A fast Legendre transform algorithm and applications to the adhesion model

1994 ◽  
Vol 9 (3) ◽  
pp. 259-281 ◽  
Author(s):  
A. Noullez ◽  
M. Vergassola
Keyword(s):  
Legendre Transform ◽  
Adhesion Model ◽  
Fast Legendre Transform

scholarly journals PRESSURE LAWS AND FAST LEGENDRE TRANSFORM

2011 ◽  
Vol 21 (04) ◽  
pp. 745-775 ◽  
Author(s):  
P. HELLUY ◽  
H. MATHIS
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Energy Minimization ◽  
Legendre Transform ◽  
Mathematical Tool ◽  
Minimization Principle ◽  
Algebra Theory ◽  
Mixture Thermodynamics ◽  
Two Phases ◽  
Fast Legendre Transform

In this paper we investigate algorithms based on the Fast Legendre Transform (FLT) in order to compute tabulated Equation Of State (EOS) for fluids with phase transition. The equation of state of a binary mixture is given by an energy minimization principle. According to the miscible or immiscible nature of the mixture, the energy of the system is either a convex envelope or an inf-convolution of the energies of the two phases. Because these operations are closely linked to Legendre transform, it is possible to construct fast algorithms that compute efficiently these operations. In addition, it appears that the natural mathematical tool for studying mixture thermodynamics in the Legendre space is the max-plus algebra theory.

scholarly journals A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3978
Author(s):  
Rocco Peter Fornari ◽  
Piotr de Silva
Keyword(s):  
Organic Molecules ◽  
Ph Value ◽  
Computational Cost ◽  
Legendre Transform ◽  
Good Prediction ◽  
Redox Potentials ◽  
Free Energies ◽  
Hybrid Functional ◽  
Data Set ◽  
State Changes

Discovering new materials for energy storage requires reliable and efficient protocols for predicting key properties of unknown compounds. In the context of the search for new organic electrolytes for redox flow batteries, we present and validate a robust procedure to calculate the redox potentials of organic molecules at any pH value, using widely available quantum chemistry and cheminformatics methods. Using a consistent experimental data set for validation, we explore and compare a few different methods for calculating reaction free energies, the treatment of solvation, and the effect of pH on redox potentials. We find that the B3LYP hybrid functional with the COSMO solvation method, in conjunction with thermal contributions evaluated from BLYP gas-phase harmonic frequencies, yields a good prediction of pH = 0 redox potentials at a moderate computational cost. To predict how the potentials are affected by pH, we propose an improved version of the Alberty-Legendre transform that allows the construction of a more realistic Pourbaix diagram by taking into account how the protonation state changes with pH.

scholarly journals New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. A. El-Deeb ◽  
Saima Rashid ◽  
Zareen A. Khan ◽  
S. D. Makharesh
Keyword(s):  
Time Scales ◽  
Legendre Transform ◽  
Independent Variables ◽  
Hilbert Type ◽  
Two Independent Variables ◽  
New Inequalities

AbstractIn this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

scholarly journals CFD-DEM Simulation of Spouted Bed Dynamics under High Temperature with an Adhesive Model

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2276
Author(s):  
Zhao Chen ◽  
Lin Jiang ◽  
Mofan Qiu ◽  
Meng Chen ◽  
Rongzheng Liu ◽  
...  
Keyword(s):  
High Temperature ◽  
Particle Surface ◽  
Particle Collision ◽  
Gas Velocity ◽  
Spouted Bed ◽  
Dem Simulation ◽  
Linear Spring ◽  
Adhesion Model ◽  
Adhesive Model ◽  
Damping Model

Particle adhesion is of great importance to coating processes due to its effect on fluidization. Currently, Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) has become a powerful tool for the study of multiphase flows. Various contact force models have also been proposed. However, particle dynamics in high temperature will be changed with particle surface properties changing. In view of this, an adhesion model is developed based on approaching-loading-unloading-detaching idea and particle surface change under high temperature in this paper. Analyses of the adhesion model are given through two particle collision process and validated by experiment. Effects of inlet gas velocity and adhesion intensity on spouted bed dynamics are investigated. It is concluded that fluidization cycle will be accelerated by adhesion, and intensity of fluidization will be marginally enhanced by slight adhesion. Within a certain range, increasing inlet gas velocity will lead to strong intensity of particle motion. A parameter sensitivity comparison of linear spring-damping model and Hertz-Mindlin Model is given, which shows in case of small overlaps, forces calculated by both models have little distinction, diametrically opposed to that of large overlaps.

scholarly journals A robust generalization of the Legendre transform for QFT

2017 ◽  
Vol 50 (22) ◽  
pp. 225201 ◽  
Author(s):  
D M Jackson ◽  
A Kempf ◽  
A H Morales
Keyword(s):  
Legendre Transform
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