Dynamic model of hysteretic elastic systems

Capogrosso-Sansone, Barbara; Guyer, R. A.

doi:10.1103/physrevb.66.224101

Cited by 117 publications

(160 citation statements)

References 14 publications

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“…When there is no disorder, Quantum Monte Carlo (QMC) studies 2,3 obtained quantitative values for the critical coupling of the superfluid-Mott insulator (SF-MI) transition at commensurate filling in one dimension, which were in good quantitative agreement with series expansion 4 and density matrix renormalization group calculations 5,6 . The critical point is now known in d = 2 to a very high accuracy 7 . Over the last decade, it became clear that trapped ultra-cold atoms provide an alternate, and more controllable, experimental realization of the bosonic Hubbard model 8 .…”

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confidence: 99%

Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap

et al. 2008

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Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the (µ/U, t/U ) phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results. has offered the first such benchmark in d = 2.However, a significant obstacle exists for such a direct comparison: The confining potential produces spatial inhomogeneities and a coexistence of SF and MI phases 10 . This naturally leads to the question as to what "critical coupling" is being accessed in the experiments. Is it the coupling at which "Mott shoulders" begin to develop about a SF core? Or is it the coupling at which a Mott region pervades the entire central region of the trap? In this paper, we provide a detailed quantitative analysis of this issue. Specifically, using the Local Density Approximation (LDA) and QMC simulations, we study, for fixed particle numbers, the evolution of the density profiles of the trapped system as a function of the interaction strength and map those "canonical trajectories" onto the phase diagram of the uniform system. We also show data for the visibility 11,12 . These measurements allow us to connect the critical points obtained in QMC with those that can be seen in experiment.The QMC results presented here were obtained using two different algorithms. In the first 15 , the imaginary time β is discretized leading to a path integral for the partition function on a rigid space-imaginary time grid with local world line updates. In the second 16,17,18 , imaginary time is continuous and there are no Trotter errors associated with discretization. Bosonic world-line updates can be non-local, and, as a consequence, the Green's function can be measured at all separations. The two algorithms give consistent results for all physical quantities calculated such as the density profiles and superfluid density.The one dimensional bosonic Hubbard Hamiltonian is,Here i = 1, 2, · · · , L where L is the number of sites andis the coordinate of the ith site as measured from the center of the system. We choose the lattice constant a = 1. The hopping parameter, t, sets the energy scale; in what follows we set t = 1, i.e., all energies are measured in units of t. n i = a † i a i is the number operator, and [a i , a † j ] = δ ij are bosonic creation and destruction operators. V T is the curvature of the trap, and the repulsive contact interaction is given by U . The chemical potential, µ, controls the average number of particles.The bosonic-Hubbard Hamiltonian can also be simulated in the ca...

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confidence: 99%

Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap

et al. 2008

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“…19, we model the specimen as a dynamical system composed of a set of N linear springs, each of which may be in one of two different states, characterized by different rest lengths l r = l 0 + ␦ o,c , with ␦ o,c = ±␦ corresponding to C 1 in the notation adopted above. Each spring switches from one state to the other depending on the stress it is required to support ͑positive stress corresponds to compression͒.…”

Section: A Three-level Examplementioning

confidence: 99%

“…The Preisach-Mayergoyz ͑PM͒ space 14,15 seems to be an appropriate general framework for this purpose. Indeed, the PM approach is based on the introduction of simple units, [16][17][18][19][20][21] characterized by some local ͑and weakly nonlocal͒ interactions that satisfy simple equilibrium and constitutive equations. A complex behavior stems from their interactions, rather than from more complicated constitutive equations introduced by hand.…”

Section: Introductionmentioning

confidence: 99%

Preisach-Mayergoyz approach to fatigue-induced irreversibility

et al. 2006

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The Preisach-Mayergoyz ͑PM͒ approach has been widely used to describe hysteresis in different fields. Among these, various types of reversible hysteretic elastic behavior have been succesfully modeled, inclusing quasi-static, fast and slow dynamics, modulation, and so on. Here, we propose an approach to extend the PM formulation to also treat irreversible phenomena, such as fatigue and damage progression. For this purpose, we introduce a multilevel scheme based on nested PM descriptions. The mathematical formulation is outlined and a phenomenological application presented.

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“…Consequently, monitoring and understanding the evolution of the mechanical state of the material when damage is in progress is a challenging goal and several methods have been proposed up to date. Among them, techniques based on nonlinear ultrasonic methods (Van den Abeele et al, 2000;Solodov et al, 2004;Chen et al, 2008;Herrmann et al, 2006;Deng and Pei, 2007) appear to be very promising. Indeed, the elastic response of a solid to an ultrasonic excitation reveals the possible presence of a damaged area by increasing its nonlinearity, even though it is to be noted that traditional ultrasonic analysis techniques (e.g.…”

Section: Introductionmentioning

confidence: 97%

“…To this purpose, models of the elastic (Delsanto and Scalerandi, 2003;Capogrosso and Guyer, 2002;Vakhnenko et al, 2005) and mechanical (Pecorari, 2004;Aleshin and Van Den Abeele, 2005) behavior of the specimen are necessary and various approaches have been developed in the last few years. Among them, models based on a Preisach-Mayergoyz (PM) space approach (McCall et al, 1994;Guyer et al, 1995Guyer et al, , 1998 have been proven to be successful in describing hysteretic nonlinearity (Delsanto and Scalerandi, 2003;Capogrosso and Guyer, 2002;Nobili and Scalerandi, 2004;Barbieri et al, 2009;Bentahar et al, 2006;Payan et al, 2007), which is a peculiar characteristic of the nonlinear elastic behavior of concrete and of the other materials mentioned above.…”

Section: Introductionmentioning

confidence: 99%

Evolution of damage-induced nonlinearity in proximity of discontinuities in concrete

Antonaci

Bruno

Gliozzi

et al. 2010

International Journal of Solids and Structures

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a b s t r a c tUnderstanding the mechanisms and modalities of damage progression close to discontinuities in solids, such as joints, is of great importance for applications in different fields. The interaction between damage and elasticity causes a nonlinear elastic response of the sample to a stress excitation (e.g. in the ultrasonic frequency range). Extracting physical or mechanical information on the sample properties from recorded ultrasonic signals requires a realistic model and an efficient detection method, as it will be discussed in this paper. We study here the successive phases that concrete samples with discontinuities enter by progressively increase the applied external load. Considerations on the mechanisms of damage progression are derived from experimental data using a Preisach-Mayergoyz space approach, developed in order to capture all the observed behaviors.

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Dynamic model of hysteretic elastic systems

Cited by 117 publications

References 14 publications

Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap

Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap

Preisach-Mayergoyz approach to fatigue-induced irreversibility

Evolution of damage-induced nonlinearity in proximity of discontinuities in concrete

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