7,271 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
Z3-graded Grassmann Variables, Parafermions and their Coherent States
A relation between the -graded Grassmann variables and parafermions is
established. Coherent states are constructed as a direct consequence of such a
relationship. We also give the analog of the Bargmann-Fock representation in
terms of these Grassmann variables.Comment: 8 page
Probabilistic Description of Traffic Breakdowns
We analyze the characteristic features of traffic breakdown. To describe this
phenomenon we apply to the probabilistic model regarding the jam emergence as
the formation of a large car cluster on highway. In these terms the breakdown
occurs through the formation of a certain critical nucleus in the metastable
vehicle flow, which enables us to confine ourselves to one cluster model. We
assume that, first, the growth of the car cluster is governed by attachment of
cars to the cluster whose rate is mainly determined by the mean headway
distance between the car in the vehicle flow and, may be, also by the headway
distance in the cluster. Second, the cluster dissolution is determined by the
car escape from the cluster whose rate depends on the cluster size directly.
The latter is justified using the available experimental data for the
correlation properties of the synchronized mode. We write the appropriate
master equation converted then into the Fokker-Plank equation for the cluster
distribution function and analyze the formation of the critical car cluster due
to the climb over a certain potential barrier. The further cluster growth
irreversibly gives rise to the jam formation. Numerical estimates of the
obtained characteristics and the experimental data of the traffic breakdown are
compared. In particular, we draw a conclusion that the characteristic intrinsic
time scale of the breakdown phenomenon should be about one minute and explain
the case why the traffic volume interval inside which traffic breakdown is
observed is sufficiently wide.Comment: RevTeX 4, 14 pages, 10 figure
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
Modelling Widely Scattered States in `Synchronized' Traffic Flow and Possible Relevance for Stock Market Dynamics
Traffic flow at low densities (free traffic) is characterized by a
quasi-one-dimensional relation between traffic flow and vehicle density, while
no such fundamental diagram exists for `synchronized' congested traffic flow.
Instead, a two-dimensional area of widely scattered flow-density data is
observed as a consequence of a complex traffic dynamics. For an explanation of
this phenomenon and transitions between the different traffic phases, we
propose a new class of molecular-dynamics-like, microscopic traffic models
based on times to collisions and discuss the properties by means of analytical
arguments. Similar models may help to understand the laminar and turbulent
phases in the dynamics of stock markets as well as the transitions among them.Comment: Comments are welcome. For related work see http://www.helbing.or
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