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 N 1% loners 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