A velocity decomposition approach for moving interfaces in viscous fluids

We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier–Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a “Stokes” part and a “regular” part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier–Stokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional time-stepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost.     

Face offsetting: A unified approach for explicit moving interfaces

Dynamic moving interfaces are central to many scientific, engineering, and graphics applications. In this paper, we introduce a novel method for moving surface meshes, called the face offsetting method, based on a generalized Huygens’ principle. Our method operates directly on a Lagrangian surface mesh, without requiring an Eulerian volume mesh. Unlike traditional Lagrangian methods, which move each vertex directly along an approximate normal or user-specified direction, our method propagates faces and then reconstructs vertices through an eigenvalue analysis locally at each vertex to resolve normal and tangential motion of the interface simultaneously. The method also includes techniques for ensuring the integrity of the surface as it evolves. Face offsetting provides a unified framework for various dynamic interface problems and delivers accurate physical solutions even in the presence of singularities and large curvatures. We present the theoretical foundation of our method, and also demonstrate its accuracy, efficiency, and flexibility for a number of benchmark problems and a real-world application.     

A covariance fitting approach for correlated acoustic source mapping

Microphone arrays are commonly used for noise source localization and power estimation in aeroacoustic measurements. The delay-and-sum (DAS) beamformer, which is the most widely used beamforming algorithm in practice, suffers from low resolution and high sidelobe level problems. Therefore, deconvolution approaches, such as the deconvolution approach for the mapping of acoustic sources (DAMAS), are often used for extracting the actual source powers from the contaminated DAS results. However, most deconvolution approaches assume that the sources are uncorrelated. Although deconvolution algorithms that can deal with correlated sources, such as DAMAS for correlated sources, do exist, these algorithms are computationally impractical even for small scanning grid sizes. This paper presents a covariance fitting approach for the mapping of acoustic correlated sources (MACS), which can work with uncorrelated, partially correlated or even coherent sources with a reasonably low computational complexity. MACS minimizes a quadratic cost function in a cyclic manner by making use of convex optimization and sparsity, and is guaranteed to converge at least locally. Simulations and experimental data acquired at the University of Florida Aeroacoustic Flow Facility with a 63-element logarithmic spiral microphone array in the absence of flow are used to demonstrate the performance of MACS.     

Aberrationless approach for diffraction of pulses at linear interfaces

The diffraction of temporally Gaussian shaped light pulses is theoretically studied by means of the aberrationless approach, a theoretical technique previously used for spatially bounded beams of unlimited time extension and which is extended here to time domain. We consider linear interfaces, that is, we assume that the spectral components of the vector field in the diffracted pulse are linearly related with the spectral components of the vector field in the incident pulse. In our analysis pulse deformations are described in terms of the following effects: time delay, focal displacement, waist modification and change in propagation velocity. Expressions for these effects, the time domain analogues of those already reported in the spatial domain, are given and compared with those obtained using the stationary phase method. The theory is used to calculate deformations of a short light pulse at a flat interface near conditions of total internal reflection.     

Defects at surfaces and interfaces — A scattering theoretical approach

A theory for isolated defects at surfaces and interfaces of semiinfinite solids is presented and applied to vacancies at or near surfaces. Vacancy-induced changes in the surface electronic structure of a simple cubic s-band model are discussed in detail and are found to converge very slowly to corresponding bulk vacancy results when the defect is moved into the solid. Results for Ga and As vacancies at GaAs surfaces are discussed in connection with recent experimental data.     

A model for bimetallic interfaces

We have developed a theoretical model by considering the charge rearrangement in the region of a bimetallic interface. By using the density functional formalism we have calculated variationally interfacial energies due to pairs of semi-infinite jellia in contact. We infer that the electronic interaction has an important role in the bimetallic adhesion.     

Metal-ferroelectric-metal current-voltage characteristics: A charge flow balance through interfaces approach

A model for current voltage characteristics of a thin film metal-ferroelectric-metalstructure is constructed by combining the electrostatics of a polarized ferroelectric filmwith the balanced flow of charge through its interfaces. Using a set of fittingparameters, good agreement with several sets of experimental data is obtained fordifferent system temperatures. The influence of model parameters on the current-voltagecharacteristic is discussed. Best fit values of some of these parameters correlate wellwith ab initio calculations in the literature, supporting the idea of low dielectricpermittivity of the interface transition layers in the ferroelectric.     

Device relevant organic films and interfaces: A surface science approach

Here the morphology, molecular orientation and electronic structure of in situ prepared para-sexiphenyl (6P) and α-sexithiophene (6T) films studied with atomic force microscopy, near edge X-ray absorption fine structure spectroscopy and valence band photoemission are presented. Attention is given to the differences between different organic crystallite orientations and the pitfalls in the interpretation of area averaging surface sensitive techniques that can arise from inhomogeneities in the films, which commonly occur even on single crystal inorganic substrates. The growth of organic-organic heterostructures is then considered for sexithiophene films grown on homogeneous upright (6P(0 0 1)) and lying (6P(2 0 3)) crystalline films. In both cases, the orientation of the substrate molecules is imposed on the molecules of the second species and thick films of upright-on-upright or lying-on-lying could be produced. The organic substrates are thus shown to be excellent templates for further organic film growth that do not require the stringent UHV conditions of inorganic templates.     

