Discussion:
This Week's Finds in Mathematical Physics (Week 293)
(too old to reply)
John Baez
2010-02-06 08:18:29 UTC
Permalink
Also available at http://math.ucr.edu/home/baez/week293.html

February 6, 2010
This Week's Finds in Mathematical Physics (Week 293)
John Baez

This week I want to list a bunch of papers and books on n-categories.
Then I'll tell you about a conference on the math of environmental
sustainability and green technology. And then I'll continue my story
about electrical circuits. But first...

This column started with some vague dreams about n-categories and
physics. Thanks to a lot of smart youngsters - and a few smart
oldsters - these dreams are now well on their way to becoming reality.
They don't need my help anymore! I need to find some new dreams. So,
"week300" will be the last issue of This Week's Finds in Mathematical
Physics.

I still like learning things by explaining them. When I start work at
the Centre for Quantum Technologies this summer, I'll want to tell you
about that. And I've realized that our little planet needs my help a
lot more than the beautiful structure of the universe does! The deep
secrets of math and physics are endlessly engrossing - but they can
wait, and other things can't. So, I'm trying to learn more about ecology,
economics, and technology. And I'd like to talk more about those.

So, I plan to start a new column. Not completely new, just a bit
different from this. I'll call it This Week's Finds, and drop the
"in Mathematical Physics". That should be sufficiently vague that I
can talk about whatever I want.

I'll make some changes in format, too. For example, I won't keep
writing each issue in ASCII and putting it on the usenet newsgroups.
Sorry, but that's too much work.

I also want to start a new blog, since the n-Category Cafe is not the
optimal place for talking about things like the melting of Arctic ice.
But I don't know what to call this new blog - or where it should
reside. Any suggestions?

I may still talk about fancy math and physics now and then. Or even
a lot. We'll see. But if you want to learn about n-categories, you
don't need me anymore. There's a *lot* to read these days. I mentioned
Carlos Simpson's book in "week291" - that's one good place to start.
Here's another introduction:

1) John Baez and Peter May, Towards Higher Categories, Springer, 2009.
Also available at http://ncatlab.org/johnbaez/show/Towards+Higher+Categories

This has a bunch of papers in it, namely:

* John Baez and Michael Shulman, Lectures on n-categories and cohomology.
* Julia Bergner, A survey of (infinity,1)-categories.
* Simona Paoli, Internal categorical structures in homotopical algebra.
* Stephen Lack, A 2-categories companion.
* Lawrence Breen, Notes on 1- and 2-gerbes.
* Ross Street, An Australian conspectus of higher categories.

After browsing these, you should probably start studying
(infinity,1)-categories, which are infinity-categories where all the
n-morphisms for n > 1 are invertible. There are a few different
approaches, but luckily they're nicely connected by some results
described in Julia Bergner's paper. Two of the most important
approaches are "Segal spaces" and "quasicategories". For the latter,
start here:

2) Andre Joyal, The Theory of Quasicategories and Its Applications,
http://www.crm.cat/HigherCategories/hc2.pdf

and then go here:

3) Jacob Lurie, Higher Topos Theory, Princeton U. Press, 2009.
Also available at http://www.math.harvard.edu/~lurie/papers/highertopoi.pdf

This book is 925 pages long! Luckily, Lurie writes well. After
setting up the machinery, he went on to use (infinity,1)-categories
to revolutionize algebraic geometry:

4) Jacob Lurie, Derived algebraic geometry I: stable infinity-categories,
available as arXiv:math/0608228.

Derived algebraic geometry II: noncommutative algebra, available as
arXiv:math/0702299.

Derived algebraic geometry III: commutative algebra, available as
arXiv:math/0703204.

Derived algebraic geometry IV: deformation theory, available as
arXiv:0709.3091.

Derived algebraic geometry V: structured spaces, available as
arXiv:0905.0459.

Derived algebraic geometry VI: E_k algebras, available as
arXiv:0911.0018.

For related work, try these:

5) David Ben-Zvi, John Francis and David Nadler, Integral transforms
and Drinfeld centers in derived algebraic geometry available as
arXiv:0805.0157.

6) David Ben-Zvi and David Nadler, The character theory of a complex
group, available as arXiv:0904.1247.

Lurie is now using (infinity,n)-categories to study topological
quantum field theory. He's making precise and proving some old
guesses James Dolan and I had:

7) Jacob Lurie, On the classification of topological field theories,
available as arXiv:0905.0465.

Jonathan Woolf is doing it in a somewhat different way, which I hope
will be unified with Lurie's work eventually:

8) Jonathan Woolf, Transversal homotopy theory, available as
arXiv:0910.3322.

All this stuff is starting to transform math in amazing ways. And I
hope physics, too - though so far, it's mainly helping us understand
the physics we already have.

Meanwhile, I've been trying to figure out something else to do. Like
a lot of academics who think about beautiful abstractions and soar
happily from one conference to another, I'm always feeling a bit
guilty, wondering what I could do to help "save the planet". Yes, we
recycle and turn off the lights when we're not in the room. If we all
do just a little bit... a little will get done. But surely mathematicians
have the skills to do more!

But what?

I'm sure lots of you have had such thoughts. That's probably why Rachel
Levy ran this conference last weekend:

9) Conference on the Mathematics of Environmental Sustainability and
Green Technology, Harvey Mudd College, Claremont, California,
Friday-Saturday, January 29-30, 2010. Organized by Rachel Levy.

Here's a quick brain dump of what I learned.

First, Harry Atwater of Caltech gave a talk on photovoltaic solar
power:

10) Atwater Research Group, http://daedalus.caltech.edu/

The efficiency of silicon crystal solar cells peaked out at 24% in
2000. Fancy "multijunctions" get up to 40% and are still improving.
But they use fancy materials like gallium arsenide, gallium indium
phosphate, and so on. The world currently uses 13 terawatts of power.
The US uses 3. But building just 1 terawatt of these fancy
photovoltaics would use up more rare substances than we can get our
hands on:

11) Gordon B. Haxel, James B. Hedrick, and Greta J. Orris, Rare earth
elements - critical resources for high technology, US Geological Survey
Fact Sheet 087-02, available at http://pubs.usgs.gov/fs/2002/fs087-02/

So, if we want solar power, we need to keep thinking about silicon and
use as many tricks as possible to boost its efficiency.

There are some limits. In 1961, Shockley and Quiesser wrote a paper
on the limiting efficiency of a solar cell. It's limited by
thermodynamical reasons! Since anything that can absorb energy
can also emit it, any solar cell also acts as a light-emitting diode,
turning electric power back into light:

12) W. Shockley and H. J. Queisser, Detailed balance limit of
efficiency of p-n junction solar cells, J. Appl. Phys. 32 (1961)
510-519.

13) Wikipedia, Schockley-Quiesser limit,
http://en.wikipedia.org/wiki/Shockley%E2%80%93Queisser_limit

What are the tricks used to approach this theoretical efficiency?
Multijunctions use layers of different materials to catch photons of
different frequencies. The materials are expensive, so people use a
lens to focus more sunlight on the photovoltaic cell. The same is true
even for silicon - see the Umuwa Solar Power Station in Australia.
But then the cells get hot and need to be cooled.

