Yes, It may be a consequence of the statistical regularity condition in the B-matrix chains which predicts a diffusion coefficient α(3D)=9/4 * α(2D)
ref: Researchgate, theory and design of audio rooms.
Dear Ismail Abbas
In general, it takes more time for molecules or energy density to diffuse in 2D (two-dimensional) systems compared to 3D (three-dimensional) systems. This is because the availability of additional dimensions in 3D allows for greater freedom of movement and more pathways for diffusion.
In a 2D system, diffusion is restricted to movement along a plane or surface, limiting the options for molecules or energy to spread. This restricted movement reduces the opportunities for encounters and interactions between particles, resulting in slower diffusion rates.
On the other hand, in a 3D system, molecules or energy can diffuse in three spatial dimensions, providing a larger space for particles to move and interact. The increased volume allows for more collisions and a higher probability of encounters, facilitating faster diffusion compared to 2D systems.
It's important to note that the specific properties of the system, such as the nature of the particles involved, temperature, pressure, and the presence of barriers or obstacles, can also influence the diffusion process and may lead to variations in diffusion rates.
In most cases, molecules or energy diffuse faster in 3D than in 2D due to the availability of space for diffusion in 3D
The chains of the matrix B predict a diffusion coefficient α(3D)=9/4 * α(2D)
Moreover, transition matrix theory B suggests different times inside different closed volumes.
In other words, time passes more slowly inside larger volumes in proportion to V/A=Lc (V=Volume, A=inner surface and Lc is the so-called characteristic length.
Here are some examples of applications of transition matrix theory B:
i- Reformulation and numerical resolution of the time-dependent 3D PDE of Laplace and Poisson as well as the heat diffusion equation with Dirichlet boundary conditions in its most general form.
ii-Numerical solution formula for complicated double and triple integration via so-called statistical weights.
iii-Numerical derivation of the Normal/Gaussian distribution, numerical statistical solution of the Gamma function and Derivation of the Imperial Sabines formula for sound rooms.
...etc.
***
If you allow it, we are now going into a minefield because most physicists and mathematicians would claim that time is absolute.
But the question arises, what does this explicitly suggest as a reform of existing concepts?
If we assume that the vital processes of life in the description of organic and biochemical chemistry are based on a diffusion mechanism, we should expect larger creatures to live longer.
In other words, we can assign different lifespans to different animals, fish, and birds based on their volume and subcutaneous surface.
Here are some very crude remarks:
i-Animals
*Lifespan of the elephant = 65 years and its Lc=2.5m.
* Lifespan of a horse = 25 years and its Lc = 1.25 m
*Lifetime of an ant less than 1 year and its Lc is about 0.04 m
For the birds
**Lifespan of an eagle = 20 years
and its Lc=1 m
**Lifespan of a duck = 6 years
and its Lc=1/4 m
**Lifespan of a small bird = 2 years
and its Lc=1/10 m
For the fish
*** Lifespan of a whale = 100 years and its Lc = 5 m
Lifespan of an average fish = 5 years and its Lc = 0.25 m
This means that the average lifetime in years is approximately equal to 20 Lc in meters.
Here I should stop and leave comments for the Research Portal contributors.
ref:
1-Researchgate, IJISRT review, theory and design of audio rooms.
2-Researchgate, IJISRT review, How Nature Works in Four-Dimensional Space: The Untold Complex Story.
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