1,138 research outputs found
Enhanced Perturbative Continuous Unitary Transformations
Unitary transformations are an essential tool for the theoretical
understanding of many systems by mapping them to simpler effective models. A
systematically controlled variant to perform such a mapping is a perturbative
continuous unitary transformation (pCUT) among others. So far, this approach
required an equidistant unperturbed spectrum. Here, we pursue two goals: First,
we extend its applicability to non-equidistant spectra with the particular
focus on an efficient derivation of the differential flow equations, which
define the enhanced perturbative continuous unitary transformation (epCUT).
Second, we show that the numerical integration of the flow equations yields a
robust scheme to extract data from the epCUT. The method is illustrated by the
perturbation of the harmonic oscillator with a quartic term and of the two-leg
spin ladders in the strong-rung-coupling limit for uniform and alternating rung
couplings. The latter case provides an example of perturbation around a
non-equidistant spectrum.Comment: 27 pages, 18 figures; separated methodological background from
introduction, added perturbed harmonic oscillator for additional
illustration, added explicit solution of deepCUT equation
Communication: XUV transient absorption spectroscopy of iodomethane and iodobenzene photodissociation
Time-resolved extreme ultraviolet (XUV) transient absorption spectroscopy of
iodomethane and iodobenzene photodissociation at the iodine pre-N4,5 edge is
presented, using femtosecond UV pump pulses and XUV probe pulses from high
harmonic generation. For both molecules the molecular core-to-valence
absorption lines fade immediately, within the pump-probe time-resolution.
Absorption lines converging to the atomic iodine product emerge promptly in
CH3I but are time-delayed in C6H5I. We attribute this delay to the initial Ï â
Ï* excitation in iodobenzene, which is distant from the iodine reporter atom.
We measure a continuous shift in energy of the emerging atomic absorption
lines in CH3I, attributed to relaxation of the excited valence shell. An
independent particle model is used to rationalize the observed experimental
findings
A stochastic flow rule for granular materials
There have been many attempts to derive continuum models for dense granular
flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb
plasticity for quasi-2D granular materials to calculate (average) stresses and
slip planes, but we propose a "stochastic flow rule" (SFR) to replace the
principle of coaxiality in classical plasticity. The SFR takes into account two
crucial features of granular materials - discreteness and randomness - via
diffusing "spots" of local fluidization, which act as carriers of plasticity.
We postulate that spots perform random walks biased along slip-lines with a
drift direction determined by the stress imbalance upon a local switch from
static to dynamic friction. In the continuum limit (based on a Fokker-Planck
equation for the spot concentration), this simple model is able to predict a
variety of granular flow profiles in flat-bottom silos, annular Couette cells,
flowing heaps, and plate-dragging experiments -- with essentially no fitting
parameters -- although it is only expected to function where material is at
incipient failure and slip-lines are inadmissible. For special cases of
admissible slip-lines, such as plate dragging under a heavy load or flow down
an inclined plane, we postulate a transition to rate-dependent Bagnold
rheology, where flow occurs by sliding shear planes. With different yield
criteria, the SFR provides a general framework for multiscale modeling of
plasticity in amorphous materials, cycling between continuum limit-state stress
calculations, meso-scale spot random walks, and microscopic particle
relaxation
Height-diameter allometry of tropical forest trees
Tropical tree height-diameter (H:D) relationships may vary by forest type and region making large-scale estimates of above-ground biomass subject to bias if they ignore these differences in stem allometry. We have therefore developed a new global tropical forest database consisting of 39 955 concurrent H and D measurements encompassing 283 sites in 22 tropical countries. Utilising this database, our objectives were:
1. to determine if H:D relationships differ by geographic region and forest type (wet to dry forests, including zones of tension where forest and savanna overlap).
2. to ascertain if the H:D relationship is modulated by climate and/or forest structural characteristics (e.g. stand-level basal area, A).
3. to develop H:D allometric equations and evaluate biases to reduce error in future local-to-global estimates of tropical forest biomass.
