mxpfit: A library for finding optimal multi-exponential approximations

Ikeno, Hidekazu

doi:10.1016/j.cpc.2018.04.015

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…In general, a short Prony series, which can accurately represent the material relaxation are desirable [31] since in the finite element models, for instance, each term of the Prony series adds a substantial number of global variables [80,81]. Detailed techniques concerning the Prony approximations are not at issue in this analysis by we may mention that nowadays there exists a MIT library named MXPFIT implemented in C++, allowing us to find optimal approximations by multi-exponential sums [77] as well some widely available commercial software packages such as Maple and OriginPro have approximations by exponentially decaying sums incorporated in their libraries.…”

Section: Discrete Relaxation Spectrum By Prony Series Decompositionmentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

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This study addresses the stress–strain relaxation functions of solid polymers in the framework of the linear viscoelasticity with aim to establish the adequate fractional operators emerging from the hereditary integrals. The analysis encompasses power-law and non-power-law materials, thus allowing to see the origins of application of the tools of the classical fractional calculus with singular memory kernels and the ideas leading towards fractional operators with non-singular (regular) kernels. A step ahead in modelling with hereditary integrals is the decomposition of non-power-law relaxation curves by Prony series, thus obtaining discrete relaxation kernels with a finite number of terms. This approach allows for seeing the physical background of the newly defined Caputo–Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories. The non-power-law relaxation curves also allow for approximations by the Mittag–Leffler function of one parameter that leads reasonably into stress–strain hereditary integrals in terms of Atangana–Baleanu fractional derivative of Caputo sense. The main outcomes of the analysis done are the demonstrated distinguishes between the relaxation curve behaviours of different materials and are therefore the adequate modelling with suitable fractional operators.

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Section: Discrete Relaxation Spectrum By Prony Series Decompositionmentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

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“…78 Here, we adapt the algorithm developed in Ref. 79 for the LTCTs and demonstrate the efficiency of the truncated PSD (TPSD) method.…”

Section: Author Declarationsmentioning

confidence: 99%

Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water

Takahashi,

Tanimura

2023

Preprint

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A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra, as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space (DHEOM-MLWS), with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.

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Discretized hierarchical equations of motion in mixed Liouville–Wigner space for two-dimensional vibrational spectroscopies of liquid water

Takahashi

Tanimura

2023

The Journal of Chemical Physics

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A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra, as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville--Wigner space (DHEOM-MLWS), with Lagrange--Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange--Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz--infrared--visible and infrared--infrared--Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.

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mxpfit: A library for finding optimal multi-exponential approximations

Cited by 5 publications

References 21 publications

Response functions in linear viscoelastic constitutive equations and related fractional operators

Response functions in linear viscoelastic constitutive equations and related fractional operators

Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water

Discretized hierarchical equations of motion in mixed Liouville–Wigner space for two-dimensional vibrational spectroscopies of liquid water

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