Contribution from the interaction Hamiltonian to the expectation value of particle number with the non-equilibrium quantum field theory

International Nuclear Information System (INIS)

Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki

2012-01-01

We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.

A novel partitioning method for block-structured adaptive meshes

Science.gov (United States)

Fu, Lin; Litvinov, Sergej; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-07-01

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

A novel partitioning method for block-structured adaptive meshes

Energy Technology Data Exchange (ETDEWEB)

Fu, Lin, E-mail: lin.fu@tum.de; Litvinov, Sergej, E-mail: sergej.litvinov@aer.mw.tum.de; Hu, Xiangyu Y., E-mail: xiangyu.hu@tum.de; Adams, Nikolaus A., E-mail: nikolaus.adams@tum.de

2017-07-15

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

Diagonalization of Hamiltonian; Diagonalization of Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Garrido, L M; Pascual, P

1960-07-01

We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.

Numerical analysis of splashing fluid using hybrid method of mesh-based and particle-based modelings

International Nuclear Information System (INIS)

Tanaka, Nobuatsu; Ogawara, Takuya; Kaneda, Takeshi; Maseguchi, Ryo

2009-01-01

In order to simulate splashing and scattering fluid behaviors, we developed a hybrid method of mesh-based model for large-scale continuum fluid and particle-based model for small-scale discrete fluid particles. As for the solver of the continuum fluid, we adopt the CIVA RefIned Multiphase SimulatiON (CRIMSON) code to evaluate two phase flow behaviors based on the recent computational fluid dynamics (CFD) techniques. The phase field model has been introduced to the CRIMSON in order to solve the problem of loosing phase interface sharpness in long-term calculation. As for the solver of the discrete fluid droplets, we applied the idea of Smoothed Particle Hydrodynamics (SPH) method. Both continuum fluid and discrete fluid interact each other through drag interaction force. We verified our method by applying it to a popular benchmark problem of collapse of water column problems, especially focusing on the splashing and scattering fluid behaviors after the column collided against the wall. We confirmed that the gross splashing and scattering behaviors were well reproduced by the introduction of particle model while the detailed behaviors of the particles were slightly different from the experimental results. (author)

Hamiltonian theory of wave and particle in quantum mechanics 2. Hamilton-Jacobi theory and particle back-reaction

International Nuclear Information System (INIS)

Holland, P.

2001-01-01

Pursuing the Hamiltonian formulation of the De Broglie-Bohm (deBB) theory presented in the preceding paper, the Hamilton-Jacobi (HJ) theory of the wave-particle system is developed. It is shown how to derive a HJ equation for the particle, which enables trajectories to be computed algebraically using Jacobi's method. Using Liouville's equation in the HJ representation it was found the restriction on the Jacobi solutions which implies the quantal distribution. This gives a first method for interpreting the deBB theory in HJ terms. A second method proceeds via an explicit solution of the field+particle HJ equation. Both methods imply that the quantum phase may be interpreted as an incomplete integral. Using these results and those of the first paper it is shown how Schroedinger's equation can be represented in Liouvilian terms, and vice versa. The general theory of canonical transformations that represent quantum unitary transformations is given, and it is shown in principle how the trajectory theory may be expressed in other quantum representations. Using the solution found for the total HJ equation, an explicit solution for the additional field containing a term representing the particle back-reaction is found. The conservation of energy and momentum in the model is established, and weak form of the action-reaction principle is shown to hold. Alternative forms for the Hamiltonian are explored and it is shown that, within this theoretical context, the deBB theory is not unique. The theory potentially provides an alternative way of obtaining the classical limit

Simulations of a single vortex ring using an unbounded, regularized particle-mesh based vortex method

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Spietz, Henrik J.; Walther, Jens Honore

2014-01-01

, unbounded particle-mesh based vortex method is used to simulate the instability, transition to turbulence and eventual destruction of a single vortex ring. From the simulation data a novel method on analyzing the dynamics of the enstrophy is presented based on the alignment of the vorticity vector...... with the principal axis of the strain rate tensor. We find that the dynamics of the enstrophy density is dominated by the local flow deformation and axis of rotation, which is used to infer some concrete tendencies related to the topology of the vorticity field....

Hamiltonian action of spinning particle with gravimagnetic moment

International Nuclear Information System (INIS)

Deriglazov, Alexei A; Ramírez, W Guzmán

2016-01-01

We develop Hamiltonian variational problem for spinning particle non-minimally interacting with gravity through the gravimagnetic moment κ. For κ = 0 our model yields Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations, the latter show unsatisfactory behavior of MPTD-particle in ultra-relativistic regime: its longitudinal acceleration increases with velocity. κ = 1 yields a modification of MPTD-equations with the reasonable behavior: in the homogeneous fields, both longitudinal acceleration and (covariant) precession of spin-tensor vanish as v→c. (paper)

Three particle scattering at high energies in a model with eikonal Hamiltonian

International Nuclear Information System (INIS)

Kharchenko, V.F.; Kuzmichev, V.E.

1980-04-01

The three particle collision process 3 → 3 with relative motion of each pair of particles described by a model with eikonal Hamiltonian is investigated. No additional restrictions on the motion of the particles (such as the fixed scattering centre approximation) are imposed. A unique, exact analytical solution of the three-particle problem is then shown to exist. An explicit expression for the 3 → 3 amplitude in the general case off the energy shell is obtained as the result of the exact summation of the multiple scattering series. It is shown that this series terminates on the energy shell. A new formula for the mutual cancellation of terms in the multiple scattering series in a model with eikonal Hamiltonian is found. (orig.)

Noncanonical Hamiltonian methods in plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1981-11-01

A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions

Noncanonical Hamiltonian methods in plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-01-01

A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)

Second-order particle-in-cell (PIC) computational method in the one-dimensional variable Eulerian mesh system

International Nuclear Information System (INIS)

Pyun, J.J.

1981-01-01

As part of an effort to incorporate the variable Eulerian mesh into the second-order PIC computational method, a truncation error analysis was performed to calculate the second-order error terms for the variable Eulerian mesh system. The results that the maximum mesh size increment/decrement is limited to be α(Δr/sub i/) 2 where Δr/sub i/ is a non-dimensional mesh size of the ith cell, and α is a constant of order one. The numerical solutions of Burgers' equation by the second-order PIC method in the variable Eulerian mesh system wer compared with its exact solution. It was found that the second-order accuracy in the PIC method was maintained under the above condition. Additional problems were analyzed using the second-order PIC methods in both variable and uniform Eulerian mesh systems. The results indicate that the second-order PIC method in the variable Eulerian mesh system can provide substantial computational time saving with no loss in accuracy

Computational performance of Free Mesh Method applied to continuum mechanics problems

Science.gov (United States)

YAGAWA, Genki

2011-01-01

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics. PMID:21558753

Multiphase flow modelling of volcanic ash particle settling in water using adaptive unstructured meshes

Science.gov (United States)

Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R. G.

2013-02-01

Small-scale experiments of volcanic ash particle settling in water have demonstrated that ash particles can either settle slowly and individually, or rapidly and collectively as a gravitationally unstable ash-laden plume. This has important implications for the emplacement of tephra deposits on the seabed. Numerical modelling has the potential to extend the results of laboratory experiments to larger scales and explore the conditions under which plumes may form and persist, but many existing models are computationally restricted by the fixed mesh approaches that they employ. In contrast, this paper presents a new multiphase flow model that uses an adaptive unstructured mesh approach. As a simulation progresses, the mesh is optimized to focus numerical resolution in areas important to the dynamics and decrease it where it is not needed, thereby potentially reducing computational requirements. Model verification is performed using the method of manufactured solutions, which shows the correct solution convergence rates. Model validation and application considers 2-D simulations of plume formation in a water tank which replicate published laboratory experiments. The numerically predicted settling velocities for both individual particles and plumes, as well as instability behaviour, agree well with experimental data and observations. Plume settling is clearly hindered by the presence of a salinity gradient, and its influence must therefore be taken into account when considering particles in bodies of saline water. Furthermore, individual particles settle in the laminar flow regime while plume settling is shown (by plume Reynolds numbers greater than unity) to be in the turbulent flow regime, which has a significant impact on entrainment and settling rates. Mesh adaptivity maintains solution accuracy while providing a substantial reduction in computational requirements when compared to the same simulation performed using a fixed mesh, highlighting the benefits of an

A Direct Method of Hamiltonian Structure

International Nuclear Information System (INIS)

Li Qi; Chen Dengyuan; Su Shuhua

2011-01-01

A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)

Nonconformal scalar field in uniform isotropic space and the method of Hamiltonian diagonalization

International Nuclear Information System (INIS)

Pavlov, Yu.V.

2001-01-01

One diagonalized metric Hamiltonian of scalar field with arbitrary relation with curvature in N-dimensional uniform isotropic space. One derived spectrum of energies of the appropriate quasi-particles. One calculated energy of quasi-particle appropriate to the canonical Hamiltonian diagonal shape. One structured a modified tensor of energy-pulse with the following features. In case of conformal scalar field it coincides with the metric tensor of energy-pulse. When it is diagonalized the energies of the appropriate particles of nonconformal field are equal to oscillation frequency and the number of such particles produced in non-stationary metric is the finite one. It is shown that Hamiltonian calculated on the basis of the modified tensor of energy-pulse may be derived as a canonical one at certain selection of variables [ru

A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

Science.gov (United States)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the Particle Finite Element Method with fixed mesh

Science.gov (United States)

Becker, P.; Idelsohn, S. R.; Oñate, E.

2015-06-01

This paper describes a strategy to solve multi-fluid and fluid-structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (FE) mesh. Our approach is an extension of the fluid-only PFEM-2 (Idelsohn et al., Eng Comput 30(2):2-2, 2013; Idelsohn et al., J Numer Methods Fluids, 2014) which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.

Application of particle-mesh Ewald summation to ONIOM theory

International Nuclear Information System (INIS)

Kobayashi, Osamu; Nanbu, Shinkoh

2015-01-01

Highlights: • Particle-mesh Ewald sum is extended to ONIOM scheme. • Non-adiabatic MD simulation in solution is performed. • The behavior of excited (Z)-penta-2,4-dieniminium cation in methanol is simulated. • The difference between gas phase and solution is predicted. - Abstract: We extended a particle mesh Ewald (PME) summation method to the ONIOM (our Own N-layered Integrated molecular Orbitals and molecular Mechanics) scheme (PME-ONIOM) to validate the simulation in solution. This took the form of a nonadiabatic ab initio molecular dynamics (MD) simulation in which the Zhu-Nakamura trajectory surface hopping (ZN-TSH) method was performed for the photoisomerization of a (Z)-penta-2,4-dieniminium cation (protonated Schiff base, PSB3) electronically excited to the S 1 state in a methanol solution. We also calculated a nonadiabatic ab initio MD simulation with only minimum image convention (MI-ONIOM). The lifetime determined by PME-ONIOM-MD was 3.483 ps. The MI-ONIOM-MD lifetime of 0.4642 ps was much shorter than those of PME-ONIOM-MD and the experimentally determined excited state lifetime. The difference eminently illustrated the accurate treatment of the long-range solvation effect, which destines the electronically excited PSB3 for staying in S 1 at the pico-second or the femto-second time scale.

Simulation study for high resolution alpha particle spectrometry with mesh type collimator

International Nuclear Information System (INIS)

Park, Seunghoon; Kwak, Sungwoo; Kang, Hanbyeol; Shin, Jungki; Park, Iljin

2014-01-01

An alpha particle spectrometry with a mesh type collimator plays a crucial role in identifying specific radionuclide in a radioactive source collected from the atmosphere or environment. The energy resolution is degraded without collimation because particles with a high angle have a longer path to travel in the air. Therefore, collision with the background increases. The collimator can cut out particles which traveling at a high angle. As a result, an energy distribution with high resolution can be obtained. Therefore, the mesh type collimator is simulated for high resolution alpha particle spectrometry. In conclusion, the collimator can improve resolution. With collimator, the collimator is a role of cutting out particles with a high angle, so, low energy tail and broadened energy distribution can be reduced. The mesh diameter is found out as an important factor to control resolution and counting efficiency. Therefore, a target particle, for example, 235 U, can be distinguished by a detector with a collimator under a mixture of various nuclides, for example: 232 U, 238 U, and 232 Th

Hamiltonian diagonalization in foliable space-times: A method to find the modes

International Nuclear Information System (INIS)

Castagnino, M.; Ferraro, R.

