Universities started to teach Latin and Greek and rhetoric to the nobility and future priests. Latin was sort of the secret code that the super-upper class talked in.
Martin Luther was not a threat to the Popes as long as he wrote in Latin. They were sort of amused. When he started writing in German, so the the public could understand what he said, the trouble began.
Surely there's a circular shadow behind the sphere, the same diameter?
What reflection illuminates that area?
Scattering is calculated asymptotically (on an indefinitely large sphere), so the angular subtense of the scatterer goes to zero.
If the sphere were large, and you were standing close behind it, you wouldn't see anything because the scattered light would all go around you.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Chuckle, OK that's your choice. Be nice to know if you were trying to detect particle bits floating in a chamber.
Snow flakes tilted the right way, reflect much more than spheres, well that's my guess. Winter has finally come here. It's ~15F at night, light fluffy snow blows in from the lake, watching it fall down is one of life's pleasures.
10-20 F (with no wind) is the perfect winter temp.George H.
Yeah I think there will be that one special direction, but out of
2*pi steraidians... seems like a pretty good approximation to ignore it. I did try glancing angles, best done early or late in the day. You get the sun in your eyes! as well as some dim ball.George H.
It's finally snowing in the Sierras. It can be beautiful. Our cabin is a couple miles from the train track, the original transcontinental railroad route. When the snow is heavy in the pines, and the train blows its whistle, we get a beautiful, faint, muffled sound. It sounds like snow.
Here's the Truckee cam:
-- John Larkin Highland Technology, Inc The best designs are necessarily accidental.
No cam needed, driving home today it was twilight, no color; but bright sky, dark trees, with white snow blotches hanging on 'em and snow covering the ground.
George H.
For the EUV application the spheres were ~30 micron droplets of molten tin crossing a ~1m diameter chamber of low-pressure hydrogen. They were vibrating violently on account of being shot out of an orifice (as in an inkjet printer). The discussion included references to YouTube videos of water balloon cannons. ;)
The shiny-sphere approximation to this situation is pretty typical of a photon budget--there's a lot you don't know in detail at the beginning, but you can usually estimate it pretty well, and the sticking points tell you where to concentrate your experimental work.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
What a planet. We have water in all its forms. Snow, clouds, waterfalls, rainbows.
-- John Larkin Highland Technology, Inc The best designs are necessarily accidental.
That was really fun. Kind of a high point.
Astoundingly enough, we are still shipping droplet detectors and ESMs and even controllers. Three years after we were smugly and ceremonially dumped.
If you apply enough money and people and management to electronic design, it never gets done.
-- John Larkin Highland Technology, Inc The best designs are necessarily accidental.
involves the problem of transforming back into the time domain.
You need to move on. Analytical solutions were for 100 yeas ago before people had computers.
Just how do you propose to solve the dynamics of colliding , rotating charged black holes using General Relativity?
There is truly to reason to piss about with analytic solutions. In any realistic real world problem, analytic solutions just don't exist, so don't even go there
Spice solves a full SMPS in 5 secs. Take the hint......
-- Kevin Aylward
Symbolic algebra does quite well at it followed by code generation.
Sometimes there is good reason to have a decent analytic or semi analytic solution to a tricky problem to get a feel for it. I am probably amongst the last of the old school theoretical physicists in that respect so much of the modern work is numerical simulation.
Newton-Raphson needs a decent initial guess or you can bounce around forever or diverge without ever converging to the solution.
-- Regards, Martin Brown
If you're applying math to a class of problem there's not good background info available on there's good reason to solve simple cases of the problem analytically before moving on to more complex real-world cases.
That is to say to get some confirmation that your "question" is even formulated correctly and isn't returning nonsense and with an analytical solution for a simple use-case you can see pretty quickly if it's sometimes returning nonsense for otherwise valid inputs and if it is there's probably not much reason to move on to numerical techniques for more complex situations with that formulation.
If all you do is solve for specific cases of classes of problem that have already been solved then no there's probably no reason to re-invent the wheel. But academic papers AFAIK are still filled with attempts at analytic solutions to simple cases of complex novel problems cuz you have to prove to someone's satisfaction either yourself or some review board or both that your thought process on how you solve that new class of problems in general isn't stupid.
Am 27.01.2021 um 04:26 schrieb Leo Baumann:
:)
Sometimes an exact solution to a particular real-world problem isn't what you're looking for immediately what you want to know is given inputs X and conditions Y does phenomena Z happen or not and under what conditions X and Y does it happen. The state-space for X and Y may be large how will you know what inputs to try in your sim for desired effect if you don't know where to look in the first place.
Am 30.01.2021 um 13:27 schrieb Leo Baumann:
sorry - it is a 10th of the first periode of a sinus ...
my mistake ...
This will be fingers down the blackboard for many, but this is the real world.
When you are sitting there with $100k of simulation software on your desk, its *quicker* and more *cost* efficient to the company that is paying you to run a sim to confirm the output of Z=!A.b + A.!B
I don't even do C=1/2.pi.f.R on a hand held calculator. Its a complete waste of time.
The reality is, in complex systems you cannot determine what the ball park park conditions are others than trivial ones already known from inspection.
Its trivial to run 1mohm to 1GOhm, 1 point per decade. My laptop runs 100 GFlops, my work software runs multiple cores.
Your point is truly academic. When its applied in practice, it only slows things down.
This is the real world......
-- Kevin Aylward
For what purpose?
Huge equations are simply hopeless to deal with in practice. Symbolic equations are, effectively, useless for real world calculations. That is, for designing real world products in an engineering environment.
I understand your point, however the underlying assumption that one doesn't get an underlying feel for what's going on by simulation, just isn't true. The ONLY way to get a feel for what's going on in todays modern designs is by simulation. It shows 100s of effects simply impossible to discover by pad and pencil. Its just the way it is. The chances of noticing a single significant effect by a closed form solution, taking months to work out, is about zero.
One example, was the construction of the H-L technique for phase noise calculations. Actually gets a following in university courses. The problem is that with all its fancy attempt to analytical calculation, it is fundamentally wrong.
There is no alternative but brute force simulations. I have literally, and I mean, literally, have run millions of simulations in my day job. For example, its quite impossible to determine a whole range of subtle effects without running processes corners when designing ASICs e.g.
Or for example, an LDO might have say 50 transistors. It has a numerous parasitic poles and zeros. It is truly imposable to optimally stabilise such a relatively simply system manually, and no one in industry does that. This is despite the reams of course in universities peddling all sorts of methods to do so.
One needs to understand some general principles of designs such as where to place say, 4 caps and 4 resisters, and then run targeted, automated, swept simulations until a spec is honed in on. Its an iterative process.
I am not Hawking, guess who long it look me to work this out?
Its a different world today, and how I am explaining it, it truly the way its run, certainly in the billion transistor ASIC universe. Its all simulation. Its only viable method.
-- Kevin Aylward
If you want to set up a real disaster can help if all the managers get pointed in the wrong direction early in the project.
The sunk cost fallacy does discourage people from sitting back and saying "this approach isn't working too well - can we come up with something different?"
If you already have a dubious solution that more or less works, it's even harder to get time to think up a few distinctly different approaches.
-- Bill Sloman, Sydney
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
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