Roughening the surface of a solar cell promotes light trapping, by
large factors! Light bounces around ergodically and has more chances
to get absorbed and turned into useful power. There are theoretical
limits on how well this trick works. But those limits were derived
using ray optics, where we assume light moves in straight lines. So,
we can beat those limits by leaving the regime where the ray-optics
approximation holds good. In other words, make the surface
complicated at length scales comparable to the wavelength at light.

For example: we can grow silicon wires from vapor! They can form
densely packed structures that absorb more light:

14) B. M. Kayes, H. A. Atwater, and N. S. Lewis, Comparison of the
device physics principles of planar and radial p-n junction nanorod
solar cells, J. Appl. Phys. 97 (2005), 114302.

Also, with such structures the charge carriers don't need to travel
so far to get from the n-type material to the p-type material. This
also boosts efficiency.

There are other tricks, still just under development. Using quasiparticles
called "surface plasmons" we can adjust the dispersion relations to
create materials with really low group velocity. Slow light has more
time to get absorbed! We can also create "meta-materials" whose
refractive index is really wacky - like n = -5!

I should explain this a bit, in case you don't understand. Remember,
the refractive index of a substance is the inverse of the speed of
light in that substance - in units where the speed of light in vacuum
equals 1. When light passes from material 1 to material 2, it takes
the path of least time - at least in the ray-optics approximation.
Using this you can show Snell's law:

sin(theta_1)/sin(theta_2) = n_2/n_1

where n_i is the index of refraction in the ith material and theta_i
is the angle between the light's path and the line normal to the
interface between materials.

Air has an index of refraction close to 1. Glass has an index of
refraction greater than 1. So, when light passes from light to glass,
it "straightens out": its path becomes closer to perpendicular to the
air-glass interface. When light passes from glass to air, the reverse
happens: the light bends more. But the sine of an angle can never exceed
1 - so sometimes Snell's law has no solution. Then the light gets
stuck! More precisely, it's forced to bounce back into the glass.
This is called "total internal reflection", and the easiest way to see
it is not with glass, but water. Dive into a swimming pool and look
up from below. You'll only see the sky in a limited disk. Outside
that, you'll see total internal reflection.

Okay, that's stuff everyone learns in optics. But *negative* indices
of refraction are much weirder! The light entering such a material
will bend *backwards*.

Materials with a negative index of refraction also exhibit a reversed
version of the ordinary Goos-Hanchen effect. In the ordinary version,
light "slips" a little before reflecting during total internal
reflection. The "slip" is actually a slight displacement of the
light's wave crests from their expected location - a "phase slip".
But for a material of negative refractive index, the light slips
*backwards*. This allows for resonant states where light gets
trapped in thin films. Maybe this can be used to make better solar
cells.

Next, Kenneth Golden gave a talk on sea ice, which covers 7-10% of the
ocean's surface and is a great detector of global warming. He's a
mathematician at the University of Utah who also does measurements in
the Arctic and Antarctic. If you want to go to math grad school
without becoming a nerd - if you want to brave 70-foot swells, dig
trenches in the snow and see Emperor penguins - you want Golden as
your advisor:

15) Ken Golden's website, http://www.math.utah.edu/~golden/

Salt gets incorporated into sea ice via millimeter-scale brine
inclusions between ice platelets, forming a "dendritic platelet
structure". Melting sea ice forms fresh water in melt ponds atop the
ice, while the brine sinks down to form "bottom water" driving the
global thermohaline conveyor belt. You've heard of the Gulf Stream,
right? Well, that's just part of this story.

When it gets hotter, the Earth's poles get less white, so they absorb
more light, making it hotter: this is "ice albedo feedback". Ice
albedo feedback is *largely controlled by melt ponds*. So if you're
interested in climate change, questions like the following become
important: when do melt ponds get larger, and when do they drain out?

Sea ice is diminishing rapidly in the Arctic - much faster than all
the existing climate models had predicted. There's a lot less sea ice
in the Antarctic, mainly in the Wedell Sea, and there it seems to be
growing, maybe due to increased precipitation. In the Arctic, winter
sea ice diminished in area by about 10% from 1978 to 2008. But summer
sea ice diminished by about 40%! It took a huge plunge in 2007,
leading to a big increase in solar heat input due to the ice albedo
effect. See:

16) Donald K. Perovich, Jacqueline A. Richter-Menge, Kathleen
F. Jones, and Bonnie Light, Sunlight, water, and ice: Extreme Arctic
sea ice melt during the summer of 2007, Geophysical Research Letters,
35 (2008), L11501. Also available at
http://www.crrel.usace.army.mil/sid/personnel/perovichweb/index1.htm

There's a lot of interesting math involved in understanding the
dynamics of sea ice. The ice thickness distribution equation was
worked out by Thorndike et al in 1975. The heat equation for ice and
snow was worked out by Maykut and Understeiner in 1971. Sea ice
dynamics was studied by Kibler.

Ice floes have two fractal regimes, one from 1 to 20 meters, another
from 100 to 1500 meters. Brine channels have a fractal
character well modeled by "diffusion limited aggregation". Brine
starts flowing when there's about 5% of brine in the ice - a kind of
percolation problem familiar in statistical mechanics. Here's what it
looks like when there's 5.7% brine:

17) Kenneth Golden, Brine inclusions in a crystal of lab-grown sea ice,
http://www.math.utah.edu/~golden/7.html

Nobody knows why polycrystalline metals have a log-normal distribution
of crystal sizes. Similar behavior, also unexplained, is seen in sea
ice.

A "polynya" is an area of open water surrounded by sea ice. Polynyas
occupy just .001% of the overall area in Antarctic sea ice, but create
1% of the icea. Icy cold catabatic winds blow off the mainland,
pushing away ice and creating patches of open water which then refreeze.

There was anomalous export of sea ice through Fran Strait in the 1990s,
which may have been one of the preconditions for high ice albedo feedback.

20-40% of sea ice is formed by surface flooding followed by refreezing.
This was *not included* in the sea ice models that gave such
inaccurate predictions.

The food chain is founded on diatoms. These form "extracellular
polymeric substances"- goopy mucus-like stuff made of polysaccharides
that protects them and serves as antifreeze. There's a lot of this
stuff; the ice gets visibly stained by it.

For more, see:

18) Kenneth M. Golden, Climate change and the mathematics of transport
in sea ice, AMS Notices, May 2009. Also available at
http://www.ams.org/notices/200905/

19) Mathematics Awareness Month, April 2009: Mathematics and Climate,
http://www.mathaware.org/mam/09/

Next, Julie Lundquist, who just moved from Lawrence Livermore Labs
to the University of Colorado, spoke about wind power:

20) Julie Lunquist, Department of Atmospheric and Oceanic Sciences,
University of Colorado, http://paos.colorado.edu/people/lundquist.php

With increased reliance on wind, the power grid will need to be
redesigned to handle fluctuating power sources. In the US, currently,
companies aren't paid for power they generate in excess of the amount
they promised to make. So, accurate prediction is a hugely important
game. Being off by 1% can cost millions of dollars! Europe has
different laws, which encourage firms to maximize the amount of wind
power they generate.

