5,169 research outputs found
An Exactly Solvable Case for a Thin Elastic Rod
We present a new exact solution for the twist of an asymmetric thin elastic
rods. The shape of such rods is described by the static Kirchhoff equations. In
the case of constant curvatire and torsion the twist of the asymmetric rod
represents a soliton lattice.Comment: 6 pages, title changed, revised versio
A parametric macromodelling technique
With the ever growing complexity of high-frequency systems in the electronic industry, formation of reduced-order models or compact macromodels of these systems is paramount. In this contribution, a Fourier series expansion technique is extended to form a modeling strategy to approximate the frequency-domain behaviour of a system based on several design variables. In particular, it is intended to provide a tool for the designer to identify the effect of manufacturer tolerances and process fluctuations or irregularities on system behaviour
Balanced truncation of perturbative representations of nonlinear systems
The paper presents a novel approach for a balanced truncation style of model reduction of a perturbative representation of a nonlinear system. Empirical controllability and observability gramians for nonlinear systems are employed to define a projection matrix. However, the projection matrix is applied to the perturbative representation of the system rather than directly to the exact nonlinear system. This is to achieve the required increase in efficiency desired of a reduced-order model. Application of the new method is illustrated through a sample test-system. The technique will be compared to the standard approach for reducing a perturbative representation of a nonlinear system
Compact models for wireless systems
For the design and analysis of wireless systems,
complex simulations are required and performed. Model order
reduction techniques enable greater efficiencies to be achieved and concomitantly, a reduction in memory-resource usage. However, maintaining a certain level of accuracy is paramount. In this contribution, two techniques are combined to enable the formation of a compact model of a high-order system, structure or component. The first is a Krylov subspace method which reduces the original model to a moderate size and the second is a Fourier series expansion method that enables speed and ease of determination of the time-domain responses of the system to
arbitrary inputs
Model reduction of weakly nonlinear systems
In general, model reduction techniques fall into two categories — moment —matching and Krylov techniques and balancing techniques. The present contribution is concerned with the former. The present contribution proposes the use of a perturbative representation as an alternative to the bilinear representation [4]. While for weakly nonlinear systems, either approximation is satisfactory, it will be seen that the perturbative method has several advantages over the bilinear representation. In this contribution, an improved reduction method is proposed. Illustrative examples are chosen, and the errors obtained from the different reduction strategies will be compared
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
The construction of a family of real Hamiltonian forms (RHF) for the special
class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus
the method, proposed in [1] for systems with finite number of degrees of
freedom is generalized to infinite-dimensional Hamiltonian systems. The
construction method is illustrated on the explicit nontrivial example of RHF of
ATFT related to the exceptional algebras E_6 and E_7. The involutions of the
local integrals of motion are proved by means of the classical R-matrix
approach.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Generalised Fourier Transform and Perturbations to Soliton Equations
A brief survey of the theory of soliton perturbations is presented. The focus
is on the usefulness of the so-called Generalised Fourier Transform (GFT). This
is a method that involves expansions over the complete basis of `squared
olutions` of the spectral problem, associated to the soliton equation. The
Inverse Scattering Transform for the corresponding hierarchy of soliton
equations can be viewed as a GFT where the expansions of the solutions have
generalised Fourier coefficients given by the scattering data.
The GFT provides a natural setting for the analysis of small perturbations to
an integrable equation: starting from a purely soliton solution one can
`modify` the soliton parameters such as to incorporate the changes caused by
the perturbation.
As illustrative examples the perturbed equations of the KdV hierarchy, in
particular the Ostrovsky equation, followed by the perturbation theory for the
Camassa- Holm hierarchy are presented.Comment: 20 pages, no figures, to appear in: Discrete and Continuous Dynamical
Systems
(De)Constructing Dimensions
We construct renormalizable, asymptotically free, four dimensional gauge
theories that dynamically generate a fifth dimension.Comment: 10 pages, late
A phenomenal basis for hybrid modelling
This work in progress extends the new mechanical philosophy from science to engineering. Engineering is the practice of organising the design and construction of artifices that satisfy needs in real-world contexts. This work shows how artifices can be described in terms of their mechanisms and composed through their observable phenomena.
Typically, the engineering of real system requires descrip- tions in many different languages: software components will be described in code; sensors and actuators in terms of their physical and electronic characteristics; plant in terms of differ- ential equations, perhaps. Another aspect of this work, then, to construct a formal framework so that diverse description languages can be used to characterise sub-mechanisms.
The work is situated in Problem Oriented Engineering, a design theoretic framework engineering defined by the first two authors
On N-wave type systems and their gauge equivalent
The class of nonlinear evolution equations - gauge equivalent to the N-wave
equations related to the simple Lie algebra g are derived and analyzed. They
are written in terms of the functions S(x,t) satisfying r= rank g nonlinear
constraints. The corresponding Lax pairs and the time evolution of the
scattering data are found. The Zakharov-Shabat dressing method is appropriately
modified to construct their soliton solutions.Comment: 5 pages, LaTeX 2e, revised versio
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