Thanks for the replies! analogdesign, can you describe what your job entails? What is involved in the projects that you and your coworkers work on? For instance, is it more common to design a specific circuit board, or to engineer how all the parts fit together to make the instrument function...
I've been considering a change in career direction recently, and have been thinking about a career in developing scientific instrumentation. I know that "scientific instrumentation" is vague and encompasses a lot, hence the reason I am posting -- to try sharpen my understanding of exactly what...
In 2 dimensions, is the geodesic deviation equation governed by a single scalar, independent of the direction of the geodesics? That is, if ξ is the separation of two nearby geodesics, do we have d^2 \xi/ds^2 + R\xi = 0 where R is a scalar that is completely independent of the direction of the...
Interpreting "diverging thermal fluctuations" as equivalent to "infinite correlation length" doesn't make sense with another article I am reading which says:
"What drives the correlation length to infinity are thermal fluctuations, which become very large close to criticality."
If large "large...
Ok, that makes sense. It brings up another question for me though. Why do people call a system "scale invariant" when the correlation length diverges? The correlations still drop off (with distance) via a power law, right? So if I zoom out they will change, and so don't seem "invariant".
According to wikipedia:
"As for a classical second order transition, a quantum second order transition has a quantum critical point (QCP) where the quantum fluctuations driving the transition diverge and become scale invariant in space and time."
I am confused about what this means. Why do the...
Suppose we apply a uniform field to an infinite conducting slab (i.e. like an infinite parallel plate capacitor, but the interior is included as part of the conductor). What is the resulting field?
The simple answer is that a surface charge develops on the boundary planes of the conductor so as...
To preface my question, I know it is related to the Gibbs paradox, but I've read the wikipedia page on it and am still confused about how to resolve the question in the particular form I state below.
Suppose a completely isolated ideal gas consisting of identical particles is confined to a...
I don't get the point of equations of state since they seem to me to just indicate that we defined too many state variables. Why not just trim down our set of state variables and do away with the equations of state (i.e. for an ideal gas, just notice that P and V are sufficient to describe the...
So while there is some notion of distance in classical spacetime, you cannot speak of a distance between two arbitrary spacetime points, right? You can only speak of the distance between points on the same time slice (this would be the spatial metric) or points at the same position slice (this...
So then is it not possible to think of classical space and time as a single spacetime since we cannot assign a definite meaning to the distance between spacetime points (independent of reference frames)?
In special relativity we have the invariant spacetime interval ds2 = dx2 - c2dt2. If we think about classical (non-relativistic) space and time as one spacetime in which the transformation between reference frames is given by the Galilean transformation, is there a corresponding spacetime...
I am reading 'Classical Dynamics: A Contemporary Approach' by J. Jose, and I am confused about a step in the author's development of potential energy for a system of many particles.
He begins by writing down a term equivalent to the total change in kinetic energy of the system:
\sum_i...
I am trying to follow the following reasoning:
Given a known matrix A, we want to find w that maximizes the quantity
w'Aw
(where w' denotes the transpose of w) subject to the constraint w'w = 1.
To do so, use a lagrange multiplier, L:
w'Aw + L(w'w - 1)
and differentiate to...