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See detailNonlinear resonant transport of Bose-Einstein condensates
Paul, T.; Richter, K.; Schlagheck, Peter ULg

in Physical Review Letters (2005), 94(2),

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a ... [more ▼]

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales. [less ▲]

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See detailNonlinear Schrödinger wave equation with linear quantum behavior
Richardson, Christopher ULg; Schlagheck, Peter ULg; Martin, John ULg et al

in Physical Review. A (2014), 89

We show that a nonlinear Schro ̈dinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the ... [more ▼]

We show that a nonlinear Schro ̈dinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schro ̈dinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantumlike features appear and is equivalent to scaling Planck’s constant. [less ▲]

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See detailNonlinear Sensitivity Analysis of Biochemical Reaction Networks, by Bilinear Approximation
Streif, Stefan; Findeisen, Rolf; Bullinger, Eric ULg

in Proc. of the 2nd Foundations of Systems Biology in Engineering FOSBE 2007, 9–12 September, Stuttgart Germany (2007)

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See detailNonlinear Structural Dynamics: Theory, Simulation and Testing, KEYNOTE LECTURE
Kerschen, Gaëtan ULg

in Proceedings of the 18th Symposium on Vibrations, Shocks and Noise (2012)

Nonlinearity is a frequent occurrence in engineering structures. It is at the origin of rich and complex dynamical phenomena that cannot be observed in linear structures. The analysis of the dynamics of ... [more ▼]

Nonlinearity is a frequent occurrence in engineering structures. It is at the origin of rich and complex dynamical phenomena that cannot be observed in linear structures. The analysis of the dynamics of nonlinear systems therefore warrants the development of rigorous and effective methods and is the focus of this presentation. Several theoretical, computational and experimental methods will be presented and applied to a real-life, full-scale nonlinear structure, the EADS- Astrium SmallSat spacecraft. [less ▲]

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See detailNonlinear System Identification in Structural Dynamics: A Short (and Biased) History
Worden, K.; Kerschen, Gaëtan ULg; Vakakis, Alexander F. et al

in 25th International Modal Analysis Conference, Orlando, 2007 (2007)

Although linear systems are now very well-understood in the context of structural dynamics, this is not at all the case for nonlinear systems. In particular, despite huge advances in the mathematical ... [more ▼]

Although linear systems are now very well-understood in the context of structural dynamics, this is not at all the case for nonlinear systems. In particular, despite huge advances in the mathematical theory of nonlinear dynamical systems, progress in the difficult field of nonlinear system identification (learning of models from measured input/output data) has largely remained fairly slow and incremental. This is not to say that there have been no major successes in the field in its comparatively short history, and the objective of this paper is to present some of the highlights, as perceived by the authors, and to pave the way for a second paper discussing new developments and possibilities for the future. [less ▲]

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See detailNonlinear System Identification in Structural Dynamics: Current Status and Future Directions
Kerschen, Gaëtan ULg; Worden, K.; Vakakis, Alexander F. et al

in 25th International Modal Analysis Conference, Orlando, 2007 (2007)

Nonlinear system identification aims at developing high-fidelity mathematical models in the presence of nonlinearity from input and output measurements performed on the real structure. The present paper ... [more ▼]

Nonlinear system identification aims at developing high-fidelity mathematical models in the presence of nonlinearity from input and output measurements performed on the real structure. The present paper is a discussion of the recent developments in this research field. Three of the latest approaches are presented, and application examples are considered to illustrate their fundamental concepts, advantages and limitations. Another objective of this paper is to identify future research needs, which would make the identification of structures with a high modal density in abroad frequency range viable. [less ▲]

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See detailNonlinear System Identification using Interpolated Short Time Fourier Transform
Shi, Dongfeng; Dimitriadis, Grigorios ULg

in Akay, A.; Arnas, O.; Cooper, J. E. (Eds.) et al Proceedings of 7th Biennial ASME Conference on Engineering Systems Design and Analysis (2004, July)

For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous ... [more ▼]

For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous amplitudes and frequencies of response signals. It is shown that the backbone curves estimated by the ISTFT agree with theoretical backbone curves very well. Additionally, the restoring force can be reconstructed to specify the type of nonlinear stiffness. A curve-fitting technique is introduced to estimate the parameters of nonlinear systems on the basis of theoretical backbone curves. It is shown that a number of typical nonlinear stiffness functions such as cubic, bilinear and pre-compressed springs can be identified accurately using this new method. [less ▲]

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See detailNonlinear Targeted Energy Transfer in Mechanical and Structural Systems I
Vakakis, Alexander F.; Gendelman, O. V.; Bergman, L. A. et al

