Showing papers in "Molecular Simulation in 2005"

On the potential of connected stars as auxetic systems

Abstract: Auxetic materials and structures exhibit the unexpected behaviour of getting wider when stretched and thinner when compressed. This behaviour requires the structures (the internal structure in the case of materials) to have geometric features, which must deform in a way that results in the structure expanding when stretched. This paper assesses the potential for auxetic behaviour of a novel class of two-dimensional periodic structures which can be described as “connected stars” as they contain star-shaped units of different rotational symmetry which are connected together to form two-dimensional periodic structures. These structures will be studied through a technique based on force-field based methods (the EMUDA technique) and it will be shown that some, but not all, of these structures can exhibit auxetic behaviour. An attempt is made to explain the reasons for the presence or absence of a negative Poisson's ratio in these systems.

Nanotube–polymer composites: insights from Flory–Huggins theory and mesoscale simulations

Abstract: Carbon nanotube (CNT)-polymer composites, with potential applications in structural materials, optoelectronics, sensors, biocatalysis, and thermal and electromagnetic shielding are an important emerging area of nanotechnology. However, progress has been slow due to difficulties in dispersing CNTs into the polymer matrix. We attack the problem from a Flory-Huggins theory point of view, and present novel simulations of the dispersion process at the mesoscale. The solubility parameter of the CNTs is mapped out as a function of tube diameter, and compared with that of well-known polymers. Parallel alignment of CNTs with the application of shear, and dispersion by attaching organic functional groups are also investigated.

Comparisons of diffusive and viscous contributions to transport coefficients of light gases in single-walled carbon nanotubes

Abstract: We examine here the relative importance of different contributions to transport of light gases in single walled carbon nanotubes, using methane and hydrogen as examples. Transport coefficients at 298 K are determined using molecular dynamics simulation with atomistic models of the nanotube wall, from which the diffusive and viscous contributions are resolved using a recent approach that provides an explicit expression for the latter. We also exploit an exact theory for the transport of Lennard-Jones fluids at low density considering diffuse reflection at the tube wall, thereby permitting the estimation of Maxwell coefficients for the wall reflection. It is found that reflection from the carbon nanotube wall is nearly specular, as a result of which slip flow dominates, and the viscous contribution is small in comparison, even for a tube as large as 8.1 nm in diameter. The reflection coefficient for hydrogen is 3-6 times as large as that for methane in tubes of 1.36 nm diameter, indicating less specular reflection for hydrogen and greater sensitivity to atomic detail of the surface. This reconciles results showing that transport coefficients for hydrogen and methane, obtained in simulation, are comparable in tubes of this size. With increase in adsorbate density, the reflection coefficient increases, suggesting that adsorbate interactions near the wall serve to roughen the local potential energy landscape perceived by fluid molecules.

Standards for molecular dynamics modelling and simulation of relaxation

Abstract: An attempt is made to formulate a set of requirements for simulation and modelling of relaxation in dense media. Each requirement is illustrated by examples of numerical simulation of particles with different types of interaction given by soft-sphere, Lennard–Jones, embedded atom method or Coulomb potential. The approaches developed are expected to be universal for some classes of relaxation processes in liquids, fluids, crystals and plasmas.

DFT study of hydrogen adsorption on Al13 clusters

Abstract: In this work, adsorption of hydrogen on Al13 clusters has been investigated theoretically using the density functional theory (DFT) approach. We have performed geometry optimization of atomic and molecular hydrogen in the proximity of Al13 and calculated the binding energy and electronic properties of the stable Al13+Hn assemblies. We have also calculated the energy barrier for the hydrogen atom transition between different adsorption sites on Al13 cluster as well as the activation energy for the dissociation and adsorption of molecular hydrogen. We found that the hydrogen atom adsorbs on the surface of Al13 cluster, without an energy barrier onto atop, bridge and hollow sites. A small barrier for H atom transition from one adsorption site to another together with the minor energy difference between the most stable isomers points towards high mobility of the hydrogen atom on the surface. The calculated dissociation–adsorption barrier for the hydrogen molecule of ∼14 kcal/mol and a desorption barrier of ∼1...

