Irony is, a lot of larger office building thermostats are really only there for display purposes (thermometer), not for control purposes (actually functional).
Often tenants can change the thermostat to whatever they want visually, but in the background it caps at a certain value or doesn't change the set point at all
It looks like it given the symbols used. P for pressure, rho for density etc. u-arrow is definitely a vector field, so it could be fluid flow. Otherwise it could be equally anything described by a vector field, like electromagnetism or gravity but they usually have a lot more E and G involved I think.
I used to solve these but then I got a certificate so now I don't have to.
Used a screen shot to Google this and it turns out to be some unsolved ancient equation regarding the laws of physics. Or something that I dont understand. And have probably misrepresented here.
73 is my ideal temp, but fuck lockin the thermostat. It should be set lowest temp desired by anyone. You can always wear a hoodie. But the human torch in your life can only get so naked.
That's all well and good until you have someone in your household with circulatory issues and can't warm themselves up effectively. Sucks having to be warm all the time so they're not cold and in pain.
If your signal looks like f(t) = K•u(t)e^at with u(t) = {1 if t≥0, 0 else}:
If Real(a) > 0, then your signal will eventually blow up.
If Real(a) < 0, then you signal will not blow up. In fact, your signal will have a maximum absolute value of |K|, and it will approach zero as time goes on.
If Real(a) = 0, it is either a complex sinusoid or a constant. In either case, it is bounded with maximum absolute value of |K|. It very much does not blow up.
So e pops up all the time in stable systems and bounded signals because the function e^at solves the common differential equation dx/dt = ax(t) with x(0)=1 regardless of the value of a, particularly regardless of whether or not the real part of a causes the solution to blow up.
Or if you know what you are doing electrically speaking pull the thermostat off the wall and connect the cooling/heating line to common for a bit;
I think it would actually be less effort
The Navier Stokes equations represent the universal laws of physics that can model any fluid in the universe.
These equations have been around since almost two centuries now but we still understand very little about them. When we have a set of equations we expect the following to happen-
Solution should exist- One should be able to solve the equations
Solution should be unique- Given particular initial conditions, one should obtain an unique solution to the problem. For example if you and your friend pour water into a container in an identical way, keeping all parameters (pouring velocity, direction, geometry and dimensions of the container, etc) identical then you both should get the same flow pattern. Water in both the containers should behave in exactly the same way. If your friend gets air bubbles at a point then you should get them at the exact same point as well.
Solution should be smooth- A finite change in the input should produce a finite change in the output. It should not be erratic and unpredictable.
Unfortunately, Navier Stokes equations do not satisfy any of the conditions mentioned above.
