An article relayed by the ASEE highlights something researchers have known for years – the boundaries between fields are coming down:
MIT Promotes Convergence as Model for 21st Century Research
At first I thought this might imply that people with interdisciplinary knowledge, like me :-), will be necessary to facilitate the teaming of super-specialists. That is, people acting analogously to catalysts, matching networks, surfactants, etc. However, I realize that it’s much bigger; it’s global, and it’s universal (essentially by diffusion). The global availability of information in this era is allowing the diffusion of disparate knowledge to everyone.
Consider the papers published by researchers at CERN… I saw at least one with 50+ authors.
While I agree with recognizing all contributors, it is increasingly apparent to me that a prevalent and perhaps necessary way to “succeed,” “stand out,” or have an “advantage,” will be to withhold information – to create or maintain barriers — to be exclusive. Trade secrets, what-have-you. Why patent something? You have to bother with litigation – the patent is written as broadly as possible, but its protection requires “pockets” as deep as possible ($$$). Maybe that’s a new metric for IP success: (Claimed Scope)*Capital. Measuring the scope could be challenging.
As fields intersect, this is why I love open software and designs. There’s inherent scalability and mutual respect in sharing. I wonder, though, what the world will be like in 20+ years. The culture of community innovation may stay, but what will be the scarce resource, the differentiating factor?
A basic but interesting fact:
At the 
point on a dispersion diagram, where 
and 
, the usual phase velocity is undefined; that is, 
.
So, what do we do when this occurs? We use L’Hospital’s rule. This yields 
. So, in the large wavelength (low momentum) and low frequency (large (rest) mass) limit, the phase velocity is mathematically identical to the group velocity – regardless the dispersion relation. In an interesting whiteboard discussion with Saeed Mohammadi, this realization seemed to be helpful.
When 
, the “original” or “root” modes (e.g. “acoustic” rather than “optical” phonons) have infinite temporal duration and spatial extent. This seems like a point of modal equilibrium. It would be interesting to check whether operating points on a dispersion curve transition toward 
when transient phenomena are considered. This point represents the “smoothest” real-(phase)space solution, which should be the proper direction for gradient descent over total energy for a general physical PDE.
I’ll go ahead and sling this out… a realization is that the group velocity, (effective)mass, etc. lose significance when spatiotemporal “texture” disappears.
Read more…
I often think about how our world reflects us, and vice versa. For instance, consider the reciprocity inherent in mass media, and how we might effectively look through the TV screen and at a blurry image of ourselves: society at-large. It’s “media as our looking glass.”
TV: “The View” and Adult Diapers
Advertisements during Oprah or The View are very different from those during football, Glee, Wipeout … prime time. Marketing companies have intently studied the viewership, and so the ads are targeted to have greatest return. I can reasonably suspect that an above average number of incontinent adults, or adult diaper-wearers (hmm, or maybe adult diaper purchasers), etc. are sitting in front of TVs watching “The View” at that moment when the commercial airs.
Google: Facebook and Babies
Today I typed “how do” into Google, and its relatively new “instant” feature displays the top few search queries, I suppose the few that are most prevalent (maybe even my suspected locale, “Peachtree City” on the left sidebar). It appears that Googlers most commonly want to know two things: how facebook works, and how to get pregnant. I guess you still can’t actually get pregnant by facebook, but maybe that’s a market-ready next step.
Google searches beginning with "how do"
Google searches beginning with "why do b"
I’m not sure what else Google is going to tell me, and I’m not really sure exactly what it means, but I’m really curious about people self-educating through the web.
In a group presentation I gave this week, I showed the math (now improved with a few corrections) for characteristics of a wave equation in general media (i.e. over a periodic basis). It is well known that Fourier techniques can be applied in partial differential equations to represent distributions of concentration, heat, electric charge, etc. This is especially appropriate for crystalline materials with well-defined periodic structure, but it is extensible to general media.
The first step was to reduce Newton’s 2nd Law from tensor form to a 1-D form, i.e. the propagation of longitudinal waves along x. (A nice feature of acoustical treatments in general, is that its formulation permits waves of general polarization, including longitudinal. Electromagnetic waves do not, except in the presence of media which can impart phase front tilt.)
I’ll eventually give the math here (and hopefully it will pass muster in my thesis), but it turns out that spatial periodicity of the material stiffness gives rise to a complex (mathematical sense) wave equation having orthogonal components. It represents a coupled heat equation and wave equation, where the dissipation term is converse to our usual expectations; it is (without coefficients):
Now there are several details and other terms which appear, but this snippet captures a form which many might find surprising. After visualizing the spatially periodic characteristics of the general PDE, I believe this has improved my understanding of dispersion diagrams: why they are generally complex (again, mathematical sense), and how we design devices using “meta” materials, and PxCs.
This investigation of periodicity-induced modal diffusion may only be novel to me, but I just haven’t seen this phenomenon described in simple terms before. See the references for some particularly impenetrable notation describing dispersion and mode coupling … but no explicit mention of inherent diffusion equation(s).
Read more…
Here’s something I’ve been curious about since the day it was constructed: the use of copper panels as a facade for a new building on Georgia Tech campus. While I understand its symbolic value as an engineering material, particularly in microelectronics, I do question its aesthetic use in new construction on a campus championing compliance with LEED standards. In my (apparently) opinionated mind, this is a highly visible waste of a precious resource.
Recently the Marcus Nanotechnology Building (known as the NRC) on the Georgia Tech campus won an award for its use of giant perforated copper panels around its exterior walls. The article is here:
http://www.copper.org/applications/architecture/awards/homepage.html
A quote:
Copper was selected for its sustainable, naturally weathering, low-maintenance and aesthetically pleasing qualities.
I’m at least a little annoyed about the use of the term “sustainable” in reference to the extracting, purifying, rolling, perforating, and mounting of architectural copper as a building facade.
