Model material points cannot be used for describing the motion of macroscopic bodies.
The derivation of the equations of continuum mechanics based on the use of limit theorems, in which the size of the domain (of a elementary volume) tends to zero, which allows the movement of the domain to describe by second law of Newton. However, the material point can not serve as a model of a domain (elementary volume) as part of a macroscopic body with its properties: any macro body consists of a large number of randomly moving structural elements (constituent particle). This suggests that the existing equations of continuum mechanics can not reflect the basic properties of real bodies.
Lev Kurlapov
A material point has no size and does not contain structural elements, so it cannot serve as a model of part of the bodies, which must be a domain (elementary volume).
Lev
The description of motion in continuum mechanics is just an approximation which, as it was already mentioned, works well to describe macroscopic and sometimes mesoscopic phenomena. The infinitesimal volumes are supposed to be small, but still made of a big number of atoms or molecules.
On the other side, we must be careful that we do not identify the mathematical artifacts we use to describe motion (like the centre of mass of an element in a continuum) with the physical systems we want to describe.
An object can be represented as a point in a first approximation if the size of this object is "far smaller" than the characteristic size of the motion you consider. For example, take the exemple of two-body systems: the Earth (r ~ 6 e6 m) is somewhat "microscopic" and can be considered as point-like when you describe its motion around the barycenter of the Solar System (R ~ 1.5 e11 m) but the Earth is "macroscopic" and cannot be considered as point-like if you deal with a close Earth-orbiting satellite (R ~ e5-e6 m).
Well, Keesom, Debye and London said that charged particles at the close proximity are no longer 'a material point', they are proportional to R3 (volume) rather than R2 (plane) while gravitational forces still depends on R2 since we can precisely measure only forces between small objects and very large objects...thus between Moon and Earth R3 forces could be used, but for simplicity we use R2 and then add some adjustments-corrections.
The World consists about of empty, as Oppi said: lot of microscopic particles at gigant distances. Each particle is of undetermined dimension and unknown density, as we suspect right now - this picture can be directly addressed to microworld scale in terms of colored subparticles. Therefore, these contradictions are if neglecting the mesostructure.
no need density and dimensions of masses, we need density of electric (electromagnetic) field and this is quite significant and even more significant in modeling VdW forces
Sure, Egidijus, fields look nice. Though, the main question, as well me understood, is on that why can one easy average a regular structure, say, with a type of crystal, starting from elementary cell, but how to average in mesoscale, for instance, a fractal structure or non periodicals, say Penrose's crystals, - this seems unresolved problem of interest - all the fields would definitely be of fatal hands up.
http://en.wikipedia.org/wiki/File:Penrose_Tiling_(Rhombi).svg
where are no such crystals in the universe, neither in the physical nor mental worlds...it is classed as a glass even if they will be stacked on top of each other in layers like in graphite...averaging is easy too, but I do not understand what do you wanna average here?
Why are you sure that the Lord missed such crystals? Just glasses? The averaging over smallest material volume, naturlich, is in the talk, - those elemental volumes which should be enough to define the mass density, and Young's modulus from the statistical ensemble, then to confirm in practice that's OK, as for standart iron #3. Else, the actual question will be in the case, even for martensite crystals.
Lord missed and computers and Mona Liza painting...no long range order along 3 orthogonal axis means there is no crystal, if order is in 2D or 1D then you will have Liquid Crystals, the rest are glasses or polycrystals (if state is solid), short range order exists in both, so your quasicrystal would be classed as a glass, but I still do not understand your english...what is your point? do you know the Lord's penrose crystal? first of all it is 2D model anyway, so even having some thin film we won't be able to distribute different atoms (or molecules) in such a way that they would preferably form Mona Liza painting...sorry
I've worried about this sort of thing for a long time. I have done a couple of rederivations of rheology built on some granular/finite scale considerations of the microstructure (not granular materials). Maybe it would interest you.
Article Objective Nontensor Rheology: Unique Flow Decompositions fro...
Dear Clifford Chafin, it is interest me. I resolved this problem using instead of material point mesoscopic particles look like in articles in attachment..
With regad , Lev
Lev, is your model (fitting) valid for all known liquid and gas systems? In other words how many distinct systems have you checked using your approach?
Dr. Kurlapov, sadly I got network errors trying to download these. Are these models for gas systems? Is yours a quasilocal approach?
That works! Thanks for that. I am mulling over eqn 3 from the Odessa paper. Can you explain it another way to me?
Dear Clifford,
In eq (3) there is flow of mass irreversible (diffusion) nature. About these term there are many discussions in Russian articles. I try to explain it in attachment.
In regards Lev
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