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Comparison of max-plus automata and joint spectral radius of tropical matrices
Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is no algorithm that takes as input a finite set of matrices M and provides as output the joint spectral radius (resp. the ultimate rank) of M. On the other hand, we prove that the joint spectral radius is nevertheless approximable and we exhibit restricted cases in which the joint spectral radius and the ultimate rank are computable. To reach this aim, we study the problem of comparing functions computed by weighted automata over the tropical semiring. This problem is known to be undecidable and we prove that it remains undecidable in some specific subclasses of automata
Kinematically Redundant Octahedral Motion Platform for Virtual Reality Simulations
We propose a novel design of a parallel manipulator of Stewart Gough type for
virtual reality application of single individuals; i.e. an omni-directional
treadmill is mounted on the motion platform in order to improve VR immersion by
giving feedback to the human body. For this purpose we modify the well-known
octahedral manipulator in a way that it has one degree of kinematical
redundancy; namely an equiform reconfigurability of the base. The instantaneous
kinematics and singularities of this mechanism are studied, where especially
"unavoidable singularities" are characterized. These are poses of the motion
platform, which can only be realized by singular configurations of the
mechanism despite its kinematic redundancy.Comment: 13 pages, 6 figure
Influence of chirping the Raman lasers in an atom gravimeter: phase shifts due to the Raman light shift and to the finite speed of light
We present here an analysis of the influence of the frequency dependence of
the Raman laser light shifts on the phase of a Raman-type atom gravimeter.
Frequency chirps are applied to the Raman lasers in order to compensate gravity
and ensure the resonance of the Raman pulses during the interferometer. We show
that the change in the Raman light shift when this chirp is applied only to one
of the two Raman lasers is enough to bias the gravity measurement by a fraction
of Gal (Gal~=~~m/s). We also show that this effect is
not compensated when averaging over the two directions of the Raman wavevector
. This thus constitutes a limit to the rejection efficiency of the
-reversal technique. Our analysis allows us to separate this effect from the
effect of the finite speed of light, which we find in perfect agreement with
expected values. This study highlights the benefit of chirping symmetrically
the two Raman lasers
Perturbations of the local gravity field due to mass distribution on precise measuring instruments: a numerical method applied to a cold atom gravimeter
We present a numerical method, based on a FEM simulation, for the
determination of the gravitational field generated by massive objects, whatever
geometry and space mass density they have. The method was applied for the
determination of the self gravity effect of an absolute cold atom gravimeter
which aims at a relative uncertainty of 10-9. The deduced bias, calculated with
a perturbative treatment, is finally presented. The perturbation reaches (1.3
\pm 0.1) \times 10-9 of the Earth's gravitational field.Comment: 12 pages, 7 figure
Pose, posture, formation and contortion in kinematic systems
The concepts of pose, posture, formation and contortion are defined for serial, parallel and hybrid kinematic systems. Workspace and jointspace structure is examined in terms of these concepts. The inter-relationships of pose, posture, formation and contortion are explored for a range of robot workspace and jointspace types
New Perspectives on the Charging Mechanisms of Supercapacitors.
