206 research outputs found
Stochastic Description of Agglomeration and Growth Processes in Glasses
We show how growth by agglomeration can be described by means of algebraic or
differential equations which determine the evolution of probabilities of
various local configurations. The minimal fluctuation condition is used to
define vitrification. Our methods have been successfully used for the
description of glass formation.Comment: 9 pages, 1 figure, LaTeX 2e, uses ws-ijmpb.cls ; submitted to
International Journal of Modern Physics
Z_3-graded exterior differential calculus and gauge theories of higher order
We present a possible generalization of the exterior differential calculus,
based on the operator d such that d^3=0, but d^2\not=0. The first and second
order differentials generate an associative algebra; we shall suppose that
there are no binary relations between first order differentials, while the
ternary products will satisfy the cyclic relations based on the representation
of cyclic group Z_3 by cubic roots of unity. We shall attribute grade 1 to the
first order differentials and grade 2 to the second order differentials; under
the associative multiplication law the grades add up modulo 3. We show how the
notion of covariant derivation can be generalized with a 1-form A, and we give
the expression in local coordinates of the curvature 3-form. Finally, the
introduction of notions of a scalar product and integration of the Z_3-graded
exterior forms enables us to define variational principle and to derive the
differential equations satisfied by the curvature 3-form. The Lagrangian
obtained in this way contains the invariants of the ordinary gauge field tensor
F_{ik} and its covariant derivatives D_i F_{km}.Comment: 13 pages, no figure
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