Legendre Transforms of Electrostatic Free-Energy Functionals

2018 ◽  
Vol 78 (6) ◽  
pp. 2973-2995
Author(s):  
Benjamin Ciotti ◽  
Bo Li
Keyword(s):  
Free Energy ◽  
Energy Functionals ◽  
Electrostatic Free Energy ◽  
Legendre Transforms

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals Existence of ground states for aggregation-diffusion equations

2019 ◽  
Vol 17 (03) ◽  
pp. 393-423 ◽  
Author(s):  
J. A. Carrillo ◽  
M. G. Delgadino ◽  
F. S. Patacchini
Keyword(s):  
Free Energy ◽  
Ground States ◽  
Energy Functional ◽  
Multi Agent Systems ◽  
Linear Diffusion ◽  
Sharp Condition ◽  
Macroscopic Models ◽  
Energy Functionals ◽  
Continuous Description ◽  
Degenerate Diffusions

We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the functional making it energetically favorable to spread, while the attraction is modeled through nonlocal forces. We give conditions on general entropies and interaction potentials for which neither ground states nor local minimizers exist. We show that these results are sharp for homogeneous functionals with entropies leading to degenerate diffusions while they are not sharp for fast diffusions. The particular relevant case of linear diffusion is totally clarified giving a sharp condition on the interaction potential under which the corresponding free energy functional has ground states or not.

An evaluation of poisson-boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

Biopolymers ◽  
2011 ◽  
pp. n/a-n/a ◽  
Author(s):  
Ronald D. Gorham ◽  
Chris A. Kieslich ◽  
Aaron Nichols ◽  
Noriko U. Sausman ◽  
Marisse Foronda ◽  
...  
Keyword(s):  
Free Energy ◽  
Free Energy Calculations ◽  
Energy Calculations ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy
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