Book published by Springer (2009)

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See detailNonlinear Targeted Energy Transfer in Mechanical and Structural Systems II
Vakakis, Alexander F.; Gendelman, O. V.; Bergman, L. A. et al

Book published by Springer (2009)

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See detailNonlinear thin shell finite element for steel and concrete structures subjected to fire: theoretical development
Talamona, Didier; Franssen, Jean-Marc ULg

in Journal of Applied Fire Science (2002), 11(4), 291-310

This article describes the features of a quadrilateral thin shell element, based on Marguerre's theory that has ben implemented in the finite element program SAFIR (from the University of Liege.) The ... [more ▼]

This article describes the features of a quadrilateral thin shell element, based on Marguerre's theory that has ben implemented in the finite element program SAFIR (from the University of Liege.) The element has four nodes (one at each corner) and each node has six degrees of freedom, i.e., three translations and three rotations (the sixth degree of freedom is a true one, which can be assimilated to the in-plane rotation.) This article presents some theoretical developments regarding the element formulation. The algorithm strategies for isotropic material (steel for example) and non-isotropic material 'concrete) and their modifications for elevated temperatures are described. Two verifications examples are presented (the patch test and Lee's frame at elevated temperatures). [less ▲]

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See detailNonlinear thin shell finite element for steel and concrete structures subjected to fire: verification and validation
Talamona, Didier; Castagne, Sylvie; Franssen, Jean-Marc ULg

in Journal of Applied Fire Science (2003), 12(1), 65-81

This article presents verification and validation examples for a nonlinear thin shell element developed for structures subjected to fire. The verification benchmarks are: a Z-shaped cantilever, a twisted ... [more ▼]

This article presents verification and validation examples for a nonlinear thin shell element developed for structures subjected to fire. The verification benchmarks are: a Z-shaped cantilever, a twisted cantilever beam, a hemispherical shell, and Lee's frame at room temperature and at elevated temperature. The element shows that it provides results in good agreement with theoretical results and other finite elements. The validation calculations have been performed on an H rolled profile and a concrete slab. The element demonstrates its ability to reproduce local buckling on a H-steel beam under fire conditions and that it predicts accurately the failure of a concrete slab subjected to fire. The theoretical development of this finite element has been published in the Journal of Applied Fire Science, Vol. 11, No. 4, pp. 291-310, "Nonlinear Thin Shell Finite Element for Steel and Concrete Structures Subjected to Fire: Theoretical Development." [less ▲]

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See detailNonlinear time-domain finite-element modeling of thin electromagnetic shells
V Sabariego, Ruth ULg; Geuzaine, Christophe ULg; Dular, Patrick ULg et al

in Proceedings of the 13th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2008) (2008, May)

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See detailNonlinear time-domain finite-element modeling of thin electromagnetic shells
V Sabariego, Ruth ULg; Geuzaine, Christophe ULg; Dular, Patrick ULg et al

in IEEE Transactions on Magnetics (2009), 45(3), 976-979

A nonlinear time-domain extension of the classical linear frequency-domain thin-shell approach is presented. The interface conditions are expressed in terms of the average magnetic flux density throughout ... [more ▼]

A nonlinear time-domain extension of the classical linear frequency-domain thin-shell approach is presented. The interface conditions are expressed in terms of the average magnetic flux density throughout the shell thickness and a number of higher order components. The method is elaborated in the frame of the magnetic vector potential formulation. The nonlinear system of algebraic equations is solved by means of the Newton–Raphson scheme. To validate the new formulation, we consider a magnetic plate placed above a double line carrying a sinusoidal current. Results are compared with those obtained with a fine finite-element model. [less ▲]

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See detailA nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models
Gyselinck, Johan; V Sabariego, Ruth ULg; Dular, Patrick ULg

in IEEE Transactions on Magnetics (2006), 42(4), 763-766

The authors present a novel nonlinear homogenization technique for laminated iron cores in three-dimensional (3-D) finite-element (FE) models of electromagnetic devices. The technique takes into account ... [more ▼]

The authors present a novel nonlinear homogenization technique for laminated iron cores in three-dimensional (3-D) finite-element (FE) models of electromagnetic devices. The technique takes into account the eddy current effects in the stacked core without the need of modeling all laminations separately. A nonlinear constitutive magnetic law is considered. The system of nonlinear algebraic equations obtained after time discretization is solved by means of the Newton-Raphson scheme. By way of validation, the method is applied to a 3-D FE model of a laminated ring core with toroidal coil. [less ▲]

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See detailNonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
Paul, T.; Hartung, M.; Richter, K. et al

in Physical Review. A (2007), 76(6),

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to ... [more ▼]

