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Last week: Highlights from
my research
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.
Adjacency defines topological species of each particle
Termini = particles
touching only one other
particle
Branching points =
particles touching three
or more other particles
Trunks = particles
touching only two other
particles
Particles become termini or three-fold branch points in stage III. In
addition there are a few loners (less than 1%). Loners are not
connected to any other particle. There are no closed loops in stage III.
Emergent property: Relative number of each species is
robust
Graphs show how the number of termini, T, and branching
points, B, scale with the total number of particles in the tree.
J. Jun, A. Hubler, PNAS 102, 536 (2005)
The number of trees is not an emergent property
J. Jun, A. Hubler, PNAS 102, 536 (2005)
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