Atomistic-continuum Model Research Articles

A novel 3D atomistic-continuum cancer invasion model: In silico simulations of an in vitro organotypic invasion assay

We develop a three-dimensional genuinely hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between these cell phenotypes in the form of epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET). The proposed model consists of a hybrid system of partial and stochastic differential equations that describe the evolution of epithelial-like and mesenchymal-like cancer cells, respectively, under the consideration of matrix-degrading enzyme concentrations and the extracellular matrix density. With the help of inverse parameter estimation and a sensitivity analysis, this three-dimensional model is then calibrated to an in vitro organotypic invasion assay experiment of oral squamous cell carcinoma cells.

Formation of Periodic Nanoridge Patterns by Ultrashort Single Pulse UV Laser Irradiation of Gold.

A direct comparison of simulation and experimental results of UV laser-induced surface nanostructuring of gold is presented. Theoretical simulations and experiments are performed on an identical spatial scale. The experimental results have been obtained by using a laser wavelength of 248 nm and a pulse length of 1.6 ps. A mask projection setup is applied to generate a spatially periodic intensity profile on a gold surface with a sinusoidal shape and periods of 270 nm, 350 nm, and 500 nm. The formation of structures at the surface upon single pulse irradiation is analyzed by scanning and transmission electron microscopy (SEM and TEM). For the simulations, a hybrid atomistic-continuum model capable of capturing the essential mechanisms responsible for the nanostructuring process is used to model the interaction of the laser pulse with the gold target and the subsequent time evolution of the system. The formation of narrow ridges composed of two colliding side walls is found in the simulation as well as in the experiment and the structures generated as a result of the material processing are categorized depending on the range of applied fluencies and periodicities.

Dynamic all-optical control in ultrashort double-pulse laser ablation

Double-pulse femtosecond laser ablation of thin aluminum films and bulk aluminum counterintuitively demonstrated a strong (60–70%) raise of the thickness-dependent thresholds for inter-pulse delays of 20–200 ps, preventing material removal at above-threshold fluencies. Time-resolved optical pump-probe reflection and double-pump transmission studies were performed and confirmed the variation of the ablation threshold depending on the interpulse delay. To support the experimental measurements, the process of double-pulse laser ablation was modelled with the combined atomistic-continuum model. The applied model can describe the laser-induced non-equilibrium phase transition processes at atomic precision, whereas the effect of free carriers, playing a determinant role for the case of ultrashort laser pulses, is accounted for in the continuum. The simulations revealed the underlying pre-ablative laser-induced stress dynamics in the hot, acoustically relaxed Al melt, crucially sensitive to the second pump-pulse compressive pressurization. The results of theoretical and experimental study enable efficient dynamic all-optical control of ultrafast laser ablation.

Practical Approach to Large-Scale Electronic Structure Calculations in Electrolyte Solutions via Continuum-Embedded Linear-Scaling Density Functional Theory

We present the implementation of a hybrid continuum-atomistic model for including the effects of a surrounding electrolyte in large-scale density functional theory (DFT) calculations within the Ord...

Metal alloy nanowire joining induced by femtosecond laser heating: A hybrid atomistic-continuum interpretation

Nanojoining is a promising nano-fabrication technique with the capability of assembling functional nanodevices with dissimilar nanoscale and/or molecular components. However, significant challenges are encountered in experimental studies owing to the extremely small scale (10−9 m), high heating rates (1016 K s−1), and high temperature gradients (1011 K m−1) inherent in the nanojoining process. A hybrid atomistic-continuum model comprised of a molecular dynamics simulation (MD) and a two-temperature model (TTM) was used to study the mechanical and thermal characteristics of copper/copper-nickel alloy nanowires during a femtosecond laser nanojoining process. The results show that the laser nanojoining of two identical copper nanowires leads to the deterioration of thermal conductivity and thermal stress due to lattice structural variations. The nanojoining process induces an interface when applied to nanowires with different crystal orientations, which leads to phonon scattering at the joining interface, significantly reducing the thermal conductivity but providing for better mechanical properties. Additional alloy impurities strongly affect the thermal and mechanical properties during the laser nanojoining process. The thermal conductivity decreases significantly with increasing of nickel content while the mechanical properties are improved with respect to the Young's modulus and elastic limit. The utility of the hybrid MD-TTM simulations employed in the present work can approximate the laser nanojoining process in accordance with reasonable physical scenarios and accurate thermal and mechanical property predictions, which can also provide an atomic-level understanding of ultra-small, ultra-fast phenomena.

