Numerical simulation of dendrite growth during solidification

A comprehensive probabilistic model for simulating dendrite morphology and investigating dendritic growth kinetics during solidification has been developed, based on a modified Cellular Automaton (mCA) for microscopic modeling of nucleation, growth of crystals and solute diffusion. The mCA model numerically calculated solute redistribution both in the solid and liquid phases, the curvature of dendrite tips and the growth anisotropy. This modeling takes account of thermal, curvature and solute diffusion effects. Therefore, it can simulate microstructure formation both on the scale of the dendrite tip length. This model was then applied for simulating dendritic solidification of an Al-7%Si alloy. Both directional and equiaxed dendritic growth has been performed to investigate the growth anisotropy and cooling rate on dendrite morphology. Furthermore, the competitive growth and selection of dendritic crystals have also investigated.

Three-dimensional electrical impedance, tomography: A topology optimization approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

Macroscopic test of quantum mechanics versus stochastic electrodynamics

We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.

Simulation of mixing in unsteady flow through a periodically obstructed channel

Fluid mixing in steady and unsteady Bow through a channel containing periodic square obstructions has been studied using a finite-difference simulation to determine fluid velocities, followed by the use of passive marker particle advection to look at fluid transport out of the cavities formed between each of the obstructions. The geometry and Bow conditions were chosen from the work by Perkins (1989, M.S. Thesis, Lehigh University; 1992, Ph.D. Thesis, Lehigh University); who investigated heat transfer enhancement due to unsteady flow through such an obstructed channel. Particle advection shows that Bow regimes which are predicted to give good mixing based on snapshots of instantaneous streamline contour plots were not necessarily able to efficiently mix fluid which started in the cavity regions throughout the channel. The use of Poincare sections shows regular regions existing under these conditions which inhibit efficient fluid transport. These regular regions are found to disappear when the unsteady Bow velocity is increased. (C) 1997 Elsevier Science Ltd.

Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Genetic algorithms for continuous optimization problems - a concept of parameter-space size adjustment

The concept of parameter-space size adjustment is pn,posed in order to enable successful application of genetic algorithms to continuous optimization problems. Performance of genetic algorithms with six different combinations of selection and reproduction mechanisms, with and without parameter-space size adjustment, were severely tested on eleven multiminima test functions. An algorithm with the best performance was employed for the determination of the model parameters of the optical constants of Pt, Ni and Cr.

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal Hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations. which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented. (C) 2001 Elsevier Science B.V. All rights reserved.

Theory of a mode-locked atom laser with toroidal geometry

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to (h) over bar /2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Simulation of interface states effect on the scanning capacitance microscopy measurement of p-n junctions

A two-dimensional numerical simulation model of interface states in scanning capacitance microscopy (SCM) measurements of p-n junctions is presented-In the model, amphoteric interface states with two transition energies in the Si band gap are represented as fixed charges to account for their behavior in SCM measurements. The interface states are shown to cause a stretch-out-and a parallel shift of the capacitance-voltage characteristics in the depletion. and neutral regions of p-n junctions, respectively. This explains the discrepancy between - the SCM measurement and simulation near p-n junctions, and thus modeling interface states is crucial for SCM dopant profiling of p-n junctions. (C) 2002 American Institute of Physics.

Current density mapping approach for design of clinical magnetic resonance imaging magnets

Novel current density mapping (CDM) schemes are developed for the design of new actively shielded, clinical magnetic resonance imaging (MRI) magnets. This is an extended inverse method in which the entire potential solution space for the superconductors has been considered, rather than single current density layers. The solution provides an insight into the required superconducting coil pattern for a desired magnet configuration. This information is then used as an initial set of parameters for the magnet structure, and a previously developed hybrid numerical optimization technique is used to obtain the final geometry of the magnet. The CDM scheme is applied to the design of compact symmetric, asymmetric, and open architecture 1.0-1.5 T MRI magnet systems of novel geometry and utility. A new symmetric 1.0-T system that is just I m in length with a full 50-cm diameter of the active, or sensitive, volume (DSV) is detailed, as well as an asymmetric system in which a 50-cm DSV begins just 14 cm from the end of the coil structure. Finally a 1.0-T open magnet system with a full 50-cm DSV is presented. These new designs provide clinically useful homogeneous regions and have appropriately restricted stray fields but, in some of the designs, the DSV is much closer to the end of the magnet system than in conventional designs. These new designs have the potential to reduce patient claustrophobia and improve physician access to patients undergoing scans. (C) 2002 Wiley Periodicals, Inc.