2,734 research outputs found
On the Fredholm property of bisingular pseudodifferential operators
For operators belonging either to a class of global bisingular
pseudodifferential operators on or to a class of bisingular
pseudodifferential operators on a product of two closed smooth
manifolds, we show the equivalence of their ellipticity (defined by the
invertibility of certain associated homogeneous principal symbols) and their
Fredholm mapping property in associated scales of Sobolev spaces. We also prove
the spectral invariance of these operator classes and then extend these results
to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added
reference
Involution and Constrained Dynamics I: The Dirac Approach
We study the theory of systems with constraints from the point of view of the
formal theory of partial differential equations. For finite-dimensional systems
we show that the Dirac algorithm completes the equations of motion to an
involutive system. We discuss the implications of this identification for field
theories and argue that the involution analysis is more general and flexible
than the Dirac approach. We also derive intrinsic expressions for the number of
degrees of freedom.Comment: 28 pages, latex, no figure
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How does dynamical downscaling affect model biases and future projections of explosive extratropical cyclones along North America’s Atlantic coast?
Explosive extratropical cyclones (EETCs) are rapidly intensifying low pressure systems that generate severe weather along North America’s Atlantic coast. Global climate models (GCMs) tend to simulate too few EETCs, perhaps partly due to their coarse horizontal resolution and poorly resolved moist diabatic processes. This study explores whether dynamical downscaling can reduce EETC frequency biases, and whether this affects future projections of storms along North America’s Atlantic coast. A regional climate model (CanRCM4) is forced with the CanESM2 GCM for the periods 1981 to 2000 and 2081 to 2100. EETCs are tracked from relative vorticity using an objective feature tracking algorithm. CanESM2 simulates 38% fewer EETC tracks compared to reanalysis data, which is consistent with a negative Eady growth rate bias (−0.1 day−1). Downscaling CanESM2 with CanRCM4 increases EETC frequency by one third, which reduces the frequency bias to −22%, and increases maximum EETC precipitation by 22%. Anthropogenic greenhouse gas forcing is projected to decrease EETC frequency (−15%, −18%) and Eady growth rate (−0.2 day−1, −0.2 day−1), and increase maximum EETC precipitation (46%, 52%) in CanESM2 and CanRCM4, respectively. The limited effect of dynamical downscaling on EETC frequency projections is consistent with the lack of impact on the maximum Eady growth rate. The coarse spatial resolution of GCMs presents an important limitation for simulating extreme ETCs, but Eady growth rate biases are likely just as relevant. Further bias reductions could be achieved by addressing processes that lead to an underestimation of lower tropospheric meridional temperature gradients
Experimental and Numerical Study of the Dispersion and Transport of Automobile Exhaust Gases from Highways
This paper describes examples of modelling and of measurements of the dispersion and transport of exhaust gases from automobiles on a highway. Model runs were performed by a large-eddy-simulation model. The measurements were carried through by the DLR environmental research aircraft lee-side of the highway between München and Augsburg
Questionable Arguments for the Correctness of Perturbation Theory in Non-Abelian Models
We analyze the arguments put forward recently by Niedermayer et al in favor
of the correctness of conventional perturbation theory in non-Abelian models
and supposedly showing that our super-instanton counterexample was sick. We
point out that within their own set of assumptions, the proof of Niedermayer et
al regarding the correctness of perturbation theory is incorrect and provide a
correct proof under more restrictive assumptions. We reply also to their claim
that the S-matrix bootstrap approach of Balog et al supports the existence of
asymptotic freedom in the O(3) model.Comment: 9 page
Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins
We present the first analytical inspiral-merger-ringdown gravitational
waveforms from binary black holes (BBHs) with non-precessing spins, that is
based on a description of the late-inspiral, merger and ringdown in full
general relativity. By matching a post-Newtonian description of the inspiral to
a set of numerical-relativity simulations, we obtain a waveform family with a
conveniently small number of physical parameters. These waveforms will allow us
to detect a larger parameter space of BBH coalescence, including a considerable
fraction of precessing binaries in the comparable-mass regime, thus
significantly improving the expected detection rates.Comment: To appear in Phys. Rev. Lett. Significant new results. One figure
removed due to page limitatio
Spectroscopy of Ne for the thermonuclear O()Ne and F()O reaction rates
Uncertainties in the thermonuclear rates of the
O()Ne and F()O reactions
affect model predictions of light curves from type I X-ray bursts and the
amount of the observable radioisotope F produced in classical novae,
respectively. To address these uncertainties, we have studied the nuclear
structure of Ne over MeV and MeV using
the F(He,t)Ne reaction. We find the values of the
4.14 and 4.20 MeV levels to be consistent with and
respectively, in contrast to previous assumptions. We confirm the recently
observed triplet of states around 6.4 MeV, and find evidence that the state at
6.29 MeV, just below the proton threshold, is either broad or a doublet. Our
data also suggest that predicted but yet unobserved levels may exist near the
6.86 MeV state. Higher resolution experiments are urgently needed to further
clarify the structure of Ne around the proton threshold before a
reliable F()O rate for nova models can be determined.Comment: 5 pages, 3 figures, Phys. Rev. C (in press
On the General Analytical Solution of the Kinematic Cosserat Equations
Based on a Lie symmetry analysis, we construct a closed form solution to the
kinematic part of the (partial differential) Cosserat equations describing the
mechanical behavior of elastic rods. The solution depends on two arbitrary
analytical vector functions and is analytical everywhere except a certain
domain of the independent variables in which one of the arbitrary vector
functions satisfies a simple explicitly given algebraic relation. As our main
theoretical result, in addition to the construction of the solution, we proof
its generality. Based on this observation, a hybrid semi-analytical solver for
highly viscous two-way coupled fluid-rod problems is developed which allows for
the interactive high-fidelity simulations of flagellated microswimmers as a
result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure
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