Numerical Investigation of Ultrashort Laser-Ablative Synthesis of Metal Nanoparticles in Liquids Using the Atomistic-Continuum Model.

We present a framework based on the atomistic continuum model, combining the Molecular Dynamics (MD) and Two Temperature Model (TTM) approaches, to characterize the growth of metal nanoparticles (NPs) under ultrashort laser ablation from a solid target in water ambient. The model is capable of addressing the kinetics of fast non-equilibrium laser-induced phase transition processes at atomic resolution, while in continuum it accounts for the effect of free carriers, playing a determinant role during short laser pulse interaction processes with metals. The results of our simulations clarify possible mechanisms, which can be responsible for the observed experimental data, including the presence of two populations of NPs, having a small (5–15 nm) and larger (tens of nm) mean size. The formed NPs are of importance for a variety of applications in energy, catalysis and healthcare.

Laser sintering of Cu nanoparticles: analysis based on modified continuum-atomistic model

This paper reports on the use of molecular dynamics simulation in conjunction with a modified two-temperature model to elucidate the dynamic behavior of copper nanoparticles (Cu-NPs) undergoing laser sintering. Simulations were conducted using seven models of Cu-NP powders to investigate the means by which particle size (SP), incident laser fluence (I0), and stacking patterns (powders comprising Cu-NPs of either one or two sizes) affect the evolution of electronic temperature (Te), lattice temperature (Tl), pressure (P), and atomic density (dAN) in Cu-NP powders under the effects of laser sintering. We also studied the evolution of sintering configurations and the radial distribution function (g(r)) of Cu-NPs. In powders comprising Cu-NPs of uniform size (2 nm $$\le$$ Sp $$\le$$ 5 nm), the apparent density (d) initially increased (i.e., the powder densified) with I0 and then decreased (i.e., the powder coarsened) with a further increase in I0. Single-size powders composed of smaller Cu-NPs (Sp = 1 nm) underwent densification followed by coarsening followed by densification. Dual-size powders comprising Cu-NPs (Sp = 1 and 3 nm) underwent coarsening almost linearly with an increase in I0, due to the fact that in this model, the incident energy was sufficient to facilitate the atomic diffusion of smaller Cu particles toward larger Cu particles.

Vibrational analysis of Ag, Cu and Ni nanobeams using a hybrid continuum-atomistic model

An important issue in the study of the nanostructures behaviors is the surface effects, which increases with the increase of the surface-to-volume ratio. Continuum theories are capable of modeling structures at micro and larger scales with enough precision and low computational costs. However, these theories are unable to predict the mechanical properties of nanostructures accurately. On the other hand, due to their high precision, atomistic modeling techniques are extensively employed for the study of systems at nanoscale; however, computational costs of these techniques are relatively high. In this research, we aim to study the vibrational behavior of nanobeams made of three FCC metals; silver, copper and nickel, for different boundary conditions. For this purpose, we develop a model which benefits from the advantages of both continuum and atomistic models. Along this line, in this research a core-shell composite model for the nanobeams is developed in which parameters of the model including the surface layer parameters such as surface elasticity, stress, and density are obtained using molecular dynamics simulations results based on genetic algorithm optimization. Subsequently, we have employed this hybrid continuum-atomistic model to predict the vibrational properties of nanobeams. Based on the conducted simulations, the error of the proposed calibrated core-shell composite model in predicting the vibrational frequency of nano beams is less than 3%, while the error of the classical continuum models without the surface effect is up to 50%.

Vibration analysis of graphene sheets resting on Winkler/Pasternak foundation: A multiscale approach

In the present article, an atomistic-continuum multiscale model is developed to study the free-vibration response of single-layered graphene sheets (SLGSs) embedded in an elastic medium based upon the higher-order Cauchy-Born (HCB) rule. In order to take both transverse shear stress and normal pressure into account, the elastic foundation is considered to be of Winkler-Pasternak type. The governing equations are derived within a variational formulation using a newly proposed method called Variational Differential Quadrature (VDQ). Using the VDQ approach together with the Generalized Differential Quadrature (GDQ) technique, the variational form of the governing equation is discretized in a computationally efficient manner. Finally, a generalized eigenvalue problem is solved to calculate the frequencies of SLGSs. The convergence and correctness of the presented numerical solutions are examined firstly. Then, a number of numerical examples are given to study the effects of boundary conditions, elastic medium and arrangement of atoms on the vibrational response of SLGSs. The present model does not involve any additional phenomenological input, and it considers size effect and material nonlinearity due to atomic interactions.

