Imperial College London

Dr Edward R Smith

Faculty of EngineeringDepartment of Mechanical Engineering

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+44 (0)7792 677 912edward.smith05 CV




149Roderic Hill BuildingSouth Kensington Campus





Publication Type

24 results found

Smith ER, Braga C, 2020, Hydrodynamics across a fluctuating interface, JOURNAL OF CHEMICAL PHYSICS, Vol: 153, ISSN: 0021-9606

Journal article

Heyes DM, Dini D, Smith ER, 2020, Statistical analysis and molecular dynamics simulations of the thermal conductivity of lennard–Jones solids including their pressure and temperature dependencies, Physica Status Solidi B: Basic Solid State Physics, Vol: 257, Pages: 1-14, ISSN: 0370-1972

Aspects of the thermal conductivity, λ, of a Lennard–Jones (LJ) solid along an isotherm and the sublimation line are studied using equilibrium molecular dynamics (MD) simulations. A reformulation of the Green–Kubo time correlation function expression for λ in the form of a probability distribution function (PDF) of single trajectory contributions (STC) exhibits the same characteristic statistical trends as found previously for liquids, even at high pressures and low temperatures. The analysis reveals that for short periods of time the thermal conductivity can be negative. This feature is evident along the sublimation line isobar and a low‐temperature isotherm going to high densities. Along the isobar and isotherm lines, λ is to a good approximation a power law in temperature and density, respectively. This behavior is used in a more general thermodynamics‐based analysis description of the state point dependence of the thermal conductivity. The heat flux autocorrelation function increasingly develops a damped oscillatory appearance as pressure increases or temperature decreases, consistent with the phonon formulation of thermal conductivity.

Journal article

Heyes DM, Dini D, Smith ER, 2020, Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations, JOURNAL OF CHEMICAL PHYSICS, Vol: 152, ISSN: 0021-9606

Journal article

Smith E, Trevelyan D, Ramos-Fernandez E, Sufian A, O'Sullivan C, Dini Det al., 2020, CPL library - a minimal framework for coupled particle and continuum simulation, Computer Physics Communications, Vol: 250, Pages: 1-11, ISSN: 0010-4655

We present an open-source library for coupling particle codes, such as molecular dynamics (MD) or the discrete element method (DEM), and grid based computational fluid dynamics (CFD). The application is focused on domain decomposition coupling, where a particle and continuum software model different parts of a single simulation domain with information exchange. This focus allows a simple library to be developed, with core mapping and communication handled by just four functions. Emphasis is on scaling on supercomputers, a tested cross-language library, deployment with containers and well-documented simple examples. Building on this core, a template is provided to facilitate the user development of common features for coupling, such as averaging routines and functions to apply constraint forces. The interface code for LAMMPS and OpenFOAM is provided to both include molecular detail in a continuum solver and model fluids flowing through a granular system. Two novel development features are highlighted which will be useful in the development of the next generation of multi-scale software: (i) The division of coupled code into a smaller blocks with testing over a range of processor topologies. (ii) The use of coupled mocking to facilitate coverage of various parts of the code and allow rapid prototyping. These two features aim to help users develop coupled models in a test-driven manner and focus on the physics of the problem instead of just software development. All presented code is open-source with detailed documentation on the dedicated website ( permitting useful aspects to be evaluated and adopted in other projects.

Journal article

Heyes D, Smith ER, Dini D, 2019, Shear stress relaxation and diffusion in simple liquids by molecular dynamics simulations: Analytic expressions and paths to viscosity, The Journal of Chemical Physics, Vol: 150, ISSN: 0021-9606

The results are reported of an equilibrium molecular dynamics simulation study of the shear viscosity, η, and self-diffusion coefficient, D, of the Lennard-Jones liquid using the Green-Kubo (GK) method. Semiempirical analytic expressions for both GK time correlation functions were fitted to the simulation data and used to derive analytic expressions for the time dependent diffusion coefficient and shear viscosity, and also the correlation function frequency transforms. In the case of the shear viscosity for a state point near the triple point, a sech function was found to fit the correlation function significantly better than a gaussian in the ballistic short time regime. A reformulation of the shear GK formula in terms of a time series of time integrals (“viscuits”) and contributions to the viscosity from components based on the initial stress (“visclets”) enable the GK expressions to be recast in terms of probability distributions which could be used in coarse grained stochastic models of nanoscale flow. The visclet treatment shows that stress relaxation is statistically independent of the initial stress for equilibrium and metastable liquids, suggesting that shear stress relaxation in liquids is diffusion controlled. By contrast, the velocity autocorrelation function is sensitive to the initial velocity. Weak oscillations and a plateau at intermediate times originate to a greater extent from the high velocity tail of the Maxwell-Boltzmann velocity distribution. Simple approximate analytic expressions for the mean square displacement and the self Van Hove correlation function are also derived.

