Programming of 3D problems

A full multigrid/full approximation storage (FMG/FAS) method is developed along with a unified pressure-based algorithm to handle the complex fluid flow problems encompassing both compressible and incompressible regimes. Besides highlighting the key elements of the present algorithm on a curvilinear staggered grid system, several flow problems, ranging from incompressible to hypersonic speeds, are computed, in conjunction with an adaptive grid method, to demonstrate its computational capability. With wide variations in geometry, fluid physics, and grid distribution, speedup between the single- and multigrid procedures can be obtained. Because different pressure boundary conditions are needed for incompressible, subsonic, and supersonic inlet and outlet, the number of grid levels that can be effectively used by the present multigrid method appears flow dependent; the implications of this observation are discussed.

Finite element methdos for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity

A numerical modelling of SAM-APDs which takes into account the effects of the guard ring on the electric field profile is presented. Starting from the knowledge of the technological parameters and from a one-dimensional model, for which Poisson's and continuity equations have been treated, we calculate the gain, the dark current, and the cut-off frequency of the device, so that it is possible to deduce the limits of those parameters to avoid parasitic breakdowns at the centre of the diode, and to get structures with high gain-bandwidth products. A two-dimensional model based on numerical solution of Poisson's equation to study the electric field profile under the guard ring is developed. Optimal conditions for implantation are deduced to avoid breakdown at the edge of the junction curvature. The results given by this modelling are compared with the experimental results concerning SAM-APDs with guard ring, which have been fabricated by C.I.T. ALCATEL.

Multidimensional modelling for the carotid artery blood flow

We show the existence of a twisted electrostatic ion-cyclotron (ESIC) wave carrying orbital angular momentum (OAM) in a magnetized dusty plasma. For our purposes, we derive a 3D wave equation for the coupled ESIC and dust ion-acoustic (DIA) waves from the hydrodynamic equations that are composed of the continuity and momentum equations, together with Poisson's equation. The 3D wave equation reveals the formation of a braided or twisted ESIC wave structure carrying OAM. The braided or twisted ESIC wave structure can trap and transport plasma particles in magnetoplasmas, such as those in Saturn's F-ring and in the forthcoming magnetized dusty plasma experiments.

A multi-physics model is developed to predict the transient nonlinear behavior of electric-sensitive hydrogel membrane, based on a multi-phasic mixture theory. In the developed model involving chemo-electro-mechanics, the transient convection-diffusion equations for ionic concentrations incorporate the migration and diffusion terms; the Poisson equation is employed to compute the distribution of electric potential directly, and the transient hydrogel deformation is implemented easily by the continuity and momentum equations. To solve the present mathematical model consisting of transient nonlinear partial differential governing equations, a true meshfree, implicit numerical scheme is conducted for solution of convection-diffusion problem and hydrogel deformation, iteratively. Unlike the mesh-based methods, the employed meshless Hermite Cloud Method (HCM) uses a fixed reproducing kernel approximation for construction of the interpolation functions, and employs the point collocation technique for discretization of partial differential boundary values and initial value problems. The transient responds of electric-sensitive hydrogels, including the membrane deformation, ionic concentrations and electric potentials, interior and exterior the membranes are numerically simulated, and the parameters having important influence on the transient hydrogel deformation are also investigated.

