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We present a scattering model based on the scalar scattering theory that allows estimating far field scattering properties in both transmission and reflection for nano-textured interfaces. We first discuss the theoretical formulation of the scattering model and validate it for nano-textures with different morphologies. Second, we combine the scattering model with the opto-electric asa simulation software and evaluate this combination by simulating and measuring the external parameters and the external quantum efficiency of solar cells with different interface morphologies. This validation shows that the scattering model is able to predict the influence of nano-textured interfaces on the solar cell performance. The scattering model presented in this manuscript can support designing nano-textured interfaces with optimized morphologies. [ABSTRACT FROM AUTHOR]

While the interaction of colloidal particles (sizes in excess of 100 nm) with liquid interfaces may be understood in terms of continuum models, which are grounded in macroscopic properties such as surface and line tensions, the behaviour of nanoparticles at liquid interfaces may be more complex. Recent simulations [D. L. Cheung and S. A. F. Bon, Phys. Rev. Lett. 102, 066103 (2009)] of nanoparticles at an idealised liquid-liquid interface showed that the nanoparticle-interface interaction range was larger than expected due, in part, to the action of thermal capillary waves. In this paper, molecular dynamics simulations of a Lennard-Jones nanoparticle in a binary Lennard-Jones mixture are used to confirm that these previous results hold for more realistic models. Furthermore by including attractive interactions between the nanoparticle and the solvent, it is found that the detachment energy decreases as the nanoparticle-solvent attraction increases. Comparison between the simulation results and recent theoretical predictions [H. Lehle and M. Oettel, J. Phys. Condens. Matter 20, 404224 (2008)] shows that for small particles the incorporation of capillary waves into the predicted effective nanoparticle-interface interaction improves agreement between simulation and theory. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations have been used to investigate the kinetics of spontaneous cavitation and crystallization in a Lennard-Jones liquid at negative pressures in the temperature range where these processes compete with each other. The nucleation rate has been calculated in NVE and NpT ensembles by the method of mean lifetime and the transition interface sampling method with parallel path swapping. The data obtained have been used to determine in the framework of classical nucleation theory the value of the ratio of the solid-liquid and the liquid-void interfacial free energy for critical crystals and cavities and the values of their volumes at points where the cavitation rate of the liquid is equal to the rate of its crystallization. [ABSTRACT FROM AUTHOR]

A common theme of studies using molecular simulation is a necessary compromise between computational efficiency and resolution of the forcefield that is used. Significant efforts have been directed at combining multiple levels of granularity within a single simulation in order to maintain the efficiency of coarse-grained models, while using finer resolution in regions where such details are expected to play an important role. A specific example of this paradigm is the development of hybrid solvent models, which explicitly sample the solvent degrees of freedom within a specified domain while utilizing a continuum description elsewhere. Unfortunately, these models are complicated by the presence of structural artifacts at or near the explicit/implicit boundary. The presence of these artifacts significantly complicates the use of such models, both undermining the accuracy obtained and necessitating the parameterization of effective potentials to counteract the artificial interactions. In this work, we introduce a novel hybrid solvent model that employs a smoothly decoupled particle interface (SDPI), a switching region that gradually transitions from fully interacting particles to a continuum solvent. The resulting SDPI model allows for the use of an implicit solvent model based on a simple theory that needs to only reproduce the behavior of bulk solvent rather than the more complex features of local interactions. In this study, the SDPI model is tested on spherical hybrid domains using a coarse-grained representation of water that includes only Lennard-Jones interactions. The results demonstrate that this model is capable of reproducing solvent configurations absent of boundary artifacts, as if they were taken from full explicit simulations. [ABSTRACT FROM AUTHOR]

Impurity atoms segregated in grain boundary (GB) regions can dramatically change the physical and chemical properties of the GBs. Such changes often appear to be attributed to the GB energy reduction and/or solute drag effect. Phase-field models have been utilized to clarify both the thermodynamic and kinetic effects of the GB segregation. In this study, we developed phase-field models for GB segregation that are diffuse interface versions of the classical two-phase model of GB segregation. The thermodynamic state at any point in the system is represented as a mixture of a GB phase and a matrix phase. There are two choices for the thermodynamic relation between the GB phase and the matrix phase that constitute the point: the equal composition condition in model I and the equal diffusion potential condition in model II. Most of the previous PFMs for GB segregation appear to be specific cases of model I. We examined the thermodynamic properties of models I and II, and compared them with each other and the classical two-phase model. Although all the models resulted in the same GB composition, the GB energy and its dependency on the composition at the equilibrium state are quite different from each other. In model I, there is a lower bound to the GB energy, which originates from the equal composition condition. The GB energy from model II shows no such lower bound, and it is represented as the vertical distance between the parallel tangent lines on the free energy diagram, as in the classical two-phase model. Nevertheless, the compositional dependence in the model II is quite different from that in the classical two-phase model. This originates from the different choices for the composition-independent parameter in the models: a constant gradient energy coefficient in model II and a constant GB width in the classical two-phase model. Model I is not suitable for simulations of alloys that show a reduction of the GB energy due to GB segregation below a certain limit (in dilute alloys, about half of the GB energy of pure solvents). Model II is a correct choice for such alloys. [ABSTRACT FROM AUTHOR]

