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Critical Dimensions of Untamped Conical Vessels

Description: Abstract: "The need often arises for determining the critical chemical concentration of uranium solution in the conical bottom of a plant reactor or storage vessel, or the dimension if the concentration is known. This report describes the mathematical analysis of Poisson's equation for a spherical sector, which approximates a right circular cone. The ratio of the critical dimension of an equivalent sphere to the height of the sector for various sector angles is derived from a comparison of first eigenvalues. No description of further relations between composition and dimensions is discussed in the report."
Date: August 25, 1947
Creator: Murray, Raymond
Partner: UNT Libraries Government Documents Department

Of FFT-based convolutions and correlations, with application to solving Poisson's equation in an open rectangular pipe

Description: A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs)to perform mixed convolutions and correlations of the charge density with the Green function. Descriptions are provided for algorithms based on theordinary Green function and for an integrated Green function (IGF). Due to its similarity to the widely used Hockney algorithm for solving Poisson'sequation in free space, this capability can be easily implemented in many existing particle-in-cell beam dynamics codes.
Date: November 7, 2011
Creator: Ryne, Robert D.
Partner: UNT Libraries Government Documents Department

A cartesian grid embedded boundary method for the heat equationand poisson's equation in three dimensions

Description: We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60-85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60-85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.
Date: November 2, 2004
Creator: Schwartz, Peter; Barad, Michael; Colella, Phillip & Ligocki, Terry
Partner: UNT Libraries Government Documents Department

A fully 3D atomistic quantum mechanical study on random dopant induced effects in 25nm MOSFETs

Description: We present a fully 3D atomistic quantum mechanical simulation for nanometered MOSFET using a coupled Schroedinger equation and Poisson equation approach. Empirical pseudopotential is used to represent the single particle Hamiltonian and linear combination of bulk band (LCBB) method is used to solve the million atom Schroedinger's equation. We studied gate threshold fluctuations and threshold lowering due to the discrete dopant configurations. We compared our results with semiclassical simulation results. We found quantum mechanical effects increase the threshold fluctuation while decreases the threshold lowering. The increase of threshold fluctuation is in agreement with previous study based on approximated density gradient approach to represent the quantum mechanical effect. However, the decrease in threshold lowering is in contrast with the previous density gradient calculations.
Date: July 11, 2008
Creator: Wang, Lin-Wang; Jiang, Xiang-Wei; Deng, Hui-Xiong; Luo, Jun-Wei; Li, Shu-Shen; Wang, Lin-Wang et al.
Partner: UNT Libraries Government Documents Department

Wavelet approach to accelerator problems. 2: Metaplectic wavelets

Description: This is the second part of a series of talks in which the authors present applications of wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to the orbit method and by using construction from the geometric quantization theory they construct the symplectic and Poisson structures associated with generalized wavelets by using metaplectic structure and corresponding polarization. The key point is a consideration of semidirect product of Heisenberg group and metaplectic group as subgroup of automorphisms group of dual to symplectic space, which consists of elements acting by affine transformations.
Date: May 1, 1997
Creator: Fedorova, A.; Zeitlin, M. & Parsa, Z.
Partner: UNT Libraries Government Documents Department

SOLVING BY PARALLEL COMPUTATION THE POISSON PROBLEM FOR HIGH INTENSITY BEAMS IN CIRCULAR ACCELERATORS.

Description: Simulation of high intensity accelerators leads to the solution of the Poisson Equation, to calculate space charge forces in the presence of acceleration chamber walls. We reduced the problem to ''two-and-a-half'' dimensions for long particle bunches, characteristic of large circular accelerators, and applied the results to the tracking code Orbit.
Date: June 18, 2001
Creator: LUCCIO,A.U.; DIMPERIO,N.L.; SAMULYAK,R. & BEEB-WANG,J.
Partner: UNT Libraries Government Documents Department

Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors

Description: Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold. Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a geodesic. The conservation of energy and momentum is assumed, which, through the use of the Bianchi identity, results in Einstein's field equation.
Date: May 2004
Creator: Burns, Michael E.
Partner: UNT Libraries