1989-01-01

A way to obtain modes diagonalizing the canonical Hamiltonian of a minimally coupled scalar quantum field, in a foliable space-time, is shown. The Cauchy data for these modes are found to be the eigenfunctions of a second-order differential operator that could be interpreted as the squared Hamiltonian for the first-quantized relativistic particle in curved space

Recently developed methods in neutral-particle transport calculations: overview

International Nuclear Information System (INIS)

Alcouffe, R.E.

1982-01-01

It has become increasingly apparent that successful, general methods for the solution of the neutral particle transport equation involve a close connection between the spatial-discretization method used and the source-acceleration method chosen. The first form of the transport equation, angular discretization which is discrete ordinates is considered as well as spatial discretization based upon a mesh arrangement. Characteristic methods are considered briefly in the context of future, desirable developments. The ideal spatial-discretization method is described as having the following attributes: (1) positive-positive boundary data yields a positive angular flux within the mesh including its boundaries; (2) satisfies the particle balance equation over the mesh, that is, the method is conservative; (3) possesses the diffusion limit independent of spatial mesh size, that is, for a linearly isotropic flux assumption, the transport differencing reduces to a suitable diffusion equation differencing; (4) the method is unconditionally acceleratable, i.e., for each mesh size, the method is unconditionally convergent with a source iteration acceleration. It is doubtful that a single method possesses all these attributes for a general problem. Some commonly used methods are outlined and their computational performance and usefulness are compared; recommendations for future development are detailed, which include practical computational considerations

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

Energy Technology Data Exchange (ETDEWEB)

Ortega, Mario Ivan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Drumm, Clifton R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-10-01

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

Cell-centered particle weighting algorithm for PIC simulations in a non-uniform 2D axisymmetric mesh

Science.gov (United States)

Araki, Samuel J.; Wirz, Richard E.

2014-09-01

Standard area weighting methods for particle-in-cell simulations result in systematic errors on particle densities for a non-uniform mesh in cylindrical coordinates. These errors can be significantly reduced by using weighted cell volumes for density calculations. A detailed description on the corrected volume calculations and cell-centered weighting algorithm in a non-uniform mesh is provided. The simple formulas for the corrected volume can be used for any type of quadrilateral and/or triangular mesh in cylindrical coordinates. Density errors arising from the cell-centered weighting algorithm are computed for radial density profiles of uniform, linearly decreasing, and Bessel function in an adaptive Cartesian mesh and an unstructured mesh. For all the density profiles, it is shown that the weighting algorithm provides a significant improvement for density calculations. However, relatively large density errors may persist at outermost cells for monotonically decreasing density profiles. A further analysis has been performed to investigate the effect of the density errors in potential calculations, and it is shown that the error at the outermost cell does not propagate into the potential solution for the density profiles investigated.

Lifting particle coordinate changes of magnetic moment type to Vlasov-Maxwell Hamiltonian dynamics

International Nuclear Information System (INIS)

Morrison, P. J.; Vittot, M.; Guillebon, L. de

2013-01-01

Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the Vlasov-Maxwell dynamics. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.

A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method

Science.gov (United States)

Bush, I. J.; Todorov, I. T.; Smith, W.

2006-09-01

The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.

Hamiltonian Approach to 2+1 Dimensional Gravity

Science.gov (United States)

Cantini, L.; Menotti, P.; Seminara, D.

2002-12-01

It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.

Form factor of relativistic two-particle system and covariant hamiltonian formulation of quantum field theory

International Nuclear Information System (INIS)

Skachkov, N.; Solovtsov, I.

1979-01-01

Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential

A coarse-mesh nodal method-diffusive-mesh finite difference method

International Nuclear Information System (INIS)

Joo, H.; Nichols, W.R.

1994-01-01

Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper

Quantization of a relativistic particle on the SL(2.R) manifold based on Hamiltonian reduction

International Nuclear Information System (INIS)

Jorjadze, G.; O'Raifeartaigh, L.; Tsutsui, I.

1994-07-01

A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2.R) group manifold. Applied to the cotangent bundle of SL(2.R). the method of Hamiltonian reduction allows us to split the reduced system into two coadjoint orbits of the group. We find that the Hilbert space consists of states given by the discrete series of the unitary irreducible representations of SL(2.R). and with a positive-definite, discrete spectrum. (author)

A Momentum-Exchange/Fictitious Domain-Lattice Boltzmann Method for Solving Particle Suspensions

Energy Technology Data Exchange (ETDEWEB)

Jeon, Seok Yun; Yoon, Joon Yong [Hanyang Univ., Seoul (Korea, Republic of); Kim, Chul Kyu [Korea Institute of Civil Engineering and Building Technology, Goyang (Korea, Republic of); Shin, Myung Seob [Korea Intellectual Property Office(KIPO), Daejeon (Korea, Republic of)

2016-06-15

This study presents a Lattice Boltzmann Method (LBM) coupled with a momentum-exchange approach/fictitious domain (MEA/FD) method for the simulation of particle suspensions. The method combines the advantages of the LB and the FD methods by using two unrelated meshes, namely, a Eulerian mesh for the flow domain and a Lagrangian mesh for the solid domain. The rigid body conditions are enforced by the momentum-exchange scheme in which the desired value of velocity is imposed directly in the particle inner domain by introducing a pseudo body force to satisfy the constraint of rigid body motion, which is the key idea of a fictitious domain (FD) method. The LB-MEA/FD method has been validated by simulating two different cases, and the results have been compared with those through other methods. The numerical evidence illustrated the capability and robustness of the present method for simulating particle suspensions.

Gauged Hamiltonians for free particle on surfaces in configuration and phase spaces

Directory of Open Access Journals (Sweden)

M Dehghani

2016-06-01

Full Text Available We present a method to gauge second class systems consisted of two constraints in the chain structure. In this method we added a momentum counterpart of Wess Zumino coordinate to primary constraint and used the first class condition to find a new and gauged Hamiltonian. Primary constraints were assumed as identities in configuration and phase space and we tried to find general Hamiltonians

Classical mechanics systems of particles and Hamiltonian dynamics

CERN Document Server

Greiner, Walter

2010-01-01

This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems. The textbook covers Newtonian mechanics in rotating coordinate systems, mechanics of systems of point particles, vibrating systems and mechanics of rigid bodies. It thoroughly introduces and explains the Lagrange and Hamilton equations and the Hamilton-Jacobi theory. A large section on nonlinear dynamics and chaotic behavior of systems takes Classical Mechanics to newest development in physics. The new edition is completely revised and updated. New exercises and new sections in canonical transformation and Hamiltonian theory have been added.

Method and system for mesh network embedded devices

Science.gov (United States)

Wang, Ray (Inventor)

2009-01-01

A method and system for managing mesh network devices. A mesh network device with integrated features creates an N-way mesh network with a full mesh network topology or a partial mesh network topology.

Non deterministic methods for charged particle transport

International Nuclear Information System (INIS)

Besnard, D.C.; Buresi, E.; Hermeline, F.; Wagon, F.

1985-04-01

The coupling of Monte-Carlo methods for solving Fokker Planck equation with ICF inertial confinement fusion codes requires them to be economical and to preserve gross conservation properties. Besides, the presence in FPE Fokker-Planck equation of diffusion terms due to collisions between test particles and the background plasma challenges standard M.C. (Monte-Carlo) techniques if this phenomenon is dominant. We address these problems through the use of a fixed mesh in phase space which allows us to handle highly variable sources, avoiding any Russian Roulette for lowering the size of the sample. Also on this mesh are solved diffusion equations obtained from a splitting of FPE. Any non linear diffusion terms of FPE can be handled in this manner. Another method, also presented here is to use a direct particle method for solving the full FPE

Relativistic non-Hamiltonian mechanics

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2010-01-01

Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

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Tetsuya Misawa

2010-01-01

Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.

Observation and Control of Hamiltonian Chaos in Wave-particle Interaction

International Nuclear Information System (INIS)

Doveil, F.; Ruzzon, A.; Elskens, Y.

2010-01-01

Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step.This contribution reviews: presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm.The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation.A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the field of

Worlds largest particle physics laboratory selects Proxim Wireless Mesh

CERN Multimedia

2007-01-01

"Proxim Wireless has announced that the European Organization for Nuclear Research (CERN), the world's largest particle physics laboratory and the birthplace of the World Wide Web, is using it's ORiNOCO AP-4000 mesh access points to extend the range of the laboratory's Wi-Fi network and to provide continuous monitoring of the lab's calorimeters" (1/2 page)

Vortex Particle-Mesh simulations of Vertical Axis Wind Turbine flows: from the blade aerodynamics to the very far wake

Science.gov (United States)

Chatelain, P.; Duponcheel, M.; Caprace, D.-G.; Marichal, Y.; Winckelmans, G.

2016-09-01

A Vortex Particle-Mesh (VPM) method with immersed lifting lines has been developed and validated. Based on the vorticity-velocity formulation of the Navier-Stokes equations, it combines the advantages of a particle method and of a mesh-based approach. The immersed lifting lines handle the creation of vorticity from the blade elements and its early development. LES of Vertical Axis Wind Turbine (VAWT) flows are performed. The complex wake development is captured in details and over very long distances: from the blades to the near wake coherent vortices, then through the transitional ones to the fully developed turbulent far wake (beyond 10 rotor diameters). The statistics and topology of the mean flow are studied. The computational sizes also allow insights into the detailed unsteady vortex dynamics, including some unexpected topological flow features.

Vortex Particle-Mesh simulations of Vertical Axis Wind Turbine flows: from the blade aerodynamics to the very far wake

International Nuclear Information System (INIS)

Chatelain, P; Duponcheel, M; Caprace, D-G; Winckelmans, G; Marichal, Y

2016-01-01

A Vortex Particle-Mesh (VPM) method with immersed lifting lines has been developed and validated. Based on the vorticity-velocity formulation of the Navier-Stokes equations, it combines the advantages of a particle method and of a mesh-based approach. The immersed lifting lines handle the creation of vorticity from the blade elements and its early development. LES of Vertical Axis Wind Turbine (VAWT) flows are performed. The complex wake development is captured in details and over very long distances: from the blades to the near wake coherent vortices, then through the transitional ones to the fully developed turbulent far wake (beyond 10 rotor diameters). The statistics and topology of the mean flow are studied. The computational sizes also allow insights into the detailed unsteady vortex dynamics, including some unexpected topological flow features. (paper)

A multilevel particle method for gas dynamics: application to multi-fluids simulation

International Nuclear Information System (INIS)

Weynans, Lisl

2006-12-01

In inertial confinement fusion, laser implosions require to know hydrodynamic flow in presence of shocks. This work is devoted to the evaluation of the ability of a particle-mesh method, inspired from Vortex-In-Cell methods, to simulate gas dynamics, especially multi-fluids. First, we develop a particle method, associated with a conservative re-meshing step, which is performed with high order interpolating kernels. We study theoretically and numerically this method. This analysis gives evidence of a strong relationship between the particle method and high order Lax-Wendroff-like finite difference schemes. We introduce a new scheme for the advection of particles. Then we implement a multilevel technique, inspired from AMR, which allows us to increase locally the accuracy of the computations. Finally we develop a level set-like technique, discretized on the particles, to simulate the interface between compressible flows. We use the multilevel technique to improve the interface resolution and the conservation of partial masses. (author)

Optimized t-expansion method for the Rabi Hamiltonian

International Nuclear Information System (INIS)

Travenec, Igor; Samaj, Ladislav

2011-01-01

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E 0 of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E 0 is assumed to be stationary with respect to the free parameters. A high accuracy of E 0 estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10 -4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E 1 , with the relative error smaller than 10 -2 (1%). -- Highlights: → We study the ground state energy of the Rabi Hamiltonian. → We use the t-expansion method with an optimized trial function. → High accuracy of estimates is achieved, the relative error being smaller than 0.01%. → The calculation of the first excited state energy is made. The method has a general applicability.

Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

International Nuclear Information System (INIS)

Castro, P.G.; Kullock, R.; Toppan, F.

2011-01-01

Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)

Optimal control methods for rapidly time-varying Hamiltonians

International Nuclear Information System (INIS)

Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.

2011-01-01

In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.

Perturbation theory corrections to the two-particle reduced density matrix variational method.

Science.gov (United States)

Juhasz, Tamas; Mazziotti, David A

2004-07-15

In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.

Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

Energy Technology Data Exchange (ETDEWEB)

Castro, P.G., E-mail: pgcastro@cbpf.b [Universidade Federal de Juiz de Fora (DM/ICE/UFJF), Juiz de Fora, MG (Brazil). Inst. de Ciencias Exatas. Dept. de Matematica; Kullock, R.; Toppan, F., E-mail: ricardokl@cbpf.b, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (TEO/CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Fisica Teorica

2011-07-01

Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)

Derivation of Hamiltonians for accelerators

Energy Technology Data Exchange (ETDEWEB)

Symon, K.R.

1997-09-12

In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.

Assessment of finite element and smoothed particles hydrodynamics methods for modeling serrated chip formation in hardened steel

Directory of Open Access Journals (Sweden)

Usama Umer

2016-05-01

Full Text Available This study aims to perform comparative analyses in modeling serrated chip morphologies using traditional finite element and smoothed particles hydrodynamics methods. Although finite element models are being employed in predicting machining performance variables for the last two decades, many drawbacks and limitations exist with the current finite element models. The problems like excessive mesh distortions, high numerical cost of adaptive meshing techniques, and need of geometric chip separation criteria hinder its practical implementation in metal cutting industries. In this study, a mesh free method, namely, smoothed particles hydrodynamics, is implemented for modeling serrated chip morphology while machining AISI H13 hardened tool steel. The smoothed particles hydrodynamics models are compared with the traditional finite element models, and it has been found that the smoothed particles hydrodynamics models have good capabilities in handling large distortions and do not need any geometric or mesh-based chip separation criterion.

On the physical applications of hyper-Hamiltonian dynamics

International Nuclear Information System (INIS)

Gaeta, Giuseppe; Rodriguez, Miguel A

2008-01-01

An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin

Coarse-mesh method for multidimensional, mixed-lattice diffusion calculations

International Nuclear Information System (INIS)

Dodds, H.L. Jr.; Honeck, H.C.; Hostetler, D.E.

1977-01-01

A coarse-mesh finite difference method has been developed for multidimensional, mixed-lattice reactor diffusion calculations, both statics and kinetics, in hexagonal geometry. Results obtained with the coarse-mesh (CM) method have been compared with a conventional mesh-centered finite difference method and with experiment. The results of this comparison indicate that the accuracy of the CM method for highly heterogeneous (mixed) lattices using one point per hexagonal mesh element (''hex'') is about the same as the conventional method with six points per hex. Furthermore, the computing costs (i.e., central processor unit time and core storage requirements) of the CM method with one point per hex are about the same as the conventional method with one point per hex

LR: Compact connectivity representation for triangle meshes

Energy Technology Data Exchange (ETDEWEB)

Gurung, T; Luffel, M; Lindstrom, P; Rossignac, J

2011-01-28

We propose LR (Laced Ring) - a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constant-time adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearly-Hamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard random-access, constant-time operators for traversing a mesh, and show that LR often saves both space and traversal time over competing representations.

Noncanonical Hamiltonian mechanics

International Nuclear Information System (INIS)

Litteljohn, R.G.

1986-01-01

Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)

Enhancements to the Combinatorial Geometry Particle Tracker in the Mercury Monte Carlo Transport Code: Embedded Meshes and Domain Decomposition

International Nuclear Information System (INIS)

Greenman, G.M.; O'Brien, M.J.; Procassini, R.J.; Joy, K.I.

2009-01-01

Two enhancements to the combinatorial geometry (CG) particle tracker in the Mercury Monte Carlo transport code are presented. The first enhancement is a hybrid particle tracker wherein a mesh region is embedded within a CG region. This method permits efficient calculations of problems with contain both large-scale heterogeneous and homogeneous regions. The second enhancement relates to the addition of parallelism within the CG tracker via spatial domain decomposition. This permits calculations of problems with a large degree of geometric complexity, which are not possible through particle parallelism alone. In this method, the cells are decomposed across processors and a particles is communicated to an adjacent processor when it tracks to an interprocessor boundary. Applications that demonstrate the efficacy of these new methods are presented

A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.

Directory of Open Access Journals (Sweden)

Jun-Qing Li

Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.

Variational and penalization methods for studying connecting orbits of Hamiltonian systems

Directory of Open Access Journals (Sweden)

Chao-Nien Chen

2000-08-01

Full Text Available In this article, we consider a class of second order Hamiltonian systems that possess infinite or finite number of equilibria. Variational arguments will be used to study the existence of connecting orbits joining pairs of equilibria. Applying penalization methods, we obtain various patterns for multibump homoclinics and heteroclinics of Hamiltonian systems.

Vortex particle-mesh simulations of vertical axis wind turbine flows: from the airfoil performance to the very far wake

Directory of Open Access Journals (Sweden)

P. Chatelain

2017-06-01

Full Text Available A vortex particle-mesh (VPM method with immersed lifting lines has been developed and validated. Based on the vorticity–velocity formulation of the Navier–Stokes equations, it combines the advantages of a particle method and of a mesh-based approach. The immersed lifting lines handle the creation of vorticity from the blade elements and its early development. Large-eddy simulation (LES of vertical axis wind turbine (VAWT flows is performed. The complex wake development is captured in detail and over up to 15 diameters downstream: from the blades to the near-wake coherent vortices and then through the transitional ones to the fully developed turbulent far wake (beyond 10 rotor diameters. The statistics and topology of the mean flow are studied. The computational sizes also allow insights into the detailed unsteady vortex dynamics and topological flow features, such as a recirculation region influenced by the tip speed ratio and the rotor geometry.

Time dependent drift Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1982-04-01

The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

Adaptive-mesh zoning by the equipotential method

Energy Technology Data Exchange (ETDEWEB)

Winslow, A.M.

1981-04-01

An adaptive mesh method is proposed for the numerical solution of differential equations which causes the mesh lines to move closer together in regions where higher resolution in some physical quantity T is desired. A coefficient D > 0 is introduced into the equipotential zoning equations, where D depends on the gradient of T . The equations are inverted, leading to nonlinear elliptic equations for the mesh coordinates with source terms which depend on the gradient of D. A functional form of D is proposed.

Trajectory Optimization Based on Multi-Interval Mesh Refinement Method

Directory of Open Access Journals (Sweden)

Ningbo Li

2017-01-01

Full Text Available In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

An expert system for automatic mesh generation for Sn particle transport simulation in parallel environment

International Nuclear Information System (INIS)

Apisit, Patchimpattapong; Alireza, Haghighat; Shedlock, D.

2003-01-01

An expert system for generating an effective mesh distribution for the SN particle transport simulation has been developed. This expert system consists of two main parts: 1) an algorithm for generating an effective mesh distribution in a serial environment, and 2) an algorithm for inference of an effective domain decomposition strategy for parallel computing. For the first part, the algorithm prepares an effective mesh distribution considering problem physics and the spatial differencing scheme. For the second part, the algorithm determines a parallel-performance-index (PPI), which is defined as the ratio of the granularity to the degree-of-coupling. The parallel-performance-index provides expected performance of an algorithm depending on computing environment and resources. A large index indicates a high granularity algorithm with relatively low coupling among processors. This expert system has been successfully tested within the PENTRAN (Parallel Environment Neutral-Particle Transport) code system for simulating real-life shielding problems. (authors)

An expert system for automatic mesh generation for Sn particle transport simulation in parallel environment

Energy Technology Data Exchange (ETDEWEB)

Apisit, Patchimpattapong [Electricity Generating Authority of Thailand, Office of Corporate Planning, Bangkruai, Nonthaburi (Thailand); Alireza, Haghighat; Shedlock, D. [Florida Univ., Department of Nuclear and Radiological Engineering, Gainesville, FL (United States)

2003-07-01

An expert system for generating an effective mesh distribution for the SN particle transport simulation has been developed. This expert system consists of two main parts: 1) an algorithm for generating an effective mesh distribution in a serial environment, and 2) an algorithm for inference of an effective domain decomposition strategy for parallel computing. For the first part, the algorithm prepares an effective mesh distribution considering problem physics and the spatial differencing scheme. For the second part, the algorithm determines a parallel-performance-index (PPI), which is defined as the ratio of the granularity to the degree-of-coupling. The parallel-performance-index provides expected performance of an algorithm depending on computing environment and resources. A large index indicates a high granularity algorithm with relatively low coupling among processors. This expert system has been successfully tested within the PENTRAN (Parallel Environment Neutral-Particle Transport) code system for simulating real-life shielding problems. (authors)

The 4-particle hydrogen-anti-hydrogen system revisited. Twofold molecular Hamiltonian symmetry and natural atom anti-hydrogen

International Nuclear Information System (INIS)

Van Hooydonk, G.

2005-01-01

The historical importance of the original quantum mechanical bond theory proposed by Heitler and London in 1927 as well as its pitfalls are reviewed. Modern ab initio treatments of H-H-bar systems are inconsistent with the logic behind algebraic Hamiltonians H ± = H 0 ± ΔH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H 2 and HH-bar. Their eigenvalues are exactly those of 1927 Heitler-London (HL) theory. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H 2 . A wrong choice leads to problems with anti-atom H-bar. In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H 2 . Their theory explains the stability of attractive system H 2 with a repulsive Hamiltonian H 0 + ΔH instead of with the attractive one H 0 - ΔH, representative for charge-asymmetrical system HH-bar. A new second order symmetry effect is detected in this attractive Hamiltonian, which leads to a 3-dimensional structure for the 4-particle system. Repulsive HL Hamiltonian H + applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H - takes over and leads to bond H 2 but in reality, HH-bar, for which we give an analytical proof. This analysis confirms and generalizes an earlier critique of the wrong long range behavior of HL-theory by Bingel, Preuss and Schmidtke and by Herring. Another wrong asymptote choice in the past also applies for atomic anti-hydrogen H-bar, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic H-bar and molecular HH-bar, including the problem with antimatter in the Universe. (author)

Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes

International Nuclear Information System (INIS)

Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.

2005-01-01

An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)

Electrical Resistance Imaging of Two-Phase Flow With a Mesh Grouping Technique Based On Particle Swarm Optimization

International Nuclear Information System (INIS)

Lee, Bo An; Kim, Bong Seok; Ko, Min Seok; Kim, Kyung Young; Kim, Sin

2014-01-01

An electrical resistance tomography (ERT) technique combining the particle swarm optimization (PSO) algorithm with the Gauss-Newton method is applied to the visualization of two-phase flows. In the ERT, the electrical conductivity distribution, namely the conductivity values of pixels (numerical meshes) comprising the domain in the context of a numerical image reconstruction algorithm, is estimated with the known injected currents through the electrodes attached on the domain boundary and the measured potentials on those electrodes. In spite of many favorable characteristics of ERT such as no radiation, low cost, and high temporal resolution compared to other tomography techniques, one of the major drawbacks of ERT is low spatial resolution due to the inherent ill-posedness of conventional image reconstruction algorithms. In fact, the number of known data is much less than that of the unknowns (meshes). Recalling that binary mixtures like two-phase flows consist of only two substances with distinct electrical conductivities, this work adopts the PSO algorithm for mesh grouping to reduce the number of unknowns. In order to verify the enhanced performance of the proposed method, several numerical tests are performed. The comparison between the proposed algorithm and conventional Gauss-Newton method shows significant improvements in the quality of reconstructed images

ELECTRICAL RESISTANCE IMAGING OF TWO-PHASE FLOW WITH A MESH GROUPING TECHNIQUE BASED ON PARTICLE SWARM OPTIMIZATION

Directory of Open Access Journals (Sweden)

BO AN LEE

2014-02-01

Full Text Available An electrical resistance tomography (ERT technique combining the particle swarm optimization (PSO algorithm with the Gauss-Newton method is applied to the visualization of two-phase flows. In the ERT, the electrical conductivity distribution, namely the conductivity values of pixels (numerical meshes comprising the domain in the context of a numerical image reconstruction algorithm, is estimated with the known injected currents through the electrodes attached on the domain boundary and the measured potentials on those electrodes. In spite of many favorable characteristics of ERT such as no radiation, low cost, and high temporal resolution compared to other tomography techniques, one of the major drawbacks of ERT is low spatial resolution due to the inherent ill-posedness of conventional image reconstruction algorithms. In fact, the number of known data is much less than that of the unknowns (meshes. Recalling that binary mixtures like two-phase flows consist of only two substances with distinct electrical conductivities, this work adopts the PSO algorithm for mesh grouping to reduce the number of unknowns. In order to verify the enhanced performance of the proposed method, several numerical tests are performed. The comparison between the proposed algorithm and conventional Gauss-Newton method shows significant improvements in the quality of reconstructed images.

