The usual way to model a vibrating membrane is by using the wave equation. Is it possible to do that from "within"? Probably the answer is yes, but where can I see it done explicitly. What I mean is can we model the membrane as a two dimensional Riemannian manifold without any specific embedding in R3 plus equations involving the metric (or form, tensors etc.) such that at any time it is isometric to the surface given by the graph of the function satisfying the wave equation at that time. Higher dimensional generalizations are also interesting.   

I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.

Problem 4.49

Sand moves without slipping at 6.0 m/s down a conveyer that is tilted at 15 ?   . The sand enters a pipe h = 3.2m below the end of the conveyer belt, as shown in the figure (Figure 1) .

Part A

What is the horizontal distance d between the conveyer belt and the pipe?

Express your answer to two significant figures and include the appropriate units.

If our universe comes from a flux compactification of string theory over 6 dimensions with a nonzero flux, then it can't be continually deformed to another compactification with zero flux as the total flux is a topological invariant. The cosmological constant of our universe is positive, which in string theory means it is a metastable state. The stable vacuum for a flux compactification in string theory is a BPS compactification with negative cosmological constant.

What if our metastable observable universe is actually embedded in a larger stable anti de Sitter background? An inflating metastable or slowly rolling or chaotically inflating patch of this asymptotically AdS universe inflates to our observable universe. By the AdS/CFT correspondence, our universe can be described by a superconformal field theory in 2+1D with no gravity.

Is there any flaw in my reasoning?

As I hope is obvious to everyone reading this, the universe contains more matter than antimatter, presumably because of some slight asymmetry in the amounts of the two generated during the Big Bang. This raises the question of whether there are any processes short of the Big Bang that produce more matter than antimatter. That is, is there any known process where a particle collider (or whatever) would convert some energy into matter not through the production of particle-antiparticle pairs but through some process that produced more matter than antimatter? This doesn't need to be restricted to current accelerators-- if there's some mechanism for this that requires impractically high energies, but is based on solid theories (i.e., the Standard Model or straightforward extensions thereof), that would be interesting, too.

I'm fairly certain that the answer is "no," because I know that the matter-antimatter asymmetry is related to CP violation, and I also know that existing measurements of CP violation are not enough to explain the asymmetry. If there were a known way to slam protons together and make more quarks than antiquarks, I wouldn't expect this to still be a mystery. My particle physics knowledge is far from comprehensive, though, so it can't hurt to ask.

(I was briefly confused into thinking that there was such an experiment a while back, but it turned out to just be sloppiness about marking the antiquarks on the part of the people writing about it...)

(This is another question prompted by the book-in-progress, on relativity, this time a single word: I wrote that matter created from energy in particle physics experiments is "generally" in the form of particle-antiparticle pairs. Then I started wondering whether that qualifier was really needed, and thus this question.)

Stop me if i'm wrong but displacement is, for example, when you enter a bathtub the water level rises around you.

What happens when displacement isnt possible?

I'll give an example. I have two blocks off steel, one at the top of a chamber and one at the bottom. there is a gap between the two blocks that is filled with water. There is NO gap between the two blocks and the side of the chamber (the water cannot escape)

What happens when the two block come together, in effect squashing the water? where does the water go?

Very unintuitive observation:

I pour myself a Guinness and the bubbles in my glass seem to move down toward the bottom of the glass instead of rising directly to the top of the glass as foam.

How can this be explained? Why is it that I observe this behavior drinking Guinness and not other carbonated drinks? What system properties (ie, temperature, nature of the solute and solvent) would affect this behavior?

Say you have a bottle of water filled up to a height H. A small hole is drilled in its side at a height d, so that water squirts out. The squirting water travels in an arc as it falls, covering some horizontal distance S away from the bottle before it hits the table top that the bottle sits on. Multi-part question to try to understand this completely:

At what height d should the hole be placed so that its horizontal travel distance S is maximized?

Will S or the optimum value of d depend on the hole diameter?

Does the answer change if you assume that the hole presents zero impedance to the water flow? This might not make sense to ask, or it might be equivalent to asking what happens in the limit of a very large-sized hole (see #2). Not sure.

Thanks to anyone who can help!

Even if the double slit experiment gives interesting (weird) results, it only concludes that each photon interacts with itself after passing the two slits. I have been thinking about a different experimental setup, where you have two well defined light sources (with specific wave lengths and phase) but no slits. And now to my questions: Has anyone ever done such an experiment, and will there be an interference pattern on the wall?

If the answer to the second question is "no", light can not be a true wave - it only has some wavelike properties. But if it is "yes", things become much more interesting.

If there is an interference pattern on the wall, there has to be an interference pattern even if both light sources are emitting single photons at random, but as seldom as, say, once per minute. That in turn would mean that the photons know about each other, even if they are separated in time with several seconds, and the light sources are independent (not entangled).

Two cannons are mounted as shown in the drawing and rigged to fire simultaneously. They are used in a circus act in which two clowns serve as human cannonballs. The clowns are fired toward each other and collide at a height of 0.95 m above the muzzles of the cannons. Clown A is launched at ?_A = 76.0

Given: Law of Conservation of Angular Momentum.

Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).
Surface same degree of aging all over.
Hypothetical large impact is not a sufficient answer.

Assuming any object large enough to alter a planets rotation or even orbit would likely destroy most of its shape, yet Venus has retained a spherical property with a seemingly flat, even terrain indicating no volcanoes,and few if any visible meteor impacts. It would be fragmented and dispersed for billions of years. Even the question of what meteor, comet, asteroid composition could survive traveling that close to the sun's temperature, radiation, electromagnetic energy, solar flares, or gravity to equal a mass reactionary change as to alter it's spin.

Your firm has been hired to design a system that allows airplane pilots to make instrument landings in rain or fog. You've decided to place two radio transmitters 48m apart on either side of the runway. These two transmitters will broadcast the same frequency, but out of phase with each other. This will cause a nodal line to extend straight off the end of the runway (see Figure 21.30b). As long as the airplane's receiver is silent, the pilot knows she's directly in line with the runway. If she drifts to one side or the other, the radio will pick up a signal and sound a warning beep. To have sufficient accuracy, the first intensity maxima need to be 64m on either side of the nodal line at a distance of 5.0km .

What frequency should you specify for the transmitters?

A car accelerates from rest at a rate of 2.2 m/s^2 for 14.3s. The car then holds this speed for 16.0s, after which there is an acceleration of -3.0 m/s^2 until the car comes to rest.

a) Sketch a position vs. time graph for the car

b) Sketch a velocity vs, time graph for the car

c) What is the total distance traveled by the car?

A glider aircraft initially traveling due west at 87.0 km/h encounters a sudden gust of wind at 39.5 km/h directed toward the northeast (see the figure below). What are the speed and direction of the glider relative to the ground during the wind gust? (The velocity of the glider with respect to the ground is the velocity of the gilder with respect to the wind plus the velocity of the wind with respect to the ground.)

A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. The horizontal velocity of the plane is 250 km/h (69.4 m/s). Rescue plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers.

1/What vertical velocity (up or down) should the supplies be given so that they arrive precisely at the climbers' position?

2/With what speed do the supplies land?