Sheared-flow Modes in Toroidal Geometry

Description: Using a Fourier-Bessel representation for the fluctuating (turbulent) electrostatic potential, an equation governing the sheared-flow modes in toroidal geometry is derived from the gyrokinetic Poisson equation, where both the adiabatic and non-adiabatic responses of the electrons are taken into account. It is shown that the principal geometrical effect on sheared-flow modes of the electrostatic potential is due to the flux-surface average of 1/B, where B is the magnetic field strength.
Date: October 1, 1999
Creator: Lewandowski, J.L.V.; Hahm, T.S.; Lee, W.W. & Lin, Z.
Partner: UNT Libraries Government Documents Department

Recent advances of strong-strong beam-beam simulation

Description: In this paper, we report on recent advances in strong-strong beam-beam simulation. Numerical methods used in the calculation of the beam-beam forces are reviewed. A new computational method to solve the Poisson equation on nonuniform grid is presented. This method reduces the computational cost by a half compared with the standard FFT based method on uniform grid. It is also more accurate than the standard method for a colliding beam with low transverse aspect ratio. In applications, we present the study of coherent modes with multi-bunch, multi-collision beam-beam interactions at RHIC. We also present the strong-strong simulation of the luminosity evolution at KEKB with and without finite crossing angle.
Date: September 15, 2004
Creator: Qiang, Ji; Furman, Miguel A.; Ryne, Robert D.; Fischer, Wolfram & Ohmi,Kazuhito
Partner: UNT Libraries Government Documents Department

A Local Corrections Algorithm for Solving Poisson's Equation inThree Dimensions

Description: We present a second-order accurate algorithm for solving thefree-space Poisson's equation on a locally-refined nested grid hierarchyin three dimensions. Our approach is based on linear superposition oflocal convolutions of localized charge distributions, with the nonlocalcoupling represented on coarser grids. There presentation of the nonlocalcoupling on the local solutions is based on Anderson's Method of LocalCorrections and does not require iteration between different resolutions.A distributed-memory parallel implementation of this method is observedto have a computational cost per grid point less than three times that ofa standard FFT-based method on a uniform grid of the same resolution, andscales well up to 1024 processors.
Date: October 30, 2006
Creator: McCorquodale, Peter; Colella, Phillip; Balls, Gregory T. & Baden,Scott B.
Partner: UNT Libraries Government Documents Department

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

Description: We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. With our 4D ({psi}, {theta}, {epsilon}, {mu}) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.
Date: November 9, 2007
Creator: Xu, X Q
Partner: UNT Libraries Government Documents Department

Quantum Monte Carlo using a Stochastic Poisson Solver

Description: Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually quantum Monte Carlo has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall quantum Monte Carlo scheme. We have developed a modified ''Walk On Spheres'' algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated within popular quantum Monte Carlo techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.
Date: May 6, 2005
Creator: Das, D; Martin, R M & Kalos, M H
Partner: UNT Libraries Government Documents Department

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

Description: This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using the finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.
Date: June 1, 2004
Creator: Evans, Gregory Herbert (Sandia National Laboratories, Livermore, CA) & Chen, Ken Shuang
Partner: UNT Libraries Government Documents Department

The dielectric boundary condition for the embedded curved boundary (ECB) method

Description: A new version of ECB has been completed that allows nonuniform grid spacing and a new dieledric boundary condition. ECB was developed to retain the simplicity and speed of an orthogonal mesh while capturing much of the fidelity of adaptive, unstructured finite element meshes. Codes based on orthogonal meshes are easy to work with and lead to well-posed elliptic and parabolic problems that are comparatively easy to solve. Generally, othogonal mesh representations lead to banded matrices while unstructured representations lead to more complicated sparse matrices. Recent advances in adapting banded linear systems to massively parallel computers reinforce our opinion that iterative field solutions utilizing banded matrix methods will continue to be competitive. Unfortunately, the underlying ``stair-step`` boundary representation in simple orthogonal mesh (and recent Adaptive Mesh Refinement) applications is inadequate. With ECB, the curved boundary is represented by piece-wise-linear representations of curved internal boundaries embedded into the orthogonal mesh- we build better, but not more, coefficients in the vicinity of these boundaries-and we use the surplus free energy on more ambitious physics models. ECB structures are constructed out of the superposition of analytically prescribed building blocks. In 2-D, we presently use a POLY4 (linear boundaries defined by 4 end points), an ANNULUS, (center, inner & outer radii, starting & stopping angle), a ROUND (starting point & angle, stopping point & angle, fillet radius). A link-list AIRFOIL has also been constructed. In the ECB scheme, we first find each intercept of the structure boundary with an I or J grid line is assigned an index K. We store the actual z,y value at the intercept, and the slope of the boundary at that intercept, in arrays whose index K is associated with the corresponding mesh point just inside the structure. In 2-D, a point just outside a structure may have up ...
Date: January 26, 1998
Creator: Hewwitt, D. W., LLNL
Partner: UNT Libraries Government Documents Department