Electrical Resistance Imaging of Two-Phase Flow With a Mesh Grouping Technique Based On Particle Swarm Optimization

Energy Technology Data Exchange (ETDEWEB)

Lee, Bo An; Kim, Bong Seok; Ko, Min Seok; Kim, Kyung Young; Kim, Sin [Jeju National Univ., Jeju (Korea, Republic of)

2014-02-15

An electrical resistance tomography (ERT) technique combining the particle swarm optimization (PSO) algorithm with the Gauss-Newton method is applied to the visualization of two-phase flows. In the ERT, the electrical conductivity distribution, namely the conductivity values of pixels (numerical meshes) comprising the domain in the context of a numerical image reconstruction algorithm, is estimated with the known injected currents through the electrodes attached on the domain boundary and the measured potentials on those electrodes. In spite of many favorable characteristics of ERT such as no radiation, low cost, and high temporal resolution compared to other tomography techniques, one of the major drawbacks of ERT is low spatial resolution due to the inherent ill-posedness of conventional image reconstruction algorithms. In fact, the number of known data is much less than that of the unknowns (meshes). Recalling that binary mixtures like two-phase flows consist of only two substances with distinct electrical conductivities, this work adopts the PSO algorithm for mesh grouping to reduce the number of unknowns. In order to verify the enhanced performance of the proposed method, several numerical tests are performed. The comparison between the proposed algorithm and conventional Gauss-Newton method shows significant improvements in the quality of reconstructed images.

The quasidiffusion method for transport problems on unstructured meshes

Science.gov (United States)

Wieselquist, William A.

2009-06-01

In this work, we develop a quasidiffusion (QD) method for solving radiation transport problems on unstructured quadrilateral meshes in 2D Cartesian geometry, for example hanging-node meshes from adaptive mesh refinement (AMR) applications or skewed quadrilateral meshes from radiation hydrodynamics with Lagrangian meshing. The main result of the work is a new low-order quasidiffusion (LOQD) discretization on arbitrary quadrilaterals and a strategy for the efficient iterative solution which uses Krylov methods and incomplete LU factorization (ILU) preconditioning. The LOQD equations are a non-symmetric set of first-order PDEs that in second-order form resembles convection- diffusion with a diffusion tensor, with the difference that the LOQD equations contain extra cross-derivative terms. Our finite volume (FV) discretization of the LOQD equations is compared with three LOQD discretizations from literature. We then present a conservative, short characteristics discretization based on subcell balances (SCSB) that uses polynomial exponential moments to achieve robust behavior in various limits (e.g. small cells and voids) and is second- order accurate in space. A linear representation of the isotropic component of the scattering source based on face-average and cell-average scalar fluxes is also proposed and shown to be effective in some problems. In numerical tests, our QD method with linear scattering source representation shows some advantages compared to other transport methods. We conclude with avenues for future research and note that this QD method may easily be extended to arbitrary meshes in 3D Cartesian geometry.

Air parcels and air particles: Hamiltonian dynamics

NARCIS (Netherlands)

Bokhove, Onno; Lynch, Peter

We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations

Adaptive and dynamic meshing methods for numerical simulations

Science.gov (United States)

Acikgoz, Nazmiye

-hoc application of the simulated annealing technique, which improves the likelihood of removing poor elements from the grid. Moreover, a local implementation of the simulated annealing is proposed to reduce the computational cost. Many challenging multi-physics and multi-field problems that are unsteady in nature are characterized by moving boundaries and/or interfaces. When the boundary displacements are large, which typically occurs when implicit time marching procedures are used, degenerate elements are easily formed in the grid such that frequent remeshing is required. To deal with this problem, in the second part of this work, we propose a new r-adaptation methodology. The new technique is valid for both simplicial (e.g., triangular, tet) and non-simplicial (e.g., quadrilateral, hex) deforming grids that undergo large imposed displacements at their boundaries. A two- or three-dimensional grid is deformed using a network of linear springs composed of edge springs and a set of virtual springs. The virtual springs are constructed in such a way as to oppose element collapsing. This is accomplished by confining each vertex to its ball through springs that are attached to the vertex and its projection on the ball entities. The resulting linear problem is solved using a preconditioned conjugate gradient method. The new method is compared with the classical spring analogy technique in two- and three-dimensional examples, highlighting the performance improvements achieved by the new method. Meshes are an important part of numerical simulations. Depending on the geometry and flow conditions, the most suitable mesh for each particular problem is different. Meshes are usually generated by either using a suitable software package or solving a PDE. In both cases, engineering intuition plays a significant role in deciding where clusterings should take place. In addition, for unsteady problems, the gradients vary for each time step, which requires frequent remeshing during simulations

Adaptive Mesh Iteration Method for Trajectory Optimization Based on Hermite-Pseudospectral Direct Transcription

Directory of Open Access Journals (Sweden)

Humin Lei

2017-01-01

Full Text Available An adaptive mesh iteration method based on Hermite-Pseudospectral is described for trajectory optimization. The method uses the Legendre-Gauss-Lobatto points as interpolation points; then the state equations are approximated by Hermite interpolating polynomials. The method allows for changes in both number of mesh points and the number of mesh intervals and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to trade the number of mesh points with the number of mesh intervals. The adaptive mesh iteration method is applied successfully to the examples of trajectory optimization of Maneuverable Reentry Research Vehicle, and the simulation experiment results show that the adaptive mesh iteration method has many advantages.

Combining the Vortex Particle-Mesh method with a Multi-Body System solver for the simulation of self-propelled articulated swimmers

Science.gov (United States)

Bernier, Caroline; Gazzola, Mattia; Ronsse, Renaud; Chatelain, Philippe

2017-11-01

We present a 2D fluid-structure interaction simulation method with a specific focus on articulated and actuated structures. The proposed algorithm combines a viscous Vortex Particle-Mesh (VPM) method based on a penalization technique and a Multi-Body System (MBS) solver. The hydrodynamic forces and moments acting on the structure parts are not computed explicitly from the surface stresses; they are rather recovered from the projection and penalization steps within the VPM method. The MBS solver accounts for the body dynamics via the Euler-Lagrange formalism. The deformations of the structure are dictated by the hydrodynamic efforts and actuation torques. Here, we focus on simplified swimming structures composed of neutrally buoyant ellipses connected by virtual joints. The joints are actuated through a simple controller in order to reproduce the swimming patterns of an eel-like swimmer. The method enables to recover the histories of torques applied on each hinge along the body. The method is verified on several benchmarks: an impulsively started elastically mounted cylinder and free swimming articulated fish-like structures. Validation will be performed by means of an experimental swimming robot that reproduces the 2D articulated ellipses.

A multiresolution remeshed particle vortex method using patches

DEFF Research Database (Denmark)

Rasmussen, Johannes Tophøj; Cottet, George-Henri; Walther, Jens Honore

vortex particle-mesh VIC algorithm interpolates particle vorticity to a mesh, solves a Poisson equation for the stream function using FFTs and calculates velocities as the curl of the stream function. With both vorticity and velocity available on the mesh, values of the substantial derivative of particle...... implementation with patches of varying resolution, is applied to the two-dimensional flow past a cylinder. The vorticity field can be divided into two regions, an arbitrary patch of vorticity and the remaining exterior vorticity field. Due to the linearity of the Poisson equation the velocity field corresponding...... to the total vorticity field is the sum of the free space solutions to the Poisson equation to each region. Hereby the flow on the patch can be simulated at a higher resolution, while including the influence from the coarser exterior region. Particles are remeshed and interpolated only to the region from which...

Numerical methods and analysis of the nonlinear Vlasov equation on unstructured meshes of phase space

International Nuclear Information System (INIS)

Besse, Nicolas

2003-01-01

This work is dedicated to the mathematical and numerical studies of the Vlasov equation on phase-space unstructured meshes. In the first part, new semi-Lagrangian methods are developed to solve the Vlasov equation on unstructured meshes of phase space. As the Vlasov equation describes multi-scale phenomena, we also propose original methods based on a wavelet multi-resolution analysis. The resulting algorithm leads to an adaptive mesh-refinement strategy. The new massively-parallel computers allow to use these methods with several phase-space dimensions. Particularly, these numerical schemes are applied to plasma physics and charged particle beams in the case of two-, three-, and four-dimensional Vlasov-Poisson systems. In the second part we prove the convergence and give error estimates for several numerical schemes applied to the Vlasov-Poisson system when strong and classical solutions are considered. First we show the convergence of a semi-Lagrangian scheme on an unstructured mesh of phase space, when the regularity hypotheses for the initial data are minimal. Then we demonstrate the convergence of classes of high-order semi-Lagrangian schemes in the framework of the regular classical solution. In order to reconstruct the distribution function, we consider symmetrical Lagrange polynomials, B-Splines and wavelets bases. Finally we prove the convergence of a semi-Lagrangian scheme with propagation of gradients yielding a high-order and stable reconstruction of the solution. (author) [fr

Reactor calculation in coarse mesh by finite element method applied to matrix response method

International Nuclear Information System (INIS)

Nakata, H.

1982-01-01

The finite element method is applied to the solution of the modified formulation of the matrix-response method aiming to do reactor calculations in coarse mesh. Good results are obtained with a short running time. The method is applicable to problems where the heterogeneity is predominant and to problems of evolution in coarse meshes where the burnup is variable in one same coarse mesh, making the cross section vary spatially with the evolution. (E.G.) [pt

A particle method for history-dependent materials

Energy Technology Data Exchange (ETDEWEB)

Sulsky, D.; Chen, Z.; Schreyer, H.L. [New Mexico Univ., Albuquerque, NM (United States)

1993-06-01

A broad class of engineering problems including penetration, impact and large rotations of solid bodies causes severe numerical problems. For these problems, the constitutive equations are history dependent so material points must be followed; this is difficult to implement in an Eulerian scheme. On the other hand, purely Lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement. Remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables, a process which can introduce errors. Proposed here is an extension of the particle-in-cell method in which particles are interpreted to be material points that are followed through the complete loading process. A fixed Eulerian grid provides the means for determining a spatial gradient. Because the grid can also be interpreted as an updated Lagrangian frame, the usual convection term in the acceleration associated with Eulerian formulations does not appear. With the use of maps between material points and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history. Example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced. Also, it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity.

Evaluating the performance of the particle finite element method in parallel architectures

Science.gov (United States)

Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.

2014-05-01

This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.

Quadratic time dependent Hamiltonians and separation of variables

International Nuclear Information System (INIS)

Anzaldo-Meneses, A.

2017-01-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

Reliability of Lyapunov characteristic exponents computed by the two-particle method

Science.gov (United States)

Mei, Lijie; Huang, Li

2018-03-01

For highly complex problems, such as the post-Newtonian formulation of compact binaries, the two-particle method may be a better, or even the only, choice to compute the Lyapunov characteristic exponent (LCE). This method avoids the complex calculations of variational equations compared with the variational method. However, the two-particle method sometimes provides spurious estimates to LCEs. In this paper, we first analyze the equivalence in the definition of LCE between the variational and two-particle methods for Hamiltonian systems. Then, we develop a criterion to determine the reliability of LCEs computed by the two-particle method by considering the magnitude of the initial tangent (or separation) vector ξ0 (or δ0), renormalization time interval τ, machine precision ε, and global truncation error ɛT. The reliable Lyapunov characteristic indicators estimated by the two-particle method form a V-shaped region, which is restricted by d0, ε, and ɛT. Finally, the numerical experiments with the Hénon-Heiles system, the spinning compact binaries, and the post-Newtonian circular restricted three-body problem strongly support the theoretical results.

A moving mesh finite difference method for equilibrium radiation diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.

