134,482 research outputs found
Port-Hamiltonian systems: an introductory survey
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models
Effective algorithm of analysis of integrability via the Ziglin's method
In this paper we continue the description of the possibilities to use
numerical simulations for mathematically rigorous computer assisted analysis of
integrability of dynamical systems. We sketch some of the algebraic methods of
studying the integrability and present a constructive algorithm issued from the
Ziglin's approach. We provide some examples of successful applications of the
constructed algorithm to physical systems.Comment: a figure added, version accepted to JDC
Duality approach to one-dimensional degenerate electronic systems
We investigate the possible classification of zero-temperature spin-gapped
phases of multicomponent electronic systems in one spatial dimension. At the
heart of our analysis is the existence of non-perturbative duality symmetries
which emerge within a low-energy description. These dualities fall into a
finite number of classes that can be listed and depend only on the algebraic
properties of the symmetries of the system: its physical symmetry group and the
maximal continuous symmetry group of the interaction. We further characterize
possible competing orders associated to the dualities and discuss the nature of
the quantum phase transitions between them. Finally, as an illustration, the
duality approach is applied to the description of the phases of two-leg
electronic ladders for incommensurate filling.Comment: 53 pages, 3 figures, published versio
Schwinger's Picture of Quantum Mechanics IV: Composition and independence
The groupoids description of Schwinger's picture of quantum mechanics is
continued by discussing the closely related notions of composition of systems,
subsystems, and their independence. Physical subsystems have a neat algebraic
description as subgroupoids of the Schwinger's groupoid of the system. The
groupoids picture offers two natural notions of composition of systems: Direct
and free products of groupoids, that will be analyzed in depth as well as their
universal character. Finally, the notion of independence of subsystems will be
reviewed, finding that the usual notion of independence, as well as the notion
of free independence, find a natural realm in the groupoids formalism. The
ideas described in this paper will be illustrated by using the EPRB experiment.
It will be observed that, in addition to the notion of the non-separability
provided by the entangled state of the system, there is an intrinsic
`non-separability' associated to the impossibility of identifying the entangled
particles as subsystems of the total system.Comment: 32 pages. Comments are welcome
A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit Element
In some applications there arises the need of a spatially distributed
description of a physical quantity inside a device coupled to a circuit. Then,
the in-space discretised system of partial differential equations is coupled to
the system of equations describing the circuit (Modified Nodal Analysis) which
yields a system of Differential Algebraic Equations (DAEs). This paper deals
with the differential index analysis of such coupled systems. For that, a new
generalised inductance-like element is defined. The index of the DAEs obtained
from a circuit containing such an element is then related to the topological
characteristics of the circuit's underlying graph. Field/circuit coupling is
performed when circuits are simulated containing elements described by
Maxwell's equations. The index of such systems with two different types of
magnetoquasistatic formulations (A* and T-) is then deduced by showing
that the spatial discretisations in both cases lead to an inductance-like
element
Index Reduction for Differential-Algebraic Equations with Mixed Matrices
Differential-algebraic equations (DAEs) are widely used for modeling of
dynamical systems. The difficulty in solving numerically a DAE is measured by
its differentiation index. For highly accurate simulation of dynamical systems,
it is important to convert high-index DAEs into low-index DAEs. Most of
existing simulation software packages for dynamical systems are equipped with
an index-reduction algorithm given by Mattsson and S\"{o}derlind.
Unfortunately, this algorithm fails if there are numerical cancellations.
These numerical cancellations are often caused by accurate constants in
structural equations. Distinguishing those accurate constants from generic
parameters that represent physical quantities, Murota and Iri introduced the
notion of a mixed matrix as a mathematical tool for faithful model description
in structural approach to systems analysis. For DAEs described with the use of
mixed matrices, efficient algorithms to compute the index have been developed
by exploiting matroid theory.
This paper presents an index-reduction algorithm for linear DAEs whose
coefficient matrices are mixed matrices, i.e., linear DAEs containing physical
quantities as parameters. Our algorithm detects numerical cancellations between
accurate constants, and transforms a DAE into an equivalent DAE to which
Mattsson--S\"{o}derlind's index-reduction algorithm is applicable. Our
algorithm is based on the combinatorial relaxation approach, which is a
framework to solve a linear algebraic problem by iteratively relaxing it into
an efficiently solvable combinatorial optimization problem. The algorithm does
not rely on symbolic manipulations but on fast combinatorial algorithms on
graphs and matroids. Furthermore, we provide an improved algorithm under an
assumption based on dimensional analysis of dynamical systems.Comment: A preliminary version of this paper is to appear in Proceedings of
the Eighth SIAM Workshop on Combinatorial Scientific Computing, Bergen,
Norway, June 201
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