General Approach to Coupled Reactive Smoluchowski Equations: Integration and Application of Discrete Variable Representation and Generalized Coordinate Methods to Diffusive Problems

Piserchia, Andrea; Banerjee, Shiladitya; Barone, Vincenzo

doi:10.1021/acs.jctc.7b00685

Cited by 3 publications

(3 citation statements)

References 46 publications

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“…The eigenvalues and eigenfunctions of this Hamiltonian can be computed, for instance, by means of DVR, the basic ideas of which go back to the 1960s. , However, the method became widely popular soon after the pioneering work of Light and others in the 1980s, − and it has been recently re-explored in connection with diffusive problems. , …”

Section: The Devil: Accuracy In Computational Spectroscopymentioning

confidence: 99%

“…139,140 However, the method became widely popular soon after the pioneering work of Light and others in the 1980s, 141−146 and it has been recently reexplored in connection with diffusive problems. 147,148 This method is related to the variational basis representation (VBR), in which an operator is represented as a matrix in a truncated basis. The elements of the matrix representation of l ( )…”

Section: Chemical Reviewsmentioning

confidence: 99%

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Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy

et al. 2019

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The past decade has witnessed an increasing interaction between experiment and theory in the field of molecular spectroscopy. On the computational side, ongoing developments of hardware and software have moved computational spectroscopy from a highly specialized research area to a general tool for researchers in different fields of chemical science. However, since its dawn, computational spectroscopy has been characterized by the dichotomies of qualitative and quantitative description, and of interpretation and accuracy. Indeed, the analysis of experiments is seldom straightforward because of the subtle interplay of several different effects, which are not easy to evaluate and isolate, and/or the complexity of the system under consideration. Often, the accuracy has to be set aside for a more qualitative analysis that will provide the means for a broad interpretation. In such a scenario, the most recent advances in theoretical treatments as well as computational tools have opened the way to the reconciliation of accuracy and interpretability, resulting in unequivocal analyses and assignments of experimental spectra and their unbiased interpretation. This Review aims at being a comprehensive, authoritative, critical, and readable account of general interest to the chemistry community because of the wealth of qualitative and quantitative information that can be obtained from spectroscopic investigations. Limiting ourselves to rotational and vibrational spectroscopy, emphasis will be put on accuracy and interpretability as well as on the routes toward their reconciliation and integration.

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Section: The Devil: Accuracy In Computational Spectroscopymentioning

confidence: 99%

Section: Chemical Reviewsmentioning

confidence: 99%

Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy

et al. 2019

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“…The model presented in this work can be used to approach problems of diusioncontrolled reaction [34,72], coupled reactive Smoluchowski equations [73], diusion with time-dependent rate coecients on reaction [74], and minimal model [38] for two species.…”

Section: Second Case: K I (T) Memory In Laplacian Termsmentioning

confidence: 99%

From continuous-time random walks to controlled-diffusion reaction

Santos¹

2019

J. Stat. Mech.

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Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised-reactions emerge through various investigations that include numerical, analytical and experimental techniques. In this work, we construct a model which involves a coupling of two diffusion equations to approach the random walkers in a medium with localised reaction point (or controlled diffusion). We present the exact analytical solutions to the model. In the following, we obtain the survival probability and mean square displacement. Moreover, we extend the model to include memory effects in reaction points. Thereby, we found a simple relation that connects the power-law memory kernels with anomalous diffusion phenomena, i.e. (x − x ) 2 ∝ t µ . The investigations presented in this work uses recent mathematical techniques to introduces a form to represent the coupled random walks in context of reaction-diffusion problem to localised reaction.

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Application of the Discrete Variable Representation Approach to Formation of Amplitude–Phase Field Distributions on a Vertical Array in a Waveguide

Макаров

2021

Acoust. Phys.

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General Approach to Coupled Reactive Smoluchowski Equations: Integration and Application of Discrete Variable Representation and Generalized Coordinate Methods to Diffusive Problems

Cited by 3 publications

References 46 publications

Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy

Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy

From continuous-time random walks to controlled-diffusion reaction

Application of the Discrete Variable Representation Approach to Formation of Amplitude–Phase Field Distributions on a Vertical Array in a Waveguide

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