Nonlinear vibration analysis of graphene sheets resting on Winkler–Pasternak elastic foundation using an atomistic-continuum multiscale model

Based on the higher-order Cauchy–Born (HCB) rule, an atomistic-continuum multiscale model is proposed to address the large-amplitude vibration problem of graphene sheets (GSs) embedded in an elastic medium under various kinds of boundary conditions. By HCB, a linkage is established between the deformation of the atomic structure and macroscopical deformation gradients without any parameter fitting. The elastic foundation is formulated according to the Winkler–Pasternak model which considers both normal pressure and transverse shear stress effects. The weak form of nonlinear governing equations is derived via a variational approach, namely based on the variational differential quadrature (VDQ) method and Hamilton’s principle. In order to solve the obtained equations, a numerical scheme is adopted in which the generalized differential quadrature (GDQ) method together with a numerical Galerkin technique is utilized for discretization in the space domain, and the time-periodic discretization method is used to discretize in the time domain. The effects of the arrangement of atoms, the Winkler and Pasternak coefficients of the elastic foundation, and boundary conditions on the frequency–response curves of GSs are illustrated. It is revealed that the nonlinear effects on the response of GSs with larger size in armchair direction are less important.

Longitudinal and Torsional Vibration Characteristics of Boron Nitride Nanotubes

Boron nitride nanotubes (BNNTs) are new cousins of carbon nanotubes (CNTs), which alternately substitute boron and nitrogen atoms for carbon atoms entirely. Its excellent physical and chemical properties, such as excellent thermal stability, chemical inertness and strong acid corrosion resistance, make BNNTs products be favorable to machine, thus scientific activities focused on them have profound practical significance and great application prospect. However, the vibration characteristics of BNNTs is still the least understood aspects. Longitudinal and torsional free vibration of single-walled boron nitride nanotubes are investigated through a coupling atomistic-continuum model with Euler beam model and atomistic simulations. Euler beam model with the involved atomistic-continuum multiscale model is capable of capturing the size effect since physical meanings of the integration for involved higher order gradient tensors are corresponding to size effect. The analytical solutions obtained by the coupling method are compared with atomistic simulation and are found to be in a good agreement. Computational results demonstrate that fundamental frequencies are in an order of 1 THz for both cantilevered and clamped boron nitride nanotubes, independent of tubular chirality. The effect of tubular radius on fundamental frequencies of both longitudinal and torsional free vibrations are large when it is small, especially the latter. The error between coupling method and atomistic simulation generally decreases as the length/diameter ratio increases. For a given length/diameter ratio, tubular radius have a distinctly decreasing effect on the error no matter what the kind of constraint is. However, a small difference observed in the study of torsional free vibration is that the clamped constraint gives rise to a slight increasing effect on the error as the tubular radius increases, but limited to a small degree. The vibrational modes confirm that the difference is originated from the involved breathing vibration in both torsional and longitudinal free vibration.

Hyperdynamics accelerated concurrent atomistic-continuum model for developing crack propagation models in elastic crystalline materials

Concurrent multiscale models that couple atomistic and continuum calculations are useful for extending the spatial limitations of atomistic models, as well as for deriving effective continuum models. This paper develops a concurrent atomistic-continuum computational model with an embedded crack in the atomistic domain. Molecular dynamics (MD) simulations are conducted in the atomistic domain, while the continuum domain is modeled using the finite element (FE) method. A major limitation of concurrent models is the time-scale mismatch between the continuum and atomistic domains that causes the two sub-domains to experience different strain-rates. To bridge the time scale difference, the MD model is augmented by a novel strain-boost hyperdynamics accelerated time marching scheme. The concurrent model is used to study strain-rate and temperature effects on crack propagation in a nickel single crystal. The continuum domain uses a nonlinear anisotropic elasticity constitutive model. Crack propagation rate is represented by a parametric continuum model, whose strain-rate and temperature dependencies are investigated. Finally, the concurrent model is used to evaluate the free energy density function for phase field modeling of crack propagation. Validation studies elucidate the potential of the concurrent model as a modeling tool for large scale continuum fracture models.

