Phase-field formulation for quantitative modeling of alloy solidification

A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than previous formulations and permits one to eliminate nonequilibrium effects at the interface. Dendrite growth simulations with vanishing solid diffusivity show that both the interface evolution and the solute profile in the solid are accurately modeled by this approach.     

Theoretical analysis of the characteristic impedance in metal-insulator-metal plasmonic transmission lines

We propose a closed form formulation for the impedance of the metal-insulator-metal (MIM) plasmonic transmission lines by solving the Maxwell's equations. We provide approximations for thin and thick insulator layers sandwiched between metallic layers. In the case of very thin dielectric layer, the surface waves on both interfaces are strongly coupled resulting in an almost linear dependence of the impedance of the plasmonic transmission line on the thickness of the insulator layer. On the other hand, for very thick insulator layer, the impedance does not vary with the insulator layer thickness due to the weak-coupling/decoupling of the surface waves on each metal-insulator interface. We demonstrate the effectiveness of our proposed formulation using two test scenarios, namely, almost zero reflection in T-junction and reflection from line discontinuity in the design of Bragg reflectors, where we compare our formulation against previously published results.     

Auxiliary field quantum Monte-Carlo simulation of interacting electrons in quantum dots

Accurate auxiliary field quantum Monte-Carlo (AFQMC) simulations of interacting electrons in quantum dots are reported. Two different formulations of this approach are presented both of which have been designed specifically for application to quantum dots. A deflation technique for calculation of anti-symmetrized traces is introduced. The auxiliary field is sampled with a hybrid algorithm and the artificial dynamics needed for use with the present formulation of AFQMC is described. The constrained path approximation is used to control the sign problem. Results for the ground state energy of two spin-polarised, interacting electrons are presented and are found to agree well with exact diagonalization results for a wide range of screening lengths. The sign problem does not appear in the regime of small screening length.     

Comparison of RANS/CMC modeling of Flame D with conventional and with Presumed Mapping Function statistics

Numerical simulations of Sandia Flame D are presented using Reynolds-averaged formulations plus a two equation turbulence model for the flow and mixing fields and a first order Conditional Moment Closure for the flame model. The distributions of probability and Conditional Scalar Dissipation (CSD) in mixture fraction space are modeled first using a Beta PDF (Probability Distribution Function) plus a theoretical model for CSD and then using the consistent, Presumed Mapping Function-based formulation of Mortensen for both PDF and CSD, in both two and three stream mixing modes. It is shown that there is an improvement in predictions compared with experiment when using the consistent models.     

Insulator—insulator—metal plasmonic waveguide for parasitic scattering suppression in plasmonic optics

We have shown using rigorous electromagnetic simulations that a planar structure consisting of two isotropic dielectric layers can be used to reduce parasitic scattering in plasmonic elements by an order-of-magnitude (to 1–3%). The proposed approach can be used for designing various plasmonic elements such as lenses, Bragg reflectors and plasmonic crystals.     

Free vibration analysis of multi-layer graphene nanoribbons incorporating interlayer shear effect via molecular dynamics simulations and nonlocal elasticity

Free vibration of cantilever multi-layer graphene nanoribbons (MLGNRs) with interlayer shear effect is investigated using molecular dynamics simulations (MD) and nonlocal elasticity. Because of similarity of MLGNRs to sandwich structures, sandwich formulations are expressed in the nonlocal form. By comparing the first two frequencies of MLGNRs with various layers and lengths obtained using MD simulations with those of the nonlocal sandwich formulation; the nonlocal parameter is calibrated to match the results of two methods. The results reveal that the calibrated nonlocal parameter for predicting the second frequencies is dependent on the number of MLGNR layers, and it increases by increasing the number of layers.     

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.     

