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PROFESSOR: Simple harmonic oscillator. So what is there about this simple harmonic oscillator? Well, it's a classical system that you understand perfectly well. An oscillator, a spring with a mass oscillates and has an energy, which is the kinetic energy plus the potential energy, and that's p squared over 2m plus 1/2 m omega squared x squared. And this may be a tiny bit unfamiliar, this way of writing it. But you may recall that omega is equal to the square root of k over m, the so-called spring constant, in which the potential in terms of k would be 1/2 k x squared. And that's the potential energy stored in a spring that you stretch at distance x. That's the total energy of a harmonic oscillator. So when physicists starting with quantum mechanics in the '20s decided, let's do a harmonic oscillator, a quantum harmonic oscillator, they had to invent the Hamiltonian. And the Hamiltonian they invented was a simple one. They looked at that and said, h...

The problem with our simple multicore system is that there is no communication when the value of a shared variable is changed. The fix is to provide the necessary communications over a shared bus that's watched by all the caches. A cache can then "snoop" on what's happening in other caches and then update its local state to be consistent. The required communications protocol is called a "cache coherence protocol". In designing the protocol, we'd like to incur the communications overhead only when there's actual sharing in progress, i.e., when multiple caches have local copies of a shared variable. To implement a cache coherence protocol, we'll change the state maintained for each cache line. The initial state for all cache lines is INVALID indicating that the tag and data fields do not contain up-to-date information. This corresponds to setting the valid bit to 0 in our original cache implementation. When the cache line state is EXC...

JUDY HOYT: It's very simple, but doesn't fully capture all of the reality. The simplest analytic expression that captures profiles reasonably well is the Pearson four, which has four moments, and those moments are generally tabulated in tables. We also presented the idea of Monte Carlo or numerical solutions, for example, Monte Carlo simulation, which is quite accurate. And another thing called the Boltzmann transport equation solution. The other thing we mentioned is that there's this process called ion channeling. Ion channeling itself is quite a challenge in calculating profiles. Calculating the profiles pretty accurately into amorphous solids, or amorphous materials, is reasonably routine. But once you have to model ion channeling, it gets a little tricky. Today I want to cover some things that we didn't get a chance to talk about. We never even talked about, last time, the physics of the modeling of the ion implantation process, that is the physical e...