A discrete phase hybrid continuum-atomistic model for electrokinetics in nanofluidics

The ever-growing field of micro- and nanotechnology has a great deal of interest in simulating dynamic phenomena of multiscale systems. Hybrid approaches that produce a trade-off between accuracy and computational costs play a key role in this area. In this study, an improved hybrid continuum-atomistic model is proposed for the simulation of electroosmotic flows in nanochannels. The aqueous solvent phase is modeled by the continuum four-way coupled Navier-Stokes equations, while a Lagrangian approach is used for the ion transport. Different forces, including the drag, buoyancy, Brownian, electrostatic, and ion-ion/wall-ion collision, and torques, including the drag and collision, govern the motion of ion particles. The ion-ion/wall-ion collision is taken into account by a discrete phase model, and the electric field is derived by the Poisson-Boltzmann closure. Results of the model, such as the change in bulk velocity with surface electric charge density, are validated by several molecular dynamics simulations and experimental observations available in the literature. It is shown that the present hybrid model is capable of predicting the main features of the problem. Moreover, the significance of different forces and the other alternative for modeling the external electric field, i.e., the discrete Coulomb’s approach with the modified particle mesh Ewald boundary treatment, are also examined. The proposed model would be extremely useful for future studies on the electrokinetics in nanochannels, especially in more complex geometries where the molecular dynamics approaches are limited due to the computational costs.

Atomistic-continuum modeling of vibrational behavior of carbon nanotubes using the variational differential quadrature method

A numerical approach is adopted for the multiscale analysis of vibrations of single-walled carbon nanotubes (SWCNTs). The SWCNT is modeled by a hyperelastic membrane whose kinematics is described using the higher-order Cauchy-Born rule. The constitutive model is formulated exclusively in terms of the interatomic potential, so, it inherits the atomistic information and involves no other phenomenological input. The variational differential quadrature (VDQ) method is employed in which the continuum model is discretized using DQ, and a weak form of equation of motion is obtained via a variational approach. VDQ is computationally advantageous since it has a fast rate of convergence and can reproduce the results of molecular dynamics simulations. Detailed investigations into frequencies and mode shapes of SWCNTs with different geometrical parameters, boundary conditions and chiralities are carried out. It is found that short nanotubes display a coupling between the axial/torsional and bending modes. Also, as the tube diameter or length increases, mode transitions are made at several critical points. If the edge supports are more flexible and tube length is longer, the critical diameters are larger. Eventually, the vibration characteristics of axially strained nanotubes are analyzed, and it is concluded that SWCNTs with smaller radii have higher strain sensitivity.

Atomistic–continuum model for probing the biomechanical properties of human erythrocyte membrane under extreme conditions

A precise first attempt is performed to quantify the biomechanical properties of human erythrocyte membrane subjects to extreme temperature and loading conditions. An improved three-dimensional (3D) atomistic–continuum model based on the Cauchy–Born rule is proposed to investigate the elastic properties and biomechanical responses of the erythrocyte membrane. A membrane rigidity model is developed to estimate the membrane elastic properties over an extreme temperature range. Our computational results reveal that the membrane is able to sustain large strains up to a certain limit; beyond which, mechanically induced hemolysis may occur as exponential stress increment, fluctuations and multiple peaks were observed in the stress–strain curves. Additionally, we found that the overall deformability of the erythrocyte membrane significantly decreases as temperature increases. It is concluded that the observed increase in membrane rigidity may be attributed to the denaturation, structural remodeling and cross-linking of membrane cytoskeletal proteins.

Graphene or h-BN paraffin composite structures for the thermal management of Li-ion batteries: A multiscale investigation

The reliability and safety of lithium-ion batteries can be affected by overheating issues. Phase change materials like paraffin due to their large heat capacities are among the best solutions for the thermal management of batteries. In this investigation, multiscale modelling techniques were developed to explore the efficiency in the thermal management of rechargeable batteries through employing the paraffin composite structures. A combined atomistic-continuum multiscale modelling was conducted to evaluate the thermal conductivity of paraffin reinforced with graphene or hexagonal boron-nitride nanosheet additives. In addition, heat generation during a battery service was simulated using the Newman's electrochemical model. Finally, three-dimensional heat transfer models were constructed to investigate the effectiveness of various paraffin composite structures in the thermal management of a battery system. Interestingly, it was found that the thermal conductivity of paraffin nanocomposites can be enhanced by several times but that does not yield significant improvement in the batteries thermal management over the pure paraffin. The acquired findings can be useful not only for the modelling of nanocomposites but more importantly for the improvement of phase change materials design to enhance the thermal management of rechargeable batteries and other electronic devices.

