opportunity for us to find really big edges.

You see, markets are pretty efficient. There are many smart players. But when things get shaken up, efficiency decreases and a few dollars fall through the cracks for smart traders to scoop up.

Understanding the opportunities around distressed market situations

Before we get into the trade research, we need to understand the scenario.

Here's an analogy I u

Larry Swedroe

The Incredible Shrinking Alpha

• Beta is a measure of a stock or market volatility in relation to the overall market. 1 = standard market risk. 2 = 2x the market risk, IE your portfolio will move 2x the market. Beta = volatility
• Alpha – The excess return of an investment relative to the return of a benchmark index is the investment's alpha
  • 20% of active managers got positive alpha in the 90's. That number is down to 2%
  • Why – The market has become more efficient. It is harder to exploit. What were sources of "alpha" are gone, dramatically reducing the ability to generate alpha. The remaining competition is going to get better and better because the men and women left standing are more skillful than the people who were playing before." 90% of trading is done by institutional investors that know what they are doing. And more money is chasing that shrinking pool of alpha that is available.
  • Taking more risks in your portfolio (IE – Leverage) doesn't not increase your alpha.
• Active management is a zero-sum game. For every winner, there must be a loser. And usually that loser is an individual investor. And more people are going toward passive management so there are less "fish" at the table to exploit
• You cannot rely on active managers to get you excess returns. You have a 1/50 chance of picking the right person.
  • This evidence shows this is true in all asset classes. Small, Large, Value, Foreign, Bonds, etc.
• You can't forecast where the market is going. Don't try to time the market.
  • Focus on what you can control. Costs, Diversify, and Tax efficiency
• Do not buy a home as an investment. It is place to live.
• Once the information is readily available, prices already reflect this and it is too late to act
• Don't buy individual stocks
• Do not buy ETN (Exchanged Traded Note) you are taking on credit risk which you are not compensated for. ETN investors with Lehman Brothers lost 85% when the company failed
• Overvaluation of stocks tend to persist longer than undervaluation. Why? More difficult and risky for the investor to short a stock
• Sinclair - "It is difficult to get a man to understand something, when his salary depends on his not understanding it"
• Markets are highly efficient in the sense that available information is rapidly digested and reflected in stock prices
• What was once alpha, now bec

Hey guys, massive Yang Guy here and I recently collided with the quandary of how 1000 dollars would be distributed to people without bank accounts;like the homeless,and people who don’t have access to a bank like the Amish. Does anybody have a definitive answer to this?

P.S -PLEASE GO CHECK OUT THE 2nd H3H3 PODCAST ANDREW WAS ON!!

be polite

Please don’t call participants in this post “shills.” There are real people you are talking to here and some of the comments have caused users to delete their insights and stop participating.

That’s not cool. Keep it cool.

tl;dr / summary

The Marshall Fire currently burning now covered in snow, known as "the most destructive fire in Colorado history," is directly over the top of known plutonium contamination, generated by radioactive waste leaking from barrels, courtesy of the Rocky Flats Plant. This facility manufactured the bulk of the plutonium pits (nuclear weapons triggers) in the height of the Cold War. In the past, strong wind events were known to spread radioactive particulates from this site and activists -- including the very FBI agent who led the historic raid on the Rocky Flats Plant -- have been sounding the alarm on this inevitability for years.

This story is a breathtaking example of the truth being stranger than fiction. In a series of events from the 1950s all the way up to the present day, there have been a series of cover-ups by the U.S. Department of Energy, its subcontractors Dow and Rockwell, the Justice Department, and at least two generations of property development powerhouses.

The clean-up effort was originally projected to take 65 years and $37 billion to do properly, but after only 10 years and $7 billion (most of which went to administrators), the clean-up effort was heralded as a success and the superfund site was opened up for both property development and recreation.

One might argue the clean-up effort was half-assed or even deliberately negligent. For example only the top 3 feet of contaminated soil was cleaned up, even though contamination is known to be much deeper and natural processes routinely bring up soil from 16 feet and below. This is the case even when excluding criminal dumping and incineration of radioactive waste clandestinely undertaken by the plant. (As an aside, uncooperative employees were known to have been deliberately exposed to "infinity levels" of radiation.) For nearly the last 20 years, there has been insufficient testing and monitoring of radioactive contamination in the area, which again is driven by commercial interests in th

I am having trouble understanding this concept.

