1,367 research outputs found
Superposition in nonlinear wave and evolution equations
Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme
superposition procedure are presented and used to generate superposition
solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE)
and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages,
2 figures, style change
Ground states and formal duality relations in the Gaussian core model
We study dimensional trends in ground states for soft-matter systems.
Specifically, using a high-dimensional version of Parrinello-Rahman dynamics,
we investigate the behavior of the Gaussian core model in up to eight
dimensions. The results include unexpected geometric structures, with
surprising anisotropy as well as formal duality relations. These duality
relations suggest that the Gaussian core model possesses unexplored symmetries,
and they have implications for a broad range of soft-core potentials.Comment: 7 pages, 1 figure, appeared in Physical Review E (http://pre.aps.org
Random perfect lattices and the sphere packing problem
Motivated by the search for best lattice sphere packings in Euclidean spaces
of large dimensions we study randomly generated perfect lattices in moderately
large dimensions (up to d=19 included). Perfect lattices are relevant in the
solution of the problem of lattice sphere packing, because the best lattice
packing is a perfect lattice and because they can be generated easily by an
algorithm. Their number however grows super-exponentially with the dimension so
to get an idea of their properties we propose to study a randomized version of
the algorithm and to define a random ensemble with an effective temperature in
a way reminiscent of a Monte-Carlo simulation. We therefore study the
distribution of packing fractions and kissing numbers of these ensembles and
show how as the temperature is decreased the best know packers are easily
recovered. We find that, even at infinite temperature, the typical perfect
lattices are considerably denser than known families (like A_d and D_d) and we
propose two hypotheses between which we cannot distinguish in this paper: one
in which they improve Minkowsky's bound phi\sim 2^{-(0.84+-0.06) d}, and a
competitor, in which their packing fraction decreases super-exponentially,
namely phi\sim d^{-a d} but with a very small coefficient a=0.06+-0.04. We also
find properties of the random walk which are suggestive of a glassy system
already for moderately small dimensions. We also analyze local structure of
network of perfect lattices conjecturing that this is a scale-free network in
all dimensions with constant scaling exponent 2.6+-0.1.Comment: 19 pages, 22 figure
Определение группового состава сырья и продуктов процесса каталитического крекинга при переработке вакуумного дистиллята из смеси казахстанской и Западно-Сибирской нефти
Experimental investigations on the fatigue resistance of automatically welded tubular X-joints for jacket support structures
The development within the offshore wind sector towards more powerful turbines combined with increasing water depth for new wind parks is challenging both the designer as well as the manufacturer of bottom fixed support structures. Besides XL-monopiles, the market developed an innovative and economic jacket support structure which is based on automatically manufactured tubular joints combined with standardized pipes. Besides the improvements for a serial manufacturing process the automatically welded tubular joints show a great potential in terms of fatigue resistance e.g. due to a smooth weld geometry without sharp notches. However, these benefits are not considered yet within the fatigue design process of automatically manufactured jacket substructures according to current standards due to the lack of suitable S-N curves. Therefore, 32 axial fatigue tests on single and double-sided automatically welded tubular X-joints have been performed to determine a new hot spot stress related S-N curve. Based on these constant amplitude fatigue tests a new S-N curve equal to a FAT 126 curve was computed which implicitly includes the benefits of the automatically welding procedure. © Published under licence by IOP Publishing Ltd
Improved treatment of the molecular final-states uncertainties for the KATRIN neutrino-mass measurement
The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to determine the
effective mass of the electron antineutrino via a high-precision measurement of
the tritium beta-decay spectrum in its end-point region. The target
neutrino-mass sensitivity of 0.2 eV / c^2 at 90% C.L. can only be achieved in
the case of high statistics and a good control of the systematic uncertainties.
One key systematic effect originates from the calculation of the molecular
final states of T_2 beta decay. In the first neutrino-mass analyses of KATRIN
the contribution of the uncertainty of the molecular final-states distribution
(FSD) was estimated via a conservative phenomenological approach to be 0.02
eV^2 / c^4. In this paper a new procedure is presented for estimating the
FSD-related uncertainties by considering the details of the final-states
calculation, i.e. the uncertainties of constants, parameters, and functions
used in the calculation as well as its convergence itself as a function of the
basis-set size used in expanding the molecular wave functions. The calculated
uncertainties are directly propagated into the experimental observable, the
squared neutrino mass m_nu^2. With the new procedure the FSD-related
uncertainty is constrained to 0.0013 eV^2 / c^4, for the experimental
conditions of the first KATRIN measurement campaign
Template-based searches for gravitational waves: efficient lattice covering of flat parameter spaces
The construction of optimal template banks for matched-filtering searches is
an example of the sphere covering problem. For parameter spaces with
constant-coefficient metrics a (near-) optimal template bank is achieved by the
A_n* lattice, which is the best lattice-covering in dimensions n <= 5, and is
close to the best covering known for dimensions n <= 16. Generally this
provides a substantially more efficient covering than the simpler hyper-cubic
lattice. We present an algorithm for generating lattice template banks for
constant-coefficient metrics and we illustrate its implementation by generating
A_n* template banks in n=2,3,4 dimensions.Comment: 10 pages, submitted to CQG for proceedings of GWDAW1
The isodiametric problem with lattice-point constraints
In this paper, the isodiametric problem for centrally symmetric convex bodies
in the Euclidean d-space R^d containing no interior non-zero point of a lattice
L is studied. It is shown that the intersection of a suitable ball with the
Dirichlet-Voronoi cell of 2L is extremal, i.e., it has minimum diameter among
all bodies with the same volume. It is conjectured that these sets are the only
extremal bodies, which is proved for all three dimensional and several
prominent lattices.Comment: 12 pages, 4 figures, (v2) referee comments and suggestions
incorporated, accepted in Monatshefte fuer Mathemati
Electrical properties of an amorphous zirconium oxide thin film and structure formation during crystallization
Metastable amorphous oxides with a strong oxygen deficiency often show surprising phenomena upon relaxation into thermodynamically stable phases. For example, Nagarajan et al. found a new type of chemically driven insulator-metal transition in highly non-stoichiometric gallium oxide films (GaOx).[1] Here, an internal solid-state disproportionation reaction leads to the growth Ga2O3 nuclei in the initially insulating GaOx matrix which thereby attains metal-like conductivity. Moreover, it has been recently shown that such films can act as memristive switches. [2]. Highly non-stoichiometric titania (TiO1.6) films show a similar disproportionation reaction upon heating but as the phase diagram for this material is more complex, various phases can be found during the relaxation [3].
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Algebraic totality, towards completeness
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose
objects can be seen as linearly topologised spaces, (a class of topological
vector spaces introduced by Lefschetz in 1942) and morphisms as continuous
linear maps. First, we recall definitions of finiteness spaces and describe
their basic properties deduced from the general theory of linearly topologised
spaces. Then we give an interpretation of LL based on linear algebra. Second,
thanks to separation properties, we can introduce an algebraic notion of
totality candidate in the framework of linearly topologised spaces: a totality
candidate is a closed affine subspace which does not contain 0. We show that
finiteness spaces with totality candidates constitute a model of classical LL.
Finally, we give a barycentric simply typed lambda-calculus, with booleans
and a conditional operator, which can be interpreted in this
model. We prove completeness at type for
every n by an algebraic method
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