Recent content by 582153236

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...