247 research outputs found
Positive approximations of the inverse of fractional powers of SPD M-matrices
This study is motivated by the recent development in the fractional calculus
and its applications. During last few years, several different techniques are
proposed to localize the nonlocal fractional diffusion operator. They are based
on transformation of the original problem to a local elliptic or
pseudoparabolic problem, or to an integral representation of the solution, thus
increasing the dimension of the computational domain. More recently, an
alternative approach aimed at reducing the computational complexity was
developed. The linear algebraic system , is considered, where is a properly normalized (scalded) symmetric
and positive definite matrix obtained from finite element or finite difference
approximation of second order elliptic problems in ,
. The method is based on best uniform rational approximations (BURA)
of the function for and natural .
The maximum principles are among the major qualitative properties of linear
elliptic operators/PDEs. In many studies and applications, it is important that
such properties are preserved by the selected numerical solution method. In
this paper we present and analyze the properties of positive approximations of
obtained by the BURA technique. Sufficient conditions for
positiveness are proven, complemented by sharp error estimates. The theoretical
results are supported by representative numerical tests
SPHERES, J\"ulich's High-Flux Neutron Backscattering Spectrometer at FRM II
SPHERES (SPectrometer with High Energy RESolution) is a third-generation
neutron backscattering spectrometer, located at the 20 MW German neutron source
FRM II and operated by the Juelich Centre for Neutron Science. It offers an
energy resolution (fwhm) better than 0.65 micro-eV, a dynamic range of +-31
micro-eV, and a signal-to-noise ratio of up to 1750:1.Comment: 12 pages, 7 figures, 2 tables. Supplemental material consists of 3
pages, 2 figures, 2 table
A note on the convergence of parametrised non-resonant invariant manifolds
Truncated Taylor series representations of invariant manifolds are abundant
in numerical computations. We present an aposteriori method to compute the
convergence radii and error estimates of analytic parametrisations of
non-resonant local invariant manifolds of a saddle of an analytic vector field,
from such a truncated series. This enables us to obtain local enclosures, as
well as existence results, for the invariant manifolds
The High-Flux Backscattering Spectrometer at the NIST Center for Neutron Research
We describe the design and current performance of the high-flux
backscattering spectrometer located at the NIST Center for Neutron Research.
The design incorporates several state-of-the-art neutron optical devices to
achieve the highest flux on sample possible while maintaining an energy
resolution of less than 1mueV. Foremost among these is a novel phase-space
transformation chopper that significantly reduces the mismatch between the beam
divergences of the primary and secondary parts of the instrument. This resolves
a long-standing problem of backscattering spectrometers, and produces a
relative gain in neutron flux of 4.2. A high-speed Doppler-driven monochromator
system has been built that is capable of achieving energy transfers of up to
+-50mueV, thereby extending the dynamic range of this type of spectrometer by
more than a factor of two over that of other reactor-based backscattering
instruments
The Complexity of Flat Freeze LTL
We consider the model-checking problem for freeze LTL on one-counter automata (OCAs). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared with one another. As the model-checking problem is undecidable in general, we focus on the flat fragment of freeze LTL, in which the usage of the freeze quantifier is restricted. Recently, Lechner et al. showed that model checking for flat freeze LTL on OCAs with binary encoding of counter updates is decidable and in 2NEXPTIME. In this paper, we prove that the problem is, in fact, NEXPTIME-complete no matter whether counter updates are encoded in unary or binary. Like Lechner et al., we rely on a reduction to the reachability problem in OCAs with parameterized tests (OCAPs). The new aspect is that we simulate OCAPs by alternating two-way automata over words. This implies an exponential upper bound on the parameter values that we exploit towards an NP algorithm for reachability in OCAPs with unary updates. We obtain our main result as a corollary
Coherent energy manipulation in single-neutron interferometry
We have observed the stationary interference oscillations of a
triple-entangled neutron state in an interferometric experiment. Time-dependent
interaction with two radio-frequency (rf) fields enables coherent manipulation
of an energy degree of freedom in a single neutron. The system is characterized
by a multiply entangled state governed by a Jaynes-Cummings Hamiltonian. The
experimental results confirm coherence of the manipulation as well as the
validity of the description.Comment: 4 pages, 3 figure
(Non)Existence of Pleated Folds: How Paper Folds Between Creases
We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zero-thickness paper. In contrast, we show that the model can be folded with additional creases, suggesting that real paper “folds” into this model via small such creases. We conjecture that the circular version of this model, consisting simply of concentric circular creases, also folds without extra creases. At the heart of our results is a new structural theorem characterizing uncreased intrinsically flat surfaces—the portions of paper between the creases. Differential geometry has much to say about the local behavior of such surfaces when they are sufficiently smooth, e.g., that they are torsal ruled. But this classic result is simply false in the context of the whole surface. Our structural characterization tells the whole story, and even applies to surfaces with discontinuities in the second derivative. We use our theorem to prove fundamental properties about how paper folds, for example, that straight creases on the piece of paper must remain piecewise-straight (polygonal) by folding.National Science Foundation (U.S.) (CAREER Award CCF-0347776
Reflection and Transmission in a Neutron-Spin Test of the Quantum Zeno Effect
The dynamics of a quantum system undergoing frequent "measurements", leading
to the so-called quantum Zeno effect, is examined on the basis of a
neutron-spin experiment recently proposed for its demonstration. When the
spatial degrees of freedom are duely taken into account, neutron-reflection
effects become very important and may lead to an evolution which is totally
different from the ideal case.Comment: 26 pages, 6 figure
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