Transcript Discussion 11

Last week:
Magnets & transformers
A magnet is a material or object that produces a
magnetic field. A method to detect a magnetic field is
to scatter iron filings and observe their pattern.
An electromagnet is a wire coil in which the
magnetic field is produced by the flow of an electric
current.
A transformer are two coils that transfer electrical
energy from one circuit to another through magnetic
coupling. A changing current in the first coil (the
primary ) creates a changing magnetic field; in turn,
this magnetic field induces a changing voltage in the
second coil (the secondary).
Iron filings that have oriented
in the magnetic field produced
by a bar magnet & a coil
Course Summary
Basic Concepts
Matter: Atoms with a heavy nucleus and some electrons “circling” around.
Electrons are negatively charged and very light.
The nucleus is made of positive protons and neutral neutrons. The mass of the atom is
proportional to the number of protons and neutrons in the nucleus.
Phase changes of matter: When heat is added to
- ice, the temperature of the ice increases till it reaches the melting temperature;
- a mixture of ice and water, the temperature stays at the melting temperature,
and more and more ice melts;
-liquid water, the temperature of the water increases till it reaches the boiling
Temperature (100oC);
-boiling water and water vapor, the temperature stays at the boiling temperature and more and
more water evaporates
-water vapor, the temperature of the vapor increases
Mass: The mass of an object is the same, everywhere in the universe. It is measured in kg.
Gravity: The gravitation force on a object is the same, everywhere on Earth, but less on the
Moon, and greater on the Sun. It is measured in lbs or Newton.
Floating: The buoyancy force is opposite and equal to the weight force of the displaced liquid.
Density of salt water > density of fresh water => object less submerged in salt water.
Mechanical equilibrium: The net force is zero and the net torque is zero (balancing beam).
Torque = (perpendicular force counter-clock-wise) * (displacement between axis and point of
attack).
Displacement =Change in position
Velocity = Displacement / Time
Motion with constant velocity:
- Net force is zero (Newton’s first law).
- Position versus time is linear (graph), - i.e. displacement = velocity * time
- Example: Rock sinking in a viscous media, parachute: air resistance = - weightforce.
Acceleration: Change in velocity / Time
Motion with constant acceleration:
-Net force is constant: Force = mass * acceleration (Newton’s second law).
- Velocity versus time is linear, -i.e. velocity = acceleration * time
-Example: Rock in free fall – y-axis points upwards – F=ma -> -m g = m a -> a = -g
Energy: Kinetic energy = mass * velocity2 /2
Potential energy = mass * gravity * height -example: ramp - kinetic energy= potential energy
Simple electronic circuits: a battery and a resistor in a closed loop (no
short cut).
Voltage drop = current * resistance
Power consumption = resistance * current2
Example: parallel light bulbs – serial light bulbs
Magnets: detected with iron filing patterns
- created by a loop current,
- two poles (North and South),
-equal poles repel, opposite poles attract (geographic North pole is a
magnetic South pole)
-there is a torque on a magnet in a magnetic field => electro motors
- changing magnetic field induces a loop current
Today: Highlights from my
research - Complex Systems
Complex systems:
A system with a large throughput of
- a fluid = turbulence, river networks
- chemicals = flames & explosion
- tension = fracture
- electrical current = lightning, dielectric breakthrough
- information = internet, social networks
The throughput is large means “sudden appearance of
a pattern or dynamics (self-organization)”
This self-organization causes emergent properties.
Complex Systems Research
Project: Predicting the
growth of ramified networks
Alfred Hübler
Center for Complex Systems Research
University of Illinois at Urbana-Champaign
Research supported in part by the National Science Foundation
(DMS-03725939 ITR)
We study:
Growth of networks in a reproducible lab
experiment, here:
the structure of materials with high-voltage
currents; which quantities a reproducible?
We find:
Materials produced in a high-voltage
current develop open-loop, fractal
structures which maximize the conductivity
for the applied current. These fractal
structures can be predicted with graphtheoretical models.