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### Propagation Of Error Calculation Of Incompressible Continuity Equation

Hello I am having trouble deriving the correct equation for error in vertical velocity from the incompressible continuity equation. We are trying to estimate vertical velocity ($w$) from the ...
110 views

### Let $Q(t,\vec x)$ solve $\partial_t^2 Q = \nabla^2Q$. Why $\partial_t^2Q = 2 (\partial_r + r^{-1})\partial_{t-r}Q$?

On page 5 of Bondi et. al. (1962) (https://doi.org/10.1098/rspa.1962.0161), a suitable method for solving the gravitational wave equation is demonstrated for the case of the scalar wave equation. ...
30 views

### Expanding the ratio between infinitesimal time elements [closed]

Given the expression $$\sqrt{\frac{1 + \frac{2}{c^{2}}\phi(r_{S}) - \left(\frac{v_{(obs)}}{c}\right)^{2}}{1 + \frac{2}{c^{2}}\phi(r_{E})}},$$ where $\phi(r_{S}), \ \phi(r_{E}), \ v_{(obs)}$ and $c$ ...
29 views

### Non-additivity of higher order terms in the intermolecular potential

The intermolecular potential energy can be written as $$u(r_{1},...,r_{N})=\sum_{i<j}^{N} u_{2} (r_{i},r_{j}) + \sum_{i<j<k}^{N} u_{3} (r_{i},r_{j},r_{k})+...$$ where the nuclear coordinates ...
1 vote
56 views

### Ruling out dependence of y and z coordinates in Lorentz transformation

Let us assume that motion is in the $x$ direction, axes of both coordinate systems are aligned and their origins meet at $t=t'=0$. The most general relation between $x$ and $x'$ then becomes (ruling ...
31 views

### How to "calculate" correctly the liquid column height in not "simple" capacities?

As I was told on a youtube lesson, to calculate the hydrostatic pressure on the bottom of a capacity, that's on the picture below, I need to use the h1 height(see that formula on the picture). And it ...
68 views

### Can a school student publish research paper? [closed]

I am a high school student. I want to publish a research paper now which I have written . Will I face any problem regarding this. Will there be any problem regarding my educational qualification . Is ...
31 views

### Does a pressure jump form as a result of surface tension even for a flat interface?

My question is fairly straightforward, is a curved interface the only way a surface tension-induced pressure jump can form over that interface, or is it also possible to occur over a flat surface? ...
49 views

20 views

### Dark Matter Axion in Toroidal Coil [closed]

I got this question for some homework, but I don't know where to start. I've tried using the 4th equation, but I can't get anywhere. Any suggestions on where to start would be appreciated, thanks. 1k views

### Can the wavelength of the standing wave be different from the wavelength of the sound it emits?

I have a question about standing waves on strings. I'll try to explain the best I can, I searched and researched the whole day yesterday but I am confused still: Every frequency has a single, and ...
78 views

### Do irreversible thermodynamic processes CONSTITUTE time or do they MOVE IN time? [closed]

Time can be associated with irreversibility. A broken egg can't reassemble. Most, if not all, processes are irreversible and this is associated with time going in one direction. Ŕemarkably, living ...
12 views

### How to calculate total sum of orientation changes in 6 DOF data from a Motion tracker?

I'm using data from a motion tracker that give provides 6 coordinates for every frame ( with frame rate of 240Hz) Position: x, y, z Orientation: azimuth(yaw), elevation(pitch), roll I can calculate ...
1 vote
34 views

### Comparison of 2 fans [closed]

I have 2 20" box fans. The first fan draws .65 Amp and claims 1780 CFM. The second fan draws .45 Amp and claims 2300 CFM. The fans are new, and the electric motors are of similar design, so I ...
40 views

2k views

### Addition of gravitational fields in general relativity

According to Newtonian gravity, when dealing with multiple sources of gravity, the net gravitational field equals the sum of the individual gravitational fields of each source. Does the same hold for ...
14 views

### Frequency dependent Purcell effect for a broadband emitter

How do I model the following system? I have an NV-center in diamond with a broad fluorescence spectrum, centered at roughly 700 nm with a FWHM of 100 nm. (The NV-center is a defect in diamond, it can ...
856 views

### Why does a stream of falling water get narrower at the bottom? [duplicate]

At first glance, I thought that the flux of the velocity field, $\mathbf u$, should be constant. The velocity of the water increases due to gravity, hence the imaginary area the velocity field is ...
I am wondering what would be the closest analogue of the matrix representation for the creation and annihilation operators arising in Gupta-Bleuler formalism, which are defined by  [a,a^\dagger] = -...