Journal article

Smith ER, Daivis PJ, Todd BD, 2019, Measuring heat flux beyond Fourier's law, JOURNAL OF CHEMICAL PHYSICS, Vol: 150, ISSN: 0021-9606

Journal article

Braga C, Smith E, Nold A, Sibley DN, Kalliadasis Set al., 2018, The pressure tensor across a liquid-vapour interface, Journal of Chemical Physics, Vol: 149, ISSN: 0021-9606

Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff and, later, Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17(3), 338 (1949); J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood’s argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F. P. Buff et al., Phys. Rev. Lett. 15, 621–623 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.

Journal article

Heyes D, Dini D, Smith E, 2018, Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model, Journal of Chemical Physics, Vol: 148, ISSN: 0021-9606

The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics(NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring’smodel (EM) for shear thinning are derived. It is argued that an “incremental viscosity,”ηi, or IV whichis the derivative of the steady state stress with respect to the shear rate is a better measure of the physicalstate of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shearstress divided by the strain rate). The stress relaxation function,Ci(t), associated withηiis consistentwith Boltzmann’s superposition principle and is computed by NEMD and the EM. The IV of the Eyringmodel is shown to be a special case of the Carreau formula for shear thinning. An analytic solutionfor the transient time correlation function for the EM is derived. An extension of the EM to allow forsignificant local shear stress fluctuations on a molecular level, represented by a gaussian distribution,is shown to have the same analytic form as the original EM but with the EM stress replaced by its timeand spatial average. Even at high shear rates and on small scales, the probability distribution functionis almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formulaapproximately satisfies the Fluctuation Theorem, which may in part explain its success in representingthe shear thinning curves of a wide range of different types of chemical systems.

Journal article

Smith ER, Theodorakis PE, Craster RV, Matar OKet al., 2018, Moving contact lines: linking molecular dynamics and continuum-scale modeling, Langmuir, Vol: 34, Pages: 12501-12518, ISSN: 0743-7463

Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.

Journal article

Heyes D, Dini D, Smith E, Branka Aet al., 2017, Nanowire stretching by Non-equilibrium Molecular Dynamics, Physica Status Solidi B: Basic Solid State Physics, Vol: 254, ISSN: 0370-1972

Non-equilibrium Molecular Dynamics (NEMD) simulations of a stretched Lennard-Jones (LJ) model single crystal nanowire with square cross-section are carried out. The microstructural and mechanical properties are examined as a function of strain and strain rate. The instantaneous Poisson's ratio and Young's modulus are shown to be strongly time (strain) dependent from the start of the pulling process. The structural transformation as a result of straining initially involves the (100) layers moving further apart and then slipping at ca. math formula when the shear slip stress along that direction is about 1% of the shear modulus, which is typical of plastic deformation of noble gas solid crystals, and in accordance with Schmid's law.

Journal article

Smith E, Heyes D, Dini D, 2017, Towards the Irving Kirkwood limit of the mechanical stress tensor, Journal of Chemical Physics, Vol: 146, ISSN: 1089-7690

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.

Journal article

Smith ER, Müller EA, Craster RV, Matar OKet al., 2016, A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics, Soft Matter, Vol: 12, Pages: 9604-9615, ISSN: 1744-6848

Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.

Journal article

Heyes DM, Dini D, Smith ER, 2016, Equilibrium fluctuations of liquid state static properties in a subvolume by molecular dynamics, Journal of Chemical Physics, Vol: 145, ISSN: 1089-7690

System property fluctuations increasingly dominate a physical process as the sampling volume decreases. The purpose of this work is to explore how the fluctuation statistics of various thermodynamic properties depend on the sampling volume, using molecular dynamics (MD) simulations. First an examination of various expressions for calculating the bulk pressure of a bulk liquid is made, which includes a decomposition of the virial expression into two terms, one of which is the Method of Planes (MOP) applied to the faces of the cubic simulation cell. Then an analysis is made of the fluctuations of local density, temperature, pressure, and shear stress as a function of sampling volume (SV). Cubic and spherical shaped SVs were used within a spatially homogeneous LJ liquid at a state point along the melting curve. It is shown that the MD-generated probability distribution functions (PDFs) of all of these properties are to a good approximation Gaussian even for SV containing only a few molecules (∼10), with the variances being inversely proportional to the SV volume, Ω. For small subvolumes the shear stress PDF fits better to a Gaussian than the pressure PDF. A new stochastic sampling technique to implement the volume averaging definition of the pressure tensor is presented, which is employed for cubic, spherical, thin cubic, and spherical shell SV. This method is more efficient for less symmetric SV shapes.

