27,098 research outputs found
Hierarchical adaptive polynomial chaos expansions
Polynomial chaos expansions (PCE) are widely used in the framework of
uncertainty quantification. However, when dealing with high dimensional complex
problems, challenging issues need to be faced. For instance, high-order
polynomials may be required, which leads to a large polynomial basis whereas
usually only a few of the basis functions are in fact significant. Taking into
account the sparse structure of the model, advanced techniques such as sparse
PCE (SPCE), have been recently proposed to alleviate the computational issue.
In this paper, we propose a novel approach to SPCE, which allows one to exploit
the model's hierarchical structure. The proposed approach is based on the
adaptive enrichment of the polynomial basis using the so-called principle of
heredity. As a result, one can reduce the computational burden related to a
large pre-defined candidate set while obtaining higher accuracy with the same
computational budget
Some Aspects of the Exact Foldy-Wouthuysen Transformation for a Dirac Fermion
The Foldy-Wouthuysen transformation (FWT) is used to separate distinct
components of relativistic spinor field, e.g. electron and positron. Usually,
the FWT is perturbative, but in some cases there is an involution operator and
the transformation can be done exactly. We consider some aspects of an exact
FWT and show that, even if the theory does not admit an involution operator,
one can use the technique of exact FWT to obtain the conventional perturbative
result. Several particular cases can be elaborated as examples
A complete characterisation of the heralded noiseless amplification of photons
Heralded noiseless amplifcation of photons has recently been shown to provide
a means to overcome losses in complex quantum communication tasks. In
particular, to overcome transmission losses that could allow for the violation
of a Bell inequality free from the detection loophole, for Device Independent
Quantum Key Distribution (DI-QKD). Several implementations of a heralded photon
amplifier have been proposed and the first proof of principle experiments
realised. Here we present the first full characterisation of such a device to
test its functional limits and potential for DI-QKD. This device is tested at
telecom wavelengths and is shown to be capable of overcoming losses
corresponding to a transmission through of single mode telecom
fibre. We demonstrate heralded photon amplifier with a gain and a
heralding probability , required by DI-QKD protocols that use the
Clauser-Horne-Shimony-Holt (CHSH) inequality. The heralded photon amplifier
clearly represents a key technology for the realisation of DI-QKD in the real
world and over typical network distances.Comment: 9 pages, 4 figure
Non-quantized Dirac monopoles and strings in the Berry phase of anisotropic spin systems
The Berry phase of an anisotropic spin system that is adiabatically rotated
along a closed circuit C is investigated. It is shown that the Berry phase
consists of two contributions: (i) a geometric contribution which can be
interpreted as the flux through C of a non-quantized Dirac monopole, and (ii) a
topological contribution which can be interpreted as the flux through C of a
Dirac string carrying a non-quantized flux, i.e., a spin analogue of the
Aharonov-Bohm effect. Various experimental consequences of this novel effect
are discussed.Comment: 4 pages, 3 figures (RevTeX + eps); v2 (revised paper): 4 pages, 4
figure
Dynamic Active Constraints for Surgical Robots using Vector Field Inequalities
Robotic assistance allows surgeons to perform dexterous and tremor-free
procedures, but robotic aid is still underrepresented in procedures with
constrained workspaces, such as deep brain neurosurgery and endonasal surgery.
In these procedures, surgeons have restricted vision to areas near the surgical
tooltips, which increases the risk of unexpected collisions between the shafts
of the instruments and their surroundings. In this work, our
vector-field-inequalities method is extended to provide dynamic
active-constraints to any number of robots and moving objects sharing the same
workspace. The method is evaluated with experiments and simulations in which
robot tools have to avoid collisions autonomously and in real-time, in a
constrained endonasal surgical environment. Simulations show that with our
method the combined trajectory error of two robotic systems is optimal.
Experiments using a real robotic system show that the method can autonomously
prevent collisions between the moving robots themselves and between the robots
and the environment. Moreover, the framework is also successfully verified
under teleoperation with tool-tissue interactions.Comment: Accepted on T-RO 2019, 19 Page
Equilibrium spin currents and magnetoelectric effect in magnetic nanostructures
We discuss the problem of equilibrium spin currents in ferromagnets with
inhomogeneous magnetization. Using simple microscopic models we explain the
physical origin of equilibrium spin currents. Next we derive the equilibrium
spin current from the Hamiltonian with a gauge field associated with local
rotations in the spin space. Several examples of magnetic systems are studied
in details, and the persistent spin current is found to exist in the ground
state of these systems. We also demonstrate the possibility to measure the
equilibrium spin current using the magnetoelectrically induced electric field
near the ring.Comment: RevTex 4 (4 pages
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