Time-filtering particle simulations with ωpeΔt ⪢ 1

Summary form only given. Atmospheric pressure non-thermal plasmas are now being used for various applications such as pollution control, light sources, medical and waste. Here a self-consistent continuum model is presented for a narrow gap plane-parallel DC glow discharge. The set of governing equations consisting of continuity and momentum equations for positive ions, fast (emitted by the cathode) and slow electrons (generated by fast electron impact ionization) coupled with Poisson's equation is treated by the technique of matched asymptotic expansions (Nayfeh, 1973). This analytic procedure reduces the unnecessary computational effort associated with Monte-Carlo approach with acceptable accuracy. In addition it is more physically transparent. Explicit results are obtained in the asymptotic limit: pL/spl Gt/1, (/spl chi//spl delta/)/spl Lt/1, where p is the gas pressure, L is the gaplength, /spl chi/ is the normalised applied voltage, and /spl delta/=(r/sub D//L)/sup 2/ where r/sub D/ is the Debye radius. In the limit of large pL the electron energy relaxation length is much smaller than gap length and local field approximation is valid. The discharge space divides naturally into a cathode fall sheath, a quasineutral plasma region and an anode fall sheath. The length of each region is derived. The electric field and charge density distribution obtained for each region (in a (semi)-analytical form) is asymptotically matched to the adjoining one in the region of overlap. The effects of the gas pressure, gap length and applied voltage on the discharge properties are investigated. The cathode fall parameters predicted by the asymptotic model are in reasonable agreement with available experimental data (Novak et al., 1987). Work is underway to apply this method for the calculation of dielectric barrier discharge characteristics.

Much interest was shown towards the studies on nonlinear stability in the late sixties. Plasma instabilities play an important role in plasma dynamics. More attention has been given towards stability analysis after recognizing that they are one of the principal obstacles in the way of a successful resolution of the problem of controlled thermonuclear fusion. Nonlinearity and dispersion are the two important characteristics of plasma instabilities. Instabilities and nonlinearity are the two important and interrelated terms. In our present work, the continuity and momentum equations for both ions and electrons together with the Poisson equation are considered as cold plasma model. Then we have adopted the modified reductive perturbation technique (MRPT) from Demiray [1] to derive the higher order equation of the Nonlinear Schrödinger equation (NLSE). In this work, detailed mathematical expressions and calculations are done to investigate the changing character of the modulation of ion acoustic plasma wave through our derived equation. Thus we have extended the application of MRPT to derive the higher order equation. Both progressive wave solutions as well as steady state solutions are derived and they are plotted for different plasma parameters to observe dark/bright solitons. Interesting structures are found to exist for different plasma parameters.

PurposeThis paper sets out to present a fully explicit smoothed particle hydrodynamics (SPH) method to solve non‐Newtonian fluid flow problems.Design/methodology/approachThe governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework. A new treatment similar to that used in Eulerian formulations is applied to viscous terms, which facilitates the implementation of various inelastic non‐Newtonian models. This approach utilizes the exact forms of the shear strain rate tensor and its second principal invariant to calculate the shear stress tensor. Three constitutive laws including power‐law, Bingham‐plastic and Herschel‐Bulkley models are studied in this work. The imposition of the incompressibility is fulfilled using a penalty‐like formulation which creates a trade‐off between the pressure and density variations. Solid walls are simulated by the boundary particles whose positions are fixed but contribute to the field variables in the same way as the fluid particles in flow field.FindingsThe performance of the proposed algorithm is assessed by solving three test cases including a non‐Newtonian dam‐break problem, flow in an annular viscometer using the aforementioned models and a mud fluid flow on a sloping bed under an overlying water. The results obtained by the proposed SPH algorithm are in close agreement with the available experimental and/or numerical data.Research limitations/implicationsIn this work, only inelastic non‐Newtonian models are studied. This paper deals with 2D problems, although extension of the proposed scheme to 3D is straightforward.Practical implicationsThis study shows that various types of flow problems involving fluid‐solid and fluid‐fluid interfaces can be solved using the proposed SPH method.Originality/valueUsing the proposed numerical treatment of viscous terms, a unified and consistent approach was devised to study various non‐Newtonian flow models.