Journal article

Smith ER, 2015, A molecular dynamics simulation of the turbulent Couette minimal flow unit, Physics of Fluids, Vol: 27, ISSN: 1070-6631

A molecular dynamics simulation of planar Couette flow is presented for the minimalchannel in which turbulence structures can be sustained. Evolution over a single break-down and regeneration cycle is compared to computational fluid dynamics simula-tions. Qualitative similar structures are observed and turbulent statistics show excellentquantitative agreement. The molecular scale law of the wall is presented in whichstick-slip molecular wall-fluid interactions replace the no-slip conditions. The impactof grid resolution is explored and the observed structures are seen to be dependenton averaging time and length scales. The kinetic energy spectra show that a range ofscales are present in the molecular system and that spectral content is dependent onthe grid resolution employed. The subgrid velocity of the molecules is studied usingjoint probability density functions, molecular trajectories, diffusion, and Lagrangianstatistics. The importance of sub-grid scales, relevance of the Kolmogorov lengthscale,and implications of molecular turbulence are discussed.

Journal article

Smith ER, Heyes DM, Dini D, Zaki TAet al., 2015, A localized momentum constraint for non-equilibrium molecular dynamics simulations, JOURNAL OF CHEMICAL PHYSICS, Vol: 142, ISSN: 0021-9606

Journal article

Heyes DM, Smith ER, Dini D, Zaki TAet al., 2014, The method of planes pressure tensor for a spherical subvolume, The Journal of Chemical Physics, Vol: 140, Pages: ---

Journal article


Molecular dynamics (MD) is a discrete modelling technique that is used to capture the nano-scale motion of molecules. MD can be used to accurately simulate a range of physical problemswhere the continuum assumption breaks down. Examples include surface interaction, complexmolecules, local phase changes, shock waves or the contact line between fluids. However, beyondvery small systems and timescales (μm and msec), MD is prohibitively expensive. Continuumcomputational fluid dynamics (CFD), on the other hand, is easily capable of simulating scales ofengineering interest, (m and s). However, CFD is unable to capture micro-scale effects vital formany modern engineering fields, such as nanofluidics, tribology, nano-electronics and integratedcircuit development. This work details the development of a set of techniques that combine theadvantages of both continuum and molecular modelling methodologies, allowing the study ofcases beyond the range of either technique alone.The present work is split into both computational and theoretical developments. The com-putational aspect involves the development of a new high-performance MD code, as well as acoupler (CPL) library to link it to a continuum solver. The MD code is fully verified, has similarperformance to existing MD software and allows simulation of a wide range of cases. The CPLlibrary is a robust, flexible and language independent API and the source code has been madefreely available under the GNU GPL v3 license. Both MD and CPL codes are developed to allowvery large scale simulation on high performance computing (HPC) facilities.The theoretical aspect includes the development of a rigorous mathematical framework andits application to develop novel coupling methodologies. The mathematical framework allowsa discrete molecular system to be expressed in terms of the control volume (CV) formulationfrom continuum fluid dynamics. A discrete form of Reynolds’ transport theorem is thus obtainedallowing both molecular an

Thesis dissertation

Smith E, Trevelyan D, Zaki T, 2013, Scalable coupling of Molecular Dynamics (MD) and Direct Numerical Simulation (DNS) of Multi-scale Flows — Part 2

The objective of this project was the development and performance optimisation of a couplingapplication. The coupler library is intended for interfacing massively-parallel algorithmsfor multi-physics simulations. The development of the coupler library adopted the same philosophyof the Message Passing Interface (MPI) library: The coupler was engineered as a setof libraries that are accessible from various applications, in order to interface their operation.However, the applications maintain independent data and scope, and only exchange informationvia calls to the coupler library. The development, validation, verification and optimisation ofthe coupling library were performed in the context of interfacing two massively parallel algorithms:a continuum Navier-Stokes solver (T ransFlow) and a molecular dynamics algorithm(StreamMD). However, the development of the coupling library has maintained generality inorder to facilitate coupling other application softwares in the future.