A moving mesh finite difference method for equilibrium radiation diffusion equations

International Nuclear Information System (INIS)

Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian

2015-01-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation

A novel three-dimensional mesh deformation method based on sphere relaxation

International Nuclear Information System (INIS)

Zhou, Xuan; Li, Shuixiang

2015-01-01

In our previous work (2013) [19], we developed a disk relaxation based mesh deformation method for two-dimensional mesh deformation. In this paper, the idea of the disk relaxation is extended to the sphere relaxation for three-dimensional meshes with large deformations. We develop a node based pre-displacement procedure to apply initial movements on nodes according to their layer indices. Afterwards, the nodes are moved locally by the improved sphere relaxation algorithm to transfer boundary deformations and increase the mesh quality. A three-dimensional mesh smoothing method is also adopted to prevent the occurrence of the negative volume of elements, and further improve the mesh quality. Numerical applications in three-dimension including the wing rotation, bending beam and morphing aircraft are carried out. The results demonstrate that the sphere relaxation based approach generates the deformed mesh with high quality, especially regarding complex boundaries and large deformations

A novel three-dimensional mesh deformation method based on sphere relaxation

Energy Technology Data Exchange (ETDEWEB)

Zhou, Xuan [Department of Mechanics & Engineering Science, College of Engineering, Peking University, Beijing, 100871 (China); Institute of Applied Physics and Computational Mathematics, Beijing, 100094 (China); Li, Shuixiang, E-mail: lsx@pku.edu.cn [Department of Mechanics & Engineering Science, College of Engineering, Peking University, Beijing, 100871 (China)

2015-10-01

In our previous work (2013) [19], we developed a disk relaxation based mesh deformation method for two-dimensional mesh deformation. In this paper, the idea of the disk relaxation is extended to the sphere relaxation for three-dimensional meshes with large deformations. We develop a node based pre-displacement procedure to apply initial movements on nodes according to their layer indices. Afterwards, the nodes are moved locally by the improved sphere relaxation algorithm to transfer boundary deformations and increase the mesh quality. A three-dimensional mesh smoothing method is also adopted to prevent the occurrence of the negative volume of elements, and further improve the mesh quality. Numerical applications in three-dimension including the wing rotation, bending beam and morphing aircraft are carried out. The results demonstrate that the sphere relaxation based approach generates the deformed mesh with high quality, especially regarding complex boundaries and large deformations.

An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

Directory of Open Access Journals (Sweden)

Jibum Kim

2014-01-01

Full Text Available We present an efficient approach for solving various mesh optimization problems. Our approach is based on Newton’s method, which uses both first-order (gradient and second-order (Hessian derivatives of the nonlinear objective function. The volume and surface mesh optimization algorithms are developed such that mesh validity and surface constraints are satisfied. We also propose several Hessian modification methods when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with nonlinear conjugate gradient and steepest descent methods in terms of both efficiency and mesh quality.

Problem on eigenfunctions and eigenvalues for effective Hamiltonians in pair channels of four-particle systems

International Nuclear Information System (INIS)

Gurbanovich, N.S.; Zelenskaya, I.N.

1976-01-01

The solution for eigenfunction and eigenvalue for effective Hamiltonians anti Hsub(p) in two-particle channels corresponding to division of four particles into groups (3.1) and (2.2) is very essential in the four-body problem as applied to nuclear reactions. The interaction of anti√sub(p) in each channel may be written in the form of an integral operator which takes account of the structure of a target nucleus or of an incident particle and satisfying the integral equation. While assuming the two-particle potentials to be central, it is possible to expand the effective interactions anti√sub(p) in partial waves and write the radial equation for anti Hsub(p). In the approximation on a mass shell the radial equations for the eigenfunctions of Hsub(p) are reduced to an algebraic equations system. The coefficients of the latter are expressed through the Fourier images for products of wave functions of bound clusters and the two-particle central potential which are localized in a momentum space

Explicit symplectic algorithms based on generating functions for charged particle dynamics

Science.gov (United States)

Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan

2016-07-01

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H (x ,p ) =pif (x ) or H (x ,p ) =xig (p ) . Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.

Hamiltonian reductions in plasma physics about intrinsic gyrokinetic

International Nuclear Information System (INIS)

Guillebon de Resnes, L. de

2013-01-01

Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including

Quadratic time dependent Hamiltonians and separation of variables

Science.gov (United States)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

A partial Hamiltonian approach for current value Hamiltonian systems

Science.gov (United States)

Naz, R.; Mahomed, F. M.; Chaudhry, Azam

2014-10-01

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

Oscillator representations for self-adjoint Calogero Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

2011-10-21

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

Oscillator representations for self-adjoint Calogero Hamiltonians

International Nuclear Information System (INIS)

Gitman, D M; Tyutin, I V; Voronov, B L

2011-01-01

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

Study on boundary search method for DFM mesh generation

Directory of Open Access Journals (Sweden)

Li Ri

2012-08-01

Full Text Available The boundary mesh of the casting model was determined by direct calculation on the triangular facets extracted from the STL file of the 3D model. Then the inner and outer grids of the model were identified by the algorithm in which we named Inner Seed Grid Method. Finally, a program to automatically generate a 3D FDM mesh was compiled. In the paper, a method named Triangle Contraction Search Method (TCSM was put forward to ensure not losing the boundary grids; while an algorithm to search inner seed grids to identify inner/outer grids of the casting model was also brought forward. Our algorithm was simple, clear and easy to construct program. Three examples for the casting mesh generation testified the validity of the program.

Adaptive upscaling with the dual mesh method

Energy Technology Data Exchange (ETDEWEB)

Guerillot, D.; Verdiere, S.

1997-08-01

The objective of this paper is to demonstrate that upscaling should be calculated during the flow simulation instead of trying to enhance the a priori upscaling methods. Hence, counter-examples are given to motivate our approach, the so-called Dual Mesh Method. The main steps of this numerical algorithm are recalled. Applications illustrate the necessity to consider different average relative permeability values depending on the direction in space. Moreover, these values could be different for the same average saturation. This proves that an a priori upscaling cannot be the answer even in homogeneous cases because of the {open_quotes}dynamical heterogeneity{close_quotes} created by the saturation profile. Other examples show the efficiency of the Dual Mesh Method applied to heterogeneous medium and to an actual field case in South America.

Renormalization of Hamiltonians

International Nuclear Information System (INIS)

Glazek, S.D.; Wilson, K.G.

1993-01-01

This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

Kinetic solvers with adaptive mesh in phase space

Science.gov (United States)

Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.

2013-12-01

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

Symmetries and the coarse-mesh method

International Nuclear Information System (INIS)

Makai, M.

1980-10-01

This report approaches the basic problem of the coarse-mesh method from a new side. Group theory is used for the determination of the space dependency of the flux. The result is a method called ANANAS after the analytic-analytic solution. This method was tested on two benchmark problems: one given by Melice and the IAEA benchmark. The ANANAS program is an experimental one. The method was intended for use in hexagonal geometry. (Auth.)

An Angular Method with Position Control for Block Mesh Squareness Improvement

Energy Technology Data Exchange (ETDEWEB)

Yao, J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Stillman, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-09-19

We optimize a target function de ned by angular properties with a position control term for a basic stencil with a block-structured mesh, to improve element squareness in 2D and 3D. Comparison with the condition number method shows that besides a similar mesh quality regarding orthogonality can be achieved as the former does, the new method converges faster and provides a more uniform global mesh spacing in our numerical tests.

Normal form for mirror machine Hamiltonians

International Nuclear Information System (INIS)

Dragt, A.J.; Finn, J.M.

1979-01-01

A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior

Coupling of smooth particle hydrodynamics with the finite element method

International Nuclear Information System (INIS)

Attaway, S.W.; Heinstein, M.W.; Swegle, J.W.

1994-01-01

A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code ppercase[pronto]. In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within ppercase[pronto] will be outlined. Example SPH ppercase[pronto] calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or ''bow tie'' elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within ppercase[pronto] allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm. ((orig.))

Mesh joinery: a method for building fabricable structures

OpenAIRE

Cignoni, Paolo; Pietroni, Nico; Malomo, Luigi; Scopigno, Roberto

2015-01-01

Mesh joinery is an innovative method to produce illustrative shape approximations suitable for fabrication. Mesh joinery is capable of producing complex fabricable structures in an efficient and visually pleasing manner. We represent an input geometry as a set of planar pieces arranged to compose a rigid structure by exploiting an efficient slit mechanism. Since slices are planar, a standard 2D cutting system is sufficient to fabricate them.

Hamiltonian Noether theorem for gauge systems and two time physics

International Nuclear Information System (INIS)

Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J

2005-01-01

The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics

Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

Science.gov (United States)

Devi, Y. D.; Kota, V. K. B.

1993-07-01

A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150Nd.

Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

International Nuclear Information System (INIS)

Devi, Y.D.; Kota, V.K.B.

1993-01-01

A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150 Nd

A simple nodal force distribution method in refined finite element meshes

Energy Technology Data Exchange (ETDEWEB)

Park, Jai Hak [Chungbuk National University, Chungju (Korea, Republic of); Shin, Kyu In [Gentec Co., Daejeon (Korea, Republic of); Lee, Dong Won [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Cho, Seungyon [National Fusion Research Institute, Daejeon (Korea, Republic of)

2017-05-15

In finite element analyses, mesh refinement is frequently performed to obtain accurate stress or strain values or to accurately define the geometry. After mesh refinement, equivalent nodal forces should be calculated at the nodes in the refined mesh. If field variables and material properties are available at the integration points in each element, then the accurate equivalent nodal forces can be calculated using an adequate numerical integration. However, in certain circumstances, equivalent nodal forces cannot be calculated because field variable data are not available. In this study, a very simple nodal force distribution method was proposed. Nodal forces of the original finite element mesh are distributed to the nodes of refined meshes to satisfy the equilibrium conditions. The effect of element size should also be considered in determining the magnitude of the distributing nodal forces. A program was developed based on the proposed method, and several example problems were solved to verify the accuracy and effectiveness of the proposed method. From the results, accurate stress field can be recognized to be obtained from refined meshes using the proposed nodal force distribution method. In example problems, the difference between the obtained maximum stress and target stress value was less than 6 % in models with 8-node hexahedral elements and less than 1 % in models with 20-node hexahedral elements or 10-node tetrahedral elements.

Moment methods with effective nuclear Hamiltonians; calculations of radial moments

International Nuclear Information System (INIS)

Belehrad, R.H.

1981-02-01

A truncated orthogonal polynomial expansion is used to evaluate the expectation value of the radial moments of the one-body density of nuclei. The expansion contains the configuration moments, , , and 2 >, where R/sup (k)/ is the operator for the k-th power of the radial coordinate r, and H is the effective nuclear Hamiltonian which is the sum of the relative kinetic energy operator and the Bruckner G matrix. Configuration moments are calculated using trace reduction formulae where the proton and neutron orbitals are treated separately in order to find expectation values of good total isospin. The operator averages are taken over many-body shell model states in the harmonic oscillator basis where all particles are active and single-particle orbitals through six major shells are included. The radial moment expectation values are calculated for the nuclei 16 O, 40 Ca, and 58 Ni and find that is usually the largest term in the expansion giving a large model space dependence to the results. For each of the 3 nuclei, a model space is found which gives the desired rms radius and then we find that the other 5 lowest moments compare favorably with other theoretical predictions. Finally, we use a method of Gordon (5) to employ the lowest 6 radial moment expectation values in the calculation of elastic electron scattering from these nuclei. For low to moderate momentum transfer, the results compare favorably with the experimental data

Mesh Refinement for Particle-In-Cell Plasma Simulations: Applications to - and benefits for - Heavy-Ion-Fusion

International Nuclear Information System (INIS)

Vay, J.-L.; Colella, P.; McCorquodale, P.; Van Straalen, B.; Friedman, A.; Grote, D.P.

2002-01-01

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and simulation of the power plant as a whole, or even of the driver, is not yet possible. Despite the rapid progress in computer power, past and anticipated, one must consider the use of the most advanced numerical techniques, if we are to reach our goal expeditiously. One of the difficulties of these simulations resides in the disparity of scales, in time and in space, which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. They discuss the challenges posed by the implementation of this technique into plasma simulations (due to the presence of particles and electromagnetic waves). They will present the prospects for and projected benefits of its application to heavy ion fusion. In particular to the simulation of the ion source and the final beam propagation in the chamber. A collaboration project is under way at LBNL between the Applied Numerical Algorithms Group (ANAG) and the HIF group to couple the Adaptive Mesh Refinement (AMR) library (CHOMBO) developed by the ANAG group to the Particle-In-Cell accelerator code WARP developed by the HIF-VNL. They describe their progress and present their initial findings

Curci-Ferrari-type condition in Hamiltonian formalism: A free spinning relativistic particle

Science.gov (United States)

Shukla, A.; Bhanja, T.; Malik, R. P.

2013-03-01

The Curci-Ferrari (CF)-type restriction emerges in the description of a free spinning relativistic particle within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of the horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of the superfield formalism. We show that the above CF condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.

