664 research outputs found
Hyperboloidal evolution of test fields in three spatial dimensions
We present the numerical implementation of a clean solution to the outer
boundary and radiation extraction problems within the 3+1 formalism for
hyperbolic partial differential equations on a given background. Our approach
is based on compactification at null infinity in hyperboloidal scri fixing
coordinates. We report numerical tests for the particular example of a scalar
wave equation on Minkowski and Schwarzschild backgrounds. We address issues
related to the implementation of the hyperboloidal approach for the Einstein
equations, such as nonlinear source functions, matching, and evaluation of
formally singular terms at null infinity.Comment: 10 pages, 8 figure
Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence
Stability properties and mode signature for equilibria of a model of electron
temperature gradient (ETG) driven turbulence are investigated by Hamiltonian
techniques. After deriving the infinite families of Casimir invariants,
associated with the noncanonical Poisson bracket of the model, a sufficient
condition for stability is obtained by means of the Energy-Casimir method. Mode
signature is then investigated for linear motions about homogeneous equilibria.
Depending on the sign of the equilibrium "translated" pressure gradient, stable
equilibria can either be energy stable, i.e.\ possess definite linearized
perturbation energy (Hamiltonian), or spectrally stable with the existence of
negative energy modes (NEMs). The ETG instability is then shown to arise
through a Kre\u{\i}n-type bifurcation, due to the merging of a positive and a
negative energy mode, corresponding to two modified drift waves admitted by the
system. The Hamiltonian of the linearized system is then explicitly transformed
into normal form, which unambiguously defines mode signature. In particular,
the fast mode turns out to always be a positive energy mode (PEM), whereas the
energy of the slow mode can have either positive or negative sign
On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson
The notions of spectral stability and the spectrum for the Vlasov-Poisson
system linearized about homogeneous equilibria, f_0(v), are reviewed.
Structural stability is reviewed and applied to perturbations of the linearized
Vlasov operator through perturbations of f_0. We prove that for each f_0 there
is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0f_0$ is perturbed by an area preserving rearrangement, f_0 will
always be stable if the continuous spectrum is only of positive signature,
where the signature of the continuous spectrum is defined as in previous work.
If there is a signature change, then there is a rearrangement of f_0 that is
unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is
analogous to Krein's theorem for the continuous spectrum. We prove that if a
discrete mode embedded in the continuous spectrum is surrounded by the opposite
signature there is an infinitesimal perturbation in C^n norm that makes f_0
unstable. If f_0 is stable we prove that the signature of every discrete mode
is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36
pages, 12 figure
Absorbing boundary conditions for the Westervelt equation
The focus of this work is on the construction of a family of nonlinear
absorbing boundary conditions for the Westervelt equation in one and two space
dimensions. The principal ingredient used in the design of such conditions is
pseudo-differential calculus. This approach enables to develop high order
boundary conditions in a consistent way which are typically more accurate than
their low order analogs. Under the hypothesis of small initial data, we
establish local well-posedness for the Westervelt equation with the absorbing
boundary conditions. The performed numerical experiments illustrate the
efficiency of the proposed boundary conditions for different regimes of wave
propagation
Universality of Performance Indicators based on Citation and Reference Counts
We find evidence for the universality of two relative bibliometric indicators
of the quality of individual scientific publications taken from different data
sets. One of these is a new index that considers both citation and reference
counts. We demonstrate this universality for relatively well cited publications
from a single institute, grouped by year of publication and by faculty or by
department. We show similar behaviour in publications submitted to the arXiv
e-print archive, grouped by year of submission and by sub-archive. We also find
that for reasonably well cited papers this distribution is well fitted by a
lognormal with a variance of around 1.3 which is consistent with the results of
Radicchi, Fortunato, and Castellano (2008). Our work demonstrates that
comparisons can be made between publications from different disciplines and
publication dates, regardless of their citation count and without expensive
access to the whole world-wide citation graph. Further, it shows that averages
of the logarithm of such relative bibliometric indices deal with the issue of
long tails and avoid the need for statistics based on lengthy ranking
procedures.Comment: 15 pages, 14 figures, 11 pages of supplementary material. Submitted
to Scientometric
Signatures for a Cosmic Flux of Magnetic Monopoles
Any early universe phase transition occurring after inflation has the
potential to populate the universe with relic magnetic monopoles. Observations
of galactic magnetic fields, as well as observations matched with models for
extragalactic magnetic fields, lead to the conclusion that monopoles of mass
\lsim 10^{15} GeV are accelerated in these fields to relativistic velocities.
We explore the possible signatures of a cosmic flux of relativistic monopoles
impinging on the earth. The electromagnetically-induced signatures of monopoles
are reliable. The hadronically-induced signatures are highly model-dependent.
Among our findings are (i) the electromagnetic energy losses of monopoles
continuously initiate a protracted shower of small intensity; (ii) monopoles
may traverse the earth's diameter, making them a probe of the earth's interior
structure; (iii) in addition to the direct monopole Cherenkov signal presently
employed, a very attractive search strategy for monopoles is detection of their
radio-Cherenkov signal produced by the coherent charge-excess in the
shower - in fact, Cherenkov-detectors have the potential to discover a monopole
flux (or limit it) several orders of magnitude below the theoretical Parker
limit of /s/sr; (iv) it is conceivable (but not compelling)
that bound states of colored monopoles may be the primary particles initiating
the air showers observed above the GZK cutoff.Comment: 33 pages, 5 figures, revtex, to appear in Astro. Part. Phy
Consensuality of Peer Nominations Among Scientists
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69069/2/10.1177_107554708200400210.pd
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