Homework Statement
In buckingham pi theorem, you have p=n-k dimensionless groups (π1, π2,...)
where n=number of total variables and k=number of total units among the variables
For example, let's say we want to relate:
ρ~m/L3 (density)
μ~m/L*t (viscosity)
v~L/t (velocity)
d~L (distance)
Da~L2/t...
Homework Statement
The following equation is presented in my textbook, with very little context and J is simply described as the "trans-membrane fluid flux, which can be modeled by using Darcy’s law."
Typically in this bioseparations class, when we discuss permeate flux, it is a unit volume...
Homework Statement
You have a cylindrical tube for which you know the length is 16±0.1 cm and the radius is 8±0.1 cm, what is the error of the volume?
Homework Equations
The Attempt at a Solution
V = π*82*16 = 3216.99 cm
But since the r term is squared, must we account for its error twice...
Homework Statement
I'm trying to plot the steady state concentration of yA vs. x, yB vs x and yu vs x using centered finite difference method.
Homework Equations
The Attempt at a Solution
τ represents the dimensionless time variable, so steady state would mean that the left hand side of...
Thanks!
If instead I had dx1/dt=-x13+x2, would it be valid to keep z1 as it is defined now (z1=x1-0) and would dz1/dt=-z13+x2 be true? Since the first term of the series expansion of x3 is x3
Homework Statement
Find whether this system is stable or unstable at the steady state (x1,x2)=(0,0)
dx1/dt = -x1+2sin(x1)+x2
dx2/dt=2sin(x2)
Homework Equations
The Attempt at a Solution
z1=x1-0
z2=x2-0
dz1/dt=-z1+z2+2z1
dz2/dt=2z2
Jacobian =
[ 1 1 ]
[ 0 2 ]
so the system is unstable.
This...
Homework Statement
dx/dt= -x2-2x(1+t+t2)
x(1)=2
estimate x(1.2) with h=0.2
Homework Equations
Implicit Euler:
I was taught that we must solve for yk+1 using Newton's method:
This doesn't seem like it will work because Newton's method assumes a function of only one variable.
According to...
Homework Statement
The Newton iteration formula is based on a Taylor series expansion of the function f(x) around an estimate of the root xn, truncated after the linear term. You are asked to derive a more accurate iteration scheme as follows: Start from the Taylor series expansion of f(x)...
Homework Statement
[T,V]=[TV-VT]ψ
Homework Equations
T=(-ħ2/2μ)∂2/∂x2
V=(1/2)kx2[/B]The Attempt at a Solution
[(-ħ2/2μ)∂2/∂x2((1/2)kx2ψ)]-[(1/2)kx2(-ħ2/2μ)∂2/∂x2(ψ)]
I think my problem is with executing the chain rule on the first term:
(-ħ2/2μ)[x2ψ''+2xψ'+2xψ'+2ψ-x2ψ''][/B]
The x2ψ''...
A remote control shot a single photon at a window that has a 50% chance of transmitting and
50% chance of reflecting photons. Once the photon wavepacket hits the glass (without an observer present), it propagates as a superposition of states, one in which it was transmitted and one in which it...
If an operator (O) acts on a function ψ and transforms the function in a scalar manner as described below, it is said to be in an eigenstate:
Oψ=kψ
in this case, O is the operator and k some scalar value.
My question is essentially if k=0, can this still be a valid eigenstate?
for example, O...
What is the origin of light the color in the following objects and does the color of these objects involves absorption, reflection, and/or transmission of light:
a beam of blue light
a white sheet of paper
a red shirt
a black shoe
a transparent yellow solution
My guesses in order:
not...