506 research outputs found
Feedback methods for inverse simulation of dynamic models for engineering systems applications
Inverse simulation is a form of inverse modelling in which computer simulation methods are used to find the time histories of input variables that, for a given model, match a set of required output responses. Conventional inverse simulation methods for dynamic models are computationally intensive and can present difficulties for high-speed
applications. This paper includes a review of established methods of inverse simulation,giving some emphasis to iterative techniques that were first developed for aeronautical applications. It goes on to discuss the application of a different approach which is based on feedback principles. This feedback method is suitable for a wide range of linear and nonlinear dynamic models and involves two distinct stages. The first stage involves
design of a feedback loop around the given simulation model and, in the second stage, that closed-loop system is used for inversion of the model. Issues of robustness within
closed-loop systems used in inverse simulation are not significant as there are no plant uncertainties or external disturbances. Thus the process is simpler than that required for the development of a control system of equivalent complexity. Engineering applications
of this feedback approach to inverse simulation are described through case studies that put particular emphasis on nonlinear and multi-input multi-output models
Spin, Statistics, and Reflections, II. Lorentz Invariance
The analysis of the relation between modular PCT-symmetry -- a
consequence of the Unruh effect -- and Pauli's spin-statistics relation is
continued. The result in the predecessor to this article is extended to the
Lorentz symmetric situation. A model \G_L of the universal covering
\widetilde{L_+^\uparrow}\cong SL(2,\complex) of the restricted Lorentz group
is modelled as a reflection group at the classical level. Based
on this picture, a representation of \G_L is constructed from pairs of
modular PCT-conjugations, and this representation can easily be verified to
satisfy the spin-statistics relation
An Algebraic Jost-Schroer Theorem for Massive Theories
We consider a purely massive local relativistic quantum theory specified by a
family of von Neumann algebras indexed by the space-time regions. We assume
that, affiliated with the algebras associated to wedge regions, there are
operators which create only single particle states from the vacuum (so-called
polarization-free generators) and are well-behaved under the space-time
translations. Strengthening a result of Borchers, Buchholz and Schroer, we show
that then the theory is unitarily equivalent to that of a free field for the
corresponding particle type. We admit particles with any spin and localization
of the charge in space-like cones, thereby covering the case of
string-localized covariant quantum fields.Comment: 21 pages. The second (and crucial) hypothesis of the theorem has been
relaxed and clarified, thanks to the stimulus of an anonymous referee. (The
polarization-free generators associated with wedge regions, which always
exist, are assumed to be temperate.
The application of parameter sensitivity analysis methods to inverse simulation models
Knowledge of the sensitivity of inverse solutions to variation of parameters of a model can be very useful in making engineering design decisions. This paper describes how parameter sensitivity analysis can be carried out for
inverse simulations generated through approximate transfer function inversion methods and also by the use of feedback principles. Emphasis is placed on the use of sensitivity models and the paper includes examples and a case study involving a model of an underwater vehicle. It is shown that the use of sensitivity models can provide physical understanding of inverse simulation solutions that is not directly available using parameter sensitivity analysis methods that involve parameter perturbations and response
differencing
Deformations of quantum field theories on spacetimes with Killing vector fields
The recent construction and analysis of deformations of quantum field
theories by warped convolutions is extended to a class of curved spacetimes.
These spacetimes carry a family of wedge-like regions which share the essential
causal properties of the Poincare transforms of the Rindler wedge in Minkowski
space. In the setting of deformed quantum field theories, they play the role of
typical localization regions of quantum fields and observables. As a concrete
example of such a procedure, the deformation of the free Dirac field is
studied.Comment: 35 pages, 3 figure
Haag duality and the distal split property for cones in the toric code
We prove that Haag duality holds for cones in the toric code model. That is,
for a cone Lambda, the algebra R_Lambda of observables localized in Lambda and
the algebra R_{Lambda^c} of observables localized in the complement Lambda^c
generate each other's commutant as von Neumann algebras. Moreover, we show that
the distal split property holds: if Lambda_1 \subset Lambda_2 are two cones
whose boundaries are well separated, there is a Type I factor N such that
R_{Lambda_1} \subset N \subset R_{Lambda_2}. We demonstrate this by explicitly
constructing N.Comment: 15 pages, 2 figures, v2: extended introductio
String-localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with
irreducible representations of the Poincar\'e group and localized in
semi-infinite strings extending to spacelike infinity. Among these are fields
that generate the irreducible representations of mass zero and infinite spin
that are known to be incompatible with point-like localized fields. For the
massive representation and the massless representations of finite helicity, all
string-localized free fields can be written as an integral, along the string,
of point-localized tensor or spinor fields. As a special case we discuss the
string-localized vector fields associated with the point-like electromagnetic
field and their relation to the axial gauge condition in the usual setting.Comment: minor correction
Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory
A summary of some lines of ideas leading to model-independent frameworks of
relativistic quantum field theory is given. It is followed by a discussion of
the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki
modular objects associated with the quantum field vacuum state and certain
algebras of observables. The distillability concept, which is significant in
specifying useful entanglement in quantum information theory, is discussed
within the setting of general relativistic quantum field theory.Comment: 26 pages. Contribution for the Proceedings of a Conference on Special
Relativity held at Potsdam, 200
Construction of Field Algebras with Quantum Symmetry from Local Observables
It has been discussed earlier that ( weak quasi-) quantum groups allow for
conventional interpretation as internal symmetries in local quantum theory.
From general arguments and explicit examples their consistency with (braid-)
statistics and locality was established. This work addresses to the
reconstruction of quantum symmetries and algebras of field operators. For every
algebra \A of observables satisfying certain standard assumptions, an
appropriate quantum symmetry is found. Field operators are obtained which act
on a positive definite Hilbert space of states and transform covariantly under
the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation
relations, these fields are demonstrated to obey local braid relation.Comment: 50 pages, HUTMP 93-B33
On the Construction of Quantum Field Theories with Factorizing S-Matrices
The subject of this thesis is a novel construction method for interacting
relativistic quantum field theories on two-dimensional Minkowski space. The
input in this construction is not a classical Lagrangian, but rather a
prescribed factorizing S-matrix, i.e. the inverse scattering problem for such
quantum field theories is studied.
For a large class of factorizing S-matrices, certain associated quantum
fields, which are localized in wedge-shaped regions of Minkowski space, are
constructed explicitely. With the help of these fields, the local observable
content of the corresponding model is defined and analyzed by employing methods
from the algebraic framework of quantum field theory.
The abstract problem in this analysis amounts to the question under which
conditions an algebra of wedge-localized observables can be used to generate a
net of local observable algebras with the right physical properties. The answer
given here uses the so-called modular nuclearity condition, which is shown to
imply the existence of local observables and the Reeh-Schlieder property.
In the analysis of the concrete models, this condition is proven for a large
family of S-matrices, including the scattering operators of the Sinh-Gordon
model and the scaling Ising model as special examples. The so constructed
models are then investigated with respect to their scattering properties. They
are shown to solve the inverse scattering problem for the considered
S-matrices, and a proof of asymptotic completeness is given.Comment: PhD thesis, Goettingen university, 2006 (advisor: D. Buchholz) 153
pages, 10 figure
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