5,482 research outputs found
McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
Evidence is presented to suggest that, in three dimensions, spherical
6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32,
34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >=
54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and
12-designs for N=84, >= 86. The existence of some of these designs is
established analytically, while others are given by very accurate numerical
coordinates. The 24-point 7-design was first found by McLaren in 1963, and --
although not identified as such by McLaren -- consists of the vertices of an
"improved" snub cube, obtained from Archimedes' regular snub cube (which is
only a 3-design) by slightly shrinking each square face and expanding each
triangular face. 5-designs with 23 and 25 points are presented which, taken
together with earlier work of Reznick, show that 5-designs exist for N=12, 16,
18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9,
that these lists of t-designs are complete and that no others exist. One of the
constructions gives a sequence of putative spherical t-designs with N= 12m
points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur
Bidirectional syntactic priming across cognitive domains: from arithmetic to language and back
Scheepers et al. (2011) showed that the structure of a correctly solved mathematical equation affects how people subsequently complete sentences containing high vs. low relative-clause attachment ambiguities. Here we investigated whether such effects generalise to different structures and tasks, and importantly, whether they also hold in the reverse direction (i.e., from linguistic to mathematical processing). In a questionnaire-based experiment, participants had to solve structurally left- or right-branching equations (e.g., 5 × 2 + 7 versus 5 + 2 × 7) and to provide sensicality ratings for structurally left- or right-branching adjective-noun-noun compounds (e.g., alien monster movie versus lengthy monster movie). In the first version of the experiment, the equations were used as primes and the linguistic expressions as targets (investigating structural priming from maths to language). In the second version, the order was reversed (language-to-maths priming). Both versions of the experiment showed clear structural priming effects, conceptually replicating and extending the findings from Scheepers et al. (2011). Most crucially, the observed bi-directionality of cross-domain structural priming strongly supports the notion of shared syntactic representations (or recursive procedures to generate and parse them) between arithmetic and language
Ground state of a large number of particles on a frozen topography
Problems consisting in finding the ground state of particles interacting with
a given potential constrained to move on a particular geometry are surprisingly
difficult. Explicit solutions have been found for small numbers of particles by
the use of numerical methods in some particular cases such as particles on a
sphere and to a much lesser extent on a torus. In this paper we propose a
general solution to the problem in the opposite limit of a very large number of
particles M by expressing the energy as an expansion in M whose coefficients
can be minimized by a geometrical ansatz. The solution is remarkably universal
with respect to the geometry and the interaction potential. Explicit solutions
for the sphere and the torus are provided. The paper concludes with several
predictions that could be verified by further theoretical or numerical work.Comment: 9 pages, 9 figures, LaTeX fil
The Rate of Type Ia Supernovae at High Redshift
We derive the rates of Type Ia supernovae (SNIa) over a wide range of
redshifts using a complete sample from the IfA Deep Survey. This sample of more
than 100 SNIa is the largest set ever collected from a single survey, and
therefore uniquely powerful for a detailed supernova rate (SNR) calculation.
Measurements of the SNR as a function of cosmological time offer a glimpse into
the relationship between the star formation rate (SFR) and Type Ia SNR, and may
provide evidence for the progenitor pathway. We observe a progressively
increasing Type Ia SNR between redshifts z~0.3-0.8. The Type Ia SNR
measurements are consistent with a short time delay (t~1 Gyr) with respect to
the SFR, indicating a fairly prompt evolution of SNIa progenitor systems. We
derive a best-fit value of SFR/SNR 580 h_70^(-2) M_solar/SNIa for the
conversion factor between star formation and SNIa rates, as determined for a
delay time of t~1 Gyr between the SFR and the Type Ia SNR. More complete
measurements of the Type Ia SNR at z>1 are necessary to conclusively determine
the SFR--SNR relationship and constrain SNIa evolutionary pathways.Comment: 37 pages, 9 figures, accepted for publication in Astrophysical
Journal. Figures 7-9 correcte
Measuring Baryon Acoustic Oscillations with Millions of Supernovae
Since type Ia Supernovae (SNe) explode in galaxies, they can, in principle,
be used as the same tracer of the large-scale structure as their hosts to
measure baryon acoustic oscillations (BAOs). To realize this, one must obtain a
dense integrated sampling of SNe over a large fraction of the sky, which may
only be achievable photometrically with future projects such as the Large
Synoptic Survey Telescope. The advantage of SN BAOs is that SNe have more
uniform luminosities and more accurate photometric redshifts than galaxies, but
the disadvantage is that they are transitory and hard to obtain in large number
at high redshift. We find that a half-sky photometric SN survey to redshift z =
0.8 is able to measure the baryon signature in the SN spatial power spectrum.
Although dark energy constraints from SN BAOs are weak, they can significantly
improve the results from SN luminosity distances of the same data, and the
combination of the two is no longer sensitive to cosmic microwave background
priors.Comment: 4 pages, 3 figures, ApJL accepte
Synchronization of Sound Sources
Sound generation and -interaction is highly complex, nonlinear and
self-organized. Already 150 years ago Lord Rayleigh raised the following
problem: Two nearby organ pipes of different fundamental frequencies sound
together almost inaudibly with identical pitch. This effect is now understood
qualitatively by modern synchronization theory (M. Abel et al., J. Acoust. Soc.
Am., 119(4), 2006). For a detailed, quantitative investigation, we substituted
one pipe by an electric speaker. We observe that even minute driving signals
force the pipe to synchronization, thus yielding three decades of
synchronization -- the largest range ever measured to our knowledge.
Furthermore, a mutual silencing of the pipe is found, which can be explained by
self-organized oscillations, of use for novel methods of noise abatement.
Finally, we develop a specific nonlinear reconstruction method which yields a
perfect quantitative match of experiment and theory.Comment: 5 pages, 4 figure
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