167,184 research outputs found
NP-hardness of the cluster minimization problem revisited
The computational complexity of the "cluster minimization problem" is
revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued
that the original NP-hardness proof does not apply to pairwise potentials of
physical interest, such as those that depend on the geometric distance between
the particles. A geometric analog of the original problem is formulated, and a
new proof for such potentials is provided by polynomial time transformation
from the independent set problem for unit disk graphs. Limitations of this
formulation are pointed out, and new subproblems that bear more direct
consequences to the numerical study of clusters are suggested.Comment: 8 pages, 2 figures, accepted to J. Phys. A: Math. and Ge
The Teacher as Servant Leader: Revisited
This essay revisits an original conference proceedings chapter from 1997, examining the biblical and educational underpinnings for the concept of teacher and servant leader
The Teacher as Servant Leader: Revisited
This essay revisits an original conference proceedings chapter from 1997, examining the biblical and educational underpinnings for the concept of teacher and servant leader
On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited
In the framework of the planar and circular restricted three-body problem, we
consider an asteroid that orbits the Sun in quasi-satellite motion with a
planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital
resonance with the planet, characterized by a non zero eccentricity and a
resonant angle that librates around zero. Likewise, in the rotating frame with
the planet it describes the same trajectory as the one of a retrograde
satellite even though the planet acts as a perturbator. In the last few years,
the discoveries of asteroids in this type of motion made the term
"quasi-satellite" more and more present in the literature. However, some
authors rather use the term "retrograde satellite" when referring to this kind
of motion in the studies of the restricted problem in the rotating frame. In
this paper we intend to clarify the terminology to use, in order to bridge the
gap between the perturbative co-orbital point of view and the more general
approach in the rotating frame. Through a numerical exploration of the
co-orbital phase space, we describe the quasi-satellite domain and highlight
that it is not reachable by low eccentricities by averaging process. We will
show that the quasi-satellite domain is effectively included in the domain of
the retrograde satellites and neatly defined in terms of frequencies.
Eventually, we highlight a remarkable high eccentric quasi-satellite orbit
corresponding to a frozen ellipse in the heliocentric frame. We extend this
result to the eccentric case (planet on an eccentric motion) and show that two
families of frozen ellipses originate from this remarkable orbit.Comment: 30 pages, 13 figures, 1 tabl
The Resonance Overlap and Hill Stability Criteria Revisited
We review the orbital stability of the planar circular restricted three-body
problem, in the case of massless particles initially located between both
massive bodies. We present new estimates of the resonance overlap criterion and
the Hill stability limit, and compare their predictions with detailed dynamical
maps constructed with N-body simulations. We show that the boundary between
(Hill) stable and unstable orbits is not smooth but characterized by a rich
structure generated by the superposition of different mean-motion resonances
which does not allow for a simple global expression for stability.
We propose that, for a given perturbing mass and initial eccentricity
, there are actually two critical values of the semimajor axis. All values
are
unstable in the Hill sense. The first limit is given by the Hill-stability
criterion and is a function of the eccentricity. The second limit is virtually
insensitive to the initial eccentricity, and closely resembles a new resonance
overlap condition (for circular orbits) developed in terms of the intersection
between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte
Movement in cluttered virtual environments
Imagine walking around a cluttered room but then having little idea of where you have traveled. This frequently happens when people move around small virtual environments (VEs), searching for targets. In three experiments, participants searched small-scale VEs using different movement interfaces, collision response algorithms, and fields of view. Participants' searches were most efficient in terms of distance traveled, time taken, and path followed when the simplest form of movement (view direction) was used in conjunction with a response algorithm that guided ("slipped") them around obstacles when collisions occurred. Unexpectedly, and in both immersive and desktop VEs, participants often had great difficulty finding the targets, despite the fact that participants could see the whole VE if they stood in one place and turned around. Thus, the trivial real-world task used in the present study highlights a basic problem with current VE systems
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