Scanning probe microscopy for silicon device fabrication

Abstract: We present a review of a detailed fabrication strategy for the realisation of nano and atomic-scale devices in silicon using phosphorus as a dopant and a combination of ultra-high vacuum scanning probe microscopy and silicon molecular beam epitaxy (MBE). In this work we have been able to overcome some of the key fabrication challenges to the realisation of atomic-scale devices including the identification of single P dopants in silicon, the controlled incorporation of P atoms in silicon with atomic precision and the minimisation of P segregation and diffusion during Si encapsulation. Recently, we have combined these results with a novel registration technique to fabricate robust electrical devices in silicon that can be contacted and measured outside the ultra-high vacuum environment. We discuss the importance of our results for the future fabrication of atomic-scale devices in silicon.

Molecular models of unlike interactions in fluid mixtures

Abstract: Recently published molecular models of two-centre Lennard–Jones plus pointquadrupole type for pure fluids are used for the quantitative description of vapour–liquid equilibria of 28 binary mixtures. The unlike interactions are described with a modified Lorentz–Berthelot combining rule that contains one binary interaction parameter in the energetic term. A recently published simple and efficient procedure is used to adjust the binary interaction parameter to a single experimental vapour pressure of the binary mixture. Vapour–liquid equilibria from these molecular models for binary mixtures are in good agreement with experimental data also at state points far away from those used for the parameter fit. Vapour–liquid equilibria of ternary mixtures are predicted reliably on that basis.

An Effective Potential for Adsorption of Polar Molecules on Graphite

Abstract: Each carbon atom in the graphite crystal has a quadrupole moment due to the symmetry of the crystal. We show that these graphite quadrupoles, along with the polarizability of graphite, have a substantial effect on adsorption of strongly polar molecules. We present an approximate method for accounting for the change in the solid–fluid potential energy due to polar interactions with graphite. The potential function is integrated over the graphite surface using a truncated Fourier series, so that the resulting potential is analogous to the Steele 10-4-3 potential. The interactions included in this potential include dipole-induced dipole, dipole–quadrupole, and quadrupole–quadrupole interactions. Hence, the potential can be used for fluid molecules with dipole and/or quadrupole moments. Fluid–fluid multipole interactions can be computed with any model; but point multipoles must be used in the solid–fluid potential. The multipole solid–fluid potential is most accurate for nearly spherical molecules.

Molecular dynamics simulation of liquid water under the influence of an external electric field

Abstract: Molecular dynamics simulations of liquid water were performed at 258K and a density of 1.0 g/cm3 under various applied external electric field, ranging 0∼1010 V/m. The influence of external field on structural and dynamical properties of water was investigated. The simple point charge (SPC) model is used for water molecules. An enhancement of the water hydrogen bond structure with increasing strength of the electric field has been deduced from the radial distribution functions and the analysis of hydrogen bonds structure. With increasing field strength, water system has a more perfect structure, which is similar to ice structure. However, the electrofreezing phenomenon of liquid water has not been detected since the self-diffusion coefficient was very large. The self-diffusion coefficient decreases remarkably with increasing strength of electric field and the self-diffusion coefficient is anisotropic.

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised organic (polymeric honeycomb) host-guest system.

Abstract: Force field-based simulations have been employed to model the mechanical properties of a range of undeformed molecular polymeric honeycombs having conventional and re-entrant hexagon pores. The conventional and re-entrant hexagon honeycombs are predicted to display positive and negative in-plane Poisson's ratios, respectively, confirming previous simulations. The structure, and mechanical and mass transport properties of a layered re-entrant honeycomb ((2,8)-reflexyne) were studied in detail for a uniaxial load applied along the x 2 direction. The mechanical properties are predicted to be stress- (strain-) dependent and the trends can be interpreted using analytical expressions from honeycomb theory. Transformation from negative to positive Poisson's ratio behaviour is predicted at an applied stress of σ2 = 2 GPa. Simulations of the loading of C60 and C70 guest molecules into the deformed layered (2,8)-reflexyne host framework demonstrate the potential for tunable size selectivity within the host framewor...

