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  2. Lattice Boltzmann methods - Wikipedia

    en.wikipedia.org/wiki/Lattice_Boltzmann_methods

    Schematic of D2Q9 lattice vectors for 2D Lattice Boltzmann. Unlike CFD methods that solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice.

  3. Lattice model (physics) - Wikipedia

    en.wikipedia.org/wiki/Lattice_model_(physics)

    In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.

  4. Map of lattices - Wikipedia

    en.wikipedia.org/wiki/Map_of_lattices

    A complete lattice is bounded. 11. A heyting algebra is bounded. (def) 12. A bounded lattice is a lattice. (def) 13. A heyting algebra is residuated. 14. A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented. [4] 17. A boolean algebra is relatively ...

  5. Mie–Grüneisen equation of state - Wikipedia

    en.wikipedia.org/wiki/Mie–Grüneisen_equation...

    A temperature-corrected version that is used in computational mechanics has the form [6] [7]: 61 = [] +;:= where is the bulk speed of sound, is the initial density, is the current density, is Grüneisen's gamma at the reference state, = / is a linear Hugoniot slope coefficient, is the shock wave velocity, is the particle velocity, and is the internal energy per unit reference volume.

  6. Flory–Huggins solution theory - Wikipedia

    en.wikipedia.org/wiki/Flory–Huggins_solution...

    Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing.

  7. Vegard's law - Wikipedia

    en.wikipedia.org/wiki/Vegard's_law

    Here, a A (1-x) B x is the lattice parameter of the solid solution, a A and a B are the lattice parameters of the pure constituents, and x is the molar fraction of B in the solid solution. Vegard's law is seldom perfectly obeyed; often deviations from the linear behavior are observed. A detailed study of such deviations was conducted by King. [3]

  8. Lattice constant - Wikipedia

    en.wikipedia.org/wiki/Lattice_constant

    Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.

  9. Bravais lattice - Wikipedia

    en.wikipedia.org/wiki/Bravais_lattice

    All primitive unit cells with different shapes for a given crystal have the same volume by definition; For a given crystal, if n is the density of lattice points in a lattice ensuring the minimum amount of basis constituents and v is the volume of a chosen primitive cell, then nv = 1 resulting in v = 1/n, so every primitive cell has the same ...