Several examples illustrating the energy balance associated with a mixing process at the interface of a planar dynamical model describing two-phase perfect fluid circulating around a circle with a sufficiently large radius within a central gravitational field are presented. The model is associated with the spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around the Earth. The fluid is supposed to be irrotational and pressure on a outer layer is constant. It is postulated that the total fluid depth is small compared to the radius of the circle and the gravity vector is directed to the center of the circle. Under these assumptions, this problem can be associated with a spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around equatorial plane. The model is the subject to the rigid lid approximation to the external boundary conditions for the outer fluid layer. One of the novelties in this work is the derivation of the nonlinear shallow water model by means of the average velocity. This introduction simplifies essentially further potential studies of mixing criteria associated with nonlinear mathematical models representing shallow water equations [ABSTRACT FROM AUTHOR]

Abstract: The interface thickness is the most crucial parameter in the phase field model (PFM) for the accuracy and the computability. However, the Gibbs–Thomson equation can be satisfied only when the interface thickness is sufficiently small, especially with a large undercooling, but this greatly limits the applications of PFM to a realistic problem. The temperature correction in the thin-interface model partially resolves the problem, but the range is rather limited. In this report, we propose a new formulation of PFM by adding extra terms stabilizing the hyperbolic tangent profile of the phase-field, and this allows us to use a much larger interface thickness for simulation, even with a large undercooling. Several benchmark comparisons with analytical solutions are carried out and discussed. [Copyright &y& Elsevier]

In this paper, we introduce a modeling methodology for field bus-based embedded systems that allows dynamic evaluation of their signal integrity characteristics at the virtual prototyping step. Our methodology is based on the following criteria: 1) a signal integrity-aware I/O interface mixed model; 2) a physical model of transmission lines to estimate signal degradation caused by the bus lines; and 3) an ICEM model to estimate the impact of a chip's internal activity on its power voltage or its I/O. Through simulations and experimental validations, we show that our methodology allows functional validation of the design and can also evaluate some low-level effects such as the influence of an embedded software instruction on the voltage drops in the power rails. [ABSTRACT FROM PUBLISHER]

Abstract: This paper presents a theoretical framework about interface states creation rate from Sieaking at the Si/SiO2 interface during Hot Carrier (HC) stress. It involves two mains mechanisms of bond breaking through incident carriers, either being very energetic or very numerous but less energetic. This concept allows physical modeling of the reliability of MOS transistors, for different HC stress conditions. Simulation is validated by measurement of both defect lateral profiles and degradation of MOS parameters. This poses a general framework for the study of HC degradation at defect level. [Copyright &y& Elsevier]

Abstract: We extend the computational method presented in for tracking an interface immersed in a given velocity field to three spatial dimensions. The proposed method is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian–Eulerian framework, and has been constructed with two goals in mind: (i) to be able to accurately follow the interface; and (ii) to automatically maintain a good distribution of the grid points along the interface. The method combines information from a pure Lagrangian approach with information from an ALE approach. The new method offers flexibility in terms of how an “optimal” point distribution should be defined, and relies on the solution of two-dimensional surface convection problems. We verify the new method by solving model problems both in the single and multiple spectral element case, and we compare this method with other traditional alternatives. We have been able to verify first, second, and third order temporal accuracy for the new method by solving these three-dimensional model problems. [Copyright &y& Elsevier]

We present an extended Cahn-Hilliard model for simulating interfacial anisotropy in thin-film dynamics by incorporating high-order terms in the energy from an expansion of the energy about an equilibrium state, following earlier work by Abinandanan and Haider [Philos. Mag. Sect. A 81,2457 (2001)]. For example, to simulate SiGe/Si thin films, where diamond cubic symmetry is needed, fourth order derivatives are included in the energy. This results in a sixth order evolution equation for the order parameter. For less symmetric crystals, one needs to add terms of higher order than fourth order. One advantage of this approach is its intrinsic regularized behavior. In particular, even for strongly anisotropic surface energy, sharp corners will not form and the extended anisotropic Cahn-Hilliard equations are well-posed. For this system we develop an energy-stable numerical scheme in which the energy decreases for any time step. We present two-dimensional (2D) and three-dimensional (3D) numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the computed equilibrium shapes using the new model and results from an analysis associated with a Wulff construction for energy minimization. The model predictions also compare well with experimental results for silicon voids. In the context of thin films, we observe the formation of interconnected ridges, wires, and fortresses similar to those observed in SiGe/Si thin films. [ABSTRACT FROM AUTHOR]

