Finite element modelling of cold formed stainless steel columns

This paper describes the results obtained from a finite element investigation into the load capacity of column members of lipped channel cross-section, cold formed from Type 304 stainless steel, subjected to concentric and eccentric compression loading. The main aims of this investigation were to determine the effects which the non-linearity of the stress-strain behaviour of the material would have on the column behaviour under concentric or eccentric loading. Stress-strain curves derived from tests and design codes are incorporated into non-linear finite element analyses of eccentrically loaded columns and the results obtained are compared with those obtained on the basis of experiments on stainless steel channel columns with the same properties and dimensions. Comparisons of the finite element results and the test results are also made with existing design specifications and conclusions are drawn on the basis of the comparisons

An application of the individual channel analysis and design approach to control of a two-input two-output coupled-tanks system

Frequency-domain methods have provided an established approach to the analysis and design of single-loop feedback control systems in many application areas for many years. Individual Channel Analysis and Design (ICAD) is a more recent development that allows neo-classical frequency-domain analysis and design methods to be applied to multi-input multi-output control problems. This paper provides a case study illustrating the use of the ICAD methodology for an application involving liquid-level control for a system based on two coupled tanks. The complete nonlinear dynamic model of the plant is presented for a case involving two input flows of liquid and two output variables, which are the depths of liquid in the two tanks. Linear continuous proportional plus integral controllers are designed on the basis of linearised plant models to meet a given set of performance specifications for this two-input two-output multivariable control system and a computer simulation of the nonlinear model and the controllers is then used to demonstrate that the overall closed-loop performance meets the given requirements. The resulting system has been implemented in hardware and the paper includes experimental results which demonstrate good agreement with simulation predictions. The performance is satisfactory in terms of steady-state behaviour, transient responses, interaction between the controlled variables, disturbance rejection and robustness to changes within the plant. Further simulation results, some of which involve investigations that could not be carried out in a readily repeatable fashion by experimental testing, give support to the conclusion that this neo-classical ICAD framework can provide additional insight within the analysis and design processes for multi-input multi-output feedback control systems

The Velocity Tensor and the Momentum Tensor

This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are derived as well as its relation with the velocity tensor. For the sake of clarity only two-dimensional case is investigated. However, general conclusions are also valid for higher dimensional spacetimes.Comment: 6 pages, 1 figur

On Partial Differential and Difference Equations with Symmetries Depending on Arbitrary Functions

In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show on a few examples, both in partial differential and partial difference equations when this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries

Broad-band variability in accreting compact objects

Cataclysmic variable stars are in many ways similar to X-ray binaries. Both types of systems possess an accretion disk, which in most cases can reach the surface (or event horizon) of the central compact object. The main difference is that the embedded gravitational potential well in X-ray binaries is much deeper than those found in cataclysmic variables. As a result, X-ray binaries emit most of their radiation at X-ray wavelengths, as opposed to cataclysmic variables which emit mostly at optical/ultraviolet wavelengths. Both types of systems display aperiodic broad-band variability which can be associated to the accretion disk. Here, the properties of the observed X-ray variability in XRBs are compared to those observed at optical wavelengths in CVs. In most cases the variability properties of both types of systems are qualitatively similar once the relevant timescales associated with the inner accretion disk regions have been taken into account. The similarities include the observed power spectral density shapes, the rms-flux relation as well as Fourier-dependant time lags. Here a brief overview on these similarities is given, placing them in the context of the fluctuating accretion disk model which seeks to reproduce the observed variability.Comment: Invited talk and accepted for publication in Acta Polytechnica, Proceedings of "The Golden Age of Cataclysmic Variables and Related Objects II

Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by the models using apparently non-Hermitian ("crypto-Hermitian") Hamiltonians with real spectra. The formalism (originally inspired by the topical need of mathematically consistent description of tobogganic quantum models) is shown to admit certain unusual nonlocal and/or "moving-frame" representations of the standard physical Hilbert space of wave functions.Comment: 10 pages, talk, int. conf. "Selected Topics in Mathematical and Particle Physics" (Prague, 5-7 May 2009, http://www.km.fjfi.cvut.cz/conference/st2009/

PT-symmetry and Integrability

We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to construct deformations of some integrable systems, the Calogero-Moser-Sutherland model and the Korteweg deVries equation. Some properties of these models are discussed.Comment: Proceeding of the Micro conference Analytic and algebraic methods II, Doppler Institute, Prague, April 200

On Two Ways to Look for Mutually Unbiased Bases

Two equivalent ways of looking for mutually unbiased bases are discussed in this note. The passage from the search for d+1 mutually unbiased bases in C(d) to the search for d(d+1) vectors in C(d*d) satisfying constraint relations is clarified. Symmetric informationally complete positive-operator-valued measures are briefly discussed in a similar vein.Comment: three pages to be published in Acta Polytechnica (Czech Technical University in Prague

On renormalization of Poisson-Lie T-plural sigma models

Covariance of the one-loop renormalization group equations with respect to Poisson-Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson-Lie sigma models with truncated matrices of parameters is investigated.Comment: 11 pages, The sources of disagreements with references [1],[2],[3] in previous versions are identified as differences in notation

Search for gravitational waves from supernovae and long GRBs

We report on evidence for black hole spindown in the light curves of the BATSE catalogue of 1491 long GRBs by application of matched filtering. This observation points to a strong interaction of the black hole with surrounding high density matter at the ISCO, inducing non-axisymmetric instabilities sustained by cooling in gravitational wave emission. Opportunities for LIGO-Virgo and the recently funded KAGRA experiments are highlighted, for long GRBs with and without supernovae and for hyper-energetic core-collapse supernovae within a distance of about 35 Mpc in the Local Universe.Comment: Invited talk at Vulcano 2012, Italy, accepted for publication in Acta Polytechnic