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STUDENT: So you're probably all familiar with the field measured in this paper here by Shrodinger, which is a quantum theory. And you surely also know that the students have a lot of problems visualizing it, and understanding its behavior in some intuitive way. For example, you know the tunneling effect. And you won't expect a classical cat to just tunnel through potential wall. What I am going to show you in this presentation is an algorithm called the split operator Fourier transform algorithm, which can be used to describe quantum tunnel evolution, and therefore, for example, the tunneling effect. And I think that it also might be interesting for you as material scientists, on the one hand, because you might be interested in time evolution of your properties, especially for nanosystems, quantum systems. But on the other hand, I will show you iteration of this algorithm which can also be used to derive other algorithms, like the [INAUDIBLE] algorithm. And you al...

You're standing at a traffic intersection. And you start to accelerate when the light turns green. Suppose that your acceleration as a function of time is a constant for some time interval t less than t one. And after that, it's zero for a time after t one less than t less than some time t two. At the exact same instant the light turns green, a bicyclist is coming through the intersection. And the bicyclist has some initial speed and is braking with an acceleration of minus b two for the entire time interval t two. And at time t two, the bicyclist comes to rest exactly where you are located. And we also know some initial conditions. So our initial conditions in this problem are that you're accelerating b one at a rate two meters per second squared. And you do this for time t one equals one second. And the bicyclist comes into the intersection. We'll call that b two naught. That's the initial speed of the bicyclist at three meters per second. And the qu...

you're so not feeling so uh might so how much do you follow if i speak if i speak italian you should try it is up to now because your favorite your favorite dish so so you also you ask that you know when you when you when you want to when you go when when you have somebody for example colloquial right and you want uh you're going to a restaurant and then you've never been and you've been with somebody that has been there yes you have them in this restaurant it's tricky with the apostrophe you always have to kind of give it that little okay um pomodoro foreign okay is around you could actually have a throw up at me it's gonna be so it's it's much nicer to say so we'll do tiramisu uh we'll go i guess i guess we go through the ingredients when we're when we're over there and there's an important component that actually is is is is relevant i guess culturally for an italian which is that we need coffee so we're gonna we...

You think you're happy? I'm happy. I'm very happy. What we will do, today is wrap up phase diagrams, make some comments about the final exam, and then we're going to get some people that aren't associated with class are going to come in, they will pass out paperwork and do the course evaluations. And, we'll get you out of here at 11:55. Before I go any further, draw your attention to another IAP subject. If you're looking for something to do during January, and this will be offered by myself and my postdoc, Patrick Trapa. We are going to offer a lab subject without a lab. It's part of an experiment that we are conducting for the National Science Foundation to see if large classes such as these that don't have a lab experience can get much of the lab experience, that is to say, planning for discovery, preparation of the background information, and then mining the data from data sets that are in the public domain, and then analyzing the d...

If you're driving down the highway and want to see how fast you're going, you look down at your speedometer. If you're in a lab and want to see how fast a chemical reaction is going, it's a little more complicated. In this video we'll look at a few factors that influence the speed of chemical reactions. This video is part of the Equilibrium video series. It is often important to determine whether or not a system is at equilibrium, to do this we must understand how a system's equilibrium state is constrained by its boundary and surroundings. Hi, my name is George Zaidan and I'm a graduate of the chemistry department here at MIT. Before watching this video, you should have a basic understanding of chemical equilibrium. After watching this video, you will be able to: Understand how reaction rate is influenced by reactant concentration Explain how reaction rates change as a system establishes equilibrium, AND Predict relative equilibrium concentrat...

Since you're enrolled in this course, let's assume that you have decided on, or perhaps are already engaged in, a managerial or professional career. And that you are developing, or have already developed the knowledge and skills necessary to do the job. That's great, but don't stop there. Experts agree that it will take a special set of competencies to succeed in tomorrow's organizations, which will be even more globalized, digitized, collaborative, and agile than those we see today. Many have written on this topic. One of the best sources, we think, is a small monograph published by the Institute of the Future, titled, The Future of Work Skills 2020. Here is a brief synopsis of the 10 competencies that the Institute suggests will be essential for your career success and the years ahead. First, relating to globalization. The Institute stresses the need for cross-cultural competency, which has a couple of key components. One is the ability to work effec...

all right you're probably wondering why there's so many pipes out here um back in um back in 1985 80 actually earlier in 93 84 we uh we had we had just we had discovered the sewage plume we were beginning to get a feeling for what it looked like and everything else and um one of the big questions at the time in in the hydro groundwater hydrology was the rate at which contaminants disperse you know how how quickly will if you put in a if you had a spill from a septic tank or a you know fuel spill or whatever else and and it got in the aquifer and it begins to migrate with the natural groundwater flow how quickly would it get diluted and dispersed to the point where it wouldn't be a problem and there were a lot of ideas about how quickly that happened and what caused it and what they what a number of folks were able to demonstrate is that the primary cause of the dispersion in groundwater unlike in surface waters or in the atmosphere which is turbulence there...

PROFESSOR: Hi. Well, if you're ready, this will be the other big side of calculus. We still have two functions, as before. Let me call them the height and the slope: y of x and the slope, s of x. Function one and function two. That's what calculus is about. And earlier, we figured out how to go from function one if we knew that, how to find the slope. Of course, it was easy when function one was just a straight line. Then the slope was just up divided by across. But when function one was curving, we had to do something. We had to take just a small distance across, a small distance up and divide, and then let small get smaller and smaller. The result of that was function two, the derivative. Today, we're going the other way. We know the slope. We know s of x, and we want to find the height, y of x, of the graph. We know how the graph is sloping at every point, and we have to put all that information together to find its height. OK. Let me say the easiest way to...