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasibound states of the quantum dot. [less ▲]

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See detailNonlinear transport of Bose-Einstein condensates through waveguides with disorder
Paul, T.; Leboeuf, P.; Pavloff, N. et al

in Physical Review. A (2005), 72(6),

We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations ... [more ▼]

We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations inherent to microfabricated guides. This model allows for analytical and numerical studies of realistic transport experiments. The repulsive interaction among the condensate atoms in the beam induces different transport regimes. Below some critical interaction (or for sufficiently small L) a stationary flow is observed. In this regime, the transmission decreases exponentially with increasing L. For strong interaction (or large L), the system displays a transition toward a time-dependent flow with an algebraic decay of the time-averaged transmission. [less ▲]

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See detailThe nonlinear tuned vibration absorber
Viguié, R.; Kerschen, Gaëtan ULg

in Proceedings of the International Conference on Structural Nonlinear Dynamics and Diagnosis (2012)

The objective of this paper is to introduce a new nonlinear dynamical absorber, the nonlinear tuned vibration absorber, through a rigorous nonlinear extension of the tuning rule for the linear tuned ... [more ▼]

The objective of this paper is to introduce a new nonlinear dynamical absorber, the nonlinear tuned vibration absorber, through a rigorous nonlinear extension of the tuning rule for the linear tuned vibration absorber. This nonlinear tuning methodology combined with the increased suppression bandwidth brought by the intentional use of nonlinearity leads to the development of an absorber that is effective in wide ranges of frequencies and motion amplitudes. The results are illustrated using a one-degree-of-freedom primary system. [less ▲]

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See detailNonlinear vibration absorber coupled to a nonlinear primary system: A tuning methodology
Viguié, Régis ULg; Kerschen, Gaëtan ULg

in Journal of Sound & Vibration (2009), 326(3-5), 780-793

This paper addresses the problem of mitigating the vibration of nonlinear mechanical systems using nonlinear dynamical absorbers. One particular feature of the proposed absorber is that it is effective in ... [more ▼]

This paper addresses the problem of mitigating the vibration of nonlinear mechanical systems using nonlinear dynamical absorbers. One particular feature of the proposed absorber is that it is effective in a wide range of forcing amplitudes. A qualitative tuning methodology is developed and validated using numerical simulations. (C) 2009 Elsevier Ltd. All rights reserved. [less ▲]

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See detailNonlinearity Characterization for Nonlinear Dynamic System Identification Using an Expert Approach
Dimitriadis, Grigorios ULg; Vio, Gareth Arthur

in Proceedings of the 2006 International Conference on Noise and Vibration Engineering (2006, September)

The identification of nonlinear dynamic systems can be rendered significantly more parsimonious if the nonlinearity present in the system is known. While there are many successful non-parametric nonlinear ... [more ▼]

The identification of nonlinear dynamic systems can be rendered significantly more parsimonious if the nonlinearity present in the system is known. While there are many successful non-parametric nonlinear system identification methods, the resulting models do not describe the nonlinearity in physical terms and are difficult to obtain due to the large number of candidate terms that must be examined. In this paper an expert approach towards the characterization of nonlinearities in a dynamic system is presented. The methodology is based on simulations of dynamic systems with a variety of commonly occurring nonlinear functions. The responses of such systems to various types of excitation are analysed and rules are developed as to what nonlinearity is likely to be present in a system given the dynamic characteristics of measured responses. [less ▲]

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See detailNonlocal magnetic field-tuned quantum criticality in cubic CeIn3-xSnx (x=0.25)
Silhanek, Alejandro ULg; Ebihara, Takao; Harrison, N. et al

in Physical Review Letters (2006), 96(20),

We show that antiferromagnetism in lightly (approximate to 8%) Sn-doped CeIn3 terminates at a critical field mu H-0(c)=42 +/- 2 T. Electrical transport and thermodynamic measurements reveal the effective ... [more ▼]

We show that antiferromagnetism in lightly (approximate to 8%) Sn-doped CeIn3 terminates at a critical field mu H-0(c)=42 +/- 2 T. Electrical transport and thermodynamic measurements reveal the effective mass m(*) not to diverge, suggesting that cubic CeIn3 is representative of a critical spin-density wave (SDW) scenario, unlike the local quantum critical points reported in anisotropic systems such as CeCu6-xAux and YbRh2Si2-xGex. The existence of a maximum in m(*) at a lower field mu H-0(x)=30 +/- 1 T may be interpreted as a field-induced crossover from local moment to SDW behavior as the Neel temperature falls below the Fermi temperature. [less ▲]

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