A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains

Description: The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.
Date: January 1997
Creator: Johansen, H. & Colella, P.
Partner: UNT Libraries Government Documents Department

Plasmas in quasi-static external electric fields

Description: This work develops some practical approximations needed to simulate a high plasma density volume bounded by walls made of dielectrics or metals which may be either biased or floating in potential. Solving Poisson`s equation in both the high-density bulk and the sheath region poses a difficult computational problem due to the large electron plasma frequency. A common approximation is to assume the electric field is computed in the ambipolar approximation in the bulk and to couple this to a sheath model at the boundaries. Unfortunately, this treatment is not appropriate when some surfaces are biased with respect to others and a net current is present within the plasma. This report develops some ideas on the application of quasi-static external electric fields to plasmas and the self-consistent treatment of boundary conditions at the surfaces. These constitute a generalization of Ohm`s law for a plasma body that entails solving for the internal fields within the plasma and the potential drop and currents through the sheaths surrounding the plasma.
Date: July 1, 1998
Creator: Riley, M.E. & Campbell, R.B.
Partner: UNT Libraries Government Documents Department

Transverse Space-Charge Effects in Circular Accelerators

Description: The particles in an accelerator interact with one another by electromagnetic forces and are held together by external focusing forces. Such a many-body system has a large number of transverse modes of oscillation (plasma oscillations) that can be excited at characteristic frequencies by errors in the external guide field. In Part I we examine one mode of oscillation in detail, namely the quadrupole mode that is excited in uniformly charged beams by gradient errors. We derive self-consistent equations of motion for the beam envelope and solve these equations for the case in which the space-charge force is much less than the external focusing force, i.e., for strong-focusing synchrotrons. We find that the resonance intensity is shifted from the value predicted by the usual transverse incoherent space-charge limit; moreover, because the space-charge force depends on the shape and size of the beam, the beam growth in always limited. For gradient errors of the magnitude normally present in strong-focusing synchrotrons, the increase in beam size is small provided the beam parameters are properly chosen; otherwise the growth may be large. Thus gradient errors need not impose a limit on the number of particles that can be accelerated. In Part II we examine the other modes of collective oscillation that are excited by machine imperfections. For simplicity we consider only one-dimensional beams that are confined by harmonic potentials, and only small-amplitude oscillations. The linearized Vlasov and Poisson equations are used to find the twofold infinity of normal modes and eigenfrequencies for the stationary distribution that has uniform charge density in real space. In practice, only the low-order modes (the dipole, quadrupole, sextupole, and one or two additional modes) will be serious, and the resonant conditions for these modes are located on a tune diagram. These results, which are valid for all beam intensities, ...
Date: October 30, 1968
Creator: Sacherer, Frank James
Partner: UNT Libraries Government Documents Department

Simulation of Electric Field in Semi Insulating Au/CdTe/Au Detector under Flux

Description: We report our simulations on the profile of the electric field in semi insulating CdTe and CdZnTe with Au contacts under radiation flux. The type of the space charge and electric field distribution in the Au/CdTe/Au structure is at high fluxes result of a combined influence of charge formed due to band bending at the electrodes and from photo generated carriers, which are trapped at deep levels. Simultaneous solution of drift-diffusion and Poisson equations is used for the calculation. We show, that the space charge originating from trapped photo-carriers starts to dominate at fluxes 10{sup 15}-10{sup 16}cm{sup -2}s{sup -1}, when the influence of contacts starts to be negligible.
Date: August 2, 2009
Creator: Franc, J.; James, R.; Grill, R.; Kubat, J.; Belas, E.; Hoschl, P. et al.
Partner: UNT Libraries Government Documents Department