Split-Cell Exponential Characteristic Transport Method for Unstructured Tetrahedral Meshes

International Nuclear Information System (INIS)

Brennan, Charles R.; Miller, Rodney L.; Mathews, Kirk A.

2001-01-01

The nonlinear, exponential characteristic (EC) method is extended to unstructured meshes of tetrahedral cells in three-dimensional Cartesian coordinates. The split-cell approach developed for the linear characteristic (LC) method on such meshes is used. Exponential distributions of the source within a cell and of the inflow flux on upstream faces of the cell are assumed. The coefficients of these distributions are determined by nonlinear root solving so as to match the zeroth and first moments of the source or entering flux. Good conditioning is achieved by casting the formulas for the moments of the source, inflow flux, and solution flux as sums of positive functions and by using accurate and robust algorithms for evaluation of those functions. Various test problems are used to compare the performance of the EC and LC methods. The EC method is somewhat less accurate than the LC method in regions of net out leakage but is strictly positive and retains good accuracy with optically thick cells, as in shielding problems, unlike the LC method. The computational cost per cell is greater for the EC method, but the use of substantially coarser meshes can make the EC method less expensive in total cost. The EC method, unlike the LC method, may fail if negative cross sections or angular quadrature weights are used. It is concluded that the EC and LC methods should be practical, reliable, and complimentary schemes for these meshes

The Effective Hamiltonian in the Scalar Electrodynamics

CERN Document Server

Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K

2002-01-01

On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.

Adjoint-based Mesh Optimization Method: The Development and Application for Nuclear Fuel Analysis

International Nuclear Information System (INIS)

Son, Seongmin; Lee, Jeong Ik

2016-01-01

In this research, methods for optimizing mesh distribution is proposed. The proposed method uses adjoint base optimization method (adjoint method). The optimized result will be obtained by applying this meshing technique to the existing code input deck and will be compared to the results produced from the uniform meshing method. Numerical solutions are calculated form an in-house 1D Finite Difference Method code while neglecting the axial conduction. The fuel radial node optimization was first performed to match the Fuel Centerline Temperature (FCT) the best. This was followed by optimizing the axial node which the Peak Cladding Temperature (PCT) is matched the best. After obtaining the optimized radial and axial nodes, the nodalization is implemented into the system analysis code and transient analyses were performed to observe the optimum nodalization performance. The developed adjoint-based mesh optimization method in the study is applied to MARS-KS, which is a nuclear system analysis code. Results show that the newly established method yields better results than that of the uniform meshing method from the numerical point of view. It is again stressed that the optimized mesh for the steady state can also give better numerical results even during a transient analysis

A novel method of the image processing on irregular triangular meshes

Science.gov (United States)

Vishnyakov, Sergey; Pekhterev, Vitaliy; Sokolova, Elizaveta

2018-04-01

The paper describes a novel method of the image processing based on irregular triangular meshes implementation. The triangular mesh is adaptive to the image content, least mean square linear approximation is proposed for the basic interpolation within the triangle. It is proposed to use triangular numbers to simplify using of the local (barycentric) coordinates for the further analysis - triangular element of the initial irregular mesh is to be represented through the set of the four equilateral triangles. This allows to use fast and simple pixels indexing in local coordinates, e.g. "for" or "while" loops for access to the pixels. Moreover, representation proposed allows to use discrete cosine transform of the simple "rectangular" symmetric form without additional pixels reordering (as it is used for shape-adaptive DCT forms). Furthermore, this approach leads to the simple form of the wavelet transform on triangular mesh. The results of the method application are presented. It is shown that advantage of the method proposed is a combination of the flexibility of the image-adaptive irregular meshes with the simple form of the pixel indexing in local triangular coordinates and the using of the common forms of the discrete transforms for triangular meshes. Method described is proposed for the image compression, pattern recognition, image quality improvement, image search and indexing. It also may be used as a part of video coding (intra-frame or inter-frame coding, motion detection).

Implementation of LDG method for 3D unstructured meshes

Directory of Open Access Journals (Sweden)

Filander A. Sequeira Chavarría

2012-07-01

Full Text Available This paper describes an implementation of the Local Discontinuous Galerkin method (LDG applied to elliptic problems in 3D. The implementation of the major operators is discussed. In particular the use of higher-order approximations and unstructured meshes. Efficient data structures that allow fast assembly of the linear system in the mixed formulation are described in detail. Keywords: Discontinuous finite element methods, high-order approximations, unstructured meshes, object-oriented programming. Mathematics Subject Classification: 65K05, 65N30, 65N55.

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

Science.gov (United States)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

A class of explicitly soluble, local, many-center hamiltonians for one-particle quantum mechanics in two and three dimensions. I

International Nuclear Information System (INIS)

Grossmann, A.; Mebkhout, M.; Centre National de la Recherche Scientifique, 13 - Marseille

1979-02-01

An explicit formula for the resolvent of a class of one-particle, many-center, local Hamiltonians is derived. This formula gives, in particular, a full description of a model molecule given by point interactions at n arbitrarily placed fixed centers in three dimensions. It also gives a three-dimensional analogue of the Kronig-Penney model

A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

Science.gov (United States)

Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

2017-12-01

A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

Intertwined Hamiltonians in two-dimensional curved spaces

International Nuclear Information System (INIS)

Aghababaei Samani, Keivan; Zarei, Mina

2005-01-01

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle

Novel methods in the Particle-In-Cell accelerator Code-Framework Warp

Energy Technology Data Exchange (ETDEWEB)

Vay, J-L [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Grote, D. P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Cohen, R. H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Friedman, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2012-12-26

The Particle-In-Cell (PIC) Code-Framework Warp is being developed by the Heavy Ion Fusion Science Virtual National Laboratory (HIFS-VNL) to guide the development of accelerators that can deliver beams suitable for high-energy density experiments and implosion of inertial fusion capsules. It is also applied in various areas outside the Heavy Ion Fusion program to the study and design of existing and next-generation high-energy accelerators, including the study of electron cloud effects and laser wakefield acceleration for example. This study presents an overview of Warp's capabilities, summarizing recent original numerical methods that were developed by the HIFS-VNL (including PIC with adaptive mesh refinement, a large-timestep 'drift-Lorentz' mover for arbitrarily magnetized species, a relativistic Lorentz invariant leapfrog particle pusher, simulations in Lorentz-boosted frames, an electromagnetic solver with tunable numerical dispersion and efficient stride-based digital filtering), with special emphasis on the description of the mesh refinement capability. In addition, selected examples of the applications of the methods to the abovementioned fields are given.

Geometric Hamiltonian structures and perturbation theory

International Nuclear Information System (INIS)

Omohundro, S.

1984-08-01

We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

Science.gov (United States)

Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak

2004-01-01

High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel

The BRST formalism and the quantization of hamiltonian systems with first class constraints

International Nuclear Information System (INIS)

Gamboa, J.; Rivelles, V.O.

1989-04-01

The quantization of hamiltonian system with first class constraints using the BFV formalism is studied. Two examples, the quantization of the relativistic particle and the relativistic spinning particle, are worked out in detail, showing that the BFV formalism is a powerful method for quantizing theories with gauge freedom. Several points not discussed is the literature are pointed out and the correct expression for the Feynman propagator in both cases is found. (L.C.)

A Hamiltonian Monte–Carlo method for Bayesian inference of supermassive black hole binaries

International Nuclear Information System (INIS)

Porter, Edward K; Carré, Jérôme

2014-01-01

We investigate the use of a Hamiltonian Monte–Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte–Carlo (MCMC) methods, such as Metropolis–Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte–Carlo treats the inverse likelihood surface as a ‘gravitational potential’ and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. This method is not as widely used as other MCMC algorithms due to the necessity of calculating gradients of the log-likelihood, which for most applications results in a bottleneck that makes the algorithm computationally prohibitive. We circumvent this problem by using accepted initial phase-space trajectory points to analytically fit for each of the individual gradients. Eliminating the waveform generation needed for the numerical derivatives reduces the total number of required templates for a 10 6 iteration chain from ∼10 9 to ∼10 6 . The result is in an implementation of the Hamiltonian Monte–Carlo that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than a Hessian MCMC. (paper)

Finite element meshing approached as a global minimization process

Energy Technology Data Exchange (ETDEWEB)

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.; LEUNG,VITUS J.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

Science.gov (United States)

Huang, W.; Zheng, Lingyun; Zhan, X.

2002-01-01

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

Hamiltonian kinetic theory of plasma ponderomotive processes

International Nuclear Information System (INIS)

McDonald, S.W.; Kaufman, A.N.

1981-12-01

The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

Hamiltonian kinetic theory of plasma ponderomotive processes

International Nuclear Information System (INIS)

McDonald, S.W.; Kaufman, A.N.

1982-01-01

The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

Mimetic finite difference method for the stokes problem on polygonal meshes

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA

2009-01-01

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

Collective Hamiltonians for dipole giant resonances

International Nuclear Information System (INIS)

Weiss, L.I.

1991-07-01

The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)

Effect of single-particle splitting in the exact wave function of the isovectorial pairing Hamiltonian

International Nuclear Information System (INIS)

Lerma H, S.

2010-01-01

The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for N=Z nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.

Two-dimensional isostatic meshes in the finite element method

OpenAIRE

Martínez Marín, Rubén; Samartín, Avelino

2002-01-01

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's...

A particle finite element method for machining simulations

Science.gov (United States)

Sabel, Matthias; Sator, Christian; Müller, Ralf

2014-07-01

The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.

Numerical form-finding method for large mesh reflectors with elastic rim trusses

Science.gov (United States)

Yang, Dongwu; Zhang, Yiqun; Li, Peng; Du, Jingli

2018-06-01

Traditional methods for designing a mesh reflector usually treat the rim truss as rigid. Due to large aperture, light weight and high accuracy requirements on spaceborne reflectors, the rim truss deformation is indeed not negligible. In order to design a cable net with asymmetric boundaries for the front and rear nets, a cable-net form-finding method is firstly introduced. Then, the form-finding method is embedded into an iterative approach for designing a mesh reflector considering the elasticity of the supporting rim truss. By iterations on form-findings of the cable-net based on the updated boundary conditions due to the rim truss deformation, a mesh reflector with a fairly uniform tension distribution in its equilibrium state could be finally designed. Applications on offset mesh reflectors with both circular and elliptical rim trusses are illustrated. The numerical results show the effectiveness of the proposed approach and that a circular rim truss is more stable than an elliptical rim truss.

BOA, Beam Optics Analyzer A Particle-In-Cell Code

International Nuclear Information System (INIS)

Bui, Thuc

2007-01-01

The program was tasked with implementing time dependent analysis of charges particles into an existing finite element code with adaptive meshing, called Beam Optics Analyzer (BOA). BOA was initially funded by a DOE Phase II program to use the finite element method with adaptive meshing to track particles in unstructured meshes. It uses modern programming techniques, state-of-the-art data structures, so that new methods, features and capabilities are easily added and maintained. This Phase II program was funded to implement plasma simulations in BOA and extend its capabilities to model thermal electrons, secondary emissions, self magnetic field and implement a more comprehensive post-processing and feature-rich GUI. The program was successful in implementing thermal electrons, secondary emissions, and self magnetic field calculations. The BOA GUI was also upgraded significantly, and CCR is receiving interest from the microwave tube and semiconductor equipment industry for the code. Implementation of PIC analysis was partially successful. Computational resource requirements for modeling more than 2000 particles begin to exceed the capability of most readily available computers. Modern plasma analysis typically requires modeling of approximately 2 million particles or more. The problem is that tracking many particles in an unstructured mesh that is adapting becomes inefficient. In particular memory requirements become excessive. This probably makes particle tracking in unstructured meshes currently unfeasible with commonly available computer resources. Consequently, Calabazas Creek Research, Inc. is exploring hybrid codes where the electromagnetic fields are solved on the unstructured, adaptive mesh while particles are tracked on a fixed mesh. Efficient interpolation routines should be able to transfer information between nodes of the two meshes. If successfully developed, this could provide high accuracy and reasonable computational efficiency.

Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

International Nuclear Information System (INIS)

Hoover, W.G.

1980-01-01

Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility

New Method for Mesh Moving Based on Radial Basis Function Interpolation

NARCIS (Netherlands)

De Boer, A.; Van der Schoot, M.S.; Bijl, H.

2006-01-01

A new point-by-point mesh movement algorithm is developed for the deformation of unstructured grids. The method is based on using radial basis function, RBFs, to interpolate the displacements of the boundary nodes to the whole flow mesh. A small system of equations has to be solved, only involving

hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes

CERN Document Server

Cangiani, Andrea; Georgoulis, Emmanuil H; Houston, Paul

2017-01-01

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and elemen...