BioMOCA—a Boltzmann transport Monte Carlo model for ion channel simulation

Abstract: With the recent availability of high-resolution structural information for several key ion channel proteins and large-scale computational resources, Molecular Dynamics has become an increasingly popular tool for ion channel simulation. However, the CPU requirements for simulating ion transport on time scales relevant to conduction still exceed the resources presently available. To address this problem, we have developed Biology Monte Carlo (BioMOCA), a three-dimensional (3D) coarsegrained particle ion channel simulator based on the Boltzmann Transport Monte Carlo (BTMC) methodology. Although this approach is widely employed in the engineering community to study charge transport in electron devices, its application to molecular biology and electrolytes in general is new and hence must be validated. The pair correlation function, which is a measure of the microscopic structure of matter, provides a suitable benchmark to compare the BTMC method against the well-established Equilibrium Monte Carlo (EMC) approach. For validation purposes BioMOCA is used to simulate several simple homogeneous equilibrium electrolytes at concentrations of physiological interest. The ion – ion pair correlation functions computed from these simulations compare very well with those obtained from EMC simulations. We also demonstrate several performance-improving techniques that result in a several-fold speed-up without compromising the pair correlation function. BioMOCA is then used to perform full 3D simulations of ion transport in the gramicidin A channel in situ in a membrane environment, as well as to study the link between the electrostatic and dielectric properties of the protein and the channel’s selectivity.

Computer simulations of two dimensional gold nanoparticle arrays: the influence of core geometry

Abstract: We report molecular dynamics computer simulations of gold passivated nanoparticles and gold nanoparticle arrays. We investigate Au140 butane and dodecanethiol passivated clusters. In particular we analyse the effect that the metal core structure has on the interparticle forces and the self assembly of small nanoparticle arrays. We find that the core geometry has very little influence on the intermolecular forces, except for interparticle distances close to contact. Also the core geometry has little influence in determining the structure of the molecular arrays. The structure of the arrays is very rich, from open structures, similar to the ones appearing in limited diffusion process, to compact structures, whose symmetry depends on the chain length of the surfactants. We discuss our results with reference to recent experiments on nanoparticle arrays.

Local density profiles are coupled to solute size and attractive potential for nanoscopic hydrophobic solutes

Abstract: We employ constant pressure molecular dynamics simulations to investigate the effects of solute size and solute–water dispersion interactions on the solvation behavior of nanoscopic hydrophobic model solutes in water at normal temperature and pressure. The hydration behavior around a single planar atomic model solute as well as a pair of such solutes have been considered. The hydration water structure of a model nanoscopic solute with standard Lennard-Jones interaction is shown to be significantly different from that of their purely repulsive analogues. The density of water in the first solvation shell of a Lennard-Jones solute is much higher than that of bulk water and it remains almost unchanged with the increase of the solute dimensions from one to a few nanometers. On the other hand, for a purely repulsive analogue of the above model, solute hydration behavior shows a marked solute size dependence. The contact density of water in this case decreases with the increasing dimension of the solute. We also...

Two exchange-correlation functionals compared for first-principles liquid water

Abstract: The first-principles description of liquid water using ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has recently been found to require long equilibration times, giving too low diffusivities and a clear over-structuring of the liquid. In the light of these findings we compare here the room-temperature description offered by two different exchange correlation functionals: BLYP, the most popular for liquid water so far, and RPBE, a revision of the widely used PBE. We find for RPBE a less structured liquid with radial distribution functions closer to experiment ones than the ones of BLYP. The diffusivity obtained with RPBE for heavy water is still 20% lower than the corresponding experimental value, but it represents a substantial improvement on the BLYP value, one order of magnitude lower than experiment. These characteristics and the hydrogen-bond (HB) network imperfection point to an effective temperature ∼3% lower than the actual simulation temperature for the RPBE liquid, ...

Quantum nature of adsorbed hydrogen on single-wall carbon nanohorns

Abstract: We have measured N2 adsorption isotherms on single-wall carbon nanohorns (SWNHs) over the temperature range of 77–92 K, and isosteric heat of adsorption, q st, were determined Adsorption measurements for SWNHs have been also done for for H2 at 20 K, and for H2 and D2 at 77 K, respectively We have performed grand canonical Monte Carlo (GCMC) simulations of N2, H2, and D2 for single-wall carbon nanotube (SWNT) models to compare with the experimental data Simulated N2 adsorption isotherm on a SWNT bundle model is in reasonably good agreement with the experimental isotherm on the SWNH assembly over a wide range of pressures at 77 K; however, simulated q st-values for the SWNT bundle suggest that the SWNH particles are incompletely arranged in the SWNH assembly Simulated endohedral isotherm of classical H2 inside an isolated SWNT model at 20 K showed that a density of adsorbed H2 in the internal space of the SWNH particle is quite smaller than that of classical H2 because of large quantum effects In simul

