Strong structural controllability and the multi-link inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Strong structural controllability and the multilink inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

The physical pendulum in an advanced undergraduate course in mechanics

The physical pendulum treated with a Hamiltonian formulation is a natural topic for study in a course in advanced classical mechanics. For the past three years, we have been offering a series of problem sets studying this system numerically in our third-year undergraduate courses in mechanics. The problem sets investigate the physics of the pendulum in ways not easily accessible without computer technology and explore various algorithms for solving mechanics problems. Our computational physics is based on Mathematica with some C communicating with Mathematica, although nothing in this paper is dependent on that choice. We have nonetheless found this system, and particularly its graphics, to be a good one for use with undergraduates.

The analytic torsion of a cone over an odd dimensional manifold

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem [3, 2] for a manifold with boundary, according to Bruning and Ma (2006) [5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved.

The analytic torsion of a cone over a sphere

We compute the analytic torsion of a cone over a sphere of dimensions 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere. (C) 2009 Elsevier Masson SAS. All rights reserved.

REIDEMEISTER TORSION AND ANALYTIC TORSION OF SPHERES

We provide a simple topological derivation of a formula for the Reidemeister and the analytic torsion of spheres.

Azo-group dihedral angle torsion dependence on temperature: A theorerical-experimental study

Quantum chemical calculations were carried out to explain the observed shifts in the absorption spectrum of different azo-aromatic compounds due to changes in the dihedral angle of the azo-group. Our results reveal that the pi-pi* transition presents a hypsochromic shift and an oscillator strength drop upon increase of the dihedral angle. Nevertheless, the pi-pi* transition exhibits the opposite behavior. This effect is attributed to the reduction in the pi-electron conjugation length of the molecule. Experimentally, we performed temperature dependence measurements of the linear absorption spectrum. Both the theoretical and experimental results demonstrate that small energy changes are mirrored in the electronic transitions of conjugated linear molecules. (C) 2010 Elsevier B.V. All rights reserved.

Torsion theories induced from commutative subalgebras

We begin a study of torsion theories for representations of finitely generated algebras U over a field containing a finitely generated commutative Harish-Chandra subalgebra Gamma. This is an important class of associative algebras, which includes all finite W-algebras of type A over an algebraically closed field of characteristic zero, in particular, the universal enveloping algebra of gl(n) (or sl(n)) for all n. We show that any Gamma-torsion theory defined by the coheight of the prime ideals of Gamma is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec Gamma have the same coheight. Hence, the coheight of these associated prime ideals is an invariant of a given simple U-module. This implies the stratification of the category of U-modules controlled by the coheight of the associated prime ideals of Gamma. Our approach can be viewed as a generalization of the classical paper by Block (1981) [4]; it allows, in particular, to study representations of gl(n) beyond the classical category of weight or generalized weight modules. (C) 2011 Elsevier B.V. All rights reserved.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Analys av förvridning vid hålning av rör : Analysis of metal torsion in rotary piercing

Hålningsprocessen är det inledande bearbetningssteget vid varmvalsning av sömlösa rör. Det är en tvärvalsningsprocess i vilken ett cylindriskt ämne valsas mellan två dubbelkoniska val¬sar över en plugg. Valsarna är snedställda med en viss mat¬ningsvinkel, vilken ger upphov till en axiell drivkraft genom ver¬ket. Hela denna pro¬cess är roterande. Detta i kombination med bl.a. de koniska valsarna leder till en förvrid¬ning av röret, dvs. en tänkt rak linje på det ingå¬ende äm¬net övergår till en spiral efter genomförd valsning. Med föreliggande uppgift är målet att studera förvridningen genom teoretisk och experimen¬tell analys. Syftet med detta är dels att få fördjupad kunskap inom området och dels att ut¬veckla en modell för pre¬diktering av förvridningen.Det experimentella arbetet är utfört på ett stål av typ Ovako 280 (SS2142). Denna mjuka stål¬sort valdes i syfte att undvika värmebehandling innan provberedning. För att visuali¬sera för¬vridningen fräs¬tes ett rakt spår längs det ingående äm¬net och hål borrades mot symmetrilinjen. De praktiska undersökningarna utfördes direkt i den löpande produktionen. Genomförda beräkningar uppvisar en längsgående förvridningsvinkel som stämmer väl över¬ens med uppmätt värde. Detta är dock under antagandet att den tangentiella hastighetskoeffi¬cienten varierar linjärt utmed deformationszonen. För en mer utvecklad modell krävs en nog¬grannare analys av kontakten mellan vals/ämne eller en grundligt genomförd uppmätning av ämnets vinkelhastighet.