New Continuum Approaches for Determining Protein-Induced Membrane Deformations

The influence of the membrane on transmembrane proteins is central to a number of biological phenomena, notably the gating of stretch activated ion channels. Conversely, membrane proteins can influence the bilayer, leading to the stabilization of particular membrane shapes, topological changes that occur during vesicle fission and fusion, and shape-dependent protein aggregation. Continuum elastic models of the membrane have been widely used to study protein-membrane interactions. These mathematical approaches produce physically interpretable membrane shapes, energy estimates for the cost of deformation, and a snapshot of the equilibrium configuration. Moreover, elastic models are much less computationally demanding than fully atomistic and coarse-grained simulation methodologies; however, it has been argued that continuum models cannot reproduce the distortions observed in fully atomistic molecular dynamics simulations. We suggest that this failure can be overcome by using chemically and geometrically accurate representations of the protein. Here, we present a fast and reliable hybrid continuum-atomistic model that couples the protein to the membrane. We show that the model is in excellent agreement with fully atomistic simulations of the ion channel gramicidin embedded in a POPC membrane. Our continuum calculations not only reproduce the membrane distortions produced by the channel but also accurately determine the channel’s orientation. Finally, we use our method to investigate the role of membrane bending around the charged voltage sensors of the transient receptor potential cation channel TRPV1. We find that membrane deformation significantly stabilizes the energy of insertion of TRPV1 by exposing charged residues on the S4 segment to solution.

Nanoscale structures generation within the surface layer of metals with short UV laser pulses

We have completed modeling of a laser pulse influence on a gold target. We have applied a hybrid atomistic-continuum model to analyze the physical mechanisms responsible for the process of nanostructuring. The model combines the advantages of Molecular Dynamics and Two Temperature Model. We have carried out a direct comparison of the modeling results and experimental data on nano-modification due to a single ps laser pulse at the energy densities significantly exceeding the melting threshold. The experimental data is obtained due to a laser pulse irradiation at the wavelength of 248 nm and duration of 1.6 ps. The mask projection (diffraction grating) creates the sinusoidal intensity distribution on a gold surface with periods of 270 nm, 350 nm, and 500 nm. The experimental data and modeling results have demonstrated a good match subject to complex interrelations between a fast material response to the laser excitation, generation of crystal defects, phase transitions and hydrodynamic motion of matter under condition of strong laser-induced non-equilibrium. The performed work confirms the proposed approach as a powerful tool for revealing the physical mechanisms underlying the process of nanostructuring of metal surfaces. Detailed understanding of the dynamics of these processes gives the possibility for designing the topology of functional surfaces on nano- and micro-scales

Multiscale modelling of heat conduction in all-MoS2 single-layer heterostructures

We developed a combined atomistic-continuum multiscale modeling to explore the effective thermal conductivity of all-MoS2 single-layer heterostructures.

A third-order Cauchy-Born rule for modeling of microtubules based on the element-free framework

The Cauchy-Born rule is an efficient formula to schematically connect the deformation of atomic structures with a reciprocal continuum field. It is especially useful to the implantation of multiscale theories and has already been successfully applied in the mechanical modeling of microtubules. In atomistic-continuum approaches, the continuum description of material properties can be evaluated by minimizing potential energy of an atomic structure. Moreover, the intrinsic interatomic potential can be obtained at the microscopic atomic level and further embedded in a macroscopic continuum model using the Cauchy-Born rule. The conventional Cauchy-Born rule, however, is not accurate enough in numerical implementations, and the errors can be removed mostly by including higher-order terms based on Taylor series. This work aims to quantitatively evaluate the influences of higher-order terms on the modeling accuracy of the mechanical behaviors of microtubules. The first-, second- and third-order Cauchy-Born rules are developed for atomistic-continuum modeling. As the continuum mechanics implementation of the third-order Cauchy-Born rule requires C2 continuity property, a specific mesh-free computational scheme based on third-order deformation gradient continuum is developed in order to suit the third-order Cauchy-Born rule for the mechanical simulation of microtubules. A series of simulation results are presented for the evaluation and discussion.