What is space time diffusion?
In a nutshell, the space-time fractional diffusion equation in (1) consists of a fractional Riesz-Feller derivative of the order α > 0 (space-derivative) that encodes the space variations and a fractional Caputo derivative of the order β > 0 (time-derivative) that measures the time variations.
What is time fractional diffusion equation?
In this work, we consider the following time-fractional diffusion equation (1) D t β u = λ ∂ 2 u ∂ x 2 − ∂ ∂ x ( F ( x ) u ( x , t ) ) , 0 < β ≤ 1 , x , t > 0 with initial condition u ( x , 0 ) = f ( x ) .
What is fractional diffusion?
The fractional diffusion equation results from the mass or energy balances,(31) ∂ u ∂ t = d d x F ( x ) where refers to the flux at position x ∈ ( 0 , L ) ⊂ R , in particular the standard or anomalous fluxes, , Q α ( x ) or ⁎ Q ⁎ α ( x ) . In what follows, we restrict our analysis to the case where and 0 < α ≤ m = 1 .
Is there diffusion in space?
“In space, molecular diffusion draws oxygen to the flame and combustion products away from the flame at a rate 100 times slower than the buoyant flow on Earth,” said Dan Dietrich, FLEX project scientist at NASA’s Glenn Research Center in Ohio.
What does Fick’s Law of diffusion state?
Fick’s law states that the rate of diffusion of a substance across unit area (such as a surface or membrane) is proportional to the concentration gradient.
Can a fire burn in space?
Fires can’t start in space itself because there is no oxygen – or indeed anything else – in a vacuum. Yet inside the confines of spacecraft, and freed from gravity, flames behave in strange and beautiful ways. They burn at cooler temperatures, in unfamiliar shapes and are powered by unusual chemistry.
Why do we not use pencil in space?
NASA wanted an alternative to pencils because the lead could easily break off and float away, creating a hazard to astronauts and sensitive electronics on the spacecraft. Cosmonauts also have been using Space Pens since 1969.
What is the difference between fickian and non fickian diffusion?
The main difference between Fickian and Non Fickian Diffusion is the presence or absence of boundaries; there are no boundaries in Fickian diffusion whereas non Fickian diffusion has a sharp boundary separating the highly swollen region from a dry, glassy region.
What pen does NASA use?
Since the late 1960s American astronauts and Russian cosmonauts have used Fisher’s pens. In fact, Fisher has created a whole line of space pens. A newer pen, called the Shuttle Pen, was used on NASA’s space shuttles and on the Russian space station, Mir.
What does fickian diffusion mean?
Fickian diffusion refers to the solute transport process in which the polymer relaxation time (tr) is much greater than the characteristic solvent diffusion time (td). When tr ≈ td, the macroscopic drug release becomes anomalous or non-Fickian [3].
https://www.youtube.com/watch?v=y5V56BWvn-s