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In this work a new method for analyzing nanostructured materials has been proposed to accelerate the simulations for solid crystalline materials. The proposed Structural Approximation Method (SAM) is based on Molecular Dynamics (MD) and the accuracy of the results can also be improved in a systematic manner by sacrificing the simulation speed. In this method a virtual material is used instead of the real one, which has less number of atoms and therefore fewer degrees of freedom, compared to the real material. The number of differential equations that must be integrated in order to specify the state of the system will decrease significantly, and the simulation speed increases. To generalize the method for different materials, we used dimensionless equations. A fuzzy estimator is designed to determine the inter-atomic potential of the virtual material such that the virtual material represents the same behavior as the real one. In this paper Gaussian membership functions, singleton fuzzifier, center average defuzzifier, and Mamdani inference engine has been used for designing the fuzzy estimator. We also used the Gear predictor-corrector numerical integration method to integrate the governing differential equations. A FCC nano-bar of copper under uniform axial loading along [1 0 0] has been considered. The Sutton-Chen inter-atomic potential is used. The strain of this nano-bar has been calculated using the MD and the proposed method. Comparing the results show that while the proposed method is much faster, its results remain in an acceptable range from the results of MD method.

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All content in this area was uploaded by Aria Alasty on Jan 19, 2014

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The size scale effect on the piezoelectric response of bulk ZnO and ZnO nanobelts has been studied using molecular dynamics simulation. Six molecular dynamics models of ZnO nanobelts are constructed and simulated with lengths of 150.97 Å and lateral dimensions ranging between 8.13 and 37.37 Å. A molecular dynamics model of bulk ZnO has also been constructed and simulated using periodic boundary conditions. The piezoelectric constants of the bulk ZnO and each of the ZnO nanobelts are predicted. The predicted piezoelectric coefficient of bulk ZnO is 1.4 C m−2, while the piezoelectric coefficient of ZnO nanobelts increases from 1.639 to 2.322 C m−2 when the lateral dimension of the ZnO NBs is reduced from 37.37 to 8.13 Å. The changes in the piezoelectric constants are explained in the context of surface charge redistribution. The results give a key insight into the field of nanopiezotronics and energy scavenging because the piezoelectric response and voltage output scale with the piezoelectric coefficient.

In this study, the ideal tensile and shear strength of the recently discovered cubic spinel silicon nitride polymorph was calculated using an ab initio density functional technique. The stress-strain curve of the cubic silicon nitride structure was calculated from simulations of applied ɛ11 and ɛ23 components of strain, and the ideal strengths were estimated at ∼45 and ∼49 GPa, respectively. In addition, the elastic constants of the cubic structure were determined and a value of ∼311 and ∼349 GPa was estimated for the bulk and shear modulus, respectively. The estimates of the elastic constants were found to be in reasonable agreement with existing data. Using a previously reported empirical relation, the hardness of the cubic phase was also estimated: ∼47 GPa.

This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, Fn(r), independent of v(r), such that the expression Ev(r)n(r)dr+Fn(r) has as its minimum value the correct ground-state energy associated with v(r). The functional Fn(r) is then discussed for two situations: (1) n(r)=n0+n(r), n/n01, and (2) n(r)= (r/r0) with arbitrary and r0. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

A practical, easily accessible guide for bench-top chemists, this book focuses on accurately applying computational chemistry techniques to everyday chemistry problems.
Provides nonmathematical explanations of advanced topics in computational chemistry.
Focuses on when and how to apply different computational techniques.
Addresses computational chemistry connections to biochemical systems and polymers.
Provides a prioritized list of methods for attacking difficult computational chemistry problems, and compares advantages and disadvantages of various approximation techniques.
Describes how the choice of methods of software affects requirements for computer memory and processing time.

Many arenas of research are rapidly advancing due to a combined effort between engineering and science. In some cases, fields of research that were stagnating under the exclusive domain of one discipline have been imbued with new discoveries through collaboration with practitioners from the second discipline. In computational mechanics, we are particularly concerned about the technological engineering interest by combining engineering technology and basic sciences through modeling and simulations. These goals have become particularly relevant due to the emergence of the field of nanotechnology, and the related burst of interest in nanoscale research. In this introductory article, we first briefly review the essential tools used by nanoscale researchers. These simulation methods include the broad areas of quantum mechanics, molecular dynamics and multiple-scale approaches, based on coupling the atomistic and continuum models. Upon completing this review, we shall conclusively demonstrate that the atomistic simulation tools themselves are not sufficient for many of the interesting and fundamental problems that arise in computational mechanics, and that these deficiencies lead to the thrust of multiple-scale methods. We summarize the strengths and limitations of currently available multiple-scale techniques, where the emphasis is made on the latest perspective approaches, such as the bridging scale method, multi-scale boundary conditions, and multi-scale fluidics. Example problems, in which multiple-scale simulation methods yield equivalent results to full atomistic simulations at fractions of the computational cost, are shown. We conclude by discussing future research directions and needs in multiple-scale analysis, and also discuss the ramifications of the integration of current nanoscale research into education.

The molecular dynamics computer simulation discovery of the slow decay
of the velocity autocorrelation function in fluids is briefly reviewed
in order to contrast that long time tail with those observed for the
stress autocorrelation function in fluids and the velocity
autocorrelation function in the Lorentz gas. For a non-localized
particle in the Lorentz gas it is made plausible that even if it behaved
quantum mechanically its long time tail would be the same as the
classical one. The generalization of Fick's law for diffusion for the
Lorentz gas, necessary to avoid divergences due to the slow decay of
correlations, is presented. For fluids, that generalization has not yet
been established, but the region of validity of generalized
hydrodynamics is discussed.

Two- and three-dimensional molecular dynamics simulations, together with finite element method simulation of continuum mechanics, have been carried out to predict the mechanical properties of a single crystalline metal with nano-holes. The stress concentration near the hole is studied from both atomistic and continuum viewpoints. The decrease in elastic modulus due to the existence of holes, the shape of holes, and the different geometries of arrangement of multiple holes are investigated.

The Born-Oppenheimer method for a normal molecule is considered, the body-fixed moving-coordinate system being defined by means of the Eckart conditions. A new method of transformation of the Hamiltonian to the set of body-fixed coordinates is proposed. The equations of electronic, vibrational, rotational and translational motion are derived in explicit form. The zeroth and the first terms are calculated in the eigenfunction expansion and the eigenvalue expansion is calculated up to the fifth term.

We study a frequency-dependent continuum model equation for electrostatics at the nano scale. It is motivated by the need to incorporate accurately the influence of dielectric correlations which are of the same length scale as the electrostatic fluctuations in protein–water systems. The model is based on a single parameter, a length scale for changes in the dielectric response, that is physically relevant. This parameter reflects the changes in the dielectric medium caused by local structuring of the molecules. We present three independent quantitative assessments of the model, including one in which the dielectric field is changing in time. The assessments involve modeling the local structuring of dielectrics around individual ions, explaining solvation of carbon nano-tube interiors and predicting accurately the electrostatic energy of ions in a carbon nano-tube. The latter involves comparing the frequency-dependent model equation directly with molecular dynamics simulations with explicit solvent. The model equation cannot be written as a differential equation but rather takes the form of a more general Fourier integral operator. It involves a non-local relationship between the polarization field and the electric field.