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised inorganic (zeolitic) host–guest system

Abstract: Force field based simulations have been employed to model the structure, and mechanical and mass transport properties of the all-silica zeolite MFI (ZSM5—Si96O192). Undeformed and deformed MFI subject to uniaxial loading in each of the three principal directions were investigated. The mechanical properties are predicted to include negative on-axis Poisson's ratios (auxetic behaviour) in the x 1–x 3 plane of the undeformed structure, and are strain-dependent. Transformation from positive-to-negative Poisson's ratio behaviour, and vice versa, is predicted for most on-axis Poisson's ratios at critical loading strains. Simulations of the simultaneous sorption of neopentane and benzene guest molecules onto the undeformed host MFI framework indicate a low neopentane-to-benzene loading ratio, consistent with experimental observation. The sorption of these two molecular species onto deformed MFI is Poisson's ratio- and strain-dependent. Uniaxial tensile loading along a direction containing a negative on-axis Pois...

Theoretical study of adhesion between graphite, polyester and silica surfaces

Abstract: This study examines the interaction between graphite and polyester-based polymers and silica in order to compare the adhesive properties of these surfaces. Surface interaction energies were calculated at different interfacial separations, and the resultant adhesion energy curves were used to determine the Work of Separation (W sep) and equilibrium interfacial separation (d 0). Adhesion between graphite and polyester was calculated to be significantly greater than between graphite and silica. Our calculations indicate that Van der Waals Forces lead to significant adhesion between graphite and polyester. However, the Van der Waals attraction is approximately 30% less between graphite and silica.

Structural and magnetic phase transitions in simple oxides using hybrid functionals

Abstract: We present the structural as well as elastic properties of the alkaline earth oxides and FeO, calculated using hybrid exchange functionals within DFT. We show that by empirically fitting the amount of Fock-exchange in the hybrid functionals, we can accurately reproduce the pressure-induced phase transitions for MgO, CaO, SrO and BaO. For FeO the hybrid functionals predict an insulator metal transition at ca. 150 GPa, associated with an i-B8 B8 structural phase transition. The structural phase transition is accompanied by a spin transition from a high- to low-spin electron configuration on the Fe2+ ions. Hence, FeO undergoes a magnetic phase transition from an anti-ferromagnetic to non-magnetic structure. We also find that as the ionicity of the polymorphs increases a higher fraction of Fock-exchange is required to reproduce the structural volumes reported from experiments.

Gibbs energy-based treatment of metallofullerenes: Ca@C72, Ca@C74, Ca@C82, and La@C82

Abstract: The paper surveys ongoing computations on endohedral fullerene systems, combining the treatments of quantum chemistry and statistical mechanics. Relative concentrations of four isomers of Ca@C72, six isomers of Ca@C74, nine isomers of Ca@C82, and four isomers of La@C82 are evaluated using the Gibbs energy based on density-functional theory (DFT) computations. The results illustrate the enthalpy–entropy interplay in the systems produced under high temperatures. Approximations for description of the encapsulate motions are analyzed.

Temperature-quench Molecular Dynamics Simulations for Fluid Phase Equilibria

Abstract: A method for locating fluid phase equilibria by means of a single canonical molecular dynamics simulation is evaluated. The temperature-quench molecular dynamics (TQMD) method consists of quenching an initially homogeneous one-phase fluid system to a lower temperature where it is mechanically and thermodynamically unstable. After a short transient, domains of coexisting phases form, which quickly acquire equilibrium-like properties. A suitable analysis of the coexisting domains in terms of local densities, compositions, or some other order parameter gives the phase equilibrium properties. We show how, contrary to expectations, one need not wait until a full global equilibration (planar interface) is resolved to obtain the correct results. As examples, the phase diagram of a cut and shift (5σ) Lennard–Jones fluid, the pressure-composition diagram of a Lennard–Jones mixture presenting three-phase vapor–liquid–liquid equilibria and the saturated liquid densities of eicosane using a united atom representation...

