scholarly journals Variational approach for nonpolar solvation analysis

2012 ◽  
Vol 137 (8) ◽  
pp. 084101 ◽  
Author(s):  
Zhan Chen ◽  
Shan Zhao ◽  
Jaehun Chun ◽  
Dennis G. Thomas ◽  
Nathan A. Baker ◽  
...  
Keyword(s):  
Variational Approach ◽  
Nonpolar Solvation ◽  
Solvation Analysis

scholarly journals Role of Dispersion Attraction in Differential Geometry Based Nonpolar Solvation Models

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhan Chen
Keyword(s):  
Differential Geometry ◽  
Electrostatic Interactions ◽  
Polar Component ◽  
Great Success ◽  
Free Energies ◽  
Dispersion Interactions ◽  
Solvation Models ◽  
Nonpolar Solvation ◽  
Solvation Analysis

AbstractDifferential geometry (DG) based solvation models have shown their great success in solvation analysis by avoiding the use of ad hoc surface definitions, coupling the polar and nonpolar free energies, and generating solvent-solute boundary in a physically self-consistent fashion. Parameter optimization is a key factor for their accuracy, predictive ability of solvation free energies, and other applications. Recently, a series of efforts have been made to improve the parameterization of these new implicit solvent models. In thiswork, we aim at studying the role of dispersion attraction in the parameterization of our DG based solvation models. To this end, we first investigate the necessity of van derWaals (vdW) dispersion interactions in the model and then carry out systematic parameterization for the model in the absence of electrostatic interactions. In particular, we explore how the changes in Lennard-Jones (L-J) potential expression, its decomposition scheme, and choices of some fixed parameter values affect the optimal values of other parameters as well as the overall modeling error. Our study on nonpolar solvation analysis offers insights into the parameterization of nonpolar components for the full DG based models by eliminating uncertainties from the electrostatic polar component. Therefore, it can be regarded as a step towards better parameterization for the full DG based model.

scholarly journals Multiple positive solutions for nonlocal elliptic problems involving the Hardy potential and concave–convex nonlinearities

2020 ◽  
pp. 2050008
Author(s):  
Shaya Shakerian
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variational Approach ◽  
Nehari Manifold ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].

scholarly journals A new variational approach for the thermodynamic topology optimization of hyperelastic structures

2020 ◽  
Author(s):  
Philipp Junker ◽  
Daniel Balzani
Keyword(s):  
Topology Optimization ◽  
Variational Approach ◽  
Large Deformations ◽  
Mathematical Structure ◽  
Detailed Model ◽  
Novel Approach ◽  
Extremal Principles ◽  
Model Derivation ◽  
Numerical Discretization ◽  
Total Structure

AbstractWe present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.

scholarly journals A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Mushtaq Ahmad Khan ◽  
Asmat Ullah ◽  
Sahib Khan ◽  
Murtaza Ali ◽  
Sheraz Khan ◽  
...  
Keyword(s):  
Image Restoration ◽  
Fractional Order ◽  
Variational Approach ◽  
Fuzzy Membership
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