Schloegl's second model on a (d ≥ 2)-dimensional hypercubic lattice involves: (i) spontaneous annihilation of particles with rate p and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of suitable pairs of neighboring particles. This model provides a prototype for nonequilibrium discontinuous phase transitions. However, it also exhibits nontrivial generic two-phase coexistence: Stable populated and vacuum states coexist for a finite range, pf(d) < p < pe(d), spanned by the orientation-dependent stationary points for planar interfaces separating these states. Analysis of interface dynamics from kinetic Monte Carlo simulation and from discrete reaction-diffusion equations (dRDEs) obtained from truncation of the exact master equation, reveals that pe(f) ∼ 0.211 3765 + ce(f),/d as d →∞, where Δc = ce -- Cf &thkap; 0.014. A metastable populated state persists above pe(d) up to a spinodal p = ps(d), which has a well-defined limit ps(d →∞) = ¼. The dRDEs display artificial propagation failure, absent in the stochastic model due to fluctuations. This feature is amplified for increasing d, thus complicating our analysis. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new phase-field model including combined effects of edge diffusion, the Ehrlich–Schwoebel barrier, deposition and desorption to simulate epitaxial growth. A new free energy function together with a correction to the initial phase variable profile is used to efficiently capture the morphological evolution when a large deposition flux is imposed. A formal matched asymptotic analysis is performed to show the reduction of the phase-field model to the classical sharp interface Burton–Cabrera–Frank model for step flow when the interfacial thickness vanishes. The phase-field model is solved by a semi-implicit finite difference scheme, and adaptive block-structured Cartesian meshes are used to dramatically increase the efficiency of the solver. The numerical scheme is used to investigate the evolution of perturbed circularly shaped small islands. The effect of edge diffusion is investigated together with the Ehrlich–Schwoebel barrier. We also investigate the linear and nonlinear regimes of a step meandering instability. We reproduce the predicted scaling law for the growth of the meander amplitude, which was based on an analysis of a long wavelength regime. New nonlinear behavior is observed when the meander wavelength is comparable to the terrace width. In particular, a previously unobserved regime of coarsening dynamics is found to occur when the meander wavelength is comparable to the terrace width. [Copyright &y& Elsevier]

Abstract: In this paper, an enriched finite element method is presented for numerical simulation of saturated porous media. The arbitrary discontinuities, such as material interfaces, are encountered via the extended finite element method (X-FEM) by enhancing the standard FEM displacements. The X-FEM technique is applied to the governing equations of porous media for the spatial discretization, followed by a generalized Newmark scheme used for the time domain discretization. In X-FEM, the material interfaces are represented independently of element boundaries and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, several numerical examples are analyzed, including the dynamic analysis of the failure of lower San Fernando dam, to demonstrate the efficiency of the X-FEM technique in saturated porous soils. [Copyright &y& Elsevier]

Abstract: A novel lubrication generator combing piezoelectric drop-on-demand (DOD) oil-jet technology is proposed for space mechanisms. A finite difference numerical model was established to analyze the design parameters of droplet ejection. The volume-of-fluid piecewise linear-interface construction (VOF-PLIC) interface-capturing method was adopted to represent the fluid domain and to track the evolution of its free boundaries whereas the continuous surface force (CSF) mode was chosen to model the interfacial physics. To explore the practicability of the proposed new lubrication generator, the flow behavior during the stages of fluid ejection and droplet formation are examined with Krytox 143AB lubricant as the baseline test fluid for a ejection cycle of 100μs. To improve the droplet ejecting performance of lubricant, the characters of inject flow part have been investigated with the variation of the pulse voltage for different spatial temperature. Injection process in the extra-low pressure is also investigated. The developed model helps to understand the drop formation process and this approach can be applied in various inject head designs. [Copyright &y& Elsevier]

A full-scale water model and mathematical simulation were used to study the fluid flow-related phenomena in a water model of an aluminum electrolysis cell. The time-dependent, multiphase fluid flow model was developed to represent the complex transient flow in the electrolysis bath. The accuracy of the mathematical model was validated by the ink dispersion and laser doppler velocimetry measurements in the water model. The shape, motion, release frequency of large-size bubbles, the fluid flow pattern, and the electrolyte-metal interface were predicted by the mathematical simulation. The design and operation of the anode were discussed, including the effect of the anode edge corner shape, the presence of a tilted bottom angle, and the magnitude of applied current density. The results indicated that coupling using a curved corner, with slot and with tilted angle at the anode, is effective for the release of bubbles and for the stability of the electrolyte-metal interface. [ABSTRACT FROM AUTHOR]

Abstract: Oscillations observed in the load–displacement response of brittle interfaces modeled by cohesive zone elements in a quasi-static finite element framework are artifacts of the discretization. The typical limit points in this oscillatory path can be traced by application of path-following techniques, or avoided altogether by adequately refining the mesh until the standard iterative Newton–Raphson method becomes applicable. Both strategies however lead to an unacceptably high computational cost and a low efficiency, justifying the development of a process driven hierarchical extension of the discretization used in the process zone of a cohesive crack. A self-adaptive enrichment scheme within individual cohesive zone elements driven by the physics governing the problem, is an efficient solution that does not require further mesh refinements. A two-dimensional mixed-mode example in a general framework with an irreversible cohesive zone law shows that an enriched formulation restores the smoothness of the solution in structures that are discretized in a relatively coarse manner. [Copyright &y& Elsevier]