The lattice Boltzmann advection-diffusion model revisited

Advection-diffusion processes can be simulated by the Lattice Boltzmann method. Two formulations have been proposed in the literature. We show that they are not fully correct (only first order accurate). A new formulation is proposed, which is shown to produce better results, both from the point of view of the Chapman-Enskog expansion or when comparing simulations with an exact time-dependent solution of the advection-diffusion equation.     

Analytic formulation and numerical implementation of an acoustic pressure gradient prediction

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams–Hawkings (FW–H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.     

On exact and approximated formulations for scaling-mode shapes in operational modal analysis by mass and stiffness change

When operational modal analysis (OMA) is used to estimate modal parameters, mode shapes cannot be mass normalized. In the past few years, some equations have been proposed to scale mode shapes using the mass-change method, which consists of repeating modal testing after changing the mass at different points of the structure where the mode shapes are known. In this paper, the structural-dynamic-modification theory is used to derive a set of equations, from which all the existing formulations can be derived. It is shown that the known equations can be divided into two types, the exact and the approximated equations, where the former type does in fact fulfill the equations derived from the theory of structural modification, whereas the remaining equations do not, mainly because the change of the mode shapes of the modified structure is not properly taken into account. By simulations, the paper illustrates the large difference in accuracy between the approximate and the exact formulations. The paper provides two new exact formulations for the scaling factors, one for the non-modified structure and – for the first time in the literature – one for the modified structure. The simulations indicate the influence of errors from the measured natural frequencies and mode shapes on the estimation of the scaling factors using the two exact formulations from the literature and the new exact formulation proposed in this paper. In addition, the paper illustrates statistics of the errors on mode-shape scaling. All simulations were carried out using a plate with closely spaced modes.     

Forward speed effects in the equations of ship motion

The explicit speed dependency of the coefficients in the linear equations of ship motion is determined from an energy formulation of the problem as opposed to the usual strip-theory formulation. For a completely symmetrical (longitudinal and lateral) ship, the cross-coupled damping coefficients resulting from the energy approach are shown to satisfy the Timman and Newman symmetry theorem identically. For ships possessing lateral symmetry only, a different form of symmetry among the cross-coupled damping coefficient is found to exist. The results of the energy approach are found to agree quite well with the results of three strip-theory formulations regarding the speed dependency of the coefficients in the heave and pitch equations.     

Reconfigurable computing for Monte Carlo simulations: Results and prospects of the Janus project

We describe Janus, a massively parallel FPGA-based computer optimized for the simulation of spin glasses, theoretical models for the behavior of glassy materials. FPGAs (as compared to GPUs or many-core processors) provide a complementary approach to massively parallel computing. In particular, our model problem is formulated in terms of binary variables, and floating-point operations can be (almost) completely avoided. The FPGA architecture allows us to run many independent threads with almost no latencies in memory access, thus updating up to 1024 spins per cycle. We describe Janus in detail and we summarize the physics results obtained in four years of operation of this machine; we discuss two types of physics applications: long simulations on very large systems (which try to mimic and provide understanding about the experimental non-equilibrium dynamics), and low-temperature equilibrium simulations using an artificial parallel tempering dynamics. The time scale of our non-equilibrium simulations spans eleven orders of magnitude (from picoseconds to a tenth of a second). On the other hand, our equilibrium simulations are unprecedented both because of the low temperatures reached and for the large systems that we have brought to equilibrium. A finite-time scaling ansatz emerges from the detailed comparison of the two sets of simulations. Janus has made it possible to perform spin-glass simulations that would take several decades on more conventional architectures. The paper ends with an assessment of the potential of possible future versions of the Janus architecture, based on state-of-the-art technology.     

