Poisson Equation

Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as three-dimensional shapes induced by the silhouettes in the space-time volume. We adopt a recent approach [14] for analyzing 2D shapes and generalize it to deal with volumetric space-time action shapes. Our method utilizes properties of the solution to the Poisson equation to extract space-time features such as local space-time saliency, action dynamics, shape structure, and orientation. We show that these features are useful for action recognition, detection, and clustering. The method is fast, does not require video alignment, and is applicable in (but not limited to) many scenarios where the background is known. Moreover, we demonstrate the robustness of our method to partial occlusions, nonrigid deformations, significant changes in scale and viewpoint, high irregularities in the performance of an action, and low-quality video.

The linearized-augmented-plane-wave (LAPW) method for thin films is generalized by removing the remaining shape approximation to the potential inside the atomic spheres. A new technique for solving Poisson's equation for a general charge density and potential is described and ...

methods are utilized as computational tools in many areas of chemical physics. In this paper, we present the theoretical basis for a dynamical Monte Carlo method in terms of the theory of Poisson processes. We show that if: (1) a "dynamical hierarchy" of transition probabilities is created which also satisfy the detailed-balance criterion; (2) time increments upon successful events are calculated appropriately; and (3) the effective independence of various events comprising the system can be achieved, then Monte Carlo methods may be utilized to simulate the Poisson process and both static and dynamic properties of model Hamiltonian systems may be obtained and interpreted consistently.

We describe an interactive, computer-assisted framework for combining parts of a set of photographs into a single composite picture, a process we call "digital photomontage." Our framework makes use of two techniques primarily: graph-cut optimization, to choose good seams within the constituent images so that they can be combined as seamlessly as possible; and gradient-domain fusion, a process based on Poisson equations, to further reduce any remaining visible artifacts in the composite. Also central to the framework is a suite of interactive tools that allow the user to specify a variety of high-level image objectives, either globally across the image, or locally through a painting-style interface. Image objectives are applied independently at each pixel location and generally involve a function of the pixel values (such as "maximum contrast") drawn from that same location in the set of source images. Typically, a user applies a series of image objectives iteratively in order to create a finished composite. The power of this framework lies in its generality; we show how it can be used for a wide variety of applications, including "selective composites" (for instance, group photos in which everyone looks their best), relighting, extended depth of field, panoramic stitching, clean-plate production, stroboscopic visualization of movement, and time-lapse mosaics.

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter ǫ = λD/L, where λD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of λDL/D (not λ 2 D /D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L 2 /D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.

A Cartesian grid method for computing flows with complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. A mixed Eulerian-Lagrangian framework is employed, which allows us to treat the immersed moving boundary as a sharp interface. The incompressible Navier-Stokes equations are discretized using a second-order-accurate finite-volume technique, and a second-orderaccurate fractional-step scheme is employed for time advancement. The fractionalstep method and associated boundary conditions are formulated in a manner that properly accounts for the boundary motion. A unique problem with sharp interface methods is the temporal discretization of what are termed "freshly cleared" cells, i.e., cells that are inside the solid at one time step and emerge into the fluid at the next time step. A simple and consistent remedy for this problem is also presented. The solution of the pressure Poisson equation is usually the most time-consuming step in a fractional step scheme and this is even more so for moving boundary problems where the flow domain changes constantly. A multigrid method is presented and is shown to accelerate the convergence significantly even in the presence of complex immersed boundaries. The methodology is validated by comparing it with experimental data on two cases: (1) the flow in a channel with a moving indentation on one wall and (2) vortex shedding from a cylinder oscillating in a uniform free-stream. Finally, the application of the current method to a more complicated moving boundary situation is also demonstrated by computing the flow inside a diaphragm-driven micropump with moving valves.

In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.

ity a nonlocal potential which could fit neutron elastic scattering data in the energy range from 0.4 to 24 MeV and where the optical-model parameters were energy independent. This is, of course, a remarkable result since we know that the absorption, for instance, is changing quite dramatically by going from 0.4 to 24 MeV incident projectile energy. We believe that these findings of Perey and Buck strongly support our result that there exists a nonlocal potential, which is not explicitly energy-dependent, which describes elastic nucleon scattering in a wide energy range. The theory presented in this paper may serve as a convenient tool in deriving such a potential. Actual calculation of an energy-independent optical-model potential as outlined in this paper is in progress.

Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born radii." Next, the atom-pair contributions are estimated by an analytical function f GB that depends upon the effective Born radii and interatomic distance of the atom pairs. Here, the relative impacts of these approximations are investigated by calculating "perfect" effective Born radii from PE theory, and enquiring as to how well the atom-pairwise energy terms from a GB model using these perfect radii in the standard f GB function duplicate the equivalent terms from PE theory. In tests on several biological macromolecules, the use of these perfect radii greatly increases the accuracy of the atom-pair terms; that is, the standard form of f GB performs quite well. The remaining small error has a systematic and a random component. The latter cannot be removed without significantly increasing the complexity of the GB model, but an alternative choice of f GB can reduce the systematic part. A molecular dynamics simulation using a perfect-radii GB model compares favorably with simulations using conventional GB, even though the radii remain fixed in the former. These results quantify, for the GB field, the importance of getting the effective Born radii right; indeed, with perfect radii, the GB model gives a very good approximation to the underlying PE theory for a variety of biomacromolecular types and conformations.

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 ]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

We present a theoretical study of electron mobility in cylindrical gated silicon nanowires at 300 K based on the Kubo-Greenwood formula and the self-consistent solution of the Schrödinger and Poisson equations. A rigorous surface roughness scattering model is derived, which takes into account the roughness-induced fluctuation of the subband wave function, of the electron charge, and of the interface polarization charge. Dielectric screening of the scattering potential is modeled within the random phase approximation, wherein a generalized dielectric function for a multi-subband quasi-one-dimensional electron gas system is derived accounting for the presence of the gate electrode and the mismatch of the dielectric constant between the semiconductor and gate insulator. A nonparabolic correction method is also presented, which is applied to the calculation of the density of states, the matrix element of the scattering potential, and the generalized Lindhard function. The Coulomb scattering due to the fixed interface charge and the intra-and intervalley phonon scattering are included in the mobility calculation in addition to the surface roughness scattering. Using these models, we study the low-field electron mobility and its dependence on the silicon body diameter, effective field, dielectric constant, and gate insulator thickness.

In this paper, a finite difference code for Direct and Large Eddy Simulation (DNS/LES) of incompressible flows is presented. This code is an intermediate tool between fully spectral Navier-Stokes solvers (limited to academic geometry through Fourier or Chebyshev representation) and more versatile codes based on standard numerical schemes (typically only second-order accurate). The interest of high-order schemes is discussed in terms of implementation easiness, computational efficiency and accuracy improvement considered through simplified benchmark problems and practical calculations. The equivalence rules between operations in physical and spectral spaces are efficiently used to solve the Poisson equation introduced by the projection method. It is shown that for the pressure treatment, an accurate Fourier representation can be used for more flexible boundary conditions than periodicity or free-slip. Using the concept of the modified wave number, the incompressibility can be enforced up to the machine accuracy. The benefit offered by this alternative method is found to be very satisfactory, even when a formal second-order error is introduced locally by boundary conditions that are neither periodic nor symmetric. The usefulness of high-order schemes combined with an immersed boundary method (IBM) is also demonstrated despite the second-order accuracy introduced by this wall modelling strategy. In particular, the interest of a partially staggered mesh is exhibited in this specific context. Three-dimensional calculations of transitional and turbulent channel flows emphasize the ability of present high-order schemes to reduce the computational cost for a given accuracy. The main conclusion of this paper is that finite difference schemes with quasi-spectral accuracy can be very efficient for DNS/LES of incompressible flows, while allowing flexibility for the boundary conditions and easiness in the code development. Therefore, this compromise fits particularly well for very high-resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments.

Due to rapid development of boundary element method (BEM), this article explores the evolution of BEM over the past half century. We here summarize the overall development and implementation of several well-known BEM variants that includes collocation BEM, galerkin BEM, dual reciprocity BEM, complex variable BEM and analog equation method. Their theoretical and mathematical backgrounds are carefully described and a generalized Laplace's equation (and Poisson's equation) is utilized in demonstrating the different approaches involved. An up-to-date review on characteristics and implementation for each of the five variants is presented and also highlighted their significant contributions in boundary element research. In addition, this article tries to cover whole aspect of interests including efficiency, applicability and accuracy in order to give better understanding of BEM evolution. Comparisons and techniques of improvement for these variants are also discussed.