If you had your choice about where to build a wind turbine, you'd
build it on the ocean or a very flat plain, where the air flows rather
smoothly. Hilly terrain leads to annoying turbulence - but sometimes
that's your only choice. Then you need to find the best spots, where
the turbulence is least bad. Complete simulation of the Navier-Stokes
equations is too computationally intensive, so people use fancier tricks.
There's a lot of math and physics here.

For weather reports people use "mesoscale simulation" which cleverly
treats smaller-scale features in an averaged way - but we need more
fine-grained simulations to see how much wind a turbine will get. This
is where "large eddy simulation" comes in.

A famous Brookhaven study suggested that the power spectrum of wind
has peaks at 4 days, 1/2 day, and 1 minute. This perhaps justifies an
approach where different time scales, and thus length scales, are
treated separately and the results then combined somehow. The study
is actually a bit controversial. But anyway, this is the approach
people are taking, and it seems to work.

Night air is stable - but day air is often not, since the ground is
hot, and hot air rises. So when a parcel of air moving along hits a
hill, it can just shoot upwards, and not come back down! This means
lots of turbulence.

Eddy diffusivity is modeled by Monin-Obukhov similarity theory:

21) American Meteorological Society Glossary, Monin-Obukhov similarity theory,
http://amsglossary.allenpress.com/glossary/search?id=monin-obukhov-similarity-theory1

The wind turbines at Altamont Pass in California kill more raptors
than all other wind farms in the world combined! Old-fashioned wind
turbines look like nice places to perch, spelling death to birds.
Cracks in concrete attract rodents, which attract raptors, who get
killed. The new ones are far better.

For more:

22) National Renewable Energy Laboratory, Research needs for winds
resource characterization, available as
http://www.nrel.gov/docs/fy08osti/43521.pdf

Finally, there was a talk by Ron Lloyd of Fat Spaniel Technologies.
This is a company that makes software for solar plants and other
sustainable energy companies:

23) Fat Spaniel Technologies, http://www.fatspaniel.com/products/

His talk was less technical so I didn't take detailed notes. One big
point I took away was this: we need better tools for modelling! This
is especially true with the coming of the "smart grid". In its
simplest form, this is a power grid that uses lots of data - for
example, data about power generation and consumption - to regulate
itself and increase efficiency. Surely there will be a lot of math
here. Maybe even the topic I've been talking about lately: bond graphs!

But now I want to talk about some very simple aspects of electrical
circuits. Last week I listed various kinds of circuits. Now let's go
into a bit more detail - starting with the simplest kind: circuits
made of just wires and linear resistors, where the currents and
voltages are independent of time.

Mathematically, such a circuit is a graph equipped with some extra data.
First, each edge has a number associated to it - the "resistance". For
example:

o----1----o----3----o
| | |
| | |
2 3 2
| | |
| | |
o----3----o----1----o

Second, we have current flowing through this circuit. To describe this,
we first arbitrarily pick an orientation on each edge:

o---->----o---->----o
| | |
| | |
V V V
| | |
| | |
o----<----o---->----o

Then we label each edge with a number saying how much "current"
is flowing through that edge, in the direction of the arrow:

2 3
o---->----o---->----o
| | |
| | |
3V V1 V 3
| | |
| | |
o----<----o---->----o
2 -3

Electrical engineers call the current I. Mathematically it's good
to think of I as a "1-chain": a linear combination of oriented edges
of our graph, with the coefficients of the linear combination being
the numbers shown above.

If we know the current, we can work out a number for each vertex of
our graph, saying how much current is flowing out of that vertex,
minus how much is flowing in:

2
1 o---->----o---->----o 0
| | |
| | |
V V V
| | |
| | |
-5 o----<----o---->----o 0
-2

Mathematically we can think of this as a "0-chain": a formal linear
combination of the vertices of our graph, with the numbers shown above
as coefficients. We call this 0-chain the "boundary" of the 1-chain
we started with. Since our current was called I, we call its boundary
delta I.

Kirchhoff's current law says that

delta I = 0

When this holds, let's say our circuit is a "closed". Physically this
follows from the law of conservation of electrical charge, together
with a reasonable assumption. Current is the flow of charge. If the
total current flowing into a vertex wasn't equal to the amount flowing
out, charge - positive or negative - would be building up there. But
for a closed circuit, we assume it's not.

If a circuit is not closed, let's call it "open". These are interesting
too. For example, we might have a circuit like this:

x
|
|
V
|
|
o---->----o
| |
| |
V V
| |
| |
o----<----o
| |
| |
V V
| |
| |
x x

where we have current flowing in the wire on top and flowing out the
two wires at bottom. We allow delta I to be nonzero at the ends of
these wires - the 3 vertices labelled x. This circuit is an "open
system" in the sense of "week290", because it has these wires dangling
out of it. It's not self-contained; we can use it as part of some
bigger circuit. We should really formalize this more, but I won't
now. Derek Wise did it more generally here:

24) Derek Wise, Lattice p-form electromagnetism and chain field theory,
available as gr-qc/0510033.

The idea here was to get a category where chain complexes are morphisms
in a category. In our situation, composing morphisms amounts to gluing
the output wires of one circuit into the input wires of another. This
is an example of the general philosophy I'm trying to pursue, where
open systems are treated as morphisms.

We've talked about 1-chains and 0-chains... but we can also back up
and talk about 2-chains! Let's suppose our graph is connected - it is
in our example - and let's fill it in with enough 2-dimensional
"faces" to get something contractible. We can do this in a god-given
way if our graph is drawn on the plane: just fill in all the holes!

o---------o---------o
|/////////|/////////|
|/////////|/////////|
|//FACE///|///FACE//|
|/////////|/////////|
|/////////|/////////|
o---------o---------o

In electrical engineering these faces are
often called "meshes".

This give us a chain complex

delta delta
C_0 <-------- C_1 <-------- C_2

and a cochain complex:

d d
C^0 -------> C^1 -------> C^2

As I've already said, it's good to think of the current I as a 1-chain,
since then

delta I = 0

is Kirchoff's current law. Since our little space is contractible the
above equation implies that

I = delta J

for some 2-chain J called the "mesh current". This assigns to each
face or "mesh" the current flowing around that face.

An electrical circuit also comes with a third piece of data, which I
haven't mentioned yet. Each oriented edge should be labelled by a
number called the "voltage" across that edge. Electrical engineers
call the voltage V. It's good to think of V as a 1-cochain, which
assigns to each edge the voltage across that edge.

Why a 1-cochain instead of a 1-chain? Because then

d V = 0

is the other basic law of electrical circuits - Kirchhoff's voltage
law! This law says that the sum of these voltages around a mesh is
zero. Since our little space is contractible the above equation
implies that

V = d phi

for some 0-cochain phi called the "electrostatic potential". In
electrostatics, this potential is a function on space. Here it
assigns a number to each vertex of our graph.

