Recent content by renormalize

But how much effort have you expended to understand and appreciate the already existing technology? For example, it took me less than a minute online to find this article from 2023: Water quality analysis using mmWave radars Abstract: Water quality and drinkability assessment are of high...

I'm unaware of practical examples of your function:$$f_{k}\left(x\right)\equiv x^{k/x}$$but a transformation of that function:$$\log\left(f_{k}\left(u^{-1}\right)\right)=-k\,u\log u$$with the specific value ##k=-1## is quite common: Stirling's Approximation:$$\log n!\approx n\log...

Perhaps you can gain intuition regarding the kind of beams that can be formed from a phased array of antennas by playing with on-line calculators. For example, here's one that allows you to adjust the number of antenna elements, their spacing and relative phase shifts...

Spectacular results! I no longer even have to refresh the page occasionally, as I used to, to get proper previewing. Kudos to Greg.

In Physics Forums you should use ## to wrap in-line LaTeX equations and $$ to wrap display equations. I've reformatted your post below: And to make our lives easier, please try using LaTeX to post your solution attempt here, rather than making us all open your PDF attachment.

Yes, the spreading of single-atom wave packets has been observed experimentally and agrees with theory: In-situ Imaging of a Single-Atom Wave Packet in Continuous Space

I don't see a function "##g##" defined anywhere in those lines.

That's of course a good point. But what empirical evidence exists that demonstrates that we don't really live in ##R^4\,##? It's been shown that spin-2 quantum field theory sums to Schwarzschild outside the event horizon, but perhaps it sums to something different at and inside the horizon. To...

How do you reconcile this claim with the actual published literature on perturbative quantum gravity? For example, here are two recent papers from Phys Rev Letters that independently sum spin-2 diagrams to all orders on flat spacetime, both of which successfully arrive at the exact Schwarzschild...

A definition is whatever size it needs to be to achieve clarity. Why do you get to define the rules for the "size" of a definition?

This is a more rigorous (https://www.britannica.com/science/equilibrium-physics): equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences...

I'm by no means expert on this topic, but doped-silicon optical modulators can apparently accomplish this (although not necessarily in the specific single-layer configuration you're proposing): This diagram is taken from the freely-available 2010 Nature review article...

I think you need to temper your expectations. According to Jackson, Classical Electrodynamics §7.5, lab-scale plasmas have electron densities in the range ##10^{12}\leq N_{e^{-}}\leq10^{16}\text{cm}^{-3}##, corresponding to plasma frequencies of ##0.01\leq f_{p}\leq1\text{THz}##. In contrast...

Yes, you can model in the "standard" way because it's directly analogous to a multilayer interference filter, but with one of the layers having an unusual dielectric constant. Yes, simply model your modulator as a layer of thickness ##t## with a frequency-dependent refractive-index...

Can you edit your post to very clearly state the problem you are trying to solve?