Supercapacitors (or electric double-layer capacitors) are high-power energy storage devices that store charge at the interface between porous carbon electrodes and an electrolyte solution. These devices are already employed in heavy electric vehicles and electronic devices, and can complement batteries in a more sustainable future. Their widespread application could be facilitated by the development of devices that can store more energy, without compromising their fast charging and discharging times. In situ characterization methods and computational modeling techniques have recently been developed to study the molecular mechanisms of charge storage, with the hope that better devices can be rationally designed. In this Perspective, we bring together recent findings from a range of experimental and computational studies to give a detailed picture of the charging mechanisms of supercapacitors. Nuclear magnetic resonance experiments and molecular dynamics simulations have revealed that the electrode pores contain a considerable number of ions in the absence of an applied charging potential. Experiments and computer simulations have shown that different charging mechanisms can then operate when a potential is applied, going beyond the traditional view of charging by counter-ion adsorption. It is shown that charging almost always involves ion exchange (swapping of co-ions for counter-ions), and rarely occurs by counter-ion adsorption alone. We introduce a charging mechanism parameter that quantifies the mechanism and allows comparisons between different systems. The mechanism is found to depend strongly on the polarization of the electrode, and the choice of the electrolyte and electrode materials. In light of these advances we identify new directions for supercapacitor research. Further experimental and computational work is needed to explain the factors that control supercapacitor charging mechanisms, and to establish the links between mechanisms and performance. Increased understanding and control of charging mechanisms should lead to new strategies for developing next-generation supercapacitors with improved performances.The authors acknowledge the Sims Scholarship Cambridge (A.C.F.), the School of the Physical Sciences of the University of Cambridge (via an Oppenheimer Research Fellowship, C.M.), EPSRC (via the Supergen consortium, A.C.F. and J.M.G.), and the EU ERC (via an Advanced Fellowship to C.P.G.) for funding. We thank Nicole Trease, Andrew Ilott, Phoebe Allan, Elizabeth Humphreys, Paul Bayley, Hao Wang, Patrice Simon, Wan-Yu Tsai, Yury Gogotsi, Mathieu Salanne, Benjamin Rotenberg, Alexei Kornyshev, Svyatoslav Kondrat and Volker Presser for collaboration, and stimulating discussions and insights into supercapacitors over the course of our research on this subject.This is the final version of the article. It first appeared from the American Chemical Society via https://doi.org/10.1021/jacs.6b0211
Rotation symmetry axes and the quality index in a 3D octahedral parallel robot manipulator system
The geometry of a 3D octahedral parallel robot manipulator system is specified in terms of two rigid octahedral structures (the fixed and moving platforms) and six actuation legs. The symmetry of the system is exploited to determine the behaviour of (a new version of) the quality index for various motions. The main results are presented graphically
Probabilistic analysis of the upwind scheme for transport
We provide a probabilistic analysis of the upwind scheme for
multi-dimensional transport equations. We associate a Markov chain with the
numerical scheme and then obtain a backward representation formula of
Kolmogorov type for the numerical solution. We then understand that the error
induced by the scheme is governed by the fluctuations of the Markov chain
around the characteristics of the flow. We show, in various situations, that
the fluctuations are of diffusive type. As a by-product, we prove that the
scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all
a>0, for a Lipschitz continuous initial datum. Our analysis provides a new
interpretation of the numerical diffusion phenomenon
The electric double layer has a life of its own
Using molecular dynamics simulations with recently developed importance
sampling methods, we show that the differential capacitance of a model ionic
liquid based double-layer capacitor exhibits an anomalous dependence on the
applied electrical potential. Such behavior is qualitatively incompatible with
standard mean-field theories of the electrical double layer, but is consistent
with observations made in experiment. The anomalous response results from
structural changes induced in the interfacial region of the ionic liquid as it
develops a charge density to screen the charge induced on the electrode
surface. These structural changes are strongly influenced by the out-of-plane
layering of the electrolyte and are multifaceted, including an abrupt local
ordering of the ions adsorbed in the plane of the electrode surface,
reorientation of molecular ions, and the spontaneous exchange of ions between
different layers of the electrolyte close to the electrode surface. The local
ordering exhibits signatures of a first-order phase transition, which would
indicate a singular charge-density transition in a macroscopic limit
Self-Motions of General 3-RPR Planar Parallel Robots
This paper studies the kinematic geometry of general 3-RPR planar parallel
robots with actuated base joints. These robots, while largely overlooked, have
simple direct kinematics and large singularity-free workspace. Furthermore,
their kinematic geometry is the same as that of a newly developed parallel
robot with SCARA-type motions. Starting from the direct and inverse kinematic
model, the expressions for the singularity loci of 3-RPR planar parallel robots
are determined. Then, the global behaviour at all singularities is
geometrically described by studying the degeneracy of the direct kinematic
model. Special cases of self-motions are then examined and the degree of
freedom gained in such special configurations is kinematically interpreted.
Finally, a practical example is discussed and experimental validations
performed on an actual robot prototype are presented
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