A stiff, 1 operator-split projection scheme is constructed for the simulation of unsteady two-dimensional reacting flow with detailed kinetics. The scheme is based on the compressible conservation equations for an ideal gas mixture in the zero-Machnumber limit. The equations of motion are spatially discretized using second-order centered differences and are advanced in time using a new stiff predictor-corrector approach. The new scheme is a modified version of the additive, stiff scheme introduced in a previous effort by H. N. Najm, P. S. Wyckoff, and O. M. Knio (1998, J. Comput. Phys. 143, 381). The predictor updates the scalar fields using a Strang-type operator-split integration step which combines several explicit diffusion sub-steps with a single stiff step for the reaction terms, such that the global time step may significantly exceed the critical diffusion stability limit. Convection terms are explicitly handled using a second-order multi-step scheme. The velocity field is advanced using a projection scheme which consists of a partial convection-diffusion update followed by a pressure correction step. A split approach is also adopted for the convection-diffusion step in the momentum update. This splitting combines an explicit treatment of the convective terms at the global time step with several explicit fractional steps for diffusion. Finally, a corrector step is implemented in order to couple the evolution of the density and velocity fields and to stabilize the computations. The corrector acts only on the convective terms and the pressure field, while the predicted updates due to diffusion and reaction are left unchanged. The correction of the scalar fields is implemented using a single-step non-split, non-stiff, second-order time integration. A similar procedure is used for the velocity field, which is followed OPERATOR-SPLIT, STIFF SCHEME 429 by a pressure projection step. The performance and behavior of the operator-split scheme are first analyzed based on tests for a nonlinear reaction-diffusion equation in one space dimension, followed by computations with a detailed C 1 C 2 methane-air mechanism in one and two dimensions. The tests are used to verify that the scheme is effectively second order in time, and to suggest guidelines for selecting integration parameters, including the number of fractional diffusion steps and tolerance levels in the stiff integration. For two-dimensional simulations with the present reaction mechanism, flame conditions, and resolution parameters, speedup factors of about 5 are achieved over the previous additive scheme, and about 25 over the original explicit scheme.

In this note, we propose and analyse a method for handling interfaces between nonmatching grids based on an approach suggested by for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.

We present a domain decomposition finite element technique for efficiently generating lower and upper bounds to outputs which are linear functionals of the solutions to symmetric or nonsymmetric second-order coercive linear partial differential equations in two space dimensions.

We present a fully distributed dynamic load balancing algorithm for parallel MIMD architectures. The algorithm can be described as a system of identical parallel processes, each running on a processor of an arbitrary interconnected network of processors. We show that the algorithm can be interpreted as a Poisson (heath) equation in a graph. This equation is analysed using Markov chain techniques and is proved to converge in polynomial time resulting in a global load balance. We also discuss some important parallel architectures and interconnection schemes such as linear processor arrays, tori, hypercubes, etc. Finally we present two applications where the algorithm has been successfully embedded (process mapping and molecular dynamic simulation).

We present a general mesh-free description of the magnetic field distribution in various electromagnetic machines, actuators, and devices. Our method is based on transfer relations and Fourier theory, which gives the magnetic field solution for a wide class of twodimensional (2-D) boundary value problems. This technique can be applied to rotary, linear, and tubular permanent-magnet actuators, either with a slotless or slotted armature. In addition to permanent-magnet machines, this technique can be applied to any 2-D geometry with the restriction that the geometry should consist of rectangular regions. The method obtains the electromagnetic field distribution by solving the Laplace and Poisson equations for every region, together with a set of boundary conditions. Here, we compare the method with finite-element analyses for various examples and show its applicability to a wide class of geometries.

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g and h. In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

Consider the partial sums {S t } of a real-valued functional F (Φ(t)) of a Markov chain {Φ(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the following conclusions are obtained:

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S n = g X 1 + • • • + g X n , where E g X 1 = 0 and E g X 1 2 < ∞. The conditions imposed restrict the moments of g and the growth of the conditional means E S n X 1. No other restrictions on the dependence structure of the chain are required. When specialized to shift processes, the conditions are implied by simple integral tests involving g.

We applied the solvation models SM8, SM8AD, and SMD in combination with the Minnesota M06-2X density functional to predict vacuum-water transfer free energies ( and tautomeric ratios in aqueous solution (Task 2) for the SAMPL2 test set. The bulkelectrostatic contribution to the free energy of solvation is treated as follows: SM8 employs the generalized Born model with the Coulomb field approximation, SM8AD employs the generalized Born approximation with asymmetric descreening, and SMD solves the nonhomogeneous Poisson equation. The non-bulk-electrostatic contribution arising from shortrange interactions between the solute and solvent molecules in the first solvation shell is treated as a sum of terms that are products of geometry-dependent atomic surface tensions and solventaccessible surface areas of the individual atoms of the solute. On average, three models tested in the present work perform similarly. In particular, we achieved mean unsigned errors of 1.4 (SM8), 2.0 (SM8AD), and 2.6 kcal/mol (SMD) for the aqueous free energies of 30 out of 31 compounds with known reference data involved in Task 1 and mean unsigned errors of 2.7 (SM8), 1.8 (SM8AD), and 2.4 kcal/mol (SMD) in the free energy differences (tautomeric ratios) for 21 tautomeric pairs in aqueous solution involved in Task 2.