Since the space of 1-cochains is the dual of the space of 1-chains, we
can take the voltage V and the current I, glom them together, and get
a number:

V(I)

This the "power": that is, the rate at which our network soaks up
energy and dissipates it into heat. Note that this is just a fancy
version of formula for power that I explained in "week290" - power is
effort times flow.

I've given you three basic pieces of data labelling our circuit: the
resistance R, the current I, and the voltage V. But these aren't
independent! Ohm's law says that the voltage across any edge is the
current through that times the resistance of that edge. But this
remember: voltage is a 1-cochain while current is a 1-chain. So
"resistance" can be thought of as a map from 1-cochains to 1-chains:

R: C^1 -> C_1

This lets us write Ohm's law like this:

V = RI

This, in turn, means the power of our circuit is

V(I) = (RI)(I)

For physical reasons, this power is always nonnegative. In fact,
let's assume it's positive unless I = 0. This is just another way of
saying that resistance labelling each edge is positive. It can be
very interesting to think about circuits with perfectly conducting
wires. These would give edges whose resistance is zero. But that's a
bit of an idealization, and right now I'd rather allow only *positive*
resistances.

Why? Because then we can think of the above formula as the inner
product of I with itself! In other words, then there's a unique inner
product on 1-cochains with

(RI)(I) = <I,I>

In this situation

R: C^1 -> C_1

is the usual isomorphism that we get between a finite-dimensional
inner product space and its dual. (For this statement to be true,
we'd better assume our graph has finitely many vertices and edges.)

Now, if you've studied de Rham cohomlogy, all this should start
reminding you of Hodge theory. And indeed, it's a baby version
of that! So, we're getting a little bit of Hodge theory, but in
a setting where our chain complexes are really morphisms in a category.

There's a lot more to say, but I want dinner.

-----------------------------------------------------------------------

Quote of the Week:

"So many young people are forced to specialize in one line or another that
a young person can't afford to try and cover this waterfront - only an old
fogy who can afford to make a fool of himself. If I don't, who will?" -
John Wheeler

-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at

http://math.ucr.edu/home/baez/

For a table of contents of all the issues of This Week's Finds, try

http://math.ucr.edu/home/baez/twfcontents.html

A simple jumping-off point to the old issues is available at

http://math.ucr.edu/home/baez/twfshort.html

If you just want the latest issue, go to

http://math.ucr.edu/home/baez/this.week.html
Dirk Bruere at NeoPax
2010-02-06 16:49:38 UTC
Permalink
John Baez wrote:
> Also available at http://math.ucr.edu/home/baez/week293.html

> February 6, 2010
> This Week's Finds in Mathematical Physics (Week 293)
> John Baez
...

> First, Harry Atwater of Caltech gave a talk on photovoltaic solar
> power:
>
> 10) Atwater Research Group, http://daedalus.caltech.edu/
>
> The efficiency of silicon crystal solar cells peaked out at 24% in
> 2000. Fancy "multijunctions" get up to 40% and are still improving.
> But they use fancy materials like gallium arsenide, gallium indium
> phosphate, and so on. The world currently uses 13 terawatts of power.
> The US uses 3. But building just 1 terawatt of these fancy
> photovoltaics would use up more rare substances than we can get our
> hands on:

Installed PV follows a version of Moore's Law
http://technocrat.net/d/2008/5/16/41454/

If we extrapolate, it hits $1 per watt in 2023 although some companies,
notably Nanosolar, claim they can produce them for that price now. What
a lot of people seem to miss is the fact that cost/Watt will continue to
fall beyond that point to where all other forms of energy are far more
expensive.

As for being resource limited, that seems a bit pessimistic. For
example, it looks like Indium will be replaced by graphene quite soon.
In fact, it looks like everything everywhere will be replaced by graphene!

Finally, PV manufactured has been doubling every 2 years. 8 more
doublings will match global electricity use. That is, around 2026.

> 11) Gordon B. Haxel, James B. Hedrick, and Greta J. Orris, Rare earth
> elements - critical resources for high technology, US Geological Survey
> Fact Sheet 087-02, available at http://pubs.usgs.gov/fs/2002/fs087-02/
>
> So, if we want solar power, we need to keep thinking about silicon and
> use as many tricks as possible to boost its efficiency.
>
> There are some limits. In 1961, Shockley and Quiesser wrote a paper
> on the limiting efficiency of a solar cell. It's limited by
> thermodynamical reasons! Since anything that can absorb energy
> can also emit it, any solar cell also acts as a light-emitting diode,
> turning electric power back into light:
>
> 12) W. Shockley and H. J. Queisser, Detailed balance limit of
> efficiency of p-n junction solar cells, J. Appl. Phys. 32 (1961)
> 510-519.

> 13) Wikipedia, Schockley-Quiesser limit,
> http://en.wikipedia.org/wiki/Shockley%E2%80%93Queisser_limit

I don't doubt the accuracy of the calculation, although I did throw away
a couple of old magazines from 1981, Proceeding of the IEEE, that had
two articles on the limits to integrated circuit density.
One showed that for fundamental theoretical reasons channels widths
would not drop below 140nm. The other claimed 100nm. We are now at 25nm.
GIGO.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
Dirk Bruere at NeoPax
2010-02-07 13:09:12 UTC
Permalink
Dirk Bruere at NeoPax wrote:
> John Baez wrote:
>> Also available at http://math.ucr.edu/home/baez/week293.html
>
>> February 6, 2010
>> This Week's Finds in Mathematical Physics (Week 293)
>> John Baez
> ...

>
> As for being resource limited, that seems a bit pessimistic. For
> example, it looks like Indium will be replaced by graphene quite soon.
> In fact, it looks like everything everywhere will be replaced by graphene!

Which reminds me - maybe one of your new Finds will feature graphene?
It really is an incredible material from a technological POV.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
Uncle Al
2010-02-08 09:40:14 UTC
Permalink
Dirk Bruere at NeoPax wrote:
>
> Dirk Bruere at NeoPax wrote:
> > John Baez wrote:
> >> Also available at http://math.ucr.edu/home/baez/week293.html
> >
> >> February 6, 2010
> >> This Week's Finds in Mathematical Physics (Week 293)
> >> John Baez
> > ...
>
> >
> > As for being resource limited, that seems a bit pessimistic. For
> > example, it looks like Indium will be replaced by graphene quite soon.
> > In fact, it looks like everything everywhere will be replaced by graphene!
>
> Which reminds me - maybe one of your new Finds will feature graphene?
> It really is an incredible material from a technological POV.

Graphene is yesterday's news. p-Doped graphane should be a 90K
superconductor,

http://arxiv.org/abs/1002.0653

and 1-D cubic diamond much higher. 1-D hexagonal diamond,
lonsdaleite, might be barely synthetically accessible as oligomers.
Good luck with making 1-D cubic short of imploding strips of
bi-graphene in hydrogen mormal to its bedding plane.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
Dirk Bruere at NeoPax
2010-02-12 13:34:19 UTC
Permalink
http://www.physorg.com/news185093054.html

(PhysOrg.com) -- Solar cells could make fossil fuels virtually
redundant if they were cheaper, but their use of rare elements and
complex manufacturing processes makes them expensive. Now IBM Research
has developed a prototype solar cell that solves both problems, using
common, cheap elements and using an inexpensive manufacturing process.
Their paper is published in the Advanced Materials journal.

