23,610 research outputs found
The Feynman-Wilson gas and the Lund model
We derive a partition function for the Lund fragmentation model and compare
it with that of a classical gas. For a fixed rapidity ``volume'' this partition
function corresponds to a multiplicity distribution which is very close to a
binomial distribution. We compare our results with the multiplicity
distributions obtained from the JETSET Monte Carlo for several scenarios.
Firstly, for the fragmentation vertices of the Lund string. Secondly, for the
final state particles both with and without decays.Comment: Latex, 21+1 pages, 11 figure
Residue currents associated with weakly holomorphic functions
We construct Coleff-Herrera products and Bochner-Martinelli type residue
currents associated with a tuple of weakly holomorphic functions, and show
that these currents satisfy basic properties from the (strongly) holomorphic
case, as the transformation law, the Poincar\'e-Lelong formula and the
equivalence of the Coleff-Herrera product and the Bochner-Martinelli type
residue current associated with when defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In
particular, corrected and clarified some things in Section 5 and 6 regarding
products of weakly holomorphic functions and currents, and the definition of
the Bochner-Martinelli type current
Time-resolved extinction rates of stochastic populations
Extinction of a long-lived isolated stochastic population can be described as
an exponentially slow decay of quasi-stationary probability distribution of the
population size. We address extinction of a population in a two-population
system in the case when the population turnover -- renewal and removal -- is
much slower than all other processes. In this case there is a time scale
separation in the system which enables one to introduce a short-time
quasi-stationary extinction rate W_1 and a long-time quasi-stationary
extinction rate W_2, and develop a time-dependent theory of the transition
between the two rates. It is shown that W_1 and W_2 coincide with the
extinction rates when the population turnover is absent, and present but very
slow, respectively. The exponentially large disparity between the two rates
reflects fragility of the extinction rate in the population dynamics without
turnover.Comment: 8 pages, 4 figure
On marginally outer trapped surfaces in stationary and static spacetimes
In this paper we prove that for any spacelike hypersurface containing an
untrapped barrier in a stationary spacetime satisfying the null energy
condition, any marginally outer trapped surface cannot lie in the exterior
region where the stationary Killing vector is timelike. In the static case we
prove that any marginally outer trapped surface cannot penetrate into the
exterior region where the static Killing vector is timelike. In fact, we prove
these result at an initial data level, without even assuming existence of a
spacetime. The proof relies on a powerful theorem by Andersson and Metzger on
existence of an outermost marginally outer trapped surface.Comment: 22 pages, 3 figures; 1 reference added, 1 figure changed, other minor
change
Shock propagation and stability in causal dissipative hydrodynamics
We studied the shock propagation and its stability with the causal
dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence
of the usual viscosity is not enough to stabilize the solution. This problem is
solved by introducing an additional viscosity which is related to the
coarse-graining scale of the theory.Comment: 14 pages, 16 figure
Gravitational-wave astronomy: the high-frequency window
This contribution is divided in two parts. The first part provides a
text-book level introduction to gravitational radiation. The key concepts
required for a discussion of gravitational-wave physics are introduced. In
particular, the quadrupole formula is applied to the anticipated
``bread-and-butter'' source for detectors like LIGO, GEO600, EGO and TAMA300:
inspiralling compact binaries. The second part provides a brief review of high
frequency gravitational waves. In the frequency range above (say) 100Hz,
gravitational collapse, rotational instabilities and oscillations of the
remnant compact objects are potentially important sources of gravitational
waves. Significant and unique information concerning the various stages of
collapse, the evolution of protoneutron stars and the details of the
supranuclear equation of state of such objects can be drawn from careful study
of the gravitational-wave signal. As the amount of exciting physics one may be
able to study via the detections of gravitational waves from these sources is
truly inspiring, there is strong motivation for the development of future
generations of ground based detectors sensitive in the range from hundreds of
Hz to several kHz.Comment: 21 pages, 5 figures, Lectures presented at the 2nd Aegean Summer
School on the Early Universe, Syros, Greece, September 200
Entanglement of distant optomechanical systems
We theoretically investigate the possibility to generate non-classical states
of optical and mechanical modes of optical cavities, distant from each other. A
setup comprised of two identical cavities, each with one fixed and one movable
mirror and coupled by an optical fiber, is studied in detail. We show that with
such a setup there is potential to generate entanglement between the distant
cavities, involving both optical and mechanical modes. The scheme is robust
with respect to dissipation, and nonlocal correlations are found to exist in
the steady state at finite temperatures.Comment: 12 pages (published with minor modifications
Adiabatic radio frequency potentials for the coherent manipulation of matter waves
Adiabatic dressed state potentials are created when magnetic sub-states of
trapped atoms are coupled by a radio frequency field. We discuss their
theoretical foundations and point out fundamental advantages over potentials
purely based on static fields. The enhanced flexibility enables one to
implement numerous novel configurations, including double wells, Mach-Zehnder
and Sagnac interferometers which even allows for internal state-dependent atom
manipulation. These can be realized using simple and highly integrated wire
geometries on atom chips.Comment: 13 pages, 2 figure
A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
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