Efficient simulation of non-linear effects in 2D optical nanostructures to TM waves

We develop a theory to study stationary TM-type waves propagating in a nanostructured layer of 2D non-linear optical metamaterial or plasmonic device. It is assumed that the layer is inhomogeneous and contains non-linear isotropic elemental materials with non-linearity and loss mechanisms, including both linear and non-linear losses. While modeling of the non-linear propagation of the TE-type scalar waves is straightforward, the TM-type waves within the standard E-field formulations of non-linear optics cannot be treated in a purely scalar H-field context since an implicit equation for the non-linear dielectric functions should be resolved otherwise. A new formulation, which is built on the solution of the implicit equation for the non-linear dielectric function, is proposed. We use a general cubic non-linearity to illustrate all of the important features of the proposed approach. The general solution for scalar H-field waves is validated versus our previously tested particular cases, and important differences are shown between those cases and the general solution. These details, for example, include the link between linear and non-linear loss mechanisms, and connection between the linear and non-linear dielectric functions. The proposed approach is used for modeling a non-linear focusing device with optically controlled isotropic Kerr-type non-linearity; the simulation results prove the predicted functioning of the device.     

Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions

Large-amplitude (geometrically nonlinear) forced vibrations of circular cylindrical shells with different boundary conditions are investigated. The Sanders-Koiter nonlinear shell theory, which includes in-plane inertia, is used to calculate the elastic strain energy. The shell displacements (longitudinal, circumferential and radial) are expanded by means of a double mixed series: harmonic functions for the circumferential variable and three different formulations for the longitudinal variable; these three different formulations are: (a) Chebyshev orthogonal polynomials, (b) power polynomials, and (c) trigonometric functions. The same formulation is applied to study different boundary conditions; results are presented for simply supported and clamped shells. The analysis is performed in two steps: first a liner analysis is performed to identify natural modes, which are then used in the nonlinear analysis as generalized coordinates. The Lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations. Different expansions involving from 14 to 34 generalized coordinates, associated with natural modes of both simply supported and clamped-clamped shells, are used to study the convergence of the solution. The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis. Numerical responses obtained in the spectral neighborhood of the lowest natural frequency are compared with results available in literature.     

Scan-based near-field acoustical holography and partial field decomposition in the presence of noise and source level variation

Practical holography measurements of composite sources are usually performed using a multireference cross-spectral approach, and the measured sound field must be decomposed into spatially coherent partial fields before holographic projection. The formulations by which the latter approach have been implemented have not taken explicit account of the effect of additive noise on the reference signals and so have strictly been limited to the case in which noise superimposed on the reference signals is negligible. Further, when the sound field is measured by scanning a subarray over a number of patches in sequence, the decomposed partial fields can suffer from corruption in the form of a spatially distributed error resulting from source level variation from scan-to-scan. In the present work, the effects of both noise included in the reference signals, and source level variation during a scan-based measurement, on partial field decomposition are described, and an integrated procedure for simultaneously suppressing the two effects is provided. Also, the relative performance of two partial field decomposition formulations is compared, and a strategy for obtaining the best results is described. The proposed procedure has been verified by using numerical simulations and has been applied to holographic measurements of a subsonic jet.     

Locally enhanced light–matter interaction of MoS2 monolayers at density-controllable nanogrooves of template-stripped Ag films

Transition metal dichalcogenide (TMD) monolayers, such as MoS_2, possess a direct optical bandgap are useful for emerging ultrathin optoelectronics in the visible light range, whereas their thin thickness limits light absorption and emission properties. To address this drawback, one promising approach is to hybridize plasmonic nanostructures with monolayer TMDs to utilize local field enhancement effects owing to localized surface plasmon resonance (LSPR). Herein, we propose a strong enhancement of the local light–matter interaction in MoS₂ monolayers on naturally generated nanoscale grooves. The nanogrooves are formed at grain boundaries (GBs) of template-stripped metal film substrates that are fabricated by mechanically stripping Ag films deposited on an ultra-flat Si substrate, wherein the nanogroove densities are systematically modulated by the Ag film thickness. We observe an effective photoluminescence enhancement factor of 758 and a Raman spectroscopy intensity enhancement of approximately 5 times in MoS₂ on the subwavelength-scale nanogrooves, compared with that on grain planes, which is attributed to a strong local field enhancement of the LSPR effect. Moreover, this plasmonic enhancement effect is elucidated by dark-field scattering spectroscopy and optical simulations. Our results can facilitate the utilization of density-controllable plasmonic nanogrooves synthesized without nanopatterning techniques for plasmonic hybrids on 2D semiconductors.     