Abstract: The domain structures of PbTiO3 epitaxial nanodots under the influences of depolarization fields and mismatch strains have been studied using three dimensional phase field simulations. The single-vortex structure and mixed domain configuration, which consisted of zigzag stripe domain and closure dipole flux near the interfaces, were found to be effective in annihilating the depolarization fields in the isotropically tensile and compressive ferroelectric nanodots, respectively. These domain structures were produced by the combined effect of electrostatic and mismatch elastic energies. The width of stripe domain was found to be related to the volume percentage of polarization dipoles along the z-axis, which varied remarkably with the change of compressive mismatch strain. In the case of nanodots under anisotropic mismatch strains, double-vortex domain patterns and stripe domains with nearly straight domain walls were formed. Moreover, the domain structures with electrostatic energy neglected were also studied. [Copyright &y& Elsevier]

We propose and study, by means of numerical simulations, the time evolution of interfaces in a generalized voter model in d = 2 dimensions. In this model, a randomly selected voter can change his or her opinion (state) with a certain probability that is an algebraic function of the average opinion of his or her nearest neighbors. By starting with well-defined (sharp) interfaces between two different states of opinion, we measure the time dependence of the interface width (w), which behaves as a power law, i.e., w ∞ tδ. In this way we characterized three different types of interfaces: (i) between an ordered phase (consensus) and a disordered one (δ = 1/2); (ii) between ordered phases having different states of opinion (δ = 1/2), which corresponds to interface coarsening without surface tension; and (iii) as in (ii) but considering surface tension. Here, we observe a finite-size induced crossover with exponents δ = 1/4 and δ = 1/2 for early and longer times, respectively. So, our study allows for the characterization of interfaces of quite different nature in a unified fashion, providing insight into the understanding of interface coarsening with and without surface tension. [ABSTRACT FROM AUTHOR]

A novel electric-circuit simulation model considering the contact and interface physics for electromagnetic railgun is suggested. The contact velocity skin-effect resistance and the contact resistance are considered. The pulsed-power supply is implemented with Simplorer V8, and the railgun is modeled by Matlab/Simulink. The data exchange is controlled by Simplorer V8. Nine experimental data have been used to validate the new model. Then, based on the validated model, a two-objective optimization pursuing both the highest velocity and the highest efficiency is carried out with the help of iSIGHT. [ABSTRACT FROM AUTHOR]

This paper presents a new neural-network method to describe the electromagnetic (EM) behavior at the interface between the substructures from an internally decomposed EM structure. A set of neural networks is used to represent the EM behavior of the substructure as seen from the interface. This allows EM coupling between substructures to be effectively represented. The method is developed in a finite-element environment. An EM transfer function matrix is formulated to produce training data, allowing neural networks to learn the spatial coupling between EM-field variables at various locations over the interface of the substructure. A new formulation is proposed where trained neural networks are integrated into the finite-element equation for efficient simulation of an overall EM structure. A technique is developed to allow the proposed model to be used with the mesh different from that in neural-network training. Examples show that the proposed method provides better accuracy than conventional neural-network approaches for modeling substructures from an internally decomposed EM problem. Using the proposed model also speeds up finite-element simulation. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the processes of thermal softening, melting and subsequent melt lubrication that occur during the high speed sliding of a metal piece on another metal block. The temperature rise in the slider arising from both high speed interface friction and from the energy dissipated during plastic deformations is computed using simple analysis and the finite element method. Subsequently, we propose a mathematical model for the transient lubrication problem that describes the behavior of the molten film at the slider–rail interface. This model successfully predicts the evolution process of the melt thickness and the melt front velocity of the liquid film; these predictions agree with the experimentally observed dynamics of molten film better than those from other existing models. [ABSTRACT FROM AUTHOR]

We have developed a mathematical model describing the process of microbial enhanced oil recovery (MEOR). The one-dimensional isothermal model comprises displacement of oil by water containing bacteria and substrate for their feeding. The bacterial products are both bacteria and metabolites. In the context of MEOR modeling, a novel approach is partitioning of metabolites between the oil and the water phases. The partitioning is determined by a distribution coefficient. The transfer part of the metabolite to oil phase is equivalent to its 'disappearance,' so that the total effect from of metabolite in the water phase is reduced. The metabolite produced is surfactant reducing oil-water interfacial tension, which results in oil mobilization. The reduction of interfacial tension is implemented through relative permeability curve modifications primarily by lowering residual oil saturation. The characteristics for the water phase saturation profiles and the oil recovery curves are elucidated. However, the effect from the surfactant is not necessarily restricted to influence only interfacial tension, but it can also be an approach for changing, e.g., wettability. The distribution coefficient determines the time lag, until residual oil mobilization is initialized. It has also been found that the final recovery depends on the distance from the inlet before the surfactant effect takes place. The surfactant effect position is sensitive to changes in maximum growth rate, and injection concentrations of bacteria and substrate, thus determining the final recovery. Different methods for incorporating surfactant-induced reduction of interfacial tension into models are investigated. We have suggested one method, where several parameters can be estimated in order to obtain a better fit with experimental data. For all the methods, the incremental recovery is very similar, only coming from small differences in water phase saturation profiles. Overall, a significant incremental oil recovery can be achieved, when the sensitive parameters in the context of MEOR are carefully dealt with. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations with many-body interactions were carried out to understand the bulk and interfacial absorption of gases in 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4). A new polarizable molecular model was developed for BMIMBF4, which was found to give the correct liquid density but which also had good agreement with experiment for its surface tension and X-ray reflectivity. The potential of mean force of CO2and SO2was calculated across the air−BMIMBF4 interface, and the bulk free energies were calculated with the free-energy perturbation method. A new polarizable model was also developed for CO2. The air−BMIMBF4 interface had enhanced BMIM density, which was mostly related to its butyl group, followed by enhanced BF4 density a few angstroms toward the liquid bulk. The density profiles were observed to exhibit oscillations between high BMIM and BF4 density indicating the presence of surface layering induced by the interface. The potential of mean force for CO2and SO2showed more negative free energies in regions of enhanced BF4 density, while more positive free energies were found in regions of high BMIM density. Moreover, these gases showed free-energy minimums at the interface, where the BMIM alkyl groups were found to be most prevalent. Our results show the importance of ionic liquid interfacial ordering for understanding gas solvation in them. [ABSTRACT FROM AUTHOR]