Molecular dynamics simulation of lipid bilayers with GROMOS96: Application of surface tension

Abstract: The GROMOS96 force fields 45A3 and 53A5, when applied to dipalmitoylphosphatidylcholine (DPPC) membranes, have a tendency to result in a reduced area per lipid in constant pressure simulations. The application of surface tension is effective in increasing the area per lipid, a measure of the phase of the membrane, but only if the area is already close to the experimental range. Therefore the surface tension cannot compensate for strong inadequacies in the force-field parameters. The behaviour of the 45A3 force field from long NP n γT simulations of tens of nanoseconds is analysed over a range of different surface tensions. Comparisons are made with the corresponding NP n AT simulations.

Collaborative grid infrastructure for molecular simulations: The eMinerals minigrid as a prototype integrated compute and data grid

Abstract: This paper describes a prototype grid infrastructure, called the “eMinerals minigrid”, for molecular simulation scientists. which is based on an integration of shared compute and data resources. We describe the key components, namely the use of Condor pools, Linux/Unix clusters with PBS and IBM's LoadLeveller job handling tools, the use of Globus for security handling, the use of Condor-G tools for wrapping globus job submit commands, Condor's DAGman tool for handling workflow, the Storage Resource Broker for handling data, and the CCLRC dataportal and associated tools for both archiving data with metadata and making data available to other workers.

Ad hoc continuum-atomistic thermostat for modeling heat flow in molecular dynamics simulations

Abstract: An ad hoc thermostating procedure that couples a molecular dynamics (MD) simulation and a numerical solution to the continuum heat flow equation is presented. The method allows experimental thermal transport properties to be modeled without explicitly including electronic degrees of freedom in a MD simulation. The method is demonstrated using two examples, heat flow from a constant temperature silver surface into a single crystal bulk, and a tip sliding along a silver surface. For the former it is shown that frictional forces based on the Hoover thermostat applied locally to grid regions of the simulation are needed for effective feedback between the atomistic and continuum equations. For fast tip sliding the thermostat results in less surface heating, and higher frictional and normal forces compared to the same simulation without the thermostat.

Dissipative particle dynamics simulation of a gold nanoparticle system

Abstract: Dissipative particle dynamics (DPD) was carried out to study systems containing gold atoms, organic ether (oligohydroquinonyl ether terminated with a thiol group) and organic solvents. The components in the simulated system are very different in size and chemical nature. Our simulation showed that the reproduction of the macroscopic experimental phase separation, properly dividing the polymeric molecule into beads, selecting the size of gold bead, and choosing the appropriate interaction parameters between beads are crucial. In addition, the solvent effect was the dominant factor for the formation of spherical aggregates of Au atoms and organic ether molecules. We report the interaction strengths between the solvent and gold clusters. Our work has demonstrated that DPD methods can be applied to the study of complex meso-scale systems.

Compact model of the quantum short-channel threshold voltage in symmetric Double-Gate MOSFET

Abstract: A compact model for the threshold voltage in Double-Gate (DG) MOSFET is developed. The model takes into account short-channel effects, carrier quantization and temperature dependence of the threshold voltage. We assume a parabolic variation of the potential with the vertical position in the silicon film at threshold. An analytical expression for the surface potential dependence as a function of bias and position in the silicon film is also developed and used for the inversion charge calculation. The model has been fully validated by 2D quantum numerical simulation and is used to predict the threshold voltage roll-off in DG MOSFET with very short channel lengths and thin films. The comparison with measured threshold voltages shows that the model reproduces with an excellent accuracy the experimental data.

2D Autocorrelation modeling of the activity of trihalobenzocycloheptapyridine analogues as farnesyl protein transferase inhibitors

Abstract: The inhibitory activity towards farnesyl protein transferase enzyme (FPT) of 49 piperidine substituted trihalobenzocycloheptapyridine analogues (thBCHPs) has been successfully modelled using 2D spatial autocorrelation vectors. Predictive linear and non-linear models were obtained by forward stepwise multilinear regression analysis (MRA) and artificial neural network (ANN) approaches, respectively. A variable selection routine that selected relevant non-linear information from the data set was employed prior to networks training. The MRA model, using three descriptors, was able to explain about 68% data variance. The model showed a linear dependence between the inhibitory activities and autocorrelation coefficients weighted by van der Waals volumes and atomic polarizabilities on the inhibitors molecules. The non-linear approach preserve several characteristics described for the linear one. Three descriptors were selected encoding the same atomic properties, but the new ones were able to explain about 92% d...

