168 research outputs found
EXACT SOLUTION OF CLASSICAL AND QUANTAL ONE-DIMENSIONAL MANY-BODY PROBLEMS WITH 2-BODY POTENTIAL VA(X)=G2A2-SINH2(AX)
No full textExact solution of the quantum Calogero-Gaudin system and of its q deformation RID A-7283-2010
No full textA complete set of commuting observables for the Calogero-Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the coalgebra invariance of the model; with the proper technical modifications this procedure can be applied to the q-deformed version of the model, which is then also exactly solved. (C) 2000 American Institute of Physics. [S0022- 2488(00)03910-4]
El derecho nacional del Reino Unido y el derecho comunitario e internacional. Una relación cada vez más tensa
No full textThis chapter in Spanish based on research carried and published in 2014, proposes to examine how international and, most of all, supranational European law and human rights jurisprudence becomes part of the law of the United Kingdom and to consider the implications for the British legal system. This will be done mainly from a legal and judicial perspective, but without ignoring the political one. Indeed, it would be highly problematic to address this theme without taking into account the growing tensions between the Cameron Government and the European Courts, in particular the court in Strasbourg. The chapter will begin by illustrating the legal mechanisms that are employed in the reception of international and supranational European law and the role played by the national and subnational parliaments and governments and then it will examine the relationship between the national courts and the supranational courts in Europe. The final part of this contribution will focus on the rising tensions over the past year between the Cameron Government, on one hand, and the European Union and, in particular, the Council of Europe: indeed one could argue that 2013 was an annus horribilis with regard to the relations between Britain and Europe
Computational Analysis of the Active Control of Incompressible Airfoil Flutter Vibration Using a Piezoelectric V-Stack Actuator
No full textThe flutter phenomenon is a potentially destructive aeroelastic vibration studied for the
design of aircraft structures as it limits the flight envelope of the aircraft. The aim of this work is to
propose a heuristic design of a piezoelectric actuator-based controller for flutter vibration suppression
in order to extend the allowable speed range of the structure. Based on the numerical model of a three
degrees of freedom (3DOF) airfoil and taking into account the FEM model of a V-stack piezoelectric
actuator, a filtered PID controller is tuned using the population decline swarm optimizer PDSO
algorithm, and gain scheduling (GS) of the controller parameters is used to make the control adaptive
in velocity. Numerical simulations are discussed to study the performance of the controller in the
presence of external disturbances
An isochronous variant of the Ruijsenaars-Toda model: equilibrium configurations, behavior in their neighborhood, Diophantine relations
No full textAn isochronous variant of the Ruijsenaars-Toda integrable many-body problem is introduced, an equilibrium configuration of this dynamical system is identified and by investigating the motions in its neighborhood Diophantine relations are obtained
On the Calogero-Moser space associated with dihedral groups
No full textInternational audienceUsing the geometry of the associated Calogero-Moser space, R. Rouquier and the author have attached to any finite complex reflection group several notions (Calogero-Moser left, right or two-sided cells, Calogero-Moser cellular characters), completing the notion of Calogero-Moser families defined by Gordon. If moreover is a Coxeter group, they conjectured that these notions coincide with the analogous notions defined using the Hecke algebra by Kazhdan and Lusztig (or Lusztig in the unequal parameters case). In the present paper, we aim to investigate these conjectures whenever is a dihedral group
Quantum versus classical integrability in Ruijsenaars-Schneider systems
No full textThe relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider systems, which are one-parameter deformations of Calogero-Moser systems, is addressed. Many remarkable properties of classical Calogero and Sutherland systems (based on any root system) at equilibrium are reported in a previous paper (Corrigan-Sasaki). For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all 'integer valued'. In this paper we report that similar features and results hold for the Ruijsenaars-Schneider type of integrable systems based on the classical root systems
Computational aspects of Calogero-Moser spaces
No full textInternational audienceWe present a series of algorithms for computing geometric and representationtheoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated with complex reflection groups. Especially, we are concerned with Calogero-Moser families (which correspond to the -fixed points of the Calogero-Moser space) and cellular characters (a proposed generalization by Rouquier and the first author of Lusztig's constructible characters based on a Galois covering of the Calogero-Moser space). To compute the former, we devised an algorithm for determining generators of the center of the rational Cherednik algebra (this algorithm has several further applications), and to compute the latter we developed an algorithmic approach to the construction of cellular characters via Gaudin operators. We have implemented all our algorithms in the Cherednik Algebra Magma Package (CHAMP) by the second author and used this to confirm open conjectures in several new cases. As an interesting application in birational geometry we are able to determine for many exceptional complex reflection groups the chamber decomposition of the movable cone of a Q-factorial terminalization (and thus the number of non-isomorphic relative minimal models) of the associated symplectic singularity
Computational aspects of Calogero-Moser spaces
No full textWe present a series of algorithms for computing geometric and
representation-theoretic invariants of Calogero-Moser spaces and rational
Cherednik algebras associated to complex reflection groups. Especially, we are
concerned with Calogero-Moser families (which correspond to the
-fixed points of the Calogero-Moser space) and cellular
characters (a proposed generalization by Rouquier and the first author of
Lusztig's constructible characters based on a Galois covering of the
Calogero-Moser space). To compute the former, we devised an algorithm for
determining generators of the center of the rational Cherednik algebra (this
algorithm has several further applications), and to compute the latter we
developed an algorithmic approach to the construction of cellular characters
via Gaudin operators. We have implemented all our algorithms in the Cherednik
Algebra Magma Package (CHAMP) by the second author and used this to confirm
open conjectures in several new cases. As an interesting application in
birational geometry we are able to determine for many exceptional complex
reflection groups the chamber decomposition of the movable cone of a
-factorial terminalization (and thus the number of non-isomorphic
relative minimal models) of the associated symplectic singularity.Comment: 42 page
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