The flow behavior of turbulent wave boundary layers with weak currents was described using a numerical model. Horizontal velocities, shear stresses, turbulent eddy viscosities, and apparent roughnesses were described. The numerical model is based upon the fluid continuity and momentum equations in the vertical plane. The momentum equations retain the advection terms with vertical orbital velocity in contrast to previous numerical models. The horizontal velocities were calculated from the momentum equations, and the vertical orbital velocity distribution was obtained from the continuity equation. The Reynolds terms were modeled by a mixing length hypothesis. The model was compared with existing models for the wave friction factor by switching off the advection terms and produced similar answers to two existing models. Next, the model was applied to a wave-only flow case with the advection terms retained. The model reproduced the measured mass transport profile by van Doorn and Godefroy reasonably well. The model was then applied to wave-current flow cases with arbitrary intersection angles. The model results for 0°, 180°, and 90° agreed well with measurements by van Doorn and Godefroy and van der Stel and Visser, respectively. The model produced significant differences between the following and opposing current cases for the same wave condition. The model results suggest that the wave boundary layer flows for relatively strong waves and weak currents can be accurately described by taking account of the nonlinear advection terms by means of the vertical wave orbital velocity.

Summary form only given. In mercury-free high-intensity-discharge (HID) lamps, mercury is often replaced by ZnI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . This substitution, along with the use of conventional metal halides such as NaI and ScI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> add both complexity and potential variability to the system. For example, has been experimentally determined that the lamp operating voltage is dependent or can be controlled by varying the amount of Znl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . This in turn has implications on the design of lamp components. The composition of the plasma, and electrical and thermal properties of the lamp are strongly influenced by the dosage of Znl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> .In this talk we report on the results from a computational investigation of the plasma properties of HID lamps having different metal halide fillings. The lamp resembles a D4 having initial mixtures containing Xe, Scl3, Znl2 and Nal. The model used in this work, nonPDPSIM, is a plasma hydrodynamics model in which continuity, momentum and energy equations are solved for charged species with solution of Poisson's equation. The model is coupled with a thermodynamics module providing local thermodynamic equilibrium (LTE) properties. Algorithms were developed to represent the transition of the lamp from a kinetics-Poisson regime during breakdown to an LTE-ambipolar regime as the arc begins to form. During the LTE phase, the plasma composition is given either by a kinetics description or by LTEderived densities on a point-by-point basis in the lamp. The plasma composition, and the effects of mixing, segregation and ionization of light and heavy additives on thermal, electrical conductivity and I-V characteristics will be discussed. The thermodynamic database constructed for these doses will also be discussed.

SIERRA is a 3-D general-purpose semiconductor-device simulation program which serves as a foundation for investigating integrated-circuit (IC) device and reliability issues. This program solves the Poisson and continuity equations in silicon under DC, transient, and small-signal conditions. Executing on a vector/parallel minisupercomputer, SIERRA utilizes a matrix solver which uses an incomplete LU (ILU) preconditioned conjugate gradient square (CGS, BCG) method. The ILU-CGS method provides a good compromise between memory size and convergence rate. The authors have observed a 5* to 7* speedup over standard direct methods in simulations of transient problems containing highly coupled Poisson and continuity equations such as those found in reliability-oriented simulations. The application of SIERRA to parasitic CMOS latchup and DRAM (dynamic random-access memory) single-event-upset studies is described. >

With the development of 3D model reconstruction, manufacturing, and 3D model vision technologies, 3D model recognition has attracted much attention recently. To handle the 3D model recognition problem, in this paper, we propose a panorama based on multi-channel-attention (MCA) CNN network for the representation of the 3D model. The proposed method is composed of three parts: extracting views, transform function learning, and generating 3D model descriptor. Concretely, we first extract the 2D panoramic views for each 3D model, and we use the multi-channel-attention neural network to extract the descriptor for each 3D model. Here, the attention model is used to find the unequal weights of each panorama view to generate the more robust 3D model descriptor. Finally, The fusion feature is used to handle the 3D model classification and retrieval problem. The popular data sets ModelNet and ShapeNet are used to demonstrate the performance of our approach. The experiments also demonstrate the superiority of our proposed method over the state-of-art methods.

