616 research outputs found
A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases
Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases
have been given in several papers (see [2,3,7,8]). In the course of evaluation,
the sigh (or unit root) ambiguities are unavoidably occurred. This paper
presents another method, different from [7] and [8], to determine the sigh
(unit root) ambiguities of Gauss sums in the index 2 case, as well as the ones
with odd order in the non-cyclic index 4 case. And we note that the method in
this paper are more succinct and effective than [8] and [7]
Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case
Let be a prime number, for some positive integer , be a
positive integer such that , and let \k be a primitive
multiplicative character of order over finite field \fq. This paper
studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2
case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function).
Firstly, the classification of the Gauss sums in index 2 case is presented.
Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2
case with order being general even integer (i.e. N=2^{r}\cd N_0 where
are positive integers and is odd.) is obtained. Thus, the
problem of explicit evaluation of Gauss sums in index 2 case is completely
solved
Multi-model simulations of the impact of international shipping on Atmospheric Chemistry and Climate in 2000 and 2030
The global impact of shipping on atmospheric chemistry and radiative forcing, as well as the associated uncertainties, have been quantified using an ensemble of ten state-of-the-art atmospheric chemistry models and a predefined set of emission data. The analysis is performed for present-day conditions ( year 2000) and for two future ship emission scenarios. In one scenario ship emissions stabilize at 2000 levels; in the other ship emissions increase with a constant annual growth rate of 2.2% up to 2030 ( termed the "Constant Growth Scenario" (CGS)). Most other anthropogenic emissions follow the IPCC ( Intergovernmental Panel on Climate Change) SRES ( Special Report on Emission Scenarios) A2 scenario, while biomass burning and natural emissions remain at year 2000 levels. An intercomparison of the model results with observations over the Northern Hemisphere (25 degrees - 60 degrees N) oceanic regions in the lower troposphere showed that the models are capable to reproduce ozone (O-3) and nitrogen oxides (NOx= NO+ NO2) reasonably well, whereas sulphur dioxide (SO2) in the marine boundary layer is significantly underestimated. The most pronounced changes in annual mean tropospheric NO2 and sulphate columns are simulated over the Baltic and North Seas. Other significant changes occur over the North Atlantic, the Gulf of Mexico and along the main shipping lane from Europe to Asia, across the Red and Arabian Seas. Maximum contributions from shipping to annual mean near-surface O-3 are found over the North Atlantic ( 5 - 6 ppbv in 2000; up to 8 ppbv in 2030). Ship contributions to tropospheric O3 columns over the North Atlantic and Indian Oceans reach 1 DU in 2000 and up to 1.8 DU in 2030. Tropospheric O-3 forcings due to shipping are 9.8 +/- 2.0 mW/m(2) in 2000 and 13.6 +/- 2.3 mW/m(2) in 2030. Whilst increasing O-3, ship NOx simultaneously enhances hydroxyl radicals over the remote ocean, reducing the global methane lifetime by 0.13 yr in 2000, and by up to 0.17 yr in 2030, introducing a negative radiative forcing. The models show future increases in NOx and O-3 burden which scale almost linearly with increases in NOx emission totals. Increasing emissions from shipping would significantly counteract the benefits derived from reducing SO2 emissions from all other anthropogenic sources under the A2 scenario over the continents, for example in Europe. Globally, shipping contributes 3% to increases in O-3 burden between 2000 and 2030, and 4.5% to increases in sulphate under A2/CGS. However, if future ground based emissions follow a more stringent scenario, the relative importance of ship emissions will increase. Inter-model differences in the simulated O-3 contributions from ships are significantly smaller than estimated uncertainties stemming from the ship emission inventory, mainly the ship emission totals, the distribution of the emissions over the globe, and the neglect of ship plume dispersion
Excited-State Effective Masses in Lattice QCD
We apply black-box methods, i.e. where the performance of the method does not
depend upon initial guesses, to extract excited-state energies from
Euclidean-time hadron correlation functions. In particular, we extend the
widely used effective-mass method to incorporate multiple correlation functions
and produce effective mass estimates for multiple excited states. In general,
these excited-state effective masses will be determined by finding the roots of
some polynomial. We demonstrate the method using sample lattice data to
determine excited-state energies of the nucleon and compare the results to
other energy-level finding techniques.Comment: 18 pages, 6 figure
Big Entropy Fluctuations in Nonequilibrium Steady State: A Simple Model with Gauss Heat Bath
Large entropy fluctuations in a nonequilibrium steady state of classical
mechanics were studied in extensive numerical experiments on a simple 2-freedom
model with the so-called Gauss time-reversible thermostat. The local
fluctuations (on a set of fixed trajectory segments) from the average heat
entropy absorbed in thermostat were found to be non-Gaussian. Approximately,
the fluctuations can be discribed by a two-Gaussian distribution with a
crossover independent of the segment length and the number of trajectories