Material properties under drawing and extrusion with cyclic torsion

A copper bar was drawn while a lead bar was extruded through a cyclically twisting die in a specifically designed experimental rig. The drawing/extrusion load fluctuated at the same frequency as that of die twisting. The load tended to be at a level of monotonic deformation when the die was changing direction. The degree of the reduction in load for both the drawing and extrusion processes depended on the deformation conditions and requires optimisation for industrial application.

The generation of new high-angle boundaries in aluminium during hot torsion

The crystallographic rotation field for deformation in torsion is such that it is possible for orientations close to stable orientations to rotate away from the stable orientation. A Taylor type model was used to demonstrate that this phenomenon has the potential to transform randomly generated low-angle boundaries into high-angle boundaries. After imposing an equivalent strain of 1.2, up to 40% of the simulated boundaries displayed a disorientation in excess of 15°. These high-angle boundaries were characterised by a disorientation axis close to parallel with the sample radial direction. A series of hot torsion tests was carried out on 1050 aluminium to seek evidence for boundaries formed by this mechanism. A number of deformation-induced high-angle boundaries were identified. Many of these boundaries showed disorientation axes and rotation senses similar to those seen in the simulations. Between 10% and 25% of all the high-angle boundary present in samples twisted to equivalent strains between 2 and 7 could be attributed to the present mechanism.

Ultrafine grained ferrite formed by interrupted hot torsion deformation of plain carbon steel

A plain carbon steel was deformed using a hot torsion deformation simulator. A schedule known to produce strain-induced ferrite was used with the strain interrupted for increasing intervals of time to determine the effect of an isothermal hold on the final microstructure. Microscopy and electron back-scattered diffraction (EBSD) were used to analyse the changes that occurred in the partially transformed microstructure during the hold and the subsequent applied strain. The strain-induced ferrite coarsened during the hold and this coarsened ferrite was refined during the second deformation. These results were compared to those obtained for a different plain carbon steel deformed in single pass rolling close to the Ar3 temperature.

Effect of thermomechanical parameters on the critical strain for ultrafine ferrite formation through hot torsion testing

A C–Mn–V steel was used to study ultrafine ferrite formation (1–3 μm) through dynamic strain-induced transformation (DSIT) using hot torsion experiments. A systematic study determined the critical strain for the start of DSIT (C,DSIT), although this may not lead to a fully ultrafine microstructure. Therefore, the strain to produce an ultrafine ferrite (UFF) as final microstructure (C,UFF) during deformation was also determined. In addition, the effect of thermomechanical parameters such as deformation temperature, prior austenite grain size, strain rate and cooling rate on C,DSIT and C,UFF has been evaluated. DSIT ferrite nucleated on prior austenite grain boundaries at an early stage of straining followed by intragranular nucleation at higher strains. The prior austenite grain size affected the distribution of DSIT ferrite nucleation sites at an early stage of transformation and the subsequent coarsening behaviour of the grain boundary and intragranular ferrite grains during post-deformation cooling. Also, C,DSIT and C,UFF increased with an increase in the prior austenite grain size and deformation temperature. The post-deformation cooling had a strong effect not only on C,UFF but also the UFF microstructure (i.e. final ferrite grain size and second phase characteristics).