50 research outputs found
Yet Another Characterization of Strong Equivalence
Strong equivalence of disjunctive logic programs is characterized here by a calculus that operates with syntactically simple formulas
Instabilities and Bifurcations of Nonlinear Impurity Modes
We study the structure and stability of nonlinear impurity modes in the
discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear
impurity emphasizing the effects of interplay between discreteness,
nonlinearity and disorder. We show how the interaction of a nonlinear localized
mode (a discrete soliton or discrete breather) with a repulsive impurity
generates a family of stationary states near the impurity site, as well as
examine both theoretical and numerical criteria for the transition between
different localized states via a cascade of bifurcations.Comment: 8 pages, 8 figures, Phys. Rev. E in pres
The Single-Particle density of States, Bound States, Phase-Shift Flip, and a Resonance in the Presence of an Aharonov-Bohm Potential
Both the nonrelativistic scattering and the spectrum in the presence of the
Aharonov-Bohm potential are analyzed. The single-particle density of states
(DOS) for different self-adjoint extensions is calculated. The DOS provides a
link between different physical quantities and is a natural starting point for
their calculation. The consequences of an asymmetry of the S matrix for the
generic self-adjoint extension are examined.
I. Introduction
II. Impenetrable flux tube and the density of states
III. Penetrable flux tube and self-adjoint extensions
IV. The S matrix and scattering cross sections
V. The Krein-Friedel formula and the resonance
VI. Regularization
VII. The R --> 0 limit and the interpretation of self-adjoint extensions
VIII. Energy calculations
IX. The Hall effect in the dilute vortex limit
X. Persistent current of free electrons in the plane pierced by a flux tube
XI. The 2nd virial coefficient of nonrelativistic interacting anyons
XII. Discussion of the results and open questionsComment: 68 pages, plain latex, 7 figures, 3 references and one figure added
plus a few minor text correction
Pearl's Causality in a Logical Setting
We provide a logical representation of Pearl's structural causal models in the causal calculus of McCain and Turner (1997) and its first-order generalization by Lifschitz. It will be shown that, under this representation, the nonmonotonic semantics of the causal calculus describes precisely the solutions of the structural equations (the causal worlds of the causal model), while the causal logic from Bochman (2004) is adequate for describing the behavior of causal models under interventions (forming submodels)
A numerical and analytical study of vortex rings with swirl
We study the growth of disturbances to vortex rings with swirl, which are exact solutions of the Euler equations of inviscid flow, using two contrasting methods. The motion of the perturbed vortex rings can be regarded as a prototype for the inviscid dynamics of vortex structures in 3D. Exact rings with swirl are computed as steady, axisymmetric flows using a variational method. Asymptotic analysis in the short wave limit, similar to geometric optics, leads to ordinary differential equations for perturbations along particle paths. These ODE's can be solved for the rings of interest, yielding predicted maximum growth rates for small disturbances. These rates are compared with the direct simulation of sample disturbances using a 3D vortex method to calculate the evolution according to the Euler equations