484 research outputs found
Expansive actions on uniform spaces and surjunctive maps
We present a uniform version of a result of M. Gromov on the surjunctivity of
maps commuting with expansive group actions and discuss several applications.
We prove in particular that for any group and any field \K, the
space of -marked groups such that the group algebra \K[G] is
stably finite is compact.Comment: 21 page
On the density of periodic configurations in strongly irreducible subshifts
Let be a residually finite group and let be a finite set. We prove
that if is a strongly irreducible subshift of finite type
containing a periodic configuration then periodic configurations are dense in
. The density of periodic configurations implies in particular that every
injective endomorphism of is surjective and that the group of automorphisms
of is residually finite. We also introduce a class of subshifts , including all strongly irreducible subshifts and all irreducible sofic
subshifts, in which periodic configurations are dense
A note on a local ergodic theorem for an infinite tower of coverings
This is a note on a local ergodic theorem for a symmetric exclusion process
defined on an infinite tower of coverings, which is associated with a finitely
generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and
Statistic
Linear cellular automata: Garden of Eden Theorem, L-surjunctivity and group rings
This paper is a slightly extended version of the
lecture given by the first author at the “5th International Algebraic
Conference in Ukraine” held on July 20–27 2005 at the Odessa I.I.
Mechnikov National University
Von Neumann Regular Cellular Automata
For any group and any set , a cellular automaton (CA) is a
transformation of the configuration space defined via a finite memory set
and a local function. Let be the monoid of all CA over .
In this paper, we investigate a generalisation of the inverse of a CA from the
semigroup-theoretic perspective. An element is von
Neumann regular (or simply regular) if there exists
such that and , where is the composition of functions. Such an
element is called a generalised inverse of . The monoid
itself is regular if all its elements are regular. We
establish that is regular if and only if
or , and we characterise all regular elements in
when and are both finite. Furthermore, we study
regular linear CA when is a vector space over a field ; in
particular, we show that every regular linear CA is invertible when is
torsion-free elementary amenable (e.g. when ) and , and that every linear CA is regular when
is finite-dimensional and is locally finite with for all .Comment: 10 pages. Theorem 5 corrected from previous versions, in A.
Dennunzio, E. Formenti, L. Manzoni, A.E. Porreca (Eds.): Cellular Automata
and Discrete Complex Systems, AUTOMATA 2017, LNCS 10248, pp. 44-55, Springer,
201
Ion dynamics and coherent structure formation following laser pulse self-channeling
The propagation of a superintense laser pulse in an underdense, inhomogeneous
plasma has been studied numerically by two-dimensional particle-in-cell
simulations on a time scale extending up to several picoseconds. The effects of
the ion dynamics following the charge-displacement self-channeling of the laser
pulse have been addressed. Radial ion acceleration leads to the ``breaking'' of
the plasma channel walls, causing an inversion of the radial space-charge field
and the filamentation of the laser pulse. At later times a number of
long-lived, quasi-periodic field structures are observed and their dynamics is
characterized with high resolution. Inside the plasma channel, a pattern of
electric and magnetic fields resembling both soliton- and vortex-like
structures is observed.Comment: 10 pages, 5 figures (visit http://www.df.unipi.it/~macchi to download
a high-resolution version), to appear in Plasma Physics and Controlled Fusion
(Dec. 2007), special issue containing invited papers from the 34th EPS
Conference on Plasma Physics (Warsaw, July 2007
Harmonic generation by atoms in circularly polarized two-color laser fields with coplanar polarizations and commensurate frequencies
The generation of harmonics by atoms or ions in a two-color, coplanar field
configuration with commensurate frequencies is investigated through both, an
analytical calculation based on the Lewenstein model and the numerical ab
initio solution of the time-dependent Schroedinger equation of a
two-dimensional model ion. Through the analytical model, selection rules for
the harmonic orders in this field configuration, a generalized cut-off for the
harmonic spectra, and an integral expression for the harmonic dipole strength
is provided. The numerical results are employed to test the predictions of the
analytical model. The scaling of the cut-off as a function of both, one of the
laser intensities and frequency ratio , as well as entire spectra for
different and laser intensities are presented and analyzed. The
theoretical cut-off is found to be an upper limit for the numerical results.
Other discrepancies between analytical model and numerical results are
clarified by taking into account the probabilities of the absorption processes
involved.Comment: 8 figure
Generalized iterated wreath products of cyclic groups and rooted trees correspondence
Consider the generalized iterated wreath product where . We
prove that the irreducible representations for this class of groups are indexed
by a certain type of rooted trees. This provides a Bratteli diagram for the
generalized iterated wreath product, a simple recursion formula for the number
of irreducible representations, and a strategy to calculate the dimension of
each irreducible representation. We calculate explicitly fast Fourier
transforms (FFT) for this class of groups, giving literature's fastest FFT
upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science
Dynamics of charge-displacement channeling in intense laser-plasma interactions
The dynamics of transient electric fields generated by the interaction of
high intensity laser pulses with underdense plasmas has been studied
experimentally with the proton projection imaging technique. The formation of a
charged channel, the propagation of its front edge and the late electric field
evolution have been characterised with high temporal and spatial resolution.
Particle-in-cell simulations and an electrostatic, ponderomotive model
reproduce the experimental features and trace them back to the ponderomotive
expulsion of electrons and the subsequent ion acceleration.Comment: 5 figures, accepted for publication in New Journal of Physic
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