3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

A Semi-Empirical Equation of Penetration Depth on Concrete Target Impacted by Ogive-Nose Projectiles

In this paper, the penetration process of ogive-nose projectiles into the semi-infinite concrete target is investigated by the dimensional analysis method and FEM simulation. With the dimensional analysis, main non-dimensional parameters which control the penetration depth are obtained with some reasonable hypothesis. Then, a new semi-empirical equation is present based on the original work of Forrestal et al., has only two non-dimensional combined variables with definite physical meanings. To verify this equation, prediction results are compared with experiments in a wide variation region of velocity. Then, a commercial FEM code, LS-DYNA, is used to simulate the complex penetration process, that also show the novel semi-empirical equation is reasonable for determining the penetration depth in a concrete target.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

A scheme for multiple sequences alignment optimization-an improvement based on family representative mechanics features

As a basic tool of modern biology, sequence alignment can provide us useful information in fold, function, and active site of protein. For many cases, the increased quality of sequence alignment means a better performance. The motivation of present work is to increase ability of the existing scoring scheme/algorithm by considering residue–residue correlations better. Based on a coarse-grained approach, the hydrophobic force between each pair of residues is written out from protein sequence. It results in the construction of an intramolecular hydrophobic force network that describes the whole residue–residue interactions of each protein molecule, and characterizes protein's biological properties in the hydrophobic aspect. A former work has suggested that such network can characterize the top weighted feature regarding hydrophobicity. Moreover, for each homologous protein of a family, the corresponding network shares some common and representative family characters that eventually govern the conservation of biological properties during protein evolution. In present work, we score such family representative characters of a protein by the deviation of its intramolecular hydrophobic force network from that of background. Such score can assist the existing scoring schemes/algorithms, and boost up the ability of multiple sequences alignment, e.g. achieving a prominent increase (50%) in searching the structurally alike residue segments at a low identity level. As the theoretical basis is different, the present scheme can assist most existing algorithms, and improve their efficiency remarkably.

Algorithm for simulating fracture processes in concrete by lattice modeling

To simulate fracture behaviors in concrete more realistically, a theoretical analysis on the potential question in the quasi-static method is presented, then a novel algorithm is proposed which takes into account the inertia effect due to unstable crack propagation and meanwhile requests much lower computational efforts than purely dynamic method. The inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, results may become questionable if a fracture process including unstable cracking is simulated by the quasi-static procedure excluding completely inertia effects. However, it requires much higher computational effort to simulate experiments with not very high loading rates by the dynamic method. In this investigation which can be taken as a natural continuation, the potential question of quasi-static method is analyzed based on the dynamic equations of motion. One solution to this question is the new algorithm mentioned above. Numerical examples are provided by the generalized beam (GB) lattice model to show both fracture processes under different loading rates and capability of the new algorithm.

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler-Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr-Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.

An Improved Ce/Se Scheme For Multi-Material Elastic-Plastic Flows And Its Applications

In this paper, a new definition of SE and CE, which is based on the hexahedron mesh and simpler than Chang's original CE/SE method (the space-time Conservation Element and Solution Element method), is proposed and an improved CE/SE scheme is constructed. Furthermore, the improved CE/SE scheme is extended in order to solve the elastic-plastic flow problems. The hybrid particle level set method is used for tracing the interfaces of materials. Proper boundary conditions are presented in interface tracking. Two high-velocity impact problems are simulated numerically and the computational results are carefully compared with the experimental data, as well as the results from other literature and LS-DYNA software. The comparisons show that the computational scheme developed currently is clear in physical concept, easy to be implemented and high accurate and efficient for the problems considered. (C) 2008 Elsevier Ltd. All rights reserved.

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

An Improved CE/SE Scheme for Numerical Simulation of Gaseous and Two-Phase Detonations

A new structure of solution elements and conservation elements based on rectangular mesh was pro- posed and an improved space-time conservation element and solution element (CE/SE) scheme with sec- ond-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas–droplet) detonation. Shock reflections were simu- lated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas–droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C–J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular pat- terns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.

A CE/SE Scheme for Flows in Porous Media and Its Applications

In this paper, a new computational scheme for solving flows in porous media was proposed. The scheme was based on an improved CE/SE method (the space-time Conservation Element and Solution Element method). We described porous flows by adopting DFB (Brinkman-Forchheimer extended Darcy) equation. The comparison between our computational results and Ghia's confirmed the high accuracy, resolution, and efficiency of our CE/SE scheme. The proposed first-order CE/SE scheme is a new reliable way for numerical simulations of flows in porous media. After investigation of effects of Darcy number on porous flow, it shows that Darcy number has dominant influence on porous flow for the Reynolds number and porosity considered.

Electronic entanglement purification scheme enhanced by charge detections

We present an entanglement purification scheme for the mixed entangled states of electrons with the aid of charge detections. Our scheme adopts the electronic polarizing beam splitters rather than the controlled-NOT (CNOT) operations, but the total successful probability of our scheme can reach the quantity as large as that of the the CNOT-operation-based protocol and twice as large as that of linear-optics-based protocol for the purification of photonic entangled states. Thus our scheme can achieve a high successful prabability without the usage of CNOT operations.

A plasma channel scheme for the interaction of an intense femtosecond laser pulse with a deuterium cluster jet

We propose a plasma channel scheme to obtain an improved table-top laser driven fusion neutron yield as a result of explosions of large deuterium clusters irradiated by an intense laser pulse. A cylindrical plasma channel is created by two moderate intensity laser prepulses at the edge of a deuterium cluster jet along which an intense main laser pulse propagates several nanoseconds later. With the aid of this plasma channel, the main laser pulse will be allowed to deposit its energy into the central region of the deuterium gas jet where the cluster sizes are larger and the atomic density is higher. The plasma channel formation and its impact on the deuterium ion energy spectrum and the consequent fusion neutron yield have been investigated. The calculated results show that a remarkable increase of the table-top laser driven fusion neutron yield would be expected.

Enhancement of Kerr nonlinearity with vanishing absorption in a tripod scheme

The giant enhancement of Kerr nonlinearity in a four-level tripod type system is investigated theoretically. By tuning the value of the Rabi frequency of the coherent control field, owing to the double dark resonances, the giant-enhanced Kerr nonlinearity can be achieved within the right transparency window. The in fluence of Doppler broadening is also discussed.