Nonequilibrium dynamics and anomalous fluctuations of …：非平衡动力学和异常波动….ppt

Unit conversions Height H= 2 m = 2 · 3.28 feet = 6.56 feet 1m=3.28 feet 2. Time of light propagation from the Sun to the Earth 8 minutes = 8·60 s = 480 s 3. Speed of a car v = 36 miles/hour = 36·1600m/3600s=16m/s 1hour=60·60s=3600s 1mile =1.6 km = 1600 m Dimensional analysis Dimensions of the physical quantities are algebraic combinations of the fundamental dimensions of length [L], mass [M], and time [ T ]. Example: x=vt ? [L] = [ L / T ] · [ T ] but x ≠ vt2 since [L] ≠ [ L / T ] · [ T ]2 = [ L ] · [ T ] Scales and units of physical quantities 1 second = 9 192 631 770 cycles of electron in cesium-133 atomic clock 1 second ≈ 1 day / (24·60·60) 1 year ≈ π·107 seconds ≈ 3·107 s 1 meter = c · (1 / 299792458) s , where a speed of light in vacuum is c=299792458 m/s ≈ 300 000 km/s. Size of an atom La~1 Angstr?m = 1? =10-10m ~ c·10-18s 1 light year = c·1year ≈ 3·108 m/s · 3·107 s ≈ 1016 m Size of the Universe is 13.7 billion years · c = 13.7·109 ly 1 kilogram= mass of a standard cylinder of platinum-iridium alloy =1000g Proton mass ≈ neutron mass is mp ~ 10-24 g = 10 -27 kg Milky Way Galaxy D ~ 100 000 light years R ~ 30 000 light years Center of Galaxy Distance to the nearest star Proxima Centauri is L=4.2 ly Sun Time of space travel to Proxima Centauri T = L/v =4.2years·c/v = 4.2 years · (300 000 km/s / 30 km/s) = 42 000 years Vector algebra Scalar is a real number independent on coordinate system: mass, volume, distance, pressure, temperature, … Tail-to -head Vector (arrow with magnitude and direction) is a set of components which transform as with a basis rotation Pythagorean theorem → Magnitude: Directi