The new photovoltaic cells are known as “kesterite” cells, which are
produced using a printing technology in which a solution containing
nanoparticles is spin-coated onto a glass substrate. According to IBM
their efficiency is close to that of established solar cells.

IBM researcher David Mitzi, who is also manager of the company’s
photovoltaic science and technology department, said they wanted to
reduce the cost and use more abundant elements for thin-film
photovoltaic cells. The current technology uses the rare elements indium
and tellurium. Indium is in particularly short supply because it is also
used in the manufacture of transparent transistors and is in high demand
for flat panel display systems. By contrast IBM’s kesterite cells uses
the common elements tin (Sn), zinc (Zn), copper (Cu), selenium (Se), and
sulfur (S).

The new solar cells are also cheaper to manufacture, using a “printing”
technique that uses a hydrazine solution containing copper and tin with
nanoparticles of zinc dispersed within it. The solution is then
spin-coated and heat treated in the presence of selenium or sulfur
vapor. This process is much cheaper than the traditional manufacturing
process, which uses an expensive vacuum-based technique.

A team at the Nagaoka National College of Technology in Japan produced a
thin-film kesterite cell in 2009, which had an efficiency of 6.8 per
cent. IBM’s kesterite cell has increased the efficiency by 40 per cent.
Mitzi said they are planning to increase the efficiency above 11 per
cent, which is equal to or better than the traditional solar cells.

Solar cells contribute under 0.1 per cent of the Earth’s electricity
supply at the moment, largely due to their expense and the rarity of
their key elements. The IBM solar cell could change all of that. IBM
will patent and license the technology and says it is open to
partnerships with existing photovoltaic cell manufacturers to bring it
to the market.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
Uncle Al
2010-02-13 12:05:17 UTC
Permalink
Dirk Bruere at NeoPax wrote:
>
> http://www.physorg.com/news185093054.html
[snip]

> Mitzi said they are planning to increase the efficiency above 11 per
> cent, which is equal to or better than the traditional solar cells.
[snip]

> IBM
> will patent and license the technology and says it is open to
> partnerships with existing photovoltaic cell manufacturers to bring it
> to the market.

Average 400 W/m^2 annual desert insolation given two-axis steering of
solar panels. A middling 1 GW power plant (daytime only!) would then
require

(10^9 W)/(400 W/m^2)(0.11 cell efficiency)(0.8 facility efficiency)

28.4x10^6 m^2 for cell area alone, or 11 square miles. If overall
fabrication cost of the *power plant* is $0.05/cm^2, that will cost
$14.2 billion. If it sells energy for $0.15/Kwhr with no overhead
whatsoever, 100% profit, payback is 95 million hours (8 hr/day average
production at full rated power). At 100% profit with zero costs and
zero interest on debts, investment reaches breakeven in 32.4 years,
with MTBF of 20 years typical.

IBM doesn't even dream of being real world.

[[Mod. note -- There are several reasons why the above calculation
is unduly pessimistic:
* The correct payback period is 95 *thousand* hours, not 95 *million*
(1 GW = 1e6 Kw = $0.15e6/hour, $14.2e9 / ($0.15e6/hour) = 95e3 hours).
* The 400 W/m^2 "annual desert insolation" is already averaged over
day and night (the daytime solar flux is over 1000 W/m^2 with clear
skies; the solar flux at the top of the Earth's atmosphere is
1400 W/m^2), so the 95 thousand hours should be converted to
a calendar time using 24 hours/day instead of 8. This lowers
the breakeven time to 10.8 years.
* Continued technology improvements should lower the manufacturing
cost of solar cells over the next decade.
* A square meter of mirror costs much less than a square meter
of solar cells, so actual solar-cell power plants usually use
large mirror arrays to concentrate sunlight onto smaller
solar-cell arrays. This greatly lowers the cost/Watt.
[This reasoning doesn't apply in space, where the
cost of the cells is utterly negligible compared to
the "astronomical" cost of launching the system,
so the design optimization is for minimum mass/power,
not for minimum manufacturing-cost/power.]
-- jt]]

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
Dirk Bruere at NeoPax
2010-02-15 05:01:08 UTC
Permalink
Uncle Al wrote:
> Dirk Bruere at NeoPax wrote:
>> http://www.physorg.com/news185093054.html
> [snip]
>
>> Mitzi said they are planning to increase the efficiency above 11 per
>> cent, which is equal to or better than the traditional solar cells.
> [snip]
[[Mod. note -- 45 excessively-quoted lines snipped. -- jt]]

Real prices - retail
http://www.solarbuzz.com/ModulePrices.htm

Currently average about $4 per peak Watt, although...
"The lowest retail price for a multi-crystalline silicon solar module is
$1.98 per watt (?1.39 per watt) from a US retailer. The lowest retail
price for a mono-crystalline silicon module is also $2.37 per watt
(?1.68 per watt), from an Asian retailer."

Which from a domestic POV, and taking into account conversion and fixing
costs etc, means that the cost of PV amortized over the life of the
system is cost competitive with conventionally produced retail
electricity in large parts of Europe and the US.

And prices are only going to fall from here onwards.
At some point soon conventional power plants are not going to be able to
compete in the domestic market during the day. Nor possibly in the
industrial market if the infrastructure exists for industrial customers
to buy domestic excess.

If you have suitable engineering knowledge and are willing to put
together the system yourself you can halve the cost again.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
Jonathan Thornburg
2010-02-15 18:36:17 UTC
Permalink
[I've changed the subject line to more accurately reflect the topic
of this posting; good newsreaders should link this to the previous
thread.]

In a moderator's note earlier in this thread, I commented on some
overly-pessimistic calculations of the economics of solar power.
In this posting I'd like to expand on this a bit, touching on both
the economics and the physics:

First, the inputs:

At the top of the atmosphere, the total intensity of sunlight is 1366
W/m^2, averaged over the annual variation due to the non-circularity of
the Earth's orbit around the Sun. At a good-for-solar-power site
(relatively low levels of clouds and dust/smoke/smog/etc to block that
sunlight from getting to the Earth's surface) the intensity is over 1000
W/m^2 at the Earth's surface during daylight hours when the Sun is well
above the horizon (say 10 hours/day). A good site should be cloudy < 20%
of the time.

There are a variety of technologies by which this can be converted
to electricity. The two most-widely-used ones at present are
* Solar-thermal, in which sunlight (concentrated via mirrors) heats
the hot side of some heat engine. In practice, this means heating
some working fluid/gas. The efficiency of such a system is
ultimately limited by by the heat engine's hot/cold absolute
temperature ratio (the Carnot-cycle efficiency limit). The
cold temperature isn't going to be any colder than ambient
(and in practice will likely be significantly above ambient),
while the hot temperature is probably limited in practice by
the requirement that the (solid) walls of the working chamber
-- including transparent windows through which the concentrated
sunlight shines to heat the working fluid -- not melt or corrode
excessively.
* Solar-cells, in which sunlight (again, probably concentrated by
mirrors, because a square meter of mirror is much cheaper than a
square meter of solar cells) is directly converted to electricity.

