How do you determine the optimal placement for a WLAN router ? For most people , this could be an physical exercise in intention , or in outlet location and cable length , or maybe where it ’s most convenient to often reset . For a physicist , it involves solving the Helmholtz equivalence .
Jason Coleis a Ph.D. physics educatee in London . He explore laser - wakefield acceleration at theJohn Adams Institute for Accelerator Science at the Imperial College of London . The field of view sounds like downright malign villainy : not subject with conventional speck accelerators , he arouse extremist high - powered lasers into thin plasm , return strong electric sphere that accelerate electron thousands of times faster . I ’m sure there ’s no chance at all that ’s go to be the inspiration for a doomsday machine … When escaping the foiling of apportion with inevitably malfunction equipment , he smatter in numerical methods . That ’s where today ’s news report start .
Instead of snaking LAN cable television service throughout his new flat tire , he switched his background computing machine to a wifi identity card . Alas , the signal was wonky , dropping out far more often than can be courteously tolerate . Undaunted by the initial lackluster performance , he sketched up a layout of his Modern flat , andset MatLab to radiate - tracingto see how the signal was bounce around the space .
Only a few lonely rays were reaching the concrete corner where the computer was situate , excuse why signaling was less than sufficient . A bit more tweaking , and Cole was able to adjust the router ’s position within the model , visually observing the sign flux map to adjudicate if reorganisation would puzzle out the job .
A fluxion mapping with 2,000 ray tracing out wifi sign throughout the unconditional . figure of speech credit : Jason Cole
Yet , Cole was disgruntled . Ray tracing was quick and simple , but not particularly tight . A little over a month later , he return to the job , this time using two - dimensional Helmholtz equation , using the wall as boundary conditions . The Helmholtz equivalence is used to mould how electromagnet Wave propagate through clock time and space ; the two - dimensional version leaves out pesky thing like elbow room height and allows Cole to check out wifi signal propagation using the flat layout he already sketched for the light beam way tracing .
Writing maths and equations without LaTeX is too objectionable for me to tackle here , but Cole does this often enough to have a visually elegant layout on his web log . channelise over to theHelmhurts entry to follow along with the working through the Helmholtz equality , using dispersion and deflexion of the electromagnetic undulation to lick for the electric field within his flat . He peppers in some excellent visualisation to reward you for slogging through the equations — the animated gif of electric node null points is particularly hypnotizing and deserving a click all by itself . ultimately , Cole progress to the point where he can bring about electromagnetic intensity maps of his flat , where warmer colours designate a stronger field , and smuggled geographical zone are null areas .
Electromagnetic intensity mathematical function with the router “ hidden away pretty uselessly in the box . ” Image credit : Jason Cole
The result was unexpected . Cole save :
I would have expect to see some neighborhood of ‘ cleverness ’ around the electromagnetic reservoir , fleet away into the distance perhaps with some funky diffraction effects going on . Instead we get a wispy social organisation with filum of strong field strength snaking their means around . There are noticeable black spots too , recognisable to anyone who ’s shifted place in a chair and have their phone conversation swing .
He started moving the router around the categoric . His analysis of how different locations impact the intensity maps are entertainingly practical ( “ tendril of internet goodness can get everywhere , even into the lav where no one at all at times reads BBC News with asleep leg . ” ) , but the math still did n’t seem entirely reflective of the reality he was experiencing within his flat tire .
That ’s when a handy commenter piped up , point out that extend the maths to allow for imaginary components would more accurately contemplate the concrete wall partly immerse signals , instead of idealized perfect reflections that were have destructive preventative and frequently nullifying the signal . look at this as further proof that just because it ’s fanciful does n’t think it is n’t important !
Cole ’s solutions were getting downright plausible , but he was still lean on one hand - wavy laying claim to simplify the job : that aside from the undulation ’s sinusoidal vibration , the trouble was time - main . Intuitively , this seems like a honest approximation — surely radiotherapy moving at the velocity of light will so quickly rebound around an flat that it may as well be instantaneous ! Yet , that sort of presumptuousness is so easy to make in physics , andnot always justified .
In a final surge of dedicated geekery , Cole abandon the simplification of Helmholtz equations , pulled up the full suite of Maxwell ’s equation of electromagnetic wafture , and apply the Finite Difference Time Domain technique to numerically mash through the problem .
After the initial wave multiplication at the start of the mannikin , the answer cursorily trace up with the Helmholtz solution from before , nicely justifying the metre independent reduction .
Image extracted fromJason Cole ’s picture
There it is : the most complicated , thorough , yet well - justified method of decide where to situation your router for optimize wifi signal is to numerically solve the Helmholtz equations , make certain to include the imaginary component of the electromagnetic wave . If that locating just happens to be in the middle of the master walk of your home , that ’s the monetary value you need to pay up for perfect response .
Tip via Charles Dayand thePhysics Today Facebook feed . Top mashup by Mika McKinnon using Jason Cole ’s image . If you adjudicate to write this story up for your science news organization , be cultured and linkback to whoever brought it to your attention .
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