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC -SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s) including moving contact angles have been developed. This article will concentrate principally on a three-dimensional version of the SMAC method. It will eschew both code verification and model validation; instead it will emphasize the applications that the MAC method can solve, from multiphase flows to rheology.

In numerous applications of image processing, e.g. astronomical and medical imaging, data-noise is well-modeled by a Poisson distribution. This motivates the use of the negative-log Poisson likelihood function for data fitting. (The fact that application scientists in both astronomical and medical imaging regularly choose this function for data fitting provides further motivation.) However difficulties arise when the negative-log Poisson likelihood is used. Chief among them are the facts that it is non-quadratic and is defined only for vectors with nonnegative values. The nonnegatively constrained, convex optimization problems that arise when the negative-log Poisson likelihood is used are therefore more challenging than when least squares is the fit-to-data function.

We consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the Piola transform, extending results previously obtained for scalar approximation. The finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element, which is then transformed to a space of vector fields on each convex quadrilateral element via the Piola transform associated to a bilinear isomorphism of the square onto the element. For affine isomorphisms, a necessary and sufficient condition for approximation of order r + 1 in L 2 is that each component of the given space of functions on the reference element contain all polynomial functions of total degree at most r. In the case of bilinear isomorphisms, the situation is more complicated and we give a precise characterization of what is needed for optimal order L 2 -approximation of the function and of its divergence. As applications, we demonstrate degradation of the convergence order on quadrilateral meshes as compared to rectangular meshes for some standard finite element approximations of H(div). We also derive new estimates for approximation by quadrilateral Raviart-Thomas elements (requiring less regularity) and propose a new quadrilateral finite element space which provides optimal order approximation in H(div). Finally, we demonstrate the theory with numerical computations of mixed and least squares finite element approximations of the solution of Poisson's equation.

Suppose that X is a positive recurrent Harris chain with invariant measure 't. We develop a Lyapunov function criterion that permits one to bound the solution g to Poisson's equation for X. This bound is then applied to obtain sufficient conditions that guarantee that the solution be an element of LP(ir). When p = 2, the square integrability of g implies the validity of a functional central limit theorem for the Markov chain. We illustrate the technique with applications to the w-ting time sequence of the single-server queue and autoregressive sequences.

Abstract. In this paper, a new method for the problem of shape representation and classification is proposed. In this method, we define a radius function on the contour of the shape which captures for each point of the boundary, attributes of its related internal part of the shape. We call ...

In this paper we introduce Enzo, a 3D MPI-parallel Eulerian blockstructured adaptive mesh refinement cosmology code. Enzo is designed to simulate cosmological structure formation, but can also be used to simulate a wide range of astrophysical situations. Enzo solves dark matter N-body dynamics using the particle-mesh technique. The Poisson equation is solved using a combination of fast fourier transform (on a periodic root grid) and multigrid techniques (on non-periodic subgrids). Euler's equations of hydrodynamics are solved using a modified version of the piecewise parabolic method. Several additional physics packages are implemented in the code, including several varieties of radiative cooling, a metagalactic ultraviolet background, and prescriptions for star formation and feedback. We also show results illustrating properties of the adaptive mesh portion of the code. Information on profiling and optimizing the performance of the code can be found in the contribution by James Bordner in this volume.

We report on the calculation of electrical characteristics of AlGaN/GaN heterojunction field effect transistors (HFETs). The model is based on the self-consistent solution of the Schrodinger and Poisson equations coupled to a quasi-2D model for the current flow. Both single and double heterojunction devices are analyzed for [0001] or [000-1] growth directions. The onset of a parasitic p-channel for particular growth directions and alloy concentrations is also shown