The renormalized Hamiltonian truncation method in the large E{sub T} expansion

Energy Technology Data Exchange (ETDEWEB)

Elias-Miró, J. [SISSA and INFN, I-34136 Trieste (Italy); Montull, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); Riembau, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); DESY, Notkestrasse 85, 22607 Hamburg (Germany)

2016-04-22

Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in refs. http://dx.doi.org/10.1103/PhysRevD.91.085011; http://dx.doi.org/10.1103/PhysRevD.93.065014; http://dx.doi.org/10.1103/PhysRevD.91.025005. The method is general but as an example we calculate the exact g{sup 2} and some of the g{sup 3} contributions for the ϕ{sup 4} theory in two dimensions. The coefficients of the local expansion calculated in ref. http://dx.doi.org/10.1103/PhysRevD.91.085011 are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.

2D automatic body-fitted structured mesh generation using advancing extraction method

Science.gov (United States)

Zhang, Yaoxin; Jia, Yafei

2018-01-01

This paper presents an automatic mesh generation algorithm for body-fitted structured meshes in Computational Fluids Dynamics (CFD) analysis using the Advancing Extraction Method (AEM). The method is applicable to two-dimensional domains with complex geometries, which have the hierarchical tree-like topography with extrusion-like structures (i.e., branches or tributaries) and intrusion-like structures (i.e., peninsula or dikes). With the AEM, the hierarchical levels of sub-domains can be identified, and the block boundary of each sub-domain in convex polygon shape in each level can be extracted in an advancing scheme. In this paper, several examples were used to illustrate the effectiveness and applicability of the proposed algorithm for automatic structured mesh generation, and the implementation of the method.

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

Science.gov (United States)

Baxes, Gregory A. (Inventor); Linger, Timothy C. (Inventor)

2011-01-01

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

Transmission probability method based on triangle meshes for solving unstructured geometry neutron transport problem

Energy Technology Data Exchange (ETDEWEB)

Wu Hongchun [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)]. E-mail: hongchun@mail.xjtu.edu.cn; Liu Pingping [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Zhou Yongqiang [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Cao Liangzhi [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)

2007-01-15

In the advanced reactor, the fuel assembly or core with unstructured geometry is frequently used and for calculating its fuel assembly, the transmission probability method (TPM) has been used widely. However, the rectangle or hexagon meshes are mainly used in the TPM codes for the normal core structure. The triangle meshes are most useful for expressing the complicated unstructured geometry. Even though finite element method and Monte Carlo method is very good at solving unstructured geometry problem, they are very time consuming. So we developed the TPM code based on the triangle meshes. The TPM code based on the triangle meshes was applied to the hybrid fuel geometry, and compared with the results of the MCNP code and other codes. The results of comparison were consistent with each other. The TPM with triangle meshes would thus be expected to be able to apply to the two-dimensional arbitrary fuel assembly.

Kinetic mesh-free method for flutter prediction in turbomachines

Indian Academy of Sciences (India)

-based mesh-free method for unsteady flows. ... Council for Scientific and Industrial Research, National Aerospace Laboratories, Computational and Theoretical Fluid Dynamics Division, Bangalore 560 017, India; Engineering Mechanics Unit, ...

Strong pairing approximation in comparison with the exact solutions to the pairing Hamiltonian

Directory of Open Access Journals (Sweden)

Lunyov A.V.

2016-01-01

Full Text Available Results of the Strong Pairing Approximation (SPA as a method with the exact particle number conservation are compared with those of the quasiparticle method (QM. It is shown that SPA comes to the same equations as QM for the gap parameter, chemical potential and one- and two-quasiparticle states. Calculations are performed for 14864Gd84 as an example, and compared with the exact solutions to the pairing Hamiltonian.

A local level set method based on a finite element method for unstructured meshes

International Nuclear Information System (INIS)

Ngo, Long Cu; Choi, Hyoung Gwon

2016-01-01

A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time

A local level set method based on a finite element method for unstructured meshes

Energy Technology Data Exchange (ETDEWEB)

Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)

2016-12-15

A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.

An Efficient Mesh Generation Method for Fractured Network System Based on Dynamic Grid Deformation

Directory of Open Access Journals (Sweden)

Shuli Sun

2013-01-01

Full Text Available Meshing quality of the discrete model influences the accuracy, convergence, and efficiency of the solution for fractured network system in geological problem. However, modeling and meshing of such a fractured network system are usually tedious and difficult due to geometric complexity of the computational domain induced by existence and extension of fractures. The traditional meshing method to deal with fractures usually involves boundary recovery operation based on topological transformation, which relies on many complicated techniques and skills. This paper presents an alternative and efficient approach for meshing fractured network system. The method firstly presets points on fractures and then performs Delaunay triangulation to obtain preliminary mesh by point-by-point centroid insertion algorithm. Then the fractures are exactly recovered by local correction with revised dynamic grid deformation approach. Smoothing algorithm is finally applied to improve the quality of mesh. The proposed approach is efficient, easy to implement, and applicable to the cases of initial existing fractures and extension of fractures. The method is successfully applied to modeling of two- and three-dimensional discrete fractured network (DFN system in geological problems to demonstrate its effectiveness and high efficiency.

Particle System Based Adaptive Sampling on Spherical Parameter Space to Improve the MDL Method for Construction of Statistical Shape Models

Directory of Open Access Journals (Sweden)

Rui Xu

2013-01-01

Full Text Available Minimum description length (MDL based group-wise registration was a state-of-the-art method to determine the corresponding points of 3D shapes for the construction of statistical shape models (SSMs. However, it suffered from the problem that determined corresponding points did not uniformly spread on original shapes, since corresponding points were obtained by uniformly sampling the aligned shape on the parameterized space of unit sphere. We proposed a particle-system based method to obtain adaptive sampling positions on the unit sphere to resolve this problem. Here, a set of particles was placed on the unit sphere to construct a particle system whose energy was related to the distortions of parameterized meshes. By minimizing this energy, each particle was moved on the unit sphere. When the system became steady, particles were treated as vertices to build a spherical mesh, which was then relaxed to slightly adjust vertices to obtain optimal sampling-positions. We used 47 cases of (left and right lungs and 50 cases of livers, (left and right kidneys, and spleens for evaluations. Experiments showed that the proposed method was able to resolve the problem of the original MDL method, and the proposed method performed better in the generalization and specificity tests.

Port-Hamiltonian approaches to motion generation for mechanical systems

NARCIS (Netherlands)

Sakai, Satoru; Stramigioli, Stefano

This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system

Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations

International Nuclear Information System (INIS)

Yamamoto, Akio

2005-01-01

This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of the GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations will be easy when the CMFD acceleration is already adopted in a transport code. By multiplying a suitable acceleration factor to a coefficient (D FD ) of a finite difference formulation, one can improve the numerical instability of the CMFD acceleration method

Coarse mesh finite element method for boiling water reactor physics analysis

International Nuclear Information System (INIS)

Ellison, P.G.

1983-01-01

A coarse mesh method is formulated for the solution of Boiling Water Reactor physics problems using two group diffusion theory. No fuel assembly cross-section homogenization is required; water gaps, control blades and fuel pins of varying enrichments are treated explicitly. The method combines constrained finite element discretization with infinite lattice super cell trial functions to obtain coarse mesh solutions for which the only approximations are along the boundaries between fuel assemblies. The method is applied to bench mark Boiling Water Reactor problems to obtain both the eigenvalue and detailed flux distributions. The solutions to these problems indicate the method is useful in predicting detailed power distributions and eigenvalues for Boiling Water Reactor physics problems

Flow simulation of a Pelton bucket using finite volume particle method

International Nuclear Information System (INIS)

Vessaz, C; Jahanbakhsh, E; Avellan, F

2014-01-01

The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets

An arbitrary curvilinear-coordinate method for particle-in-cell modeling

International Nuclear Information System (INIS)

Fichtl, C A; Finn, J M; Cartwright, K L

2012-01-01

A new approach to kinetic simulation of plasmas in complex geometries, based on the particle-in-cell (PIC) simulation method, is explored. In the two-dimensional (2D) electrostatic version of our method, called the arbitrary curvilinear-coordinate PIC method, all essential PIC operations are carried out in 2D on a uniform grid on the unit square logical domain, and mapped to a nonuniform boundary-fitted grid on the physical domain. As the resulting logical grid equations of motion are not separable, we have developed an extension of the semi-implicit modified leapfrog integration technique to preserve the symplectic nature of the logical grid particle mover. A generalized, curvilinear-coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid is also developed. By our formulation, we compute the plasma charge density on the logical grid based on the particles' positions on the logical domain. That is, the plasma particles are weighted to the uniform logical grid and the self-consistent mean electrostatic fields obtained from the solution of the logical grid Poisson equation are interpolated to the particle positions on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid and allows us to run the PIC method on arbitrary boundary-fitted meshes. (paper)

Quantization of a Hamiltonian system with an infinite number of degrees of freedom

International Nuclear Information System (INIS)

Zhidkov, P.E.

1994-01-01

We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schroedinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. In the paper rigorous mathematical methods are used. 9 refs. (author)

Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method

Science.gov (United States)

Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.

2013-01-01

Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…

Empirical Hamiltonians

International Nuclear Information System (INIS)

Peggs, S.; Talman, R.

1987-01-01

As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases

Phase space eigenfunctions of multidimensional quadratic Hamiltonians

International Nuclear Information System (INIS)

Dodonov, V.V.; Man'ko, V.I.

1986-01-01

We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

Upper bounds on entangling rates of bipartite Hamiltonians

International Nuclear Information System (INIS)

Bravyi, Sergey

2007-01-01

We discuss upper bounds on the rate at which unitary evolution governed by a nonlocal Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c log(d) parallel H parallel, where d is the smallest dimension of the interacting particles parallel H parallel is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove an analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate - a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily

Effective Hamiltonian for travelling discrete breathers

Science.gov (United States)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

Patched based methods for adaptive mesh refinement solutions of partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Saltzman, J.

1997-09-02

This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

Hamiltonian systems in accelerator physics

International Nuclear Information System (INIS)

Laslett, L.J.

1985-06-01

General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs

Boundary Hamiltonian Theory for Gapped Topological Orders

Science.gov (United States)

Hu, Yuting; Wan, Yidun; Wu, Yong-Shi

2017-06-01

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.

Comparison of three different methods for effective introduction of platelet-rich plasma on PLGA woven mesh.

Science.gov (United States)

Lee, Ji-Hye; Nam, Jinwoo; Kim, Hee Joong; Yoo, Jeong Joon

2015-03-11

For successful tissue regeneration, effective cell delivery to defect site is very important. Various types of polymer biomaterials have been developed and applied for effective cell delivery. PLGA (poly lactic-co-glycolic acid), a synthetic polymer, is a commercially available and FDA approved material. Platelet-rich plasma (PRP) is an autologous growth factor cocktail containing various growth factors including PDGF, TGFβ-1 and BMPs, and has shown positive effects on cell behaviors. We hypothesized that PRP pretreatment on PLGA mesh using different methods would cause different patterns of platelet adhesion and stages which would modulate cell adhesion and proliferation on the PLGA mesh. In this study, we pretreated PRP on PLGA using three different methods including simple dripping (SD), dynamic oscillation (DO) and centrifugation (CE), then observed the amount of adhered platelets and their activation stage distribution. The highest amount of platelets was observed on CE mesh and calcium treated CE mesh. Moreover, calcium addition after PRP coating triggered dramatic activation of platelets which showed large and flat morphologies of platelets with rich fibrin networks. Human chondrocytes (hCs) and human bone marrow stromal cells (hBMSCs) were next cultured on PRP-pretreated PLGA meshes using different preparation methods. CE mesh showed a significant increase in the initial cell adhesion of hCs and proliferation of hBMSCs compared with SD and DO meshes. The results demonstrated that the centrifugation method can be considered as a promising coating method to introduce PRP on PLGA polymeric material which could improve cell-material interaction using a simple method.