Abstract: A model for unifying a viscoelastic fluid and a Newtonian fluid is established, in which the governing equations for the viscoelastic fluid and the Newtonian fluid are successfully united into a system of generalized Navier–Stokes equations. A level set method is set up to solve the model for capturing the moving interface in the mold filling process. The physical governing equations are solved by the finite volume method on a non-staggered grid and the interpolation technique on the collocated grid is used for the pressure-velocity and the stress-velocity decoupling problems. The level set and its reinitialization equation are solved by the finite difference method, in which the spatial derivatives are discretized by the 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme, and the temporal derivatives are discretized by the 3rd-order Total Variation Diminishing Runge–Kutta (TVD-R–K) scheme. The validity of the method is verified by some benchmark problems. Then a simulation of viscoelastic fluid mold filling process is pursued with the method. The moving interface and all the information of the physical quantities during the injection process are captured. The die swelling phenomenon is found in the simulation. The influences of elasticity and viscosity on the physical quantities such as stresses etc. in the mold filling process are analyzed. Numerical results show that elastic characteristics such as the stretch and die swelling etc. reinforce accordingly as Weissenberg number increases. Pressures increase continuously in the mold filling process and the pressure maintains the maximum value at the inlet. Injection velocity is proportional to injection pressure. A higher viscosity leads to a higher pressure distribution, that is, the pressure decreases as Reynolds number increases. [Copyright &y& Elsevier]

Abstract: In this work, a multi scale modeling approach has been developed to simulate the impact of woven fabrics using a finite element (FE) analysis. A yarn level of resolution is used in the model. This approach, referred to as the hybrid element analysis (HEA) is based on decreasing the complexity of the finite element model with distance away from the impact zone based on the multiscale nature of the fabric architecture and the physics of the impact event. Solid elements are used to discretize the yarns around the impact region, which transition to shell elements in the surrounding region. A new method for modeling the shell yarns is incorporated that more accurately represents the contours of the yarn cross section. Impedances have been matched across the solid–shell interface to prevent interfacial reflections of the longitudinal strain wave. The HEA method is validated by first applying it to the FE model of a single yarn for which an analytical solution is known. The HEA method is then applied to a woven fabric model and validated by comparing it against a baseline model consisting of yarns discretized using only solid elements. [Copyright &y& Elsevier]

Abstract: The main point of this paper is to propose a non-local three-dimensional hydraulic conductivity full tensor upscaling algorithm and code. The algorithm is capable of transforming very refined cell conductivity models into coarse block conductivity models for quick and accurate solution of the groundwater flow equation. Flow rate and hydraulic head gradient are the variables used to relate the outputs from the fine scale model to the outputs from the coarse scale model. The flows and gradients computed at the coarse scale blocks should match the average values of the corresponding quantities observed at the fine scale. The algorithm is geared towards its use in conjunction with finite-difference codes for the solution of the groundwater flow equation capable of handling full tensor hydraulic conductivities. The finite-difference formulation of the groundwater flow equation requires specifying the hydraulic conductivity at the block interface in order to compute the discharge crossing the interface. Most finite-difference codes take as input conductivities at the blocks and then perform some type of averaging to come up with the interblock conductivity. Typically the harmonic mean of the conductivities of neighboring blocks is used. We propose computing directly the interblock conductivity during the upscaling process thus avoiding the need to average already averaged (upscaled) values of adjacent blocks. This approach also circumvents the problem associated with averaging conductivity tensors when their principal directions are not aligned with the Cartesian axes. The proposed algorithm is successfully demonstrated in four synthetic examples with spatially isotropic, anisotropic and bimodal conductivities fields at the fine scale. The computer code is provided with explanation of the input parameters and output results. [Copyright &y& Elsevier]