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is

We show by simulation that electron mobility and velocity overshoot are greater when strained inversion layers are grown on SiGe-On-insulator substrates ͑strained Si/SiGe-OI͒ than when unstrained silicon-on-insulator ͑SOI͒ devices are employed. In addition, mobility in these strained inversion layers is only slightly degraded compared with strained bulk Si/SiGe inversion layers, due to the phonon scattering increase produced by greater carrier confinement. Poisson and Schroedinger equations are self-consistently solved to evaluate the carrier distribution in this structure. A Monte Carlo simulator is used to solve the Boltzmann transport equation. Electron mobility in these devices is compared to that in SOI inversion layers and in bulk Si/SiGe inversion layers. The effect of the germanium mole fraction x, the strained-silicon layer thickness, T Si , and the total width of semiconductor ͑SiϩSiGe͒ slab sandwiched between the two oxide layers, T w were carefully analyzed. We observed strong dependence of the electron mobility on T Si , due to the increase in the phonon scattering rate as the silicon layer thickness is reduced, a consequence of the greater confinement of the carriers. This effect is less important as the germanium mole fraction, x, is reduced, and as the value of T Si increases. For T Si Ͼ20 nm, mobility does not depend on T Si , and maximum mobility values are obtained.

Long-time states of a turbulent, decaying, two-dimensional, Navier-Stokes flow are shown numerically to relax toward maximum-entropy configurations, as defined by the "sinh-Poisson" equation. The large-scale Reynolds number is about 14 000, the spatial resolution is ( 512>2, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large-scale eddy-turnover times.

We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topology. The singular vertices are chosen automatically. As opposed to most previous methods, our flattening process involves only the solution of linear systems of Poisson equations, thus is very efficient. Our method is shown to be faster than existing methods, yet generates parameterizations having comparable quasi-conformal distortion.

We consider the approximation of a microelectronic device corresponding to a n + − n − n + diode consisting in a channel flanked on both sides by two highly doped regions. This is modelled through a system of equations: ballistic for the channel and drift-diffusion elsewhere. The overall coupling stems from the Poisson equation for the self-consistent potential. We propose an original numerical method for its processing, being realizable, explicit in time and nonnegativity preserving on the density. In particular, the boundary conditions at the junctions express the continuity of the current and don't destabilize the general scheme. At last, efficiency is shown by presenting results on test-cases of some practical interest.

We introduce a new code, ECOSMOG, to run N -body simulations for a wide class of modified gravity and dynamical dark energy theories. These theories generally have one or more new dynamical degrees of freedom, the dynamics of which are governed by their (usually rather nonlinear) equations of motion. Solving these non-linear equations has been a great challenge in cosmology. Our code is based on the RAMSES code, which solves the Poisson equation on adaptively refined meshes to gain high resolutions in the high-density regions. We have added a solver for the extra degree(s) of freedom and performed numerous tests for the f (R) gravity model as an example to show its reliability. We find that much higher efficiency could be achieved compared with other existing mesh/grid-based codes thanks to two new features of the present code: (1) the efficient parallelisation and (2) the usage of the multigrid relaxation to solve the extra equation(s) on both the regular domain grid and refinements, giving much faster convergence even under much more stringent convergence criteria. This code is designed for performing high-accuracy, high-resolution and large-volume cosmological simulations for modified gravity and general dark energy theories, which can be utilised to test gravity and the dark energy hypothesis using the upcoming and future deep and high-resolution galaxy surveys.

Proper orthogonal decomposition (POD) has been used to develop a reduced-order model of the hydrodynamic forces acting on a circular cylinder. Direct numerical simulations of the incompressible Navier-Stokes equations have been performed using a parallel computational fluid dynamics (CFD) code to simulate the flow past a circular cylinder. Snapshots of the velocity and pressure fields are used to calculate the divergence-free velocity and pressure modes, respectively. We use the dominant of these velocity POD modes (a small number of eigenfunctions or modes) in a Galerkin procedure to project the Navier-Stokes equations onto a low-dimensional space, thereby reducing the distributed-parameter problem into a finite-dimensional nonlinear dynamical system in time. The solution of the reduced dynamical system is a limit cycle corresponding to vortex shedding. We investigate the stability of the limit cycle by using long-time integration and propose to use a shooting technique to home on the system limit cycle. We obtain the pressure-Poisson equation by taking the divergence of the Navier-Stokes equation and then projecting it onto the pressure POD modes. The pressure is then decomposed into lift and drag components and compared with the CFD results.

