1,155 research outputs found
Generalized quasiperiodic Rauzy tilings
We present a geometrical description of new canonical -dimensional
codimension one quasiperiodic tilings based on generalized Fibonacci sequences.
These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual
Penrose and icosahedral tilings. Thanks to a natural indexing of the sites
according to their local environment, we easily write down, for any
approximant, the sites coordinates, the connectivity matrix and we compute the
structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change
Easy plane baby skyrmions
The baby Skyrme model is studied with a novel choice of potential, . This "easy plane" potential vanishes at the equator of the target
two-sphere. Hence, in contrast to previously studied cases, the boundary value
of the field breaks the residual SO(2) internal symmetry of the model.
Consequently, even the unit charge skyrmion has only discrete symmetry and
consists of a bound state of two half lumps. A model of long-range
inter-skyrmion forces is developed wherein a unit skyrmion is pictured as a
single scalar dipole inducing a massless scalar field tangential to the vacuum
manifold. This model has the interesting feature that the two-skyrmion
interaction energy depends only on the average orientation of the dipoles
relative to the line joining them. Its qualitative predictions are confirmed by
numerical simulations. Global energy minimizers of charges B=1,...,14,18,32 are
found numerically. Up to charge B=6, the minimizers have 2B half lumps
positioned at the vertices of a regular 2B-gon. For charges B >= 7, rectangular
or distorted rectangular arrays of 2B half lumps are preferred, as close to
square as possible.Comment: v3: replaced with journal version, one new reference, one deleted
reference; 8 pages, 5 figures v2: fixed some typos and clarified the
relationship with condensed matter systems 8 pages, 5 figure
Milton\u27s Adherence to Aristotle\u27s Antient Rule in the Composition of Samson Agonistes
The vast body of Milton scholarship is rich in studies of Samson Agonistes. Almost every imaginable facet of the work has received careful consideration: its biographical significance, its historical backgrounds, its link to Greek tragedy, its Hebraic source and inspiration, its structure, language, and verse forms, Throughout the critical examinations of the play, references are frequent to Aristotle\u27s Poetics, particularlyto Milton\u27s interpretation of the Aristotelian katharsis and to the quantitative parts of tragedy as applied to Samson Agonistes. The emphasis has been upon Milton\u27s indebtedness to Greek tragedy, however, rather than upon his debt to the Poetics. This paper is concerned, therefore, in bringing together what has been said on the subject of Milton\u27s debt to Aristotle, and in applying directly to Samson Agonistes Aristotle\u27s antient rule as set forth in the Poetics
Adaptive finite element method assisted by stochastic simulation of chemical systems
Stochastic models of chemical systems are often analysed by solving the corresponding\ud
Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability\ud
distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density
Points of Ninth Order on Cubic Curves
In this paper we geometrically provide a necessary and sufficient condition for points on a cubic to be associated with an infinite family of other cubics who have nine-pointic contact at that point. We then provide a parameterization of the family of cubics with nine-pointic contact at that point, based on the osculating quadratic
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