In any such system, the concentrating mirrors can be either fixed
or sun-tracking. Sun-tracking gives higher sun intensity, but costs
more (and is more vulnerable to wind storms etc). Fixed is cheaper,
but gives lower sun intensity at the focus. One compromise which
is sometimes used in solar-thermal plants is a parabolic trough
oriented east-west, with a working-fluid pipe running along the
mirror's line focus.

The big problem for any solar power plant is that no power is produced
at night (which is at least perfectly predictable) or when it's cloudy
(which isn't predictable very far in advance, except in a statistical
sense).
[Solar cells still produce some power in cloudy
weather, but it's still much less than during
full-sunlight conditions.]
It helps a bit that power demand in most industrialized countries
is quite diurnal (low at night, high in day/evening), but still, the
solar-power supply curve (power available as a function of time) isn't
very well matched to the electric-utility-demand curve (customer demand
for power as a function of time). Long-term storage of energy on the
relevant scales (many Gigawatt-hours) is a *very* difficult problem,
i.e., all the currently-available solutions (pump water uphill, compress
air into a huge resirvoir, charge batteries, heat a molten salt) are
very expensive.

Possible solutions include:
* Statistical multiplexing, where you have a lot of solar power
plants scattered across different local-climate zones (so their
cloud covers aren't highly correlated). You can get bonus points
if you also spread your plants across multiple time zones, to match
the production and electric-utility-demand curves a bit better.
(This implies lots of long-distance power lines, although cities
in cloudy climates would need plenty of long-distance power
transmission to be solar-powered anyway.)
* Using chemical conversion cycles where sunlight drives endothermic
(energy-absorbing) chemical reactions (e.g., 2 H2O --> 2H2 + O2)
to give energy-rich products (e.g., hydrogen gas), then shipping
thyese products to places where energy is wanted. (For hydrogen
gas, the shipping infrastructure might resemble that currently
used for (possibly liquified) natural gas.) About 2 months ago
there was a news feature on such "solar fuels" in Science,
"Solar Fuels: Sunlight in Your Tank"
Science 11 December 2009:
Vol. 326. no. 5959, pp. 1472 - 1475
DOI: 10.1126/science.326.5959.1472
http://www.sciencemag.org/cgi/content/summary/326/5959/1472
(subscription required)
which reported that such systems exist at the prototype stage,
but are currently quite expensive, and still need further
(chemical-engineering) development before they're ready for
large-scale gigawatt-scale deployment.
[It's an interesting gedanken question to compare
that "further development" with that needed to go
from today's Tokamaks to practical nuclear-*fusion*
power plants, a project likely to require at least
25 years and many 10s of giga-{dollars,euros}.]

Right now oil/coal/gas are very cheap, and their global-warming
costs will be paid by (mostly poor) people far away in space and
time from those designing the plants or paying the up-front bills.
Nuclear (fission) power has historically often been subsidized by
government insurance and loan guarantees, and (for example) most
future nuclear fission power in the USA will be similarly subsidised.

Thus right now solar-power electricity is substantially (perhaps
a factor of 2-5) more expensive than oil/coal/gas/nuclear in
industrialized countries/areas.
[The economics are more favorable for solar power
in isolated areas where regular utility power isn't
available, i.e., where the competition is with Diesel
generators.]
However, the long-term trends are that solar-power technology is
rapidly developing, making solar power steadily cheaper over time,
whereas most other types of power plants are getting steadily more
expensive.
Dirk Bruere at NeoPax
2010-02-15 19:28:38 UTC
Permalink
Jonathan Thornburg wrote:

> However, the long-term trends are that solar-power technology is
> rapidly developing, making solar power steadily cheaper over time,
> whereas most other types of power plants are getting steadily more
> expensive.

The limitation for PV conversion comes down to 2 factors - efficiency
and cost per sq metre. With the former, 20% is easily achievable and to
date the most efficient are around 40%. But let's stick with a modest
20% and make a couple of assumptions. The first is that material costs
will not be major constraint. This seems reasonable given major research
into the use of alternative materials rather than rare metals like
Indium. The second assumption is that the "ultimate" fabrication process
is more like screen printing that vacuum deposition.

How cheap could our hypothetical 1 sq metre 20% efficient PV panel be
made? If we compare it to the cost of 1 sq m of LCD TV screen, which is
quite a complex bit of tech, then maybe $200. That immediately gives us
a price of $1 per peal Watt.

I suggest that making a PV panel by a printing process will ultimately
be less than one tenth of this price in genuine mass production and that
the final costs of a PV installation circa 2025 will not be determined
by the cost of panels, but by the ironwork and grid connections.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
Gerard Westendorp
2010-02-15 23:09:03 UTC
Permalink
Dirk Bruere at NeoPax wrote:
[..]

> How cheap could our hypothetical 1 sq metre 20% efficient PV panel be
> made?

One important cost factor is energy. You need quite pure silicon, made
form SiO2 (sand). This purification is unfortunately energy intensive. I
think they changed the process now, but the old process was repeatedly
melting it.

One thing that will help is making the layer very thin.

Gerard
Dirk Bruere at NeoPax
2010-02-16 08:05:57 UTC
Permalink
Gerard Westendorp wrote:
> Dirk Bruere at NeoPax wrote:
> [..]
>
>> How cheap could our hypothetical 1 sq metre 20% efficient PV panel be
>> made?
>
> One important cost factor is energy. You need quite pure silicon, made
> form SiO2 (sand). This purification is unfortunately energy intensive. I
> think they changed the process now, but the old process was repeatedly
> melting it.
>
> One thing that will help is making the layer very thin.
>
> Gerard
>
But thin film technology relies more on exotic inks than processed
Silicon. For example, Nanosolar:

http://www.nanosolar.com/technology

I have heard, but cannot verify, that they can make PV panels for
70c/Watt. However, they charge what the market can stand. The bad news
is that their ink is a pretty exotic mix that uses some rare elements.

http://en.wikipedia.org/wiki/Nanosolar

"Nanosolar claims to have produced "the world's lowest-cost solar
panel."[31] This cost has been variously reported as "cell costs [of]
only $0.36 per peak watt,"[32] a "raw uninstalled cost of solar
electricity [of] about 40 to 60 cents per watt,"[26] and an "aim to
produce the panels for 99 cents a watt."[33] It has been reported that
Nanosolar CEO Martin Roscheisen declined to comment on the $0.36 per
peak watt figure.[25] It should be noted that a cell cost of $0.36/watt
is consistent with a wholesale solar panel cost of $0.99/watt and
Nanosolar has not been criticized for being inconsistent in its claims;
rather, skeptics have expressed doubt that Nanosolar can produce a
product at the costs claimed in the foreseeable future.[25]. Meanwhile,
thin-film competitor, First Solar, has announced the achievement of
$0.98/watt panel production cost"

Ultimately, screen printing PV cells using semiconductor inks must be
the way to go. What I would like to know is the cost of the ink, per sq
metre.

Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
j***@specsol.spam.sux.com
2010-02-17 09:27:28 UTC
Permalink
In sci.physics Dirk Bruere at NeoPax <***@gmail.com> wrote:
> Jonathan Thornburg wrote:
>
>> However, the long-term trends are that solar-power technology is
>> rapidly developing, making solar power steadily cheaper over time,
>> whereas most other types of power plants are getting steadily more
>> expensive.
>
> The limitation for PV conversion comes down to 2 factors - efficiency
> and cost per sq metre. With the former, 20% is easily achievable and to
> date the most efficient are around 40%. But let's stick with a modest
> 20% and make a couple of assumptions. The first is that material costs
> will not be major constraint. This seems reasonable given major research
> into the use of alternative materials rather than rare metals like
> Indium. The second assumption is that the "ultimate" fabrication process
> is more like screen printing that vacuum deposition.

[Moderator's note: Quoted text snipped. -P.H.]

Don't forget the cost of the fail safe inverter contoller you have to
have to connect to the grid. They aren't cheap.

--
Jim Pennino

Remove .spam.sux to reply.
Yevgen Barsukov
2010-02-17 09:27:28 UTC
Permalink
[Moderator's note: Quoted text snipped. -P.H.]

On Feb 15, 1:28 pm, Dirk Bruere at NeoPax <***@gmail.com>
wrote:

> How cheap could our hypothetical 1 sq metre 20% efficient PV panel be
> made? If we compare it to the cost of 1 sq m of LCD TV screen, which is
> quite a complex bit of tech, then maybe $200. That immediately gives us
> a price of $1 per peal Watt.
>
> I suggest that making a PV panel by a printing process will ultimately
> be less than one tenth of this price in genuine mass production and that
> the final costs of a PV installation circa 2025 will not be determined
> by the cost of panels, but by the ironwork and grid connections.

1W/$ with 10% efficiency is already history, since that is why CdTe
cells are being sold for.

As for going the next order of magnitude cheaper - it is coming.
Slury custing, and no rare elements, already 9% efficiency.
See kesterite cells, Cu2ZnSn(S,Se):
http://www.physorg.com/news185093054.html

Regards,
Yevgen
Dirk Bruere at NeoPax
2010-02-18 18:34:35 UTC
Permalink
Yevgen Barsukov wrote:
> [Moderator's note: Quoted text snipped. -P.H.]
>
> On Feb 15, 1:28 pm, Dirk Bruere at NeoPax <***@gmail.com>
> wrote:
>
>> How cheap could our hypothetical 1 sq metre 20% efficient PV panel be
>> made? If we compare it to the cost of 1 sq m of LCD TV screen, which is
>> quite a complex bit of tech, then maybe $200. That immediately gives us
>> a price of $1 per peal Watt.
>>
>> I suggest that making a PV panel by a printing process will ultimately
>> be less than one tenth of this price in genuine mass production and that
>> the final costs of a PV installation circa 2025 will not be determined
>> by the cost of panels, but by the ironwork and grid connections.
>
> 1W/$ with 10% efficiency is already history, since that is why CdTe
> cells are being sold for.
>
> As for going the next order of magnitude cheaper - it is coming.
> Slury custing, and no rare elements, already 9% efficiency.
> See kesterite cells, Cu2ZnSn(S,Se):
> http://www.physorg.com/news185093054.html
>
> Regards,
> Yevgen
>

Agreed.
I am interested in the social and economic impact of daytime electricity
that is one tenth the cost of any "conventional" source. Especially if
domestic generators sell excess capacity, or even load leveling backup
in the form of batteries.

--
Dirk

http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
Dr J R Stockton
2010-02-16 08:06:10 UTC
Permalink
In sci.physics.research message <***@hate.spam.net>, Sat,
13 Feb 2010 07:05:17, Mod posted:

> ...

>[[Mod. note -- There are several reasons why the above calculation
>is unduly pessimistic:
> ...
>* A square meter of mirror costs much less than a square meter
> of solar cells, so actual solar-cell power plants usually use
> large mirror arrays to concentrate sunlight onto smaller
> solar-cell arrays. This greatly lowers the cost/Watt.
> [This reasoning doesn't apply in space, where the
> cost of the cells is utterly negligible compared to
> the "astronomical" cost of launching the system,
> so the design optimization is for minimum mass/power,
> not for minimum manufacturing-cost/power.]

OTOH, in space mirrors can be very thin - think light-sail material -
and so it could well be worth using mirrors of very little mass/area to
increase the insolation of cells of only moderately little mass/area,
thereby reducing the overall mass/power.

>-- jt]]


--
(c) John Stockton, near London. *@merlyn.demon.co.uk/?.?***@physics.org
Web <URL:http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links.
Correct <= 4-line sig. separator as above, a line precisely "-- " (RFC5536/7)
Do not Mail News to me. Before a reply, quote with ">" or "> " (RFC5536/7)
J. Clarke
2010-02-16 22:30:27 UTC
Permalink
Dr J R Stockton wrote:
> In sci.physics.research message <***@hate.spam.net>,
> Sat, 13 Feb 2010 07:05:17, Mod posted:
>
>> ...
>
>> [[Mod. note -- There are several reasons why the above calculation
>> is unduly pessimistic:
>> ...
>> * A square meter of mirror costs much less than a square meter
>> of solar cells, so actual solar-cell power plants usually use
>> large mirror arrays to concentrate sunlight onto smaller
>> solar-cell arrays. This greatly lowers the cost/Watt.
>> [This reasoning doesn't apply in space, where the
>> cost of the cells is utterly negligible compared to
>> the "astronomical" cost of launching the system,
>> so the design optimization is for minimum mass/power,
>> not for minimum manufacturing-cost/power.]
>
> OTOH, in space mirrors can be very thin - think light-sail material -
> and so it could well be worth using mirrors of very little mass/area
> to increase the insolation of cells of only moderately little
> mass/area, thereby reducing the overall mass/power.

So you've reduced the mass to practically nothing. What keeps this thing
from heading off for Epsilon Eridani or wherever? Google "light sail".
Dr J R Stockton
2010-02-18 00:31:55 UTC
Permalink
In sci.physics.research message <***@news3.newsguy.com>, Tue, 16
Feb 2010 23:30:27, J. Clarke <***@cox.net> posted:
>Dr J R Stockton wrote:
>> In sci.physics.research message <***@hate.spam.net>,
>> Sat, 13 Feb 2010 07:05:17, Mod posted:
>>
>>> ...
>>
>>> [[Mod. note -- There are several reasons why the above calculation
>>> is unduly pessimistic:
>>> ...
>>> * A square meter of mirror costs much less than a square meter
>>> of solar cells, so actual solar-cell power plants usually use
>>> large mirror arrays to concentrate sunlight onto smaller
>>> solar-cell arrays. This greatly lowers the cost/Watt.
>>> [This reasoning doesn't apply in space, where the
>>> cost of the cells is utterly negligible compared to
>>> the "astronomical" cost of launching the system,
>>> so the design optimization is for minimum mass/power,
>>> not for minimum manufacturing-cost/power.]
>>
>> OTOH, in space mirrors can be very thin - think light-sail material -
>> and so it could well be worth using mirrors of very little mass/area
>> to increase the insolation of cells of only moderately little
>> mass/area, thereby reducing the overall mass/power.
>
>So you've reduced the mass to practically nothing. What keeps this thing
>from heading off for Epsilon Eridani or wherever? Google "light sail".