Bandstructure effects in the electronic transport of strongly quantized silicon nanowire field-effect-transistors (FET) in various transport orientations are examined. A 10-band sp 3 d 5 s* semi-empirical atomistic tight-binding model coupled to a self consistent Poisson solver is used for the dispersion calculation. A semi-classical, ballistic FET model is used to evaluate the current-voltage characteristics. It is found that the total gate capacitance is degraded from the oxide capacitance value by 30% for wires in all the considered transport orientations ([100], [110], [111]). Different wire directions primarily influence the carrier velocities, which mainly determine the relative performance differences, while the total charge difference is weakly affected. The velocities depend on the effective mass and degeneracy of the dispersions. The [110] and secondly the [100] oriented 3nm thick nanowires examined, indicate the best ON-current performance compared to [111] wires. The dispersion features are strong functions of quantization. Effects such as valley splitting can lift the degeneracies especially for wires with cross section sides below 3nm. The effective masses also change significantly with quantization, and change differently for different transport orientations. For the cases of [100] and [111] wires the masses increase with quantization, however, in the [110] case, the mass decreases. The mass variations can be explained from the non-parabolicities and anisotropies that reside in the first Brillouin zone of silicon. Index terms -nanowire, bandstructure, tight binding, transistors, MOSFETs, nonparabolicity, effective mass, injection velocity, quantum capacitance, anisotropy. carrier velocities, closely followed by the [100] devices with a little higher masses. [111]

Glow discharge at atmospheric pressure using a dielectric barrier discharge can induce fluid flow and operate as an actuator for flow control. In this paper, we simulate the physics of a two-dimensional asymmetric actuator operating in helium gas using a high-fidelity first-principles-based numerical modeling approach to help improve our understanding of the physical mechanisms associated with such actuators. Fundamentally, there are two processes in the two half-cycles of the actuator operation, largely due to the difference in mobility between faster electrons and slower ions, and the geometric configurations of the actuator ͑insulator and electrodes͒. The first half-cycle is characterized by the deposition of the slower ion species on the insulator surface while the second half-cycle by the deposition of the electrons at a faster rate. A power-law dependence on the voltage for the resulting force is observed, which indicates that larger force can be generated by increasing the amplitude. Furthermore, one can enhance the effectiveness of the actuator by either increasing the peak value of the periodic force generation or by increasing the asymmetry between the voltage half-cycles or both. Overall, the increase in the lower electrode size, applied voltage, and dielectric constant tends to contribute to the first factor, and the decrease in frequency of applied voltage tends to contribute to the second factor. However, the complex interplay between the above factors determines the actuator performance.

In this paper, we propose a new numerical method for treating two-phase incompressible flow where one phase is being converted into the other, e.g., the vaporization of liquid water. We consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow. This method was designed as an extension of the Ghost Fluid Method 1999, J. Comput. Phys. 152, 457) and relies heavily on the boundary condition capturing technology developed in Liu et al. (2000, J. Comput. Phys. 154, 15) for the variable coefficient Poisson equation and in Kang et al. (in press J. Comput. Phys.) for multiphase incompressible flow. Our new numerical method admits a sharp interface representation similar to the method proposed in Helenbrook et al. (1999, J. Comput. . Since the interface boundary conditions are handled in a simple and straightforward fashion, the code is very robust, e.g. no special treatment is required to treat the merging of flame fronts. The method is presented in three spatial dimensions, with numerical examples in one, two, and three spatial dimensions.

An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynominals expansions is given for this scheme. An example demonstrating the applicability of the method is given.

A shear-lag analysis is presented for estimating sliding friction stress at fibermatrix intevfaces in ceramic-matrix composites using the single-fiber push-out test. The analysis includes an approximate correction for the increased interfacial compression and, therefore, the interfacial friction stress arising from the trunsverse (Poisson) expansion of the fibers subjected to the compressive load. An exponential decrease of the interfacial shear stress along the fiber length is predicted. This result is similar to the results of a finite-element analysis reported in the literature. The analysis also provides a basis for the experimental determination of a coefficient of interfacial friction (p) and a residual interfacial compression (~0 ) . It is shown that the sliding friction stress (rf=puao) can be overestimated i f the transverse expansion of the fibers is not taken into account.

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed.

The current dipole is a widely used source model in forward and inverse electroencephalography and magnetoencephalography applications. Analytic solutions to the governing field equations have been developed for several approximations of the human head using ideal dipoles as the source model. Numeric approaches such as the finite-element and finite-difference methods have become popular because they allow the use of anatomically realistic head models and the increased computational power that they require has become readily available. Although numeric methods can represent more realistic domains, the sources in such models are an approximation of the ideal dipole. In this paper, we examine several methods for representing dipole sources in finite-element models and compare the resulting surface potentials and external magnetic field with those obtained from analytic solutions using ideal dipoles.