Lecture 14: Strange attractors
14.2 Fractals
In the last lecture we discussed the properties of the Lorenz model and,
Q: We saw in Lecture 13 that the strange attractor describes an infinitely
in particular, the existence of a strange attractor above a cr
Running head: BUTTON EXPERIMENT
1
Button experiment
Institution:
Name:
BUTTON EXPERIMENT
2
Statement of the problem
There have been different materials that are used to measure the distance of the small objects.
The aim of the study was to find out the us
2.2.2 Importance of automated assessment
In teaching programs, assessment is a very important tool for better progress. Assessment can bring a
strong positive effect on the student. Students will learn the when they are frequently assessed, and
feedback i
CHAPTER 4: DATA ANALYSIS AND DISCUSSION
1. Introduction
This chapter of the work include an in depth analysis of data with the help of graphical
presentation methods and thematic analysis method[Tho15]. Along with this, in the section
focused on answering
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Examples 4
1. Verify that
Z
(i)
(Y21 (, ) Y11 (, )d
Z
(iii)
Z
= 0,
(ii)
(Y44 (, ) Y53 (, )d = 0,
0
Y1 (, )2 d = 1.
(Hint: in (ii) you do not need to know the full form of the spherical har
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Solutions 4
(Y21 (, ) Y11 (, )d
cos sin sin sin d d = (2)[sin4 /4]0 = 0.
R
R 2
R
ii) (Y44 (, ) Y53 (, )d 0 ei(4+3) . . . d [ei ]2
0 = 0.
R 0
R
2
iii) |Y1 (, )| d = (3/4) 2 0 cos2 sin d = (
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Examples 2
You may use the following result for Gaussian integrals:
p
R x2
R
p
2
dn
e
dx = /, and x2n ex dx = (1)n d
.
n
1. Which of the following are well-constructed expressions? State wh
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Solutions 2
1. i) Ket; bra is hb|A + hd| .
ii) Bra; ket is |di + |ci. Note the placement of the scalars is purely conventional.
iii) Strictly, nothing. Assuming I is meant, it is an operato
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Solutions 5
(1) = sin(x/a) for 0 < x < a and 0 elsewhere. The
1. For this case, the perturbation is H
p
ground state wavefunction of the unperturbed square well is 0 (x) = 2/a sin(x/a), so
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Examples 1
The questions marked * are problems which everyone should attempt. The rest are proofs that
fill in some of the more important gaps in the notes (or in one case (13) a harder exa
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2015-16:
Examples 5
1. A particle mass m moves in the 1-D potential given by V (x) = for x < 0 and x > a, and
V (x) = sin(x/a) for 0 < x < a. Treating this as a perturbation on an infinite square
we
PHYS30201 Mathematical Fundamentals of Quantum Mechanics 2016-17:
Examples 3
1. Let |i and |i be possible states of a quantum mechanical particle in 1-D, which moves in a
potential V (x). Write down position-space representations of the following expressi
Running head: CHAPTER THREE: METHODOLOGY
Chapter Three: Research Methodology
Institution
Name:
Date:
1
CHAPTER THREE: METHODOLOGY
2
Chapter three: Research Design
This chapter explains the methods that will be used to get the data that will be used in the
Running head: ISLAMIC AND CONVENTIONAL BANKS
Comparison between the performances of Islamic banks with that of the conventional
banks
Institution:
Name:
1
ISLAMIC AND CONVENTIONAL BANKS
2
Abstract
The economic growth of a country is determined by how the
Lecture 13: Lorenz model and chaos
Over the next two lectures we consider a simple nonlinear model of RayleighBernard convection that led to the discovery of chaos by Ed Lorenz (1963).
13.1 Equations of motion
The Lorenz equations were originally derived
Note:
No = No, in general
Note: all of these are
Newtonian fluids
Not on syllabus
Steady-state
Incompressible
Inviscid
Uniform
density
Barotropic
(density only
a function of
pressure)
Constant
dynamic
viscosity
Dimensionality
Vorticity
Momentum equation
C
Flows, Fluctuations and Complexity
Problem set 4
(d) Using the continuity equation for flows in phase space, show that volume elements
contract exponentially in time at a rate,
V = (V )0 e(+1+b)t .
1. (a) Write down the Lorenz equations and solve for the
Lecture 16: Turbulence
16.2 Kolmogorov theory: turbulent cascade
(mathematical details non-examinable)
16.1 What is turbulence?
Salmon (1998) nicely sums up the challenge of defining turbulence:
Every aspect of turbulence is controversial. Even the defini
harmonic
motion and
normal modes
edited AL, CP, JJL November 2012
1
GP06
Introduction
This experiment is a study of the one-dimensional oscillations of a number of bodies undergoing coupled simple harmonic motion (SHM). The physics and mathematical descri
Lecture 15: Fluctuations and dissipation
Now suppose we produce a stochastic (random) time series with the same
The previous two lectures we found that apparently unpredictable, random-
frequency spectrum:
1
looking behaviour can arise in deterministic sy
driven
harmonic
motion
revised CWPP January 2012
GP04
Handle this equipment carefully. It is delicate and if it breaks, recoiling cords and dropping weights
could present a hazard.
1
Introduction
The aim of the experiment is to test the mathematical theor
Lecture 9: Convection and flow instability
The instability can also be viewed from an energetic perspective. Suppose
two fluid parcels, volume V , are exchanged in a stratified fluid:
9.1 Convective instability
z2
l2
Consider an incompressible fluid in wh
Note:
No = No, in general
Note: all of these are
Newtonian fluids
Not on syllabus
Steady-state
Incompressible
Inviscid
Uniform
density
Barotropic
(density only
a function of
pressure)
Constant
dynamic
viscosity
Dimensionality
Vorticity
Momentum equation
N
Surname: 1
Course:
Name:
Tutor:
Date:
Capacity management in health care centers
It has been found that every hospital will prioritize on how the expenses will be reduced
and what can be done to increase the efficiency of the services[Reg10]. It is with v
Surname: 1
Course:
Name:
Tutor:
Date:
Computer science questions
3.3
The operating system must keep track of main memory address space so that there will be no
other programs in the memory that will affect the working of the normal programs.
Time overhead
Running Head: CAR ACCIDENTS IN UAE
1
Car accidents in UAE
Name:
Institution:
Introduction
Car accidents are really disgusting to happen to a driver. Most of the road users are
clearly aware of the rules and regulations for driving. They also know the impa
Running head: COMPLY OR EXPLAIN
1
Comply or explain is the right approach
Institution:
Name:
COMPLY OR EXPLAIN
2
Introduction
Comply or explain is an approach that has been used in companies and organizations to
positively recognize that an alternative to