Annual precipitation coefficient of variation (PV), dry season length (SD), and mean annual air temperature (TA) emerged as key drivers of variation in H:D relationships at the pantropical and region scales. Vegetation structure also played a role with trees in forests of a high A being, on average, taller at any given D. After the effects of environment and forest structure are taken into account, two main regional groups can be identified. Forests in Asia, Africa and the Guyana Shield all have, on average, similar H:D relationships, but with trees in the forests of much of the Amazon Basin and tropical Australia typically being shorter at any given D than their counterparts elsewhere. The region-environment-structure model with the lowest Akaike\u27s information criterion and lowest deviation estimated stand-level H across all plots to within amedian â2.7 to 0.9% of the true value. Some of the plot-to-plot variability in H:D relationships not accounted for by this model could be attributed to variations in soil physical conditions. Other things being equal, trees tend to be more slender in the absence of soil physical constraints, especially at smaller D. Pantropical and continental-level models provided less robust estimates of H, especially when the roles of climate and stand structure in modulating H:D allometry were not simultaneously taken into account
Consistent Treatment of Soft and Hard Processes in Hadronic Interactions
The QCD improved parton model is a very successful concept to treat processes
in hadronic interactions, whenever large partonic transverse momenta are
involved. However, cross sections diverge in the limit p_T -> 0, and the usual
treatment is the definition of a lower cutoff p_T_min, such that processes with
a smaller p_T -- so-called soft processes -- are simply ignored, which is
certainly not correct for example at RHIC energies. A more consistent procedure
amounts to introduce a technical parameter Q_0^2, referred to as soft
virtuality scale, which is nothing but an artificial borderline between soft
and hard physics. We will discuss such a formalism, which coincides with the
improved parton model for high p_T processes and with the phenomenological
treatment of soft scattering, when only small virtualities are involved. The
most important aspect of our approach is that it allows to obtain a smooth
transition between soft and hard scattering, and therefore no artificial
dependence on a cutoff parameter should appear.Comment: 19 pages, 19 figure
Introducing LoCo, a Logic for Configuration Problems
In this paper we present the core of LoCo, a logic-based high-level
representation language for expressing configuration problems. LoCo shall allow
to model these problems in an intuitive and declarative way, the dynamic
aspects of configuration notwithstanding. Our logic enforces that
configurations contain only finitely many components and reasoning can be
reduced to the task of model construction.Comment: In Proceedings LoCoCo 2011, arXiv:1108.609
On the Role of Energy Conservation in High-Energy Nuclear Scattering
We argue that most commonly used models for nuclear scattering at
ultra-relativistic energies do not treat energy conservation in a consistent
fashion. Demanding theoretical consistency as a minimal requirement for a
realistic model, we provide a solution for the above-mentioned problem, the
so-called ``Parton-Based Gribov-Regge Theory''. In order to keep a clean
picture, we do not consider secondary interactions. We provide a very
transparent extrapolation of the physics of more elementary interactions
towards nucleus-nucleus scattering, without considering any nuclear effects due
to final state interactions. In this sense we consider our model a realistic
and consistent approach to describe the initial stage of nuclear collisions.Comment: 17 pages, LaTeX created with LyX, 10 figure
The KATRIN Pre-Spectrometer at reduced Filter Energy
The KArlsruhe TRItium Neutrino experiment, KATRIN, will determine the mass of
the electron neutrino with a sensitivity of 0.2 eV (90% C.L.) via a measurement
of the beta-spectrum of gaseous tritium near its endpoint of E_0 =18.57 keV. An
ultra-low background of about b = 10 mHz is among the requirements to reach
this sensitivity. In the KATRIN main beam-line two spectrometers of MAC-E
filter type are used in a tandem configuration. This setup, however, produces a
Penning trap which could lead to increased background. We have performed test
measurements showing that the filter energy of the pre-spectrometer can be
reduced by several keV in order to diminish this trap. These measurements were
analyzed with the help of a complex computer simulation, modeling multiple
electron reflections both from the detector and the photoelectric electron
source used in our test setup.Comment: 22 pages, 12 figure
Static Friction Phenomena in Granular Materials: Coulomb Law vs. Particle Geometry
The static as well as the dynamic behaviour of granular material are
determined by dynamic {\it and} static friction. There are well known methods
to include static friction in molecular dynamics simulations using scarcely
understood forces. We propose an Ansatz based on the geometrical shape of
nonspherical particles which does not involve an explicit expression for static
friction. It is shown that the simulations based on this model are close to
experimental results.Comment: 11 pages, Revtex, HLRZ-33/9
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