A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models

A nonlocal continuum electrostatic model,defined as integro-differential equations,can significantly improve the classic Poisson dielectric model,but is too costly to be applied to large protein simulations.To sharply reduce the model’s complexity,a modified nonlocal continuum electrostatic model is presented in this paper for a protein immersed in water solvent,and then transformed equivalently as a system of partial differential equations.By using this new differential equation system,analytical solutions are derived for three different nonlocal ionic Born models,where a monoatomic ion is treated as a dielectric continuum ball with point charge either in the center or uniformly distributed on the surface of the ball.These solutions are analytically verified to satisfy the original integro-differential equations,thereby,validating the new differential equation system.

A review on the application of modified continuum models in modeling and simulation of nanostructures

Analysis of the mechanical behavior of nanos- tructures has been very challenging. Surface energy and non- local elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are men- tioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomateri- als are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires fur- ther applications of modified continuum models in modeling nanomaterials and nanostructures.

Effect of Longitudinal Magnetic Field on Vibration Response of Double-Walled Carbon Nanotubes Embedded in Viscoelastic Medium

This paper aims to study the effect of externally applied longitudinal magnetic field on the transverse vibration of viscoelastic double-walled carbon nanotubes （visco-DWCNTs） embedded in a viscoelastic medium. The analyses are carried out based on the nonlocal viscoelastic model and Euler-Bernoulli beam theory. Governing equations are derived for the vibration of the embedded visco-DWCNT subjected to a magnetic field, where the Lorentz magnetic force, the surrounding viscoelastic medium, the intertube van der Waals forces and viscoelasticity of the DWCNT are taken into consideration. In this study, the transfer function method is employed to solve the governing equations, which enables one to obtain the natural frequencies and the corresponding mode shapes in closed form for the DWCNTs with arbitrary boundary conditions. Here the developed mechanics model is first compared with the existing techniques available in the literature in a few particular cases, where excellent agreement is achieved. The validation of the model is followed by a detailed parametric study of the effects of longitudinal magnetic field, nonlocal parameter, boundary conditions, structural damping coefficient and aspect ratio of the DWCNTs on their vibration. The study demonstrates the efficiency of the present technique designed for vibration analysis of a complicated multi-physics system comprising DWCNTs, the viscoelastic medium and a magnetic field in longitudinal direction.