Abstract: We present a new 3D steady-state saturated groundwater-flow forward-simulator with full conductivity tensors using a 19-points block-centered finite-difference method. Hydraulic conductivity tensors are defined at the block interfaces eliminating the need to average conductivity tensors at adjacent blocks to approximate their values at the interfaces. The capabilities of the code are demonstrated in three heterogeneous formulations, two of the examples are 2D, and the third one is 3D and uses a nonuniform discretization grid. A benchmark, in the context of conductivity upscaling, is carried out with the MODFLOW LVDA module, which uses hydraulic conductivity tensors at block centers and then approximates their values at the interfaces. The results show that our code gives more accurate predictions for the interblock fluxes than the MODFLOW LVDA module when the block conductivity principal directions are not parallel to the Cartesian axis. [Copyright &y& Elsevier]

Abstract: A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equations on the same mesh. For long simulations, the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation. This is done in the spirit of shock-capturing schemes, for which numerical dissipation effectively preserves a sharp but mesh-representable shock profile. For contact capturing, the formulation is modified so that interface representations remain sharp like captured shocks, countering their tendency to diffuse via the same numerical diffusion needed for shock-capturing. Special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed. The interface compression method is coupled to a shock-capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries. Convergence to weak solutions of the governing equations is proved for the new contact capturing approach. Comparisons with exact Riemann problems for model one-dimensional multi-material flows show that the interface compression technique is accurate. The method employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions. Examples of two- and three-dimensional flows are also presented, including a demonstration with significantly disparate equations of state: a shock induced collapse of three-dimensional van der Waal’s bubbles (air) in a stiffened equation of state liquid (water) adjacent to a Mie-Grüneisen equation of state wall (copper). [Copyright &y& Elsevier]

Abstract: The mechanical behaviour and failure properties of adhesive joints are influenced not only by adhesive properties but also by interface characteristics. Various modelling methods have been proposed to predict the failure behaviour of adhesive joints. Among those methods, cohesive zone modelling, which consists of introducing a cohesive law in the numerical models to reproduce the adhesive layer, is widely used to simulate the behaviour of adhesive joints. The cohesive parameters of the traction–separation laws in each pure mode should be determined for application of this technique. It is known that the cohesive parameters are affected by both adhesive properties and interface characteristics so, in most cases, these parameters are iteratively obtained by matching numerical results to experimental results. In this paper, a systematic procedure for the determination of the cohesive parameters is proposed by introducing an optimization technique (design of experiment and the kriging metamodel). The first step is to identify design variables affecting a response of a system. In this study, the cohesive parameters are selected as the design variables. Once the design variables are identified, design ranges or sampling ranges of the design variables are determined in order to result in a near optimal response with the determined sampling ranges. If the design variables and the sampling ranges are obtained then the design of experiment is performed to determine appropriate sampling points in the sampling ranges and a minimum number of simulations. Then, the load difference between numerical and experimental load–displacement results at several values of displacements are defined as an error, and the kriging metamodel, which surrogates the error, is constructed based on the sampling points. Cohesive parameters are determined by applying the numerical nonlinear optimization algorithm to minimize the error. The proposed procedure is applied to a co-cured Single Leg Bending (SLB) joint under mode I and mode II-dominant modes and the cohesive parameters are determined. From these parameters, the mixed-mode cohesive zone model is constructed and applied to the simulation of the co-cured SLB joint under varying mode-mixities. Simulation results are compared with the experimental results. It is shown that the failure behaviour of the SLB joint is well-described by using the mixed-mode cohesive zone model with the determined parameters. [Copyright &y& Elsevier]

Abstract: We developed a new rigorous mathematical model of the first order and proposed a methodology for determination of kinetic parameters of organic particle adhesion at electrified interface. Mathematical model of consecutive multi-step processes contains analytical solutions of the product amount and the rate of product formation, which correspond to an electrical equivalent of charge and current transients, respectively. Synthetic data simulating amperometric measurement of particle adhesion are offered to illustrate the proposed methodology. Methodology refers to a unique experiment, which is analyzed according to the mathematical model of the two- and the three-step processes in order to discuss the validity and pertinence of both model variants. The methodology shows the principle how to sequentially separate individual components of the two- and the three-step processes using both data sets (current and charge transients), in order to accurately determine the corresponding kinetic parameters. Transition from the model of the two- to the three-step processes is examined and the criteria for their differentiation are pointed out. [Copyright &y& Elsevier]

Photoluminescence measurements on hydrogenated amorphous silicon/crystalline silicon (a-Si : H/c-Si) heterostructures have been used for two aspects of their characterization: the monitoring of the crystalline silicon wafers and of their interface properties after different steps of solar cell processing and the tracking of interface properties on purpose-built symmetrical structures with different amorphous silicon overlayers. The difference in the quasi-Fermi level splittings in these symmetrical structures, determined both experimentally and by numerical modelling, suggests an energetic position of the interface defect distribution with a peak at around 0.7-0.8 eV above the c-Si valence band edge. Numerical modelling is also applied to the structures after solar cell processing steps and consistently tracks the variation in quasi-Fermi level splitting, i.e. excess carrier densities, in the c-Si layer. The agreement in the experimental and simulated open-circuit voltages for the final cell adds confidence to the interface defect parameters determined. [ABSTRACT FROM AUTHOR]