The frequency ω is plotted against the wave vector k, but how do I actually read it? Do I search for a frequency and look which modes are "(co)existing" at that frequency? Or do I pick a wave vector (a direction) and look which frequencies are allowed for these values of k? I can probably read it both ways, but where is cause and effect exactly?

Here's what I know: Let's assume a 2D case with a simple Brillouin Zone Γ-X-Y-Γ. The sections of the dispersion relation correspond to values of k, where Γ denotes the point where k is very small and the wavelength λ is very large. Traveling along the x-axis is basically like traversing the edges of the Brillouin Zone, covering all possible directions of the wave vector.

1. Suppose, a dispersion branch for Γ-X has two possible frequencies. What is the "real world meaning" of that? Do both these modes exist at a certain excitation frequency?
2. Now assume there are two different branches that occur at the same frequency inside Γ-X. Does that make it any different than case 1 where the same branch has one frequency twice?
3. So for example, does Γ-X tell me the size of the wavelength propagating in that direction?

I am having trouble understanding this concept.

The frequency ωω is plotted against the wave vector kk, but how do I actually read it? Do I search for a frequency and look which modes are "(co)existing" at that frequency? Or do I pick a wave vector (a direction) and look which frequencies are allowed for these values of kk? I can probably read it both ways, but where is cause and effect exactly?

Here's what I know: Let's assume a 2D case with a simple Brillouin Zone ΓΓ-X-Y-ΓΓ. The sections of the dispersion relation correspond to values of kk, where ΓΓ denotes the point where kk is very small and the wavelength λλ is very large. Traveling along the x-axis is basically like traversing the edges of the Brillouin Zone, covering all possible directions of the wave vector.

1. Suppose, a dispersion branch for ΓΓ-X has two possible frequencies. What is the "real world meaning" of that? Do both these modes exist at a certain excitation frequency?
2. Now assume there are two different branches that occur at the same frequency inside ΓΓ-X. Does that make it any different than case 1 where the same branch has one frequency twice?
3. So for example, does ΓΓ-X tell me the size of the wavelength propagating in that direction?

Hi everyone, Bob here,

This is going to be part 2 of the series where we check out how things are lining up. I really feel like our wrinkles are coming together nicely with the DD we are independently doing, and arriving at very similar conclusions. In this chapter, We will be reviewing some choice DD and making some really neat connections.

https://preview.redd.it/39nrny3r9mb81.jpg?width=500&format=pjpg&auto=webp&s=c08fc380d92ef16c0cadfb584169ad23e47e9c59

PS, get jacked, because this DD has been reviewed by some of the greatest wrinkly minds I know of before posting. Hope you learn something, and gain some wrinkles yourself - god knows we need ‘em.

Table of Contents

I will be breaking this up into a couple posts because reddit is retarded - so retarded you cannot post over 40,000 characters per post. I guess they never anticipated the level of autism we could muster. 🤷🏽‍♂️. I hope you enjoy the first part of this series.

Looking for Part 1? Go Here!

Chapter 1:

• 1.0 - Recap on understanding the T+ cycles and how they work, along with some insight to market mechanics

1. 1.1 - T+ Cycles & How They Work
2. 1.2 - Supplemental Liquidity Deposits
3. 1.3 - CBOE Futures Cycles
4. 1.4 - Key Terms

In This Chapter:

• 2.0 - Notable Theories & Observations

1. 2.1 - Leenixus SLD Theory
2. 2.2 - Gherkinit Futures Theory
3. 2.3 - Zinko83 Variance Swaps
4. 2.4 - Turdfurg23 Heartbeats
5. 2.5 - My Own Observations
6. 2.6 - Tying it All Together

• 3.0 - Conclusions

1. 3.1 - For The Wrinkles
   1. 3.1-🌈🐻 - Is Moass Inevitable? - An Exercise in Rationality
   2. 3.1-🚀🦧 - Is Moass Possible? And Could it Be Near?
2. 3.2 - For The Smoothest Among Us (Yes there’s a TADR)

• 69.420 - Disclaimers & Sources