('particles'). The distribution itself does depend on both, approaching the
single standard Gaussian distribution as any of those parameters increases. The
global time-dependent fluctuations turned out to be qualitatively different in
that they have a strict upper bound much less than the average entropy
production. Thus, unlike the equilibrium steady state, the recovery of the
initial low entropy becomes impossible, after a sufficiently long time, even in
the largest fluctuations. However, preliminary numerical experiments and the
theoretical estimates in the special case of the critical dynamics with
superdiffusion suggest the existence of infinitely many Poincar\'e recurrences
to the initial state and beyond. This is a new interesting phenomenon to be
farther studied together with some other open questions. Relation of this
particular example of nonequilibrium steady state to a long-standing persistent
controversy over statistical 'irreversibility', or the notorious 'time arrow',
is also discussed. In conclusion, an unsolved problem of the origin of the
causality 'principle' is touched upon.Comment: 21 pages, 7 figure
Loop Representations
The loop representation plays an important role in canonical quantum gravity
because loop variables allow a natural treatment of the constraints. In these
lectures we give an elementary introduction to (i) the relevant history of
loops in knot theory and gauge theory, (ii) the loop representation of Maxwell
theory, and (iii) the loop representation of canonical quantum gravity. (Based
on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)Comment: 38 pages, MPI-Ph/93-9
Radiative forcing in the 21st century due to ozone changes in the troposphere and the lower stratosphere
Radiative forcing due to changes in ozone is expected for the 21st century. An assessment on changes in the tropospheric oxidative state through a model intercomparison ("OxComp'') was conducted for the IPCC Third Assessment Report (IPCC-TAR). OxComp estimated tropospheric changes in ozone and other oxidants during the 21st century based on the "SRES'' A2p emission scenario. In this study we analyze the results of 11 chemical transport models (CTMs) that participated in OxComp and use them as input for detailed radiative forcing calculations. We also address future ozone recovery in the lower stratosphere and its impact on radiative forcing by applying two models that calculate both tropospheric and stratospheric changes. The results of OxComp suggest an increase in global-mean tropospheric ozone between 11.4 and 20.5 DU for the 21st century, representing the model uncertainty range for the A2p scenario. As the A2p scenario constitutes the worst case proposed in IPCC-TAR we consider these results as an upper estimate. The radiative transfer model yields a positive radiative forcing ranging from 0.40 to 0.78 W m(-2) on a global and annual average. The lower stratosphere contributes an additional 7.5-9.3 DU to the calculated increase in the ozone column, increasing radiative forcing by 0.15-0.17 W m(-2). The modeled radiative forcing depends on the height distribution and geographical pattern of predicted ozone changes and shows a distinct seasonal variation. Despite the large variations between the 11 participating models, the calculated range for normalized radiative forcing is within 25%, indicating the ability to scale radiative forcing to global-mean ozone column change
Isomorphs in model molecular liquids
Isomorphs are curves in the phase diagram along which a number of static and
dynamic quantities are invariant in reduced units. A liquid has good isomorphs
if and only if it is strongly correlating, i.e., the equilibrium
virial/potential energy fluctuations are more than 90% correlated in the NVT
ensemble. This paper generalizes isomorphs to liquids composed of rigid
molecules and study the isomorphs of two systems of small rigid molecules, the
asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for
both systems we find that the isochoric heat capacity, the excess entropy, the
reduced molecular center-of-mass self part of the intermediate scattering
function, the reduced molecular center-of-mass radial distribution function to
a good approximation are invariant along an isomorph. In agreement with theory,
we also find that an instantaneous change of temperature and density from an
equilibrated state point to another isomorphic state point leads to no
relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be
more approximative than those of the asymmetric dumbbell model, which is
consistent with the OTP model being less strongly correlating. For both models
we find "master isomorphs", i.e., isomorphs have identical shape in the
virial/potential energy phase diagram.Comment: 20 page
Least-squares inversion for density-matrix reconstruction
We propose a method for reconstruction of the density matrix from measurable
time-dependent (probability) distributions of physical quantities. The
applicability of the method based on least-squares inversion is - compared with
other methods - very universal. It can be used to reconstruct quantum states of
various systems, such as harmonic and and anharmonic oscillators including
molecular vibrations in vibronic transitions and damped motion. It also enables
one to take into account various specific features of experiments, such as
limited sets of data and data smearing owing to limited resolution. To
illustrate the method, we consider a Morse oscillator and give a comparison
with other state-reconstruction methods suggested recently.Comment: 16 pages, REVTeX, 6 PS figures include
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