Abstract: Numerical modeling of linear friction welding (LFW) of TC4 titanium alloy was conducted using ABAQUS/Explicit with a 2D model. The coupled thermo-mechanical analysis was performed with the Johnson–Cook material model. The effects of processing parameters on the temperature evolution and axial shortening of LFW joints were numerically investigated. It is shown that the temperature at the interface can first increase quickly to about 1000°C within 1s, then increases slowly, and finally tends to become uniform across the interface under certain processing conditions. The temperature gradient across the joint from the interface is very high during the friction process. Consequently, significant axial shortening and fast formation of flash start to happen as the interface temperature becomes more uniform. During cooling, the interface temperature decreases steeply at a rate of several hundred degrees per second because of the fast heat conduction to the cold end of the specimen. The temperature distribution appears to be uniform in the joint after about 30s. At a higher oscillation frequency, the interface temperature rises more quickly and the axial dimension shortens more and at a faster rate. The same phenomena are observed for the amplitude and friction pressure. The effects of these three factors can be integrated into one parameter of heat input. The axial shortening increases with increasing heat input almost linearly as the heat input exceeds a critical value. [Copyright &y& Elsevier]

Abstract: This paper describes the development of an efficient numerical model, namely scaled boundary finite-element method (SBFEM) for linear waves interaction with cylindrical structures of arbitrary shapes. The two-dimensional Helmholtz equation is firstly weakened in the circumferential direction, so that the governing partial differential equation is transformed to an ordinary matrix differential equation in radial direction, and is solved fully analytically. As a key element, a virtual porous circular cylinder surrounding the cylindrical structures is introduced so that the entire computational domain is partitioned along the virtual cylinder into an unbounded and several bounded sub-domains with common interfaces. The principle innovation is that, the present SBFEM model chooses Hankel function as a base solution for the unbounded sub-domain, while a power series is used for the internal bounded sub-domains. The approach discretises only the common interfaces of the sub-domains with surface finite-elements, and fewer elements are required to obtain very accurate results. Numerical simulations show that the new SBFEM model offers a considerable improvement by far in its numerical performance, as well as in the range of physical phenomena that is capable of simulating. The wave forces and run-ups are presented for a single and multiple cylindrical structures of different cross sectional shapes. Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined. [Copyright &y& Elsevier]

Abstract: Metastable pit growth, a critical stage of pitting corrosion, has an important role in understanding pitting corrosion which involves a series of complicated interface electrochemical reactions. In this paper, a computational model which simulates metastable pit growth and its transition to stable growth is developed. The model based on the cellular automata approach contains several evolution rules that govern electrochemical reactions, solution reactions and diffusion. The results of simulated metastable pit growth kinetics are compared with the experiment data quoted from the literature. The influence of different factors including the diffusion of cations, the extent of the rupture of protective film, the pit radius and the existence of salt film on growth transition is analyzed. In order to improve the simulation efficiency, the Block algorithm is introduced which can accelerate the simulation of reaction–diffusion system. The mechanism of transition to passivity is discussed through comparing the simulation results with experimental data. [Copyright &y& Elsevier]

Abstract: Recent experiments have shown failure in flip chip micro solder joints induced by electromigration. This paper proposes a three-dimensional computational model to simulate the evolution of micro and sub-micro scale solder joints due to electromigration induced diffusion. The evolving morphology of the solder joint related with multiple mechanisms causes a computational challenge. This is addressed by employing a diffuse interface model with multiple concentrations. To efficiently resolve complications, a semi-implicit Fourier spectral scheme and a biconjugate-gradient method are adopted. Results have demonstrated rich dynamics and solder breakage at the interface on the cathode side. Furthermore, the effect of the designed interface region on the reliability of solder joints has been investigated with the developed model. [Copyright &y& Elsevier]

Abstract: We present a new method for tracking an interface immersed in a given velocity field which is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian–Eulerian (ALE) framework. The new method has been constructed with two goals in mind: (i) to be able to accurately follow the interface; and (ii) to automatically achieve a good distribution of the grid points along the interface. In order to achieve these goals, information from a pure Lagrangian approach is combined with information from an ALE approach. Our implementation relies on the solution of several pure convection problems along the interface in order to obtain the relevant information. The new method offers flexibility in terms of how an “optimal” point distribution should be defined. We have proposed several model problems, each with a prescribed time-dependent velocity field and starting with a prescribed interface; these problems should be useful in order to validate the accuracy of interface-tracking algorithms, e.g., as part of an ALE solver for free surface flows. We have been able to verify first, second, and third order temporal accuracy for the new method by solving these two-dimensional model problems. [Copyright &y& Elsevier]

Abstract: An expression for anisotropic interfacial energy of hexagonal close-packed metals has been formulated which is able to reproduce published data obtained using the modified embedded-atom method, covering the variation in interface energy as a function of orientation for a number of metals. The coefficients associated with the expression can be determined fully by measured or calculated interfacial energies of just three independent crystal planes. Three-dimensional phase-field model simulations using this representation of interfacial energy have been found to yield convincing crystal morphologies. The apparent rate of crystal growth as a function of orientation in the phase-field simulation agrees with predictions made by surface energy theory. [Copyright &y& Elsevier]

