4,087 research outputs found
Comment on "Spin-1 aggregation model in one dimension"
M. Girardi and W. Figueiredo have proposed a simple model of aggregation in
one dimension to mimic the self-assembly of amphiphiles in aqueous solution
[Phys. Rev. E 62, 8344 (2000)]. We point out that interesting results can be
obtained if a different set of interactions is considered, instead of their
choice (the s=1 Ising model).Comment: Accepted for publication in Phys. Rev.
Well-orders in the transfinite Japaridze algebra
This paper studies the transfinite propositional provability logics
\glp_\Lambda and their corresponding algebras. These logics have for each
ordinal a modality \la \alpha \ra. We will focus on the closed
fragment of \glp_\Lambda (i.e., where no propositional variables occur) and
\emph{worms} therein. Worms are iterated consistency expressions of the form
\la \xi_n\ra \ldots \la \xi_1 \ra \top. Beklemishev has defined
well-orderings on worms whose modalities are all at least and
presented a calculus to compute the respective order-types.
In the current paper we present a generalization of the original
orderings and provide a calculus for the corresponding generalized order-types
. Our calculus is based on so-called {\em hyperations} which are
transfinite iterations of normal functions.
Finally, we give two different characterizations of those sequences of
ordinals which are of the form \la {\formerOmega}_\xi (A) \ra_{\xi \in \ord}
for some worm . One of these characterizations is in terms of a second kind
of transfinite iteration called {\em cohyperation.}Comment: Corrected a minor but confusing omission in the relation between
Veblen progressions and hyperation
Hyperations, Veblen progressions and transfinite iterations of ordinal functions
In this paper we introduce hyperations and cohyperations, which are forms of
transfinite iteration of ordinal functions.
Hyperations are iterations of normal functions. Unlike iteration by pointwise
convergence, hyperation preserves normality. The hyperation of a normal
function f is a sequence of normal functions so that f^0= id, f^1 = f and for
all ordinals \alpha, \beta we have that f^(\alpha + \beta) = f^\alpha f^\beta.
These conditions do not determine f^\alpha uniquely; in addition, we require
that the functions be minimal in an appropriate sense. We study hyperations
systematically and show that they are a natural refinement of Veblen
progressions.
Next, we define cohyperations, very similar to hyperations except that they
are left-additive: given \alpha, \beta, f^(\alpha + \beta)= f^\beta f^\alpha.
Cohyperations iterate initial functions which are functions that map initial
segments to initial segments. We systematically study cohyperations and see how
they can be employed to define left inverses to hyperations.
Hyperations provide an alternative presentation of Veblen progressions and
can be useful where a more fine-grained analysis of such sequences is called
for. They are very amenable to algebraic manipulation and hence are convenient
to work with. Cohyperations, meanwhile, give a novel way to describe slowly
increasing functions as often appear, for example, in proof theory
Soft interactions in jet quenching
We study the collisional aspects of jet quenching in a high energy nuclear
collision, especially in the final state pion gas. The jet has a large energy,
and acquires momentum transverse to its axis more effectively by multiple soft
collisions than by few hard scatterings (as known from analogous systems such
as J/\psi production at Hera). Such regime of large E and small momentum
transfer corresponds to Regge kinematics and is characteristically dominated by
the pomeron. From this insight we estimate the jet quenching parameter in the
hadron medium (largely a pion gas) at the end of the collision, which is
naturally small and increases with temperature in line with the gas density.
The physics in the quark-gluon plasma/liquid phase is less obvious, and here we
revisit a couple of simple estimates that suggest indeed that the
pomeron-mediated interactions are very relevant and should be included in
analysis of the jet quenching parameter. Finally, the ocasional hard collisions
produce features characteristic of a L\`evy flight in the q_perp^2 plane
perpendicular to the jet axis. We suggest one- and two-particle q_perp
correlations as interesting experimental probes.Comment: 14 pages, 16 figure
REGIONAL AND URBAN SCIENCE IN FRANCE: RANKINGS OF AUTHORS AND INSTITUTIONS AND PUBLICATION PATTERNS DURING THE NINETIES
This article analyses the evolution experienced by research in urban and regional science in France between 1991 and 2000, comparing these changes with wider international trends. Nine of the leading international journals of regional and urban studies were used in drawing up rankings of countries, authors and institutions and in exploring publication patterns. We examine the strategy adopted by the French in establishing themselves within the world's top five in regional and urban research and report a number of interesting findings when comparisons are drawn internationally.REGIONAL AND URBAN SCIENCE, BIBLIOMETRICS, RANKINGS
X(3872) and its Partners in the Heavy Quark Limit of QCD
In this letter, we propose interpolating currents for the X(3872) resonance,
and show that, in the Heavy Quark limit of QCD, the X(3872) state should have
degenerate partners, independent of its internal structure. Magnitudes of
possible I=0 and I=1 components of the X(3872) are also discussed.Comment: 12 page
- …