Polarization mapping of nanoparticle plasmonic coupling

We propose the use of polarization mapping as a tool to better separate the effects of plasmonic coupling from the local refractive index for molecular imaging and biosensing using gold nanoparticles. Polarization mapping allows identification of the orthogonal excitation mode when the particle dimer orientation is unknown, as may be the case when using plasmonic nanoparticles for cell labeling. This information can be used to sense relative changes in the dielectric environment, or for absolute dielectric sensing with additional a priori interparticle distance information. First, the theoretical scattering by nanoparticle pairs is modeled under parallel and orthogonal polarization orientations and increasing interparticle separation. Second, polarization mapping of substrate bound nanoparticles using dark-field microspectroscopy is investigated as a method to isolate the individual plasmonic coupling modes associated with a pair of nanoparticles without reorientation of the sample. The results of this study provide useful insight toward potential avenues for monitoring distances using plasmonic nanoparticles and sensing the local refractive index using nanoparticle pairs when the pair orientation is not known, as may be the case when using nanoparticles for cell receptor labeling.     

MC-Smooth: A mass-conserving,smooth vorticity–velocity formulation for multi-dimensional flows

A novel vorticity–velocity formulation of the Navier–Stokes equations – the Mass-Conserving, Smooth (MC-Smooth) vorticity–velocity formulation – is developed in this work. The governing equations of the MC-Smooth formulation include a new second-order Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and N_spec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity–velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity–velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benefits, other important features of the MC-Smooth formulation include: (1) it does not require the use of a staggered grid, and (2) it does not require excessive grid refinement to ensure mass conservation. The MC-Smooth formulation is a computationally attractive approach that can effectively extend the applicability of the vorticity–velocity formulation.     

加装印刷电路板的圆孔阵矩形机壳屏蔽效能

 为评估矩形金属机壳抗外部电磁干扰的能力,建立加装印刷电路板(PCB)有圆孔孔阵矩形机壳的波导等效电路模型,导出其电场屏蔽效能的简洁表达式,提出一种简单高效的新方法,对于没有加装印刷电路板的机壳,该方法的简化结果与现有文献结果完全一致;对于加装PCB的机壳屏蔽效能,该方法计算结果与CST仿真结果良好吻合。结果表明:电场极化方向与孔阵长度方向平行,同其与孔阵长度方向垂直比较,前者屏蔽效能显著优于后者;所考虑的频率范围内,加装PCB可以显著提高机壳的屏蔽效能;正交排列孔阵的屏蔽效能优于交错排列孔阵的屏蔽效能;保持孔阵中孔数目不变,孔间距越大,屏蔽效能越高。     

A parallel solution – adaptive method for three-dimensional turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed and applied to the prediction of steady turbulent non-premixed compressible combusting flows in three space dimensions. The parallel solution-adaptive algorithm solves the system of partial-differential equations governing turbulent compressible flows of reactive thermally perfect gaseous mixtures using a fully coupled finite-volume formulation on body-fitted multi-block hexahedral meshes. The compressible formulation adopted herein can readily accommodate large density variations and thermo-acoustic phenomena. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. For calculations of near-wall turbulence, an automatic near-wall treatment readily accommodates situations during adaptive mesh refinement where the mesh resolution may not be sufficient for directly calculating near-wall turbulence using the low-Reynolds-number formulation. Numerical results for turbulent diffusion flames, including cold- and hot-flow predictions for a bluff-body burner, are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting fine-scale features of complex turbulent non-premixed flames.