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3
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1answer
47 views

Electromagnetic field and continuous and differentiable vector fields

We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields. We know electrostatic and ...
4
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0answers
85 views

On Cohomological Gauge theory Calculation

I am in trouble with calculation details of Witten's Two dimensional Gauge Theories Revisited. My questions is about (3.21) and (3.27). From section 3, we have $$\delta A_i=i\epsilon \psi_i\\ \delta ...
3
votes
0answers
97 views

Heat transfer from hot water through a copper pipe to oil in a tank

I want to build a geyser attached to a pump with copper tubing running into an oil tank. This is done because the oil solidifies at a temperature below 15 degrees Celsius. I have done a few ...
1
vote
0answers
88 views

How to calculate these integrals about propagator of QFT analytically?

How to get these three analytical solutions? Thanks very much! $$ G_{ret}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0+i\epsilon)^2 - \vec{p}^2 - m^2} = ...
1
vote
0answers
32 views

velocity function in slip effect

$$\frac{dp_l}{dx}-\mu_l\frac{\partial^2 u}{\partial y^2}=0$$ where $\mu_l$ and $p_l$ is the liquid phase viscosity and pressure, respectively; and $u$ is the flow velocity. The boundary ...
1
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0answers
122 views

insulator based gauss law questions

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply. Here's a question I'm working on that isn't part of my book. where the radii ...
1
vote
0answers
105 views

Uniform load applied to a parabolic curve

As I have to design the vertebra bone and its natural boundary conditions I came across a problem. How can I applied a uniform load if the place where the force is applied is a parabolic curve. Ok ...
0
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0answers
57 views

Finding the total space that an oscillating body has gone through via complex analysis

I was solving my homework and I got to an exercise that stated: An harmonic oscillating body has an equation of $$y(t) = A \sin(t)$$ Find the total space that the body has travelled during $t \in ...
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0answers
39 views

Integration of Forchheimer equation for unsteady-state permeability determination

I would like to know the steps for the integration of Equation 17 in Section 6.2.1.2 of American Petroleum Institute Recommended Practices 40 for Core Analysis to yield: ...
0
votes
0answers
60 views

Ricci/Tensor Calculus and Matrix Calculus

What are the differences in the types of problems Ricci/Tensor Calculus and Matrix Calculus can solve? One formulation is generally used by the physics community and the other by statisticians and ...
0
votes
0answers
99 views

g as a function of Theta

I slide an object down a ramp of a certain length, which is inclined at a certain angle $\theta$. It reaches the bottom in time $t$. Assuming that no forces act on the object other than gravity and ...
0
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0answers
120 views

Nicholas Kollerstrom article on the history of Calculus

Today, Newton┬┤s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom http://www.arxiv.org/abs/1212.2666 That basically claims that Newton did not invent Calculus. The article does ...