The formation of an air gap at the mould–metal interface in vertical continuous casting has long been known to have a detrimental effect on the efficiency of the process, and has therefore attracted attempts at mathematical modelling. While almost all current efforts consist of complex three-dimensional numerical simulations of the phenomenon, this paper considers instead an asymptotic model that captures the essential characteristics. The model is thermomechanical and is derived for a geometry, where the generalized plane strain approximation is appropriate. Although two-way coupling between the thermal and mechanical problems is accounted for, it is found that the problems decouple at leading order anyway, and that the thickness of the air gap does not depend on the constitutive relation used for describing the inelastic strains. Furthermore, a criterion for the onset of air-gap formation is derived in terms of the process operating parameters. Mathematically, we obtain a moving boundary problem for a parabolic partial differential equation with a degenerate initial condition and a non-standard Neumann-type boundary condition. Sample computations are performed using parameters for the continuous casting of the copper, and the results, qualitative trends and possible extensions are discussed. [ABSTRACT FROM AUTHOR]

This paper employs the phase-field method to study the splitting behaviour of a single coherent particle under an applied uniaxial stress. It finds that the splitting behaviour is greatly influenced by the initial shape of precipitates, the bulk free energy condition, the degree of supersaturation and the ratio of the interfacial energy to the elastic strain energy, etc. The simulated results demonstrate that the aspect ratio of the particle determines whether the splitting can occur and how many split plates can be obtained. The splitting of particle is sensitive to the interfacial energy, i.e. the splitting becomes more and more difficult with increasing the ratio of the interfacial energy to the elastic strain energy. And increasing the magnitude of the applied stress is favourable to the splitting. The splitting process is also explained from the point of view of the corresponding diffusion potential. [ABSTRACT FROM AUTHOR]

Composition gradients in miscible liquids can create volume forces resulting in various interfacial phenomena. Experimental observations of these phenomena are related to some difficulties because they are transient, sufficiently weak and can be hidden by gravity driven flows. As a consequence, the question about their existence and about adequate mathematical models is not yet completely elucidated. In this work we present some experimental evidences of interfacial phenomena in miscible liquids and numerical simulations of miscible drops and diffuse interfaces. [ABSTRACT FROM AUTHOR]

Using cellular automata dynamics, a discrete technique to study stochastic growth equations (SGE) is presented. By analogy to deposition models in which the growth rule depends on height differences between neighbours, we introduce an interface growth process with synchronous updating in which the transition probability for a given site i to receive a particle at a time t is defined as pi(t) = rexp [kGi(t)]. r and k are the model parameters and Gi(t) is a function which depends on the height of the site i and its neighbours, and its functional form is specified through discretization of the deterministic part of the growth equation associated with a given deposition process. To validate the method, we study its application to two linear SGE--the Edwards-Wilkinson equation and the Mullins-Herring equation, and a nonlinear one--the Kardar-Parisi-Zhang equation. The statistical analysis of the height distributions in simulations recovered the correct values for roughening exponents, confirming that the processes generated are indeed in the universality classes of the original growth equations. We also observed a crossover from random deposition to the correlated regime when the parameter k is varied in each case studied. [ABSTRACT FROM AUTHOR]

Plasma etching of thin films is essential for microelectronics manufacturing. With current feature sizes of 35 nm in production and processes for smaller devices being developed, the sidewall roughness is within the order of magnitude of the gate length of the device, and therefore significantly impacts the devices' performance. In this paper we review the modelling of the surface profile evolution in plasma etching. Both two-dimensional (2D) and three-dimensional (3D) models have been developed using a number of representations and solution algorithms. String algorithms and the method of characteristics use a segmented string which is incrementally advanced. Level-set representations describe the profile evolution as a moving interface in response to a velocity field. Cellular representations in which the area or volume domain is divided into discrete cells have been used with flux and surface kinetics based on Monte Carlo calculations. We discuss our work in the modelling of profile evolution with surface roughening using a 3D cellular Monte Carlo simulation. The formation of perpendicular and parallel ripple formation on planar surfaces as a function of ion bombardment incidence angle and the transformation from perpendicular to parallel as etching progresses has been modelled. The smoothing and/or roughening of resist masks has been demonstrated along with the pattern transfer of roughness into the underlying layers being etched. [ABSTRACT FROM AUTHOR]

A novel method is proposed to simulate Rayleigh[?]Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh[?]Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh[?]Taylor instabilities of turbulent flows. [ABSTRACT FROM AUTHOR]

A mathematical model is developed to investigate the dynamics of vapor bubble growth in a thin liquid film, movement of the interface between two fluids and the surface heat transfer characteristics. The model takes into account the effects of phase change between the vapor and liquid, gravity, surface tension and viscosity. The details of the multiphase now and heat transfer are discussed for two cases: (1) when a water micro-droplet impacts a thin liquid film with a vapor bubble growing and (2) when the vapor bubble grows and merges with the vapor layer above the liquid film without the droplet impacting. The development trend of the interface between the vapor and liquid is coincident qualitatively with the available literature, mostly at the first stage. We also provide an important method to better understand the mechanism of nucleate spray cooling. [ABSTRACT FROM AUTHOR]