I do not need to; I understand physics, including its numerical aspects
- see St Luke: Chapter 10, Verse 37, tail.

No solar-power system will be in a strictly geocentric orbit; it will be
displaced to some extent because of the momenta of the solar photons
that it absorbs and of the microwave (+-) photons that it emits.

But for solar pressure to match solar gravity, the material must "weigh"
of the order of 1.6 gsm (common paper is 80 gsm); and, in Earth orbit,
the Earth's gravity is necessarily substantially greater than the Sun's.
Details can be found on my Web site.

ISTM that there is negligible prospect of keeping the overall mass of an
SPS, per unit area of sunlight intercepted, down to anything remotely
approaching substantially less than 1.6 gsm. Radiation pressure will
probably have an observable effect on the orbit - present-day tracking
is rather accurate - but an SPS will remain orbiting Earth as desired.

--
(c) John Stockton, near London. *@merlyn.demon.co.uk/?.?***@physics.org
Web <URL:http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links.
Correct <= 4-line sig. separator as above, a line precisely "-- " (RFC5536/7)
Do not Mail News to me. Before a reply, quote with ">" or "> " (RFC5536/7)
jmfbahciv
2010-02-07 14:04:15 UTC
Permalink
[s.p.r removed]

Dirk Bruere at NeoPax wrote:
> John Baez wrote:
>> Also available at http://math.ucr.edu/home/baez/week293.html

<snip>

>> There are some limits. In 1961, Shockley and Quiesser wrote a paper
>> on the limiting efficiency of a solar cell. It's limited by
>> thermodynamical reasons! Since anything that can absorb energy can
>> also emit it, any solar cell also acts as a light-emitting diode,
>> turning electric power back into light:
>>
>> 12) W. Shockley and H. J. Queisser, Detailed balance limit of
>> efficiency of p-n junction solar cells, J. Appl. Phys. 32 (1961)
>> 510-519.
>
>> 13) Wikipedia, Schockley-Quiesser limit,
>> http://en.wikipedia.org/wiki/Shockley%E2%80%93Queisser_limit
>
> I don't doubt the accuracy of the calculation, although I did throw away
> a couple of old magazines from 1981, Proceeding of the IEEE, that had
> two articles on the limits to integrated circuit density.
> One showed that for fundamental theoretical reasons channels widths
> would not drop below 140nm. The other claimed 100nm. We are now at 25nm.
> GIGO.
>

What did they do? Multi-leave? Or is that multi-leaf?

/BAH
nuny@bid.nes
2010-02-07 07:40:33 UTC
Permalink
On Feb 6, 12:18 am, ***@math.removethis.ucr.andthis.edu (John Baez)
wrote:
> Also available athttp://math.ucr.edu/home/baez/week293.html
>
> February 6, 2010
> This Week's Finds in Mathematical Physics (Week 293)
> John Baez
>
> This week I want to list a bunch of papers and books on n-categories.
> Then I'll tell you about a conference on the math of environmental
> sustainability and green technology.  And then I'll continue my story
> about electrical circuits.  But first...
>
> This column started with some vague dreams about n-categories and
> physics.  Thanks to a lot of smart youngsters - and a few smart
> oldsters - these dreams are now well on their way to becoming reality.
> They don't need my help anymore!  I need to find some new dreams.  So,
> "week300" will be the last issue of This Week's Finds in Mathematical
> Physics.

NOOOOO! Even though I can't follow most of what you write, this is
AWFUL!

> I still like learning things by explaining them.  When I start work at
> the Centre for Quantum Technologies this summer, I'll want to tell you
> about that.  And I've realized that our little planet needs my help a
> lot more than the beautiful structure of the universe does!  The deep
> secrets of math and physics are endlessly engrossing - but they can
> wait, and other things can't.  So, I'm trying to learn more about ecology,
> economics, and technology.  And I'd like to talk more about those.
>
> So, I plan to start a new column.  Not completely new, just a bit
> different from this.  I'll call it This Week's Finds, and drop the
> "in Mathematical Physics".  That should be sufficiently vague that I
> can talk about whatever I want.

Phew! Please, I'm getting too old for shocks like that!

> I'll make some changes in format, too.  For example, I won't keep
> writing each issue in ASCII and putting it on the usenet newsgroups.
> Sorry, but that's too much work.

Where can I find it?

> The efficiency of silicon crystal solar cells peaked out at 24% in
> 2000.  Fancy "multijunctions" get up to 40% and are still improving.
> But they use fancy materials like gallium arsenide, gallium indium
> phosphate, and so on.  The world currently uses 13 terawatts of power.
> The US uses 3.  But building just 1 terawatt of these fancy
> photovoltaics would use up more rare substances than we can get our
> hands on:

> So, if we want solar power, we need to keep thinking about silicon and
> use as many tricks as possible to boost its efficiency.
>
> There are some limits.
There's also graphene showing great promise, and the recent
discovery of QM tricks chlorophyll plays to make sure every captured
photon gets used by making it possible for an incoming photon's
wavefunction to spread over many molecules.

http://www.nature.com/nature/journal/v463/n7281/abs/nature08811.html
SIlicon's limits don't apply to these newer materials.

> Nobody knows why polycrystalline metals have a log-normal distribution
> of crystal sizes. Similar behavior, also unexplained, is seen in sea ice.

Any comparison in pseudocrystalline materials?

> If you had your choice about where to build a wind turbine, you'd
> build it on the ocean or a very flat plain, where the air flows rather
> smoothly. Hilly terrain leads to annoying turbulence - but sometimes
> that's your only choice.

Savonius turbines don't care as much about turbulence as do
"conventional" propeller-style windmills, but are also less efficient.
Where's the breakeven? What does it take to convince a Kennedy that
Savinius turbines are not ugly?

> A famous Brookhaven study suggested that the power spectrum of wind
> has peaks at 4 days, 1/2 day, and 1 minute.

I see a possible correlation with the crystal size distribution
subject above. What's the size distribution of weather cells?

As for the rest, I can't make heads or tails of it.

Circuits I can analyze and build though.


Mark L. Fergerson
OwlHoot
2010-02-24 08:33:38 UTC
Permalink
On Feb 6, 8:18 am, ***@math.removethis.ucr.andthis.edu (John Baez)
wrote:
>
> ...
>
> I also want to start a new blog, since the n-Category Cafe is not the
> optimal place for talking about things like the melting of Arctic ice.
> But I don't know what to call this new blog - or where it should
> reside. Any suggestions?

Not sure how your surname is pronounced, as I've only ever seen it in
print; but if it is "Bays", how about something like "Back to Baezics" ?

Cheers

John R Ramsden
Continue reading on narkive:
Loading...