2,411 research outputs found
Simultaneous Coherent Structure Coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity
The clustering of data into physically meaningful subsets often requires
assumptions regarding the number, size, or shape of the subgroups. Here, we
present a new method, simultaneous coherent structure coloring (sCSC), which
accomplishes the task of unsupervised clustering without a priori guidance
regarding the underlying structure of the data. sCSC performs a sequence of
binary splittings on the dataset such that the most dissimilar data points are
required to be in separate clusters. To achieve this, we obtain a set of
orthogonal coordinates along which dissimilarity in the dataset is maximized
from a generalized eigenvalue problem based on the pairwise dissimilarity
between the data points to be clustered. This sequence of bifurcations produces
a binary tree representation of the system, from which the number of clusters
in the data and their interrelationships naturally emerge. To illustrate the
effectiveness of the method in the absence of a priori assumptions, we apply it
to three exemplary problems in fluid dynamics. Then, we illustrate its capacity
for interpretability using a high-dimensional protein folding simulation
dataset. While we restrict our examples to dynamical physical systems in this
work, we anticipate straightforward translation to other fields where existing
analysis tools require ad hoc assumptions on the data structure, lack the
interpretability of the present method, or in which the underlying processes
are less accessible, such as genomics and neuroscience
Submanifolds with parallel second fundamental form studied via the GauĂź map
For an arbitrary n-dimensional riemannian manifold N and an integer m between 1 and n-1 a covariant derivative on the GraĂźmann bundle G_m(TN) is introduced which has the property that an m-dimensional submanifold M of N has parallel second fundamental form if and only if its GauĂź map (defined on M with values in G_m(TN)) is affine. (For the case that N is the euclidian space this result was already obtained by J.Vilms in 1972.) By means of this relation a generalization of E. Cartan's theorem on the total geodesy of a geodesic umbrella can be derived: Suppose, initial data (p,W,b) prescribing an m-dimensional tangent space W and a second fundamental form b at p in N are given; for these data we construct an m-dimensional ``umbrella'' M=M(p,W,b) in N, the rays of which are helical arcs of N; moreover we present tensorial conditions (not involving the covariant derivative on G_m(TN)) which guarantee that the umbrella M has parallel second fundamental form. These conditions are as well necessary, and locally every submanifold with parallel second fundamental form can be obtained in this way
Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
NaIrO, a honeycomb 5 oxide, has been recently identified as a
potential realization of the Kitaev spin lattice. The basic feature of this
spin model is that for each of the three metal-metal links emerging out of a
metal site, the Kitaev interaction connects only spin components perpendicular
to the plaquette defined by the magnetic ions and two bridging ligands. The
fact that reciprocally orthogonal spin components are coupled along the three
different links leads to strong frustration effects and nontrivial physics.
While the experiments indicate zigzag antiferromagnetic order in NaIrO,
the signs and relative strengths of the Kitaev and Heisenberg interactions are
still under debate. Herein we report results of ab initio many-body electronic
structure calculations and establish that the nearest-neighbor exchange is
strongly anisotropic with a dominant ferromagnetic Kitaev part, whereas the
Heisenberg contribution is significantly weaker and antiferromagnetic. The
calculations further reveal a strong sensitivity to tiny structural details
such as the bond angles. In addition to the large spin-orbit interactions, this
strong dependence on distortions of the IrO plaquettes singles out the
honeycomb 5 oxides as a new playground for the realization of
unconventional magnetic ground states and excitations in extended systems.Comment: 13 pages, 2 tables, 3 figures, accepted in NJ
Emission coordinates for the navigation in space
A general approach to the problem of positioning by means of pulsars or other
pulsating sources located at infinity is described. The counting of the pulses
for a set of different sources whose positions in the sky and periods are
assumed to be known, is used to provide null emission, or light, coordinates
for the receiver. The measurement of the proper time intervals between
successive arrivals of the signals from the various sources is used to give the
final localization of the receiver, within an accuracy controlled by the
precision of the onboard clock. The deviation from the flat case is discussed,
separately considering the different possible causes: local gravitational
potential, finiteness of the distance of the source, proper motion of the
source, period decay, proper acceleration due to non-gravitational forces.
Calculations turn out to be simple and the result is highly positive. The
method can also be applied to a constellation of satellites orbiting the Earth.Comment: 13 pages, 1 figure, appearing on the Proceedings of the 60th
International Astronautical Conference IAC 2009, October 12-16, Daejeong,
Kore
Quantum clocks observe classical and quantum time dilation
At the intersection of quantum theory and relativity lies the possibility of
a clock experiencing a superposition of proper times. We consider quantum
clocks constructed from the internal degrees of relativistic particles that
move through curved spacetime. The probability that one clock reads a given
proper time conditioned on another clock reading a different proper time is
derived. From this conditional probability distribution, it is shown that when
the center-of-mass of these clocks move in localized momentum wave packets they
observe classical time dilation. We then illustrate a quantum correction to the
time dilation observed by a clock moving in a superposition of localized
momentum wave packets that has the potential to be observed in experiment. The
Helstrom-Holevo lower bound is used to derive a proper time-energy/mass
uncertainty relation.Comment: Updated to match published versio
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