EXAMINATION OF THE PCICE METHOD IN THE NEARLY INCOMPRESSIBLE, AS WELL AS STRICTLY INCOMPRESSIBLE, LIMITS

Description: The conservative-form, pressure-based PCICE numerical method (Martineau and Berry, 2004) (Berry, 2006), recently developed for computing transient fluid flows of all speeds from very low to very high (with strong shocks), is simplified and generalized. Though the method automatically treats a continuous transition of compressibility, three distinct, limiting compressibility regimes are formally defined for purposes of discussion and comparison with traditional methods – the strictly incompressible limit, the nearly incompressible limit, and the f ully compressible limit. The PCICE method’s behavior is examined in each limiting regime. In the strictly incompressible limit the PCICE algorithm reduces to the traditional MAC-type method with velocity divergence driving the pressure Poisson equation. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of traditional incompressible methods, i.e. to one in which not only the velocity divergence effect, but also the density gradient effect is included as a driving function in the pressure Poisson equation. This nearly incompressible regime has received little attention, and it appears that in the past, strictly incompressible methods may have been conveniently applied to flows in this regime at the expense of ignoring a potentially important coupling mechanism. This could be significant in many important flows; for example, in natural convection flows resulting from high heat flux. In the f ully compressible limit or regime, the algorithm is found to reduce to an expression equivalent to density-based methods for high-speed flow.
Date: April 1, 2007
Creator: Berry, Ray A. & Martineau, Richard C.
Partner: UNT Libraries Government Documents Department

Performance of particle in cell methods on highly concurrent computational architectures

Description: Particle in cell (PIC) methods are effective in computing Vlasov-Poisson system of equations used in simulations of magnetic fusion plasmas. PIC methods use grid based computations, for solving Poisson’s equation or more generally Maxwell’s equations, as well as Monte-Carlo type methods to sample the Vlasov equation. The presence of two types of discretizations, deterministic field solves and Monte-Carlo methods for the Vlasov equation, pose challenges in understanding and optimizing performance on today large scale computers which require high levels of concurrency. These challenges arises from the need to optimize two very different types of processes and the interactions between them. Modern cache based high-end computers have very deep memory hierarchies and high degrees of concurrency which must be utilized effectively to achieve good performance. The effective use of these machines requires maximizing concurrency by eliminating serial or redundant work and minimizing global communication. A related issue is minimizing the memory traffic between levels of the memory hierarchy because performance is often limited by the bandwidths and latencies of the memory system. This paper discusses some of the performance issues, particularly in regard to parallelism, of PIC methods. The gyrokinetic toroidal code (GTC) is used for these studies and a new radial grid decomposition is presented and evaluated. Scaling of the code is demonstrated on ITER sized plasmas with up to 16K Cray XT3/4 cores.
Date: September 23, 2009
Creator: Adams, M. F.; Ethier, S. & Wichmann, N.
Partner: UNT Libraries Government Documents Department

Equilibrium Initialization and Stability of Three-Dimensional Gas Disks

Description: We present a new systematic way of setting up galactic gas disks based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disk. We first show that the required circular velocity has no dependence on the height above or below the midplane so long as the gas pressure is a function of density only. The assumption of disks being very thin enables us to decouple the vertical structure from the radial direction. Based on that, the equation of hydrostatic equilibrium together with the reduced Poisson equation leads to two sets of second-order non-linear differential equation, which are easily integrated to set-up a stable disk. We call one approach 'density method' and the other one 'potential method'. Gas disks in detailed balance are especially suitable for investigating the onset of the gravitational instability. We revisit the question of global, axisymmetric instability using fully three-dimensional disk simulations. The impact of disk thickness on the disk instability and the formation of spontaneously induced spirals is studied systematically with or without the presence of the stellar potential. In our models, the numerical results show that the threshold value for disk instability is shifted from unity to 0.69 for self-gravitating thick disks and to 0.75 for combined stellar and gas thick disks. The simulations also show that self-induced spirals occur in the correct regions and with the right numbers as predicted by the analytic theory.
Date: August 25, 2010
Creator: Wang, Hsiang-Hsu; /Heidelberg, Max Planck Inst. Astron. /ZAH, Heidelberg; Klessen, Ralf S.; /ZAH, Heidelberg /KIPAC, Menlo Park; Dullemond, Cornelis P.; /Heidelberg, Max Planck Inst. Astron. et al.
Partner: UNT Libraries Government Documents Department