Smith E, Trevelyan D, Ramos-Fernandez E, 2013, CPL library

The coupler (CPL) consists of a series of function calls which are loosely based on the MPI framework in terms of both functionality and scope. Their aim is to facilitate the exchange of data between two parallel solvers -- Molecular Dynamics (MD) and continuum Computational Fluid Dynamics (CFD). For details of the methods, the reader is referred to our websitewww.cpl-library.orgThe routines have been developed in Fortran 2008 with sufficient generality that they could be used as a language independent API through External functional interfaces. These routines are compiled into a library module which can be linked to both the Molecular Dynamics (MD) and Computational Fluid Dynamics (CFD) codes. Both codes should be run using the MPI multiple program multiple data paradigm (MPMD).


Smith E, Anton L, 2012, Scalable coupling of Molecular Dynamics (MD) and Direct Numerical Simulation (DNS) of multi-scale flows,

The goal of this dCSE project was to develop the software infrastructure to couple highpreformance fluid and molecular dynamics solvers. This captures important details of localisedfluid flow at the molecular level whilst preserving the efficiency of the continuum computationin the rest of the domain. The result is a verified and scalable library which links a continuumfluid dynamics (CFD) code to a molecular dynamics code.


Smith ER, Heyes DM, Dini D, Zaki TAet al., 2012, Control-volume representation of molecular dynamics, Physical Review E, Vol: 85, Pages: 056705-056705, ISSN: 1539-3755

A molecular dynamics (MD) parallel to the control volume (CV) formulation of fluid mechanics is developedby integrating the formulas of Irving and Kirkwood [J. Chem. Phys.18, 817 (1950)] over a finite cubic volumeof molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, whichyields an equivalent to Reynolds’ transport theorem for the discrete system. This approach casts the dynamics ofthe molecular system into a form that can be readily compared to the continuum equations. The MD equationsof motion are reinterpreted in terms of a Lagrangian-to-control-volume (LCV) conversion functionθifor eachmoleculei.TheLCVfunction and its spatial derivatives are used to express fluxes and relevant forces across thecontrol surfaces. The relationship between the local pressures computed using the volume average [Lutsko,J.Appl. Phys.64, 1152 (1988)] techniques and the method of planes [Toddet al.,Phys.Rev.E52, 1627 (1995)]emerges naturally from the treatment. Numerical experiments using the MD CV method are reported forequilibrium and nonequilibrium (start-up Couette flow) model liquids, which demonstrate the advantages ofthe formulation. The CV formulation of the MD is shown to be exactly conservative and is, therefore, ideallysuited to obtain macroscopic properties from a discrete system.

Journal article

Heyes DM, Smith ER, Dini D, Spikes HA, Zaki TAet al., 2012, Pressure dependence of confined liquid behavior subjected to boundary-driven shear, J. Chem. Phys, Vol: 136, Pages: 134705-134705

Journal article

Heyes DM, Smith ER, Dini D, Zaki TAet al., 2011, The equivalence between Volume Averaging and Method of Planes definitions of the pressure tensor at a plane, J. Chem. Phys, Vol: 135, Pages: 024512-024512

Journal article

Yamtich J, Starcevic D, Lauper J, Smith E, Shi I, Rangarajan S, Jaeger J, Sweasy JBet al., 2010, Hinge residue I174 is critical for proper dNTP selection by DNA polymerase beta., Biochemistry, Vol: 49, Pages: 2326-2334

DNA polymerase beta (pol beta) is the key gap-filling polymerase in base excision repair, the DNA repair pathway responsible for repairing up to 20000 endogenous lesions per cell per day. Pol beta is also widely used as a model polymerase for structure and function studies, and several structural regions have been identified as being critical for the fidelity of the enzyme. One of these regions is the hydrophobic hinge, a network of hydrophobic residues located between the palm and fingers subdomains. Previous work by our lab has shown that hinge residues Y265, I260, and F272 are critical for polymerase fidelity by functioning in discrimination of the correct from incorrect dNTP during ground state binding. Our work aimed to elucidate the role of hinge residue I174 in polymerase fidelity. To study this residue, we conducted a genetic screen to identify mutants with a substitution at residue I174 that resulted in a mutator polymerase. We then chose the mutator mutant I174S for further study and found that it follows the same general kinetic pathway as and has an overall protein folding similar to that of wild-type (WT) pol beta. Using single-turnover kinetic analysis, we found that I174S exhibits decreased fidelity when inserting a nucleotide opposite a template base G, and this loss of fidelity is due primarily to a loss of discrimination during ground state dNTP binding. Molecular dynamics simulations show that mutation of residue I174 to serine results in an overall tightening of the hinge region, resulting in aberrant protein dynamics and fidelity. These results point to the hinge region as being critical in the maintenance of the proper geometry of the dNTP binding pocket.

Journal article

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