Interfacial potential approach for Ag/ZnO （0001） interfaces

Systematic approaches are presented to extract the interfacial potentials from the ab initio adhesive energy of the interface system by using the Chen–M ¨obius inversion method. We focus on the interface structure of the metal（111）/Zn O（0001）in this work. The interfacial potentials of Ag–Zn and Ag–O are obtained. These potentials can be used to solve some problems about Ag/Zn O interfacial structure. Three metastable interfacial structures are investigated in order to check these potentials. Using the interfacial potentials we study the procedure of interface fracture in the Ag/Zn O（0001） interface and discuss the change of the energy, stress, and atomic structures in tensile process. The result indicates that the exact misfit dislocation reduces the total energy and softens the fracture process. Meanwhile, the formation and mobility of the vacancy near the interface are observed.     

A direct approach to generalised multiple mapping conditioning for selected turbulent diffusion flame cases

This work presents a direct and transparent interpretation of two concepts for modelling turbulent combustion: generalised Multiple Mapping Conditioning (MMC) and sparse-Lagrangian Large Eddy Simulation (LES). The MMC approach is presented as a hybrid between the Probability Density Function (PDF) method and approaches based on conditioning (e.g. Conditional Moment Closure, flamelet, etc.). The sparse-Lagrangian approach, which allows for a dramatic reduction of computational cost, is viewed as an alternative interpretation of the Filtered Density Function (FDF) methods. This work presents simulations of several turbulent diffusion flame cases and discusses the universality of the localness parameter between these cases and the universality of sparse-Lagrangian FDF methods with MMC.     

Multidimensional chemistry coordinate mapping approach for combustion modelling with finite-rate chemistry

A multidimensional chemistry coordinate mapping (CCM) approach is presented for efficient integration of chemical kinetics in numerical simulations of turbulent reactive flows. In CCM the flow transport is integrated in the computational cells in physical space, whereas the integration chemical reactions are carried out in a phase space made up of a few principal variables. Each cell in the phase space corresponds to several computational cells in the physical space, resulting in a speedup of the numerical integration. In reactive flows with small hydrocarbon fuels two principal variables have been shown to be satisfactory to construct the phase space. The two principal variables are the temperature (T) and the specific element mass ratio of the H atom (J _H). A third principal variable, σ=?J _H·?J _H, which is related to the dissipation rate of J _H, is required to construct the phase space for combustion processes with an initially non-premixed mixture. For complex higher hydrocarbon fuels, e.g. n-heptane, care has to be taken in selecting the phase space in order to model the low-temperature chemistry and ignition process. In this article, a multidimensional CCM algorithm is described for a systematic selection of the principal variables. The method is evaluated by simulating a laminar partially remixed pre-vaporised n-heptane jet ignition process. The CCM approach is then extended to simulate n-heptane spray combustion by coupling the CCM and Reynolds averaged Navier–Stokes (RANS) code. It is shown that the computational time for the integration of chemical reactions can be reduced to only 3–7%, while the result from the CCM method is identical to that of direct integration of the chemistry in the computational cells.     

A nonconforming combination for solving elliptic problems with interfaces

Nonconforming combinations are provided for solving interface problems of elliptic equations. In these approaches, the Ritz-Galerkin method with particular solutions is used for the part of a solution domain where there are interface singular points; and the conventional finite element method is used for the rest of the solution domain. In addition, admissible functions chosen are constrained to be continuous only at the element nodes on the common boundary of the subdomains. Error bounds are derived in the Sobolev norms, and numerical experiments are given for solving a model interface problem of the equation, −Δu + U = 0. Moreover, a significant coupling relation, L + 1 = O(|ln h|), is found for interface problems by using the nonconforming combinations, where (L + 1) is the total number of particular solutions used in the Ritz-Galerkin method, and h is the maximal boundary length of triangular elements in the finite element method.     

A novel approach for the quantitative kinetic study of reactions at solid/liquid interfaces in the presence of power ultrasound

A novel cell and procedure is described which permits the quantitative mechanistic study of ultrasonically enhanced reactions which occur at solid/liquid interfaces. A model of a controlled and calculable time-average rate of mass transport to and from the interface is used in order to compare experimental results with theoretical predictions based on mechanistic reaction schemes. In this way concentrations of mechanistically significant species near the interface can be related to those in bulk solution and hence the sonochemical effects of ultrasound dissected from those arising purely from mass transport. The effect of ultrasound is demonstrated for the reaction dissolution of p-chloranil in the presence of aqueous base and for the reaction of the same substrate with the aromatic amine, N,N-dimethyl-phenylenediamine, both systems which have been studied previously in the absence of ultrasound. Complementary atomic force microscopy images are also reported.     

Efficient approach to metal/metal oxide interfaces within variable charge model

A modified procedure of calculating the energy of metal/oxide interfaces and surfaces in the frame of the CTIP + EAM model (charge transfer ionic potential + embedded atom method) has been developed. According to the proposed approach, local charges and positions of atoms are determined only in a restricted zone surrounding the interface, while in the remaining region they are fixed. As a result, the number of variables undergoes a significant reduction, which enables carrying out efficient calculations for metal/oxide systems. The modified procedure has been applied to studying the relaxation of the α-Al₂O₃ surface. Using three different forms of the CTIP + EAM model present in literature, it has been shown that the correctness of the obtained results is conditioned by the appropriate relation between the CTIP and EAM components. Finally, the relaxation of the Ni/α-Al₂O₃ interface has been examined.     

Effective Hamiltonian for fluid interfaces

Based on a microscopic theory of inhomogeneous fluids we derive a non-Gaussian and nonlocal effetive Hamiltonian of a liquid-vapor interface. A partial resummation of a gradient expansion yields terms proportional to the area as well as to the Gaussian and the square of the mean curvature of the interface. For van der Waals fluids the gradient expansion breaks down and leads to a singularity in the momentum dependent surface tension. The nonlocal Hamiltonian and various approximations thereof are compared quantitatively.