Thought I would follow up here and try to more succinctly describe the problem. At its core, I have three random variables that are normally distributed:
x_1 \sim N(\mu_1, \sigma_1) \\
x_2 \sim N(\mu_2, \sigma_2) \\
x_3 \sim N(\mu_3, \sigma_3)
I also know there is a relationship among...
Thanks for the reply. I do check assumptions about distributions with high-stat simulations to try and catch mistakes. In the situation I'm describing above, it is the high-stat sims that show I must be doing something wrong... but not horribly so. I have both a bias in my final results as...
I run into this issue with my research when modeling particle detector responses with a normal distribution since it will on occasion try to produce a negative energy particle (clearly not realistic). There are options but they produce biases. One is to just cap the low end at zero (or nearly...
Hello PF! It's been a while. How are things?
In my research I'm faced with determining a probability distribution from a function built as follows:
Perform three measurements X, Y, Z that have normally distributed errors.
Impose a constraint and variable change that allows me to...
Sometimes you can get in (not top tier) with less than 3.0 on probation. Your scores on the Physics GRE would probably be a primary factor.
Depending on the school you may even hedge your bet a little and apply for M.S. program, then move on to the Ph.D. after a couple semesters once you've...
I suppose that depends. Are you still an undergrad? In grad school? If an undergrad, taking classes certainly wouldn't hurt. Full disclosure: I have degrees in both comp sci and physics so I'm biased. I have found the comp sci background to be extremely useful since I encounter multiple...
Yes, yes, and yes. Those three are a good start ;) C++ and Java are very close in structure and syntax, so not a big deal to know both. Python is just, well, awesome. Ok, not in all aspects, but for certain things (fast prototyping of an idea) it is. Plus it's really easy to learn.
Your situation sounds very familiar. My first degree was Computer Science. I actually went back to get an undergrad in Physics before going on to grad school. It took four semesters because of the class sequence (I also picked up a math degree while I was at it).
In my school, IF one...
If I understand the definition correctly, then I think so. Y, A, B, C are normally distributed about a mean, but not necessarily independent (i.e. covariance != 0).
A thought I had was to perform principle component analysis on A, B, C so I then would have some new (independent) eigenvectors...
You are correct, I am looking to calculate the expected value of Y given A, B, C and known correlations YA, YB, YC, AB, AC, BC (and necessary variances, etc...)
I've searched the forums but am unable to find an answer to this:
Given two variables with a correlation, you can predict one from the other using the familiar
E(Y|X) = EY + r * s_y * (X - EX) / s_x
What I want to know is how to predict values from multiple variables, especially when these...
I very briefly did some exploration working directly with OpenGL, but it seemed like a ton of work to handle things at that level. So then I learned 3D in Java using java3d. I found a tutorial and very diligently followed it step by step. A few days in, I was able to do some cool stuff from...
I am facing an issue in my research where I need to enumerate all combinations of an underlying set. BUT the set has some special features. Here is an example:
Given a set {A,B,C,D,E, F} where each item in the set consists of two values. Something like:
A = (1,2)
B = (3,4)
C = (5,6)...
It's true, lepton-lepton collisions are much nicer to deal with. Plus *all* center of mass beam energy is available to make a particle (which is generally not the case for hadrons). You need to have much more energy in your hadron beam than the energy of physics you are actually exploring...
Centripetal acceleration is acceleration directed towards the center of circular motion. So this is usually
a_c=-\omega^2 r
or
a_c=-\frac{v^2}{r}.
In either case you need to know how fast the disc is rotating (and its radius). So how would you determine how fast the disc is...
Tricky :) You may recall that in Newtonian mechanics, the Lagrangian L = T - V (potential energy - kinetic energy). The energy equations are in terms of position and velocity and are in "generalized coordinates". That is to say, you can use any coordinate system you like. A sometimes...
The first can be thought of as a conservation of energy problem. Consider how much work it would take to stop the person. (this assumes the distance he falls through the snow adds a negligible amount of potential energy... even if it doesn't you can still solve this in a similar way).
For...
What is the acceleration "a" when the object is at terminal velocity?
Using your equations, what is the terminal velocity in terms of m, g, and b?
Now, what is "a" when you cut "v" in half?
I would like to see a general solution to this as well. I poked at it but nothing immediately jumped out at me. The general solution must determine how -pq compares to \sqrt{(pq)^{2} - p^{2} q^{2}}} as q-->0. It's not obvious to me that the latter approaches zero any order "faster" so the...
The case you are describing here seems like a situation where the wave functions combine to act like a single particle (like Bose-Einstein condensate).
Also, this might be just like saying free quarks cannot be seen, but always as part of something. Yet, a quark is generally considered more...
On the immediate horizon, around 1TeV, an e+ e- linear collider could probe super symmetry models (where every "normal" particle is paired with another, higher mass particle that differs in spin by 1/2). Information from the LHC *should* give us some clues as to what's going on here. Either it...
It's a good question and hard to answer. When we "look" with our eyes at a regular object, what we actually see are the photons (light) reflecting off (or being emitted by) the object. This works well for even small objects, but there is a limit (primarily related to the wavelength of light)...
College is expensive, no doubt. I managed without my parent's help though. I used a combination of Stafford loans (I think there is something different now) and a campus job. I found a balance of 30 hours work and 9 hours classes worked very well for me. It took longer, but what's important...
I would have to say a C.S. degree would be very valuable to a computational physicist. I worked briefly with COSMOS (a hydrodynamics simulator) and the code base was quite large. Understanding how to plan and organize your code is necessary to efficiently manage such a project.
Ah, I see what they are getting at. Yes, you are correct, "right past B" is to be considered the point when you have to take into account centripetal acceleration since it is now on the curved portion of the track.
So, if you get an expression for velocity at this point, and then work it...
If you are asking does gravity affect the magnitude and direction of a magnetic field as decribed by classical equations, then strictly speaking, I believe it does. BUT this would only be in cases of very high gravitational fields (like near black holes, etc...).
But on the earth, I would...
There are two ways to look at this problem. One way is conservation of energy, the other is kinematic.
For kinematic, you might first look at what velocity is necessary to "throw" an object straight up 0.80 m. Once you have this, then you can look at what acceleration is necessary to reach...
Right at point B, you are correct, the normal force should be zero. It is only after this point when it starts to increase.
For the normal force at point C you will need to take into account both the acceleration of gravity as well as centripetal acceleration.
As a sanity check, given your diagram, it is clear that when theta is zero, the force pushing at C should be only in the -x direction and with magnitude you calculated above. Now, at theta approaches 90 degrees, I would expect that the force normal to the support surface C is sitting on to...