Shear viscosity and thermal conductivity of quadrupolar real fluids from molecular simulation

Abstract: In the present work, equilibrium molecular dynamics was used with the Green-Kubo formalism to simultaneously calculate shear viscosity and thermal conductivity of ten real fluids, i.e. F2, N2, O2, CO2, C2H6, C2H4, C2F6, C3H4, C3H6 and SF6. The fluids were consistently described by the two-center Lennard–Jones plus point quadrupole (2CLJQ) pair potential, whose parameters were adjusted to vapor–liquid equilibria only [J. Phys. Chem. B, 2001, 105, 12126–12133]. The predicted shear viscosities and thermal conductivities show an overall average deviation of only about 10% from correlations of experimental data where comparison was possible. At low temperature and high density state points, the Green–Kubo integral for shear viscosity shows slow convergence. This problem can be overcome by a new approach developed in the present work. It is based on the adjustment of a suitable function describing the long time behavior of the autocorrelation function and yields reliable results without the need of excessively ...

Size-dependent mobility of platinum cluster on a graphite surface

Abstract: Molecular dynamics simulations of platinum (Pt) clusters on a graphite surface were performed to study their diffusion and aggregation. The Sutton-Chen many-body potential was used for the Pt–Pt interaction, whereas, a Steele potential was used to calculate the interaction between Pt atoms and carbon (C) atoms of graphite. The results show that at room temperature, the Pt clusters with less than 40 atoms are very mobile with a two-dimensional diffusion coefficient higher than 10−11m2 s−1, but decreasing rapidly with size. The diffusion coefficient of larger cluster has variable size-dependence with local minima at cluster sizes of 50 and 300 Pt atoms and a local maximum at cluster size of 100 atoms. In additional to the overall size of the Pt cluster or nanoparticle, the mismatch between the bottom layer of Pt and graphite also affected the overall Pt–graphite affinity and hence the Pt cluster mobility. The presence of a neighboring Pt cluster can greatly affect mobility. The aggregation of two 50-atom cl...

Hybrid MD-Nernst Planck Model of Alpha-hemolysin Conductance Properties

Abstract: Motivated by experiments in which an applied electric field translocates polynucleotides through an alpha-hemolysin protein channel causing ionic current transient blockade, a hybrid simulation model is proposed to predict the conductance properties of the open channel. Time scales corresponding to ion permeation processes are reached using the Poisson-Nemst-Planck (PNP) electro-diffusion model in which both solvent and local ion concentrations are represented as a continuum. The diffusion coefficients of the ions (K(+) and Cl(-)) input in the PNP model are, however, calculated from all-atom molecular dynamics (MD). In the MD simulations, a reduced representation of the channel is used. The channel is solvated in a 1 M KCI solution, and an external electric field is applied. The pore specific diffusion coefficients for both ionic species are reduced 5-7 times in comparison to bulk values. Significant statistical variations (17-45%) of the pore-ions diffusivities are observed. Within the statistics, the ionic diffusivities remain invariable for a range of external applied voltages between 30 and 240mV. In the 2D-PNP calculations, the pore stem is approximated by a smooth cylinder of radius approx. 9A with two constriction blocks where the radius is reduced to approx. 6A. The electrostatic potential includes the contribution from the atomistic charges. The MD-PNP model shows that the atomic charges are responsible for the rectifying behaviour and for the slight anion selectivity of the a-hemolysin pore. Independent of the hierarchy between the anion and cation diffusivities, the anionic contribution to the total ionic current will dominate. The predictions of the MD-PNP model are in good agreement with experimental data and give confidence in the present approach of bridging time scales by combining a microscopic and macroscopic model.

A continuum-atomistic method for incorporating Joule heating into classical molecular dynamics simulations

Abstract: A hybrid atomistic-continuum method is presented for incorporating Joule heating into large-scale molecular dynamics (MD) simulations. When coupled to a continuum thermostat, the method allows resistive heating and heat transport in metals to be modeled without explicitly including electronic degrees of freedom. Atomic kinetic energies in a MD simulation are coupled via an ad hoc feedback loop to continuum current and heat transfer equations that are solved numerically on a finite difference grid (FDG). For resistive heating, the resistance in each region of the FDG is calculated from the experimental resistivity, atomic density, and average kinetic energy in the MD simulation. A network of resistors is established from which the potential at every FDG region is calculated given an applied voltage. The potential differences and the resistance between connected FDG regions are used to calculate the current between the two points and the heat generated from that current. This information is then added back ...