8,273 research outputs found
Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems
We present the mixed Galerkin discretization of distributed parameter
port-Hamiltonian systems. On the prototypical example of hyperbolic systems of
two conservation laws in arbitrary spatial dimension, we derive the main
contributions: (i) A weak formulation of the underlying geometric
(Stokes-Dirac) structure with a segmented boundary according to the causality
of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac
structure by a finite-dimensional Dirac structure is realized using a mixed
Galerkin approach and power-preserving linear maps, which define minimal
discrete power variables. (iii) With a consistent approximation of the
Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models.
By the degrees of freedom in the power-preserving maps, the resulting family of
structure-preserving schemes allows for trade-offs between centered
approximations and upwinding. We illustrate the method on the example of
Whitney finite elements on a 2D simplicial triangulation and compare the
eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the
CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0
Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic
quantum error-correcting code to provide a toy model for bulk gauge fields or
linearized gravitons. The key new elements are the introduction of degrees of
freedom on the links (edges) of the associated tensor network and their
connection to further copies of the HaPPY code by an appropriate isometry. The
result is a model in which boundary regions allow the reconstruction of bulk
algebras with central elements living on the interior edges of the (greedy)
entanglement wedge, and where these central elements can also be reconstructed
from complementary boundary regions. In addition, the entropy of boundary
regions receives both Ryu-Takayanagi-like contributions and further corrections
that model the term of Faulkner, Lewkowycz,
and Maldacena. Comparison with Yang-Mills theory then suggests that this
term can be reinterpreted as a part of the
bulk entropy of gravitons under an appropriate extension of the physical bulk
Hilbert space.Comment: 20 pages, 11 figure
Neural Embeddings of Graphs in Hyperbolic Space
Neural embeddings have been used with great success in Natural Language
Processing (NLP). They provide compact representations that encapsulate word
similarity and attain state-of-the-art performance in a range of linguistic
tasks. The success of neural embeddings has prompted significant amounts of
research into applications in domains other than language. One such domain is
graph-structured data, where embeddings of vertices can be learned that
encapsulate vertex similarity and improve performance on tasks including edge
prediction and vertex labelling. For both NLP and graph based tasks, embeddings
have been learned in high-dimensional Euclidean spaces. However, recent work
has shown that the appropriate isometric space for embedding complex networks
is not the flat Euclidean space, but negatively curved, hyperbolic space. We
present a new concept that exploits these recent insights and propose learning
neural embeddings of graphs in hyperbolic space. We provide experimental
evidence that embedding graphs in their natural geometry significantly improves
performance on downstream tasks for several real-world public datasets.Comment: 7 pages, 5 figure
Hybrid fuzzy and sliding-mode control for motorised tether spin-up when coupled with axial vibration
A hybrid fuzzy sliding mode controller is applied to the control of motorised tether spin-up coupled with an axial oscillation phenomenon. A six degree of freedom dynamic model of a motorised momentum exchange tether is used as a basis for interplanetary payload exchange. The tether comprises a symmetrical double payload configuration, with an outrigger counter inertia and massive central facility. It is shown that including axial elasticity permits an enhanced level of performance prediction accuracy and a useful departure from the usual rigid body representations, particularly for accurate payload positioning at strategic points. A special simulation program has been devised in MATLAB and MATHEMATICA for a given initial condition data case
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Accepted versio
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