As modern field effect transistors (FETs) scale down into the sub-10-nm regime, the approaching end of CMOS scaling becomes evident. Recently, we have performed a series of three-dimensional, fully quantum-mechanical, charge-self-consistent transport simulations and optimizations to show [1] that all FETs, irrespective of their channel material, will reach a fundamental downscaling limit around 4-5 nm technology node, due to unacceptably high levels of thermally induced errors. To investigate alternatives to FET/CMOS scaling, many emerging devices and technologies have been under active research in recent years. Among them, oxide-based memristors have become one of the strongest candidates to replace flash, and possibly DRAM and SRAM in the near future [2]. Moreover, memristors have a high potential to enable beyond-CMOS technology advances in novel architectures for high performance computing [3]. However, despite the spectacular progress in experimental demonstration of oxide memristors, their microscopic transport theory and even some key operational principles, essential to advance experimental progress, remain uncertain [4]. To facilitate the understanding of physical switching mechanisms and accelerate experimental development in oxide memristors, we have developed a 3D fully-coupled electrical and thermal transport model [5] that solves simultaneously the time-dependent continuity equations for electrons, holes, and oxygen vacancies, the time-dependent heat equation including Joule heating sources, and the Poisson equation for all the charged species. The model captures all the most important processes that drive memristive switching, including field drift due to the electrical potential gradient, Fick diffusion due to the concentration gradient, and the Soret effect due to the temperature gradient. To properly simulate the movement of oxygen vacancies, the rigid point ion model [5] is used, in which the vacancy velocity exponentially depends on the temperature and the electric field when the field exceeds a critical value. The fully-coupled equations and relevant physical models are implemented in CHARON, a multi-dimensional parallel TCAD code developed at Sandia National Labs. CHARONis built upon the open-source Trilinos packages [6], which support finite element and finite volume discretization methods, state-of-the-art nonlinear and linear solvers, MPI parallel capability, and many more. It can simulate arbitrary device geometry and supports multi-physics capability (i.e., allowing for solving different equations in different regions). The coupled model has been applied to simulate the switching process in a 3D filamentary tantalum oxide memristor shown in Fig. 1(a). The layer material and thickness come from an experimental device published in Ref. [7]. Making use of the multi-physics capability in CHARON, we solve the coupled Poisson, electron, oxygen vacancy, and heat equations in the active Ta and conduction filament (CF) regions, with vacancies confined in Ta and CF regions, while in the Pt and Ta2O5 regions, due to absence of mobile vacancies, the coupled Poisson, electron, and heat equations are solved, with Pt treated as a highly doped n-type semiconductor using immobile dopants, and Ta2O5 as an undoped semiconductor. Extensive simulations show that both field drift and thermal processes play crucial roles in determining the switching dynamics of the bipolar TaOx device. Specifically, (i) during OFF switching, when a sufficient negative voltage is applied to the top Pt electrode, Joule heating causes the increase of temperature with the hottest spot located in the CF, and consequently, oxygen vacancies move away from CF into Ta under the influence of both heating and field, which leads to a vacancy density gap and possible depletion of vacancies in the entire CF at high negative voltage, resulting in the OFF state; (ii) during ON switching, a sufficient positive voltage causes Joule heating and the increase of temperature, and increased temperature causes vacancies moving from Ta into CF to refill the vacancy gap, resulting in the ON state. Interestingly, we show that the thermally activated field-dominated switching in the considered devices can lead to more than three orders of magnitude speed-up in switching time, with only 50% voltage/current increase. Simulated resistances during OFF and ON switching as a function of time and voltage show very good qualitative agreement with experimental measurement in Ref. [7]. Furthermore, under a triangular voltage sweep, the simulated current-voltage hysteresis curve is shown in Fig. 1(b), which also shows good qualitative agreement with the measured data in Ref. [8]. The generality of the proposed model allows to simulate and investigate the underlying physical switching mechanisms in a wide spectrum of oxide memristors ranging from field-dominant, field-thermal-driven to thermal-dominant memristive devices. Figure 1