1,624 research outputs found
Barotropic fluid compatible parametrizations of dark energy
Parametrizations of Equation of state parameter as a function of the scale
factor or redshift are frequently used in dark energy modeling. The question
investigated in this paper is if parametrizations proposed in the literature
are compatible with the dark energy being a barotropic fluid. The test of this
compatibility is based on the functional form of the speed of sound squared,
which for barotropic fluid dark energy follows directly from the function for
the Equation of state parameter. The requirement that the speed of sound
squared should be between 0 and speed of light squared provides constraints on
model parameters using analytical and numerical methods. It is found that this
fundamental requirement eliminates a large number of parametrizations as
barotropic fluid dark energy models and puts strong constraints on parameters
of other dark energy parametrizations.Comment: v1: 19 pages, 1 table, 4 figures. v2: minor changes, references
added. v3: version accepted in EPJ
Improved Magnetic Information Storage using Return-Point Memory
The traditional magnetic storage mechanisms (both analog and digital) apply
an external field signal H(t) to a hysteretic magnetic material, and read the
remanent magnetization M(t), which is (roughly) proportional to H(t). We
propose a new analog method of recovering the signal from the magnetic
material, making use of the shape of the hysteresis loop M(H). The field H,
``stored'' in a region with N domains or particles, can be recovered with
fluctuations of order 1/N using the new method - much superior to the 1/sqrt{N}
fluctuations in traditional analog storage.Comment: 9 pages, 15 figure
The Stretch Factor of - and -Delaunay Triangulations
In this paper we determine the stretch factor of the -Delaunay and
-Delaunay triangulations, and we show that this stretch is
. Between any two points of such
triangulations, we construct a path whose length is no more than
times the Euclidean distance between and , and this
bound is best possible. This definitively improves the 25-year old bound of
by Chew (SoCG '86). To the best of our knowledge, this is the first
time the stretch factor of the well-studied -Delaunay triangulations, for
any real , is determined exactly
Does Australia Need Universities?
Scholarships & Prizes Office. University of Sydne
On the Time Variation of Fundamental Constants
We will define the mass of an electron in the context of Weinberg's empirical formula that relates the mass of a pion to fundamental physical constants, namely the gravitational and Planck constants, the speed of light in vacuum and the Hubble constant. After redefining the Weinberg formula to apply for electrons instead of pions we will add density parameters, used in modern Cosmology, to the Hubble constant in an attempt to persevere the universality of free fall which is one of the corner stones of General Relativity. Universality of free fall is not violated if fundamental physical constants do not vary with time which will be demonstrated in the aforementioned empirical formula for the electron mass and thus, subsequently the proton-to-electron mass ratio, the fine structure constant as well as for the gravitational constant
K-pop and Authoritarianism: Political Histories and Aesthetic Reflections in South Korea
Scholarships & Prizes Office. University of Sydne
Degree Four Plane Spanners: Simpler and Better
Let P be a set of n points embedded in the plane, and let C be the complete Euclidean graph whose point-set is P. Each edge in C between two points p, q is realized as the line segment [pq], and is assigned a weight equal to the Euclidean distance |pq|. In this paper, we show how to construct in O(nlg{n}) time a plane spanner of C of maximum degree at most 4 and of stretch factor at most 20. This improves a long sequence of results on the construction of bounded degree plane spanners of C. Our result matches the smallest known upper bound of 4 by Bonichon et al. on the maximum degree while significantly improving their stretch factor upper bound from 156.82 to 20. The construction of our spanner is based on Delaunay triangulations defined with respect to the equilateral-triangle distance, and uses a different approach than that used by Bonichon et al. Our approach leads to a simple and intuitive construction of a well-structured spanner, and reveals useful structural properties of the Delaunay triangulations defined with respect to the equilateral-triangle distance
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