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Let's take a brief look at how to think about submitting your photographs as potential cover art in their presentations. The first thing that's essential is for you to study the journal layout to which you are submitting your image, how they might be placed in a particular cover format. Most covers these days are full bleeds. That is, the image takes up the whole cover and is therefore vertical. Some of them still have, let's say, rectangle places within the larger vertical format. But most of them are bleeds at this point. So you have to think about that when you do submit an idea for a cover. Think about where the journal's logo is placed, where additional text might be dropped. You have to take all these things into consideration to help the art director decide whether or not the image is good enough for a cover. But I do suggest not submitting a cover idea with the journal logo. Just let the folks at the journal use their imaginations. Let's start ...

PROFESSOR: So let's think of a specific virus, the coronavirus, including the case of interest today, which is the SARS-CoV-2 novel coronavirus. So this virus comes in the form of virion, which is the capsid containing RNA, which is then going to infect a cell. And the size of that virion is around 120 nanometer diameter, and it's nearly a perfect sphere. Now, the size here of 120 nanometers compared to bacteria is about 1,000 times smaller than [some] bacteria. So this actually has a very big implication in terms of how a virion can be spread from one organism to another. So the bacteria, if you recall, are the size of several microns. That's the scale of large droplets, which sediment -- or larger than that, they would begin to sediment out of the air. And we can think about transmission through coughing. Also, besides the fact that the virus is much smaller, it cannot swim. So bacteria have various means of locomotion -- cilia, flagella, et cetera, whereas ...

PROFESSOR: So let's look at a little more detail at the equilibrium size of respiratory droplets that are emitted during breathing, or coughing, or speaking. And the key idea is that these droplets are not pure liquid. As explained in the wells curve, pure droplets that are small enough will shrink completely and evaporate. However, these droplets contain a significant amount of solutes. And those solutes, in the case of mucus coming from your lungs or from your vocal cords, your nasal pharynx, are full of proteins and other macromolecules, carbohydrates. And also there are always in bodily fluids plenty of dissolved salts such as sodium and chloride or calcium or potassium ions. Also, in saliva, many of these species are present, although it's not quite as thick of a liquid. And of course, virions as well will find themselves in here, and it also constitutes solutes. So the idea is that we don't just have a pure liquid. So there is some initial volume fractio...

PROFESSOR: So let's build on this concept of diffusion of virions in droplets to understand how we would expect a size dependent infectivity of virions in different sized droplets. So an important concept in epidemiology that we will come to later is the infectivity, which is the probability that if a virion is transferred that it actually causes an infection in the host. That can be further broken down into a product of two probabilities. The first is that if the virus has escaped from the droplet, it actually causes an infection. And that's perhaps something which is roughly constant. It has to do with the physiology of the host. But then there is the escape of the virion from the droplet. And as we've already discussed, that's a strongly size dependent quantity. And from very large droplets, it's very difficult in a mucus droplet, especially, for the virion to diffuse out in a reasonable amount of time. And in fact, virions are typically found to ha...

PROFESSOR: So let's talk about the transfer of respiratory pathogens, and in particular, contagious pathogens such as viruses and bacteria, that infect the respiratory system. The way that such pathogens are normally transferred is through droplets which are emitted by respiration, which could be by just normal breathing, coughing, sneezing, et cetera. And so here is a sketch of an infected person who is undergoing respiration and is emitting droplets into the air. And so let's think about what is the fate of those droplets, what it could be. So one possibility is if the droplets are very heavy, they're just going to settle to the ground. And then they may collect on the ground or on some other surface. And then somebody else could touch that surface and transmit it, perhaps by touching their eyes or some other-- or their nose or some bodily entrance point. And that sort of transmission is called fomite transmission. So these dried up bits of droplets on the s...

Today, let's start our little look at history. We've actually been here before is sort of the theme I want to develop, because I want us to put us back as if you are entering the labor force around 1930. You've just come off what we call the roaring '20s. And while you should feel better because the economy was going so well in the 1920s and profits were up and the stock market was at record levels, you probably don't feel very optimistic. Because despite all this good news, family income was falling in the 1920s as it is today. Most of the income went to the top 10%, just as it is today in our society. And then of course 1929 comes along, and we get the Great Stock Market Crash, and everything starts to fall to pieces. At that point, over the next several years, if you were entering the labor force or an existing, more mature worker, you were expected to lose between 8% to 20% percent of your income. If you got unemployed, over 25% of the labor force,...

STUDENT: Let's talk about the Mohr's Circle, an important tool in materials science and mechanical engineering. What is Mohr's Circle, and what does it do? Assume you have a rod, and you want to break it with your hands. What can you do about it? You can pull it, compress it, or twist it. Each of these will induce a stress in the rod in a different way. And the Mohr's Circle helps you analyze this. Mohr's Circle is a graphical tool, a visual way to see how to go from one state of stress to another. Usually you are given a state of stress that you calculated from using stress equations. Then you want to find a state of stress at a new angle of orientation, or principal stresses at that orientation, or the maximum in-plane shear stresses. And Mohr's Circle allows you to draw this representative element to visualize the calculations for you. Now, let's derive the Mohr's Circle. So now we take a look at the piece of material that we cut from th...

PROFESSOR: Simultaneous eigenstates. So let's begin with that. We decided that we could pick 1 l and l squared, and they would commute. And we could try to find functions that are eigenstates of both. So if we have functions that are eigenstates of those, we'll try to expand in terms of those functions. And all this operator will become a number acting on those functions. And that's why the Laplacian simplifies, and that's why we'll be able to reduce the Schrodinger equation to a radial equation. This is the goal. Schrodinger equation has r theta and phi. But theta and phi will deal with all the angular dependents. We'll find functions for which that operator gives a number acting on them. And therefore, the whole differential equation will simplify. So simultaneous eigenstates, and given the simplicity of l z, everybody chooses l z. So we should find simultaneous eigenstates of this two things. And let's call them psi l m of theta and phi. Whe...

PROFESSOR: So let's review prominence a little bit. The first thing you want to think about is content words versus function words, all right? You see a sentence. OK. How many stresses difference-- how many levels of stressors do we have? Four, right? First one unstressed, right? So which word do you not stress? Which syllables? AUDIENCE: Function words. PROFESSOR: Function words. Function words. And when you do not stress function words, what happened? What's the most important thing? AUDIENCE: Vowels get reduced. PROFESSOR: Vowels get reduced, right? Vowels get reduced. That's the most important thing. Vowels get reduced. OK, and what happens to content words, every content word? There is some stress, right? There's some stress on every content word, which means you're not going to reduce the vowel, right? The third level, you need to find out if you put equal amount of stress on every content word, you're going to go uh-uh-uh-uh-uh-uh. You'r...