Suppose I have an box (set) containing two different colored balls, red and blue, say.
Now, suppose the balls differ in size, where the size of the red balls has one particular distribution and those of the blue another.
How can we describe the distribution of the balls in the box?
This is a vague question and I apologize in advance for not being able to explain it better.
I'm combining r.v.'s from different populations (distributions). The resulting population can be thought to come from a mixture distribution. I think another way of describing the resulting...
Ok. So the answer to finding the solution of
(-1)^x=1
is clear.
But say we didnt know it and wanted to solve it. One approach is to take the log of both sides
x\cdot log(-1)=log(1)=0
But now the right hand side is defined where as the left is not!
What am I missing?
Hi,
I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this.
Suppose we have a dielectric in space subjected to some external static electric field.
I have read (without explanation)...
Hi,
One of the boundary conditions when solving for the potential, \Phi, outside a dielectric sphere placed within a uniform electric field is
\lim_{r→0}\Phi(r,θ)<\infty
Can anyone explain/prove why this so.
Thanks,
Hi,
I was reading about Markov chains and came across the following statement:
"The conditional distribution p(x_n|x_{n-1}) will be specified by a set of K-1 parameters for each of the K states of x_{n-1} giving a total of K(K-1) parameters."
In the above we have assumed that the...
Acadamia vs. Industry -- supervisors role
Is there an incentive for supervisors to guide their Ph.D. students to follow an academic career rather than move to industry?
Hi,
When solving a 2nd order Linear DE with constant coefficients (ay''+by'+cy=0) we are told to look for solutions of the form y=e^{rt} and then the solution (if we have 2 distinct roots of the characteristic) is given by
y(t)=c_1 e^{r_1 t}+c_2 e^{r_2 t}
This is clearly a solution, but...
Hi,
I'm interested in how a dielectric sphere effects a (spatially) uniform time varying field.
I'm sure I'm not the first to inquire about this very topic. Could anyone direct me to a resource?
Thanks,
Hi,
Do material posses both dielectric as well as resistance properties?
I imagine that when there is a difference in potential across a volume of some material, some current will flow (I=V/R <-- the material's resistance), but also the material may become polarized to a certain degree...
Suppose X and Y are r.v.
Suppose also that we get N samples of a r.v. Z which depends on X and Y. That is Z=g(X,Y).
Which is a better estimate of the true value of Z?
Z=E[g(X,Y)]
or
Z=g(E[X],E[Y])
Hi,
I'm getting some confusing results and cant figure out what is wrong
Suppose we have a uniform field
E=[0,0,E_z] in a dielectric media.
By E=-\nabla\psi we can deduce that \psi(x,y,z)=-z E_z
But, taking the Laplacian
\nabla^2\psi=\frac{\partial^2 (-zE_z)}{\partial z^2}=0
does...
Hi,
I have a random variable X with some zero-mean distribution.
I have a function Y of this r.v. given by something complicated
Y=(a+X)^\frac{2}{3}
Is there an explicit way of finding the distribution of Y or even its mean?
Thanks
Often a time varying E-field is represented in complex format. I have a simple E-field (uniform in space) given by
\vec{E}(t)=E_o\cos(\omega t)\cdot\hat{k}
or equivalently, the real part of
\vec{E}(t)=E_o e^{\omega t}\cdot\hat{k}.
We know the potential is the negative gradient of the...
Confused.. please help!
Often when an electric field varies sinusoidally with time, it is represented as a complex number. Say,
\vec{E}(t)=A\cos(t) \cdot \hat{k}
We know at any time, the magnitude of E is A\cos(t).
Alternatively the same vector E is understood to be the real part of the...
Hi,
The Poisson equation (or Gauss Law) in a vacuum is given by
\nabla^2\phi=-\frac{\rho}{\epsilon_0}
where \rho \mbox{ and } \epsilon_0 are the charge density and vacuum permittivity or (electric constant of space).
My question is what is the Gauss's Law in a dielectric material? Do...
Solving the Laplace equation in Cartesian Coordinates leads to the 2nd order ODEs:
\frac{X''}{X}=k_1, \qquad \frac{Y''}{Y}=k_2 \qquad \frac{Z''}{Z}=k_3
In each case the sign of k_i will determine if the solution (to the particular ODE) is harmonic or not.
Hence, if two people solve the...
Hi,
If
k_3 \cdot (A_1 \cos k_1 x + A_2 \sin k_1 x)\cdot(B_1 \cos k_2 y + B_2 \sin k_2 y)\cdot(C_1 e^{k_3 z}-C_2 e^{-k_3 z})=E
in the limit as \sqrt{x^2+y^2+z^2}\rightarrow\infty
Can we infer anything about any of the constants?
Hi
I'm getting confused solving the Laplace eqn in Cartesian coordinates.
The equation can be solved by solving each of
\frac{X''(x)}{X(x)}=-k_x^2, \qquad\qquad
\frac{Y''(y)}{Y(y)}=-k_y^2, \qquad\qquad
\frac{Z''(z)}{Z(z)}=k_z^2
and then substituting into the equation...
Hi,
I'm given a sensitivity threshold for a system in terms of the electric field. Is there any way of finding what the threshold is in terms of electric potential?
I know the relation E=-\nabla\Phi , but I dont see how I can apply it here.
ex.
Given E_{t} \mbox{ in } [\frac{V}{m}] what...
Hi,
Is there any way to analytically calculate the perturbation of a uniform electrostatic ﬁeld by a dielectric cube.
I know a solution exists for dielectric spheres but I haven't been able to come across the solution, when dealing with a cube.
Ohh.. and I'm assuming the simplest case...
Hi
The following structure has 2 elements.
people = struct(...
'name',{'bob', 'john'},...
'numKids',{0, 2}, ...
'kidsage',{[],[12,9]});
each element people(1), people(2) has three frields (name, numKids, kidsage)
Instead of declaring the structure in one line as above...
Hi,
I have a quick question regarding MatLab.
I have 3 matracies A, B and C.
For every entry equal to 1 in B, I want to let the corresponding entry in A be an integral of x from 0 to C.
ex.
for all (i,j)
if B(i,j)==1 then let A(i,j)=quad(@(x) x, 0, C(i,j))
A quick way to do...
Solving a cubic.... sort of!
Hi,
Can the equation \sqrt{Ax-x^3}+\sqrt{Bx-x^3}=C be solved explicitly?
All of MathLab, Maple and WolframAlpha seem to give an explicit solution but they dont show how they come to it. I'm afraid they may be missing other possible solutions.
Thanks,
I once came across a Wikipedia page describing a system where indifferent of the initial starting position, at some final time t=T the system would always reach the same equilibrium position.
Does anyone know what the name of such a system is?
I recall there was an animation of 4 balls each...
I have an implicit function f(x,y,z) which represents a surface in the XYZ Cartesian reference frame. I would like to change this current XYZ reference frame by a matrix M.
ie.
M: XYZ \rightarrow X'Y'Z'
If I have a vector v in XYZ, then v'=Mv is my representation of v in the X'Y'Z'...
I have found in physics literature a periodic function of time is many times written in complex form.
For example,f(x,t)=g(x)e^{i\omega t}
As a non-physicist this has proven a bit confusing.
Is it generally understood that the function we are really interested in the real part of the...
Hi Everyone,
I'm told that the following formula represents Kirchhoff's current law
g_1 E_{1 n}+\varepsilon_1 \frac{\partial E_{1 n}}{\partial t}=g_2 E_{2 n}+\varepsilon_2 \frac{\partial E_{2 n}}{\partial t}
where the first term on each side is Ohm's law and the conductive current
and...