Comparison of three different methods for effective introduction of platelet-rich plasma on PLGA woven mesh

International Nuclear Information System (INIS)

Lee, Ji-Hye; Nam, Jinwoo; Kim, Hee Joong; Yoo, Jeong Joon

2015-01-01

For successful tissue regeneration, effective cell delivery to defect site is very important. Various types of polymer biomaterials have been developed and applied for effective cell delivery. PLGA (poly lactic-co-glycolic acid), a synthetic polymer, is a commercially available and FDA approved material. Platelet-rich plasma (PRP) is an autologous growth factor cocktail containing various growth factors including PDGF, TGFβ-1 and BMPs, and has shown positive effects on cell behaviors. We hypothesized that PRP pretreatment on PLGA mesh using different methods would cause different patterns of platelet adhesion and stages which would modulate cell adhesion and proliferation on the PLGA mesh. In this study, we pretreated PRP on PLGA using three different methods including simple dripping (SD), dynamic oscillation (DO) and centrifugation (CE), then observed the amount of adhered platelets and their activation stage distribution. The highest amount of platelets was observed on CE mesh and calcium treated CE mesh. Moreover, calcium addition after PRP coating triggered dramatic activation of platelets which showed large and flat morphologies of platelets with rich fibrin networks. Human chondrocytes (hCs) and human bone marrow stromal cells (hBMSCs) were next cultured on PRP-pretreated PLGA meshes using different preparation methods. CE mesh showed a significant increase in the initial cell adhesion of hCs and proliferation of hBMSCs compared with SD and DO meshes. The results demonstrated that the centrifugation method can be considered as a promising coating method to introduce PRP on PLGA polymeric material which could improve cell-material interaction using a simple method. (paper)

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

Science.gov (United States)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Measure synchronization in a coupled Hamiltonian associated with ...

African Journals Online (AJOL)

We report here, the existence of measure synchronization (MS) in a coupled Hamiltonian system associated with the motion of particles in a periodic potential of the pendulum type. We show that the oscillators can assume chaotic MS stares vis quasiperiodic measure desynchrononized state. In the chaotic MS state, the ...

A nonlinear equivalent circuit method for analysis of passive intermodulation of mesh reflectors

Directory of Open Access Journals (Sweden)

Jiang Jie

2014-08-01

Full Text Available Passive intermodulation (PIM has gradually become a serious electromagnetic interference due to the development of high-power and high-sensitivity RF/microwave communication systems, especially large deployable mesh reflector antennas. This paper proposes a field-circuit coupling method to analyze the PIM level of mesh reflectors. With the existence of many metal–metal (MM contacts in mesh reflectors, the contact nonlinearity becomes the main reason for PIM generation. To analyze these potential PIM sources, an equivalent circuit model including nonlinear components is constructed to model a single MM contact so that the transient current through the MM contact point induced by incident electromagnetic waves can be calculated. Taking the electric current as a new electromagnetic wave source, the far-field scattering can be obtained by the use of electromagnetic numerical methods or the communication link method. Finally, a comparison between simulation and experimental results is illustrated to verify the validity of the proposed method.

Sdg interacting boson hamiltonian in the seniority scheme

Energy Technology Data Exchange (ETDEWEB)

Yoshinaga, N.

1989-03-06

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

sdg Interacting boson hamiltonian in the seniority scheme

Science.gov (United States)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Wahlen-Strothman, J. M. [Rice Univ., Houston, TX (United States); Henderson, T. H. [Rice Univ., Houston, TX (United States); Hermes, M. R. [Rice Univ., Houston, TX (United States); Degroote, M. [Rice Univ., Houston, TX (United States); Qiu, Y. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)

2018-01-03

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems, but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.

On Using Particle Finite Element for Hydrodynamics Problems Solving

Directory of Open Access Journals (Sweden)

E. V. Davidova

2015-01-01

Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \

A Tissue Relevance and Meshing Method for Computing Patient-Specific Anatomical Models in Endoscopic Sinus Surgery Simulation

Science.gov (United States)

Audette, M. A.; Hertel, I.; Burgert, O.; Strauss, G.

This paper presents on-going work on a method for determining which subvolumes of a patient-specific tissue map, extracted from CT data of the head, are relevant to simulating endoscopic sinus surgery of that individual, and for decomposing these relevant tissues into triangles and tetrahedra whose mesh size is well controlled. The overall goal is to limit the complexity of the real-time biomechanical interaction while ensuring the clinical relevance of the simulation. Relevant tissues are determined as the union of the pathology present in the patient, of critical tissues deemed to be near the intended surgical path or pathology, and of bone and soft tissue near the intended path, pathology or critical tissues. The processing of tissues, prior to meshing, is based on the Fast Marching method applied under various guises, in a conditional manner that is related to tissue classes. The meshing is based on an adaptation of a meshing method of ours, which combines the Marching Tetrahedra method and the discrete Simplex mesh surface model to produce a topologically faithful surface mesh with well controlled edge and face size as a first stage, and Almost-regular Tetrahedralization of the same prescribed mesh size as a last stage.

A moving mesh method with variable relaxation time

OpenAIRE

Soheili, Ali Reza; Stockie, John M.

2006-01-01

We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \\tau is employed as a regularization parameter. Previously reported results on MMPDEs have invariably employed a constant value of the parameter \\tau. We extend this standard approach by incorporating a variable relaxation time that is calculated adaptively alongside the solution in orde...

Action-minimizing methods in Hamiltonian dynamics

CERN Document Server

Sorrentino, Alfonso

2015-01-01

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a

Dynamical decoupling of unbounded Hamiltonians

Science.gov (United States)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

Science.gov (United States)

Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.

2017-12-01

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Fock-space diagonalization of the state-dependent pairing Hamiltonian with the Woods-Saxon mean field

International Nuclear Information System (INIS)

Molique, H.; Dudek, J.

1997-01-01

A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H pair =summation αβ G αβ c α † c bar α † c bar β c β with an arbitrary set of matrix elements G αβ . Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p∼40 particles on n∼80 levels and for several dozens of lowest lying states with precision ∼(1 endash 2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei. copyright 1997 The American Physical Society

Contact Hamiltonian mechanics

Energy Technology Data Exchange (ETDEWEB)

Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)

2017-01-15

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

Hamiltonian formulation for the Martin-Taylor model

International Nuclear Information System (INIS)

Vasconcelos, D.B.; Viana, R.L.

1993-01-01

Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)

Adsorption and kinetics study of manganesse (II) in waste water using vertical column method by sugar cane bagasse

Science.gov (United States)

Zaini, H.; Abubakar, S.; Rihayat, T.; Suryani, S.

2018-03-01

Removal of heavy metal content in wastewater has been largely done by various methods. One effective and efficient method is the adsorption method. This study aims to reduce manganese (II) content in wastewater based on column adsorption method using absorbent material from bagasse. The fixed variable consisted of 50 g adsorbent, 10 liter adsorbate volume, flow rate of 7 liters / min. Independent variable of particle size with variation 10 – 30 mesh and contact time with variation 0 - 240 min and respon variable concentration of adsorbate (ppm), pH and conductivity. The results showed that the adsorption process of manganese metal is influenced by particle size and contact time. The adsorption kinetics takes place according to pseudo-second order kinetics with an equilibrium adsorption capacity (qe: mg / g) for 10 mesh adsorbent particles: 0.8947; 20 mesh adsorbent particles: 0.4332 and 30 mesh adsorbent particles: 1.0161, respectively. Highest removal efficience for 10 mesh adsorbent particles: 49.22% on contact time 60 min; 20 mesh adsorbent particles: 35,25% on contact time 180 min and particle 30 mesh adsorbent particles: 51,95% on contact time 150 min.

The Role of Chronic Mesh Infection in Delayed-Onset Vaginal Mesh Complications or Recurrent Urinary Tract Infections: Results From Explanted Mesh Cultures.

Science.gov (United States)

Mellano, Erin M; Nakamura, Leah Y; Choi, Judy M; Kang, Diana C; Grisales, Tamara; Raz, Shlomo; Rodriguez, Larissa V

2016-01-01

Vaginal mesh complications necessitating excision are increasingly prevalent. We aim to study whether subclinical chronically infected mesh contributes to the development of delayed-onset mesh complications or recurrent urinary tract infections (UTIs). Women undergoing mesh removal from August 2013 through May 2014 were identified by surgical code for vaginal mesh removal. Only women undergoing removal of anti-incontinence mesh were included. Exclusion criteria included any women undergoing simultaneous prolapse mesh removal. We abstracted preoperative and postoperative information from the medical record and compared mesh culture results from patients with and without mesh extrusion, de novo recurrent UTIs, and delayed-onset pain. One hundred seven women with only anti-incontinence mesh removed were included in the analysis. Onset of complications after mesh placement was within the first 6 months in 70 (65%) of 107 and delayed (≥6 months) in 37 (35%) of 107. A positive culture from the explanted mesh was obtained from 82 (77%) of 107 patients, and 40 (37%) of 107 were positive with potential pathogens. There were no significant differences in culture results when comparing patients with delayed-onset versus immediate pain, extrusion with no extrusion, and de novo recurrent UTIs with no infections. In this large cohort of patients with mesh removed for a diverse array of complications, cultures of the explanted vaginal mesh demonstrate frequent low-density bacterial colonization. We found no differences in culture results from women with delayed-onset pain versus acute pain, vaginal mesh extrusions versus no extrusions, or recurrent UTIs using standard culture methods. Chronic prosthetic infections in other areas of medicine are associated with bacterial biofilms, which are resistant to typical culture techniques. Further studies using culture-independent methods are needed to investigate the potential role of chronic bacterial infections in delayed vaginal mesh

New Hamiltonian constraint operator for loop quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

2015-12-17

A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

New Hamiltonian constraint operator for loop quantum gravity

Directory of Open Access Journals (Sweden)

Jinsong Yang

2015-12-01

Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

International Nuclear Information System (INIS)

Yahiaoui, S.-A.; Bentaiba, M.

2011-01-01

We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)

Solving kinetic equations with adaptive mesh in phase space for rarefied gas dynamics and plasma physics (Invited)

International Nuclear Information System (INIS)

Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna

2014-01-01

The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers

Solving kinetic equations with adaptive mesh in phase space for rarefied gas dynamics and plasma physics (Invited)

Energy Technology Data Exchange (ETDEWEB)

Kolobov, Vladimir [CFD Research Corporation, Huntsville, AL 35805, USA and The University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Arslanbekov, Robert [CFD Research Corporation, Huntsville, AL 35805 (United States); Frolova, Anna [Computing Center of the Russian Academy of Sciences, Moscow, 119333 (Russian Federation)

2014-12-09

The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.

PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils

Science.gov (United States)

Johnson, Scott; Walton, Otis; Settgast, Randolph

2013-01-01

PowderSim is a calculation tool that combines a discrete-element method (DEM) module, including calibrated interparticle-interaction relationships, with a mesh-free, continuum, SPH (smoothed-particle hydrodynamics) based module that utilizes enhanced, calibrated, constitutive models capable of mimicking both large deformations and the flow behavior of regolith simulants and lunar regolith under conditions anticipated during in situ resource utilization (ISRU) operations. The major innovation introduced in PowderSim is to use a mesh-free method (SPH-based) with a calibrated and slightly modified critical-state soil mechanics constitutive model to extend the ability of the simulation tool to also address full-scale engineering systems in the continuum sense. The PowderSim software maintains the ability to address particle-scale problems, like size segregation, in selected regions with a traditional DEM module, which has improved contact physics and electrostatic interaction models.

An immersed boundary method for the interaction of turbulence with particles of arbitrary shape

Science.gov (United States)

Wang, Shizhao; Vanella, Marcos; Balaras, Elias

2014-11-01

In this work we present a computational scheme applicable to turbulence/particle interactions, targeting applications involving millions of particles of arbitrary shape. Immersed boundary methods have been frequently applied in simulating such problems, but are usually confined to spherical particles. Extension to rigid/deformable particles of arbitrary shape introduces significant challenges in achieving parallel efficiency. The proposed method is based on the moving least squares immersed boundary approach (Vanella & Balaras, J. Comput. Physics, 228(18), 6617, 2009) on uniform and adaptive block-structured grids. We will present a novel parallelization strategy based on a master/slave model: the processor on which a body/structure resides is designated the master processor, while all the processors that contain at least one block overlapping with the body are designated the slaves. As the particle moves through the fluid, its blocks association and therefore the participating processors change. Effective ways of replicating the mesh metadata on all processors will be discussed. Results for homogeneous turbulence interacting with spherical and ellipsoidal particles and comparisons with experimental results will be given.

Nyx: Adaptive mesh, massively-parallel, cosmological simulation code

Science.gov (United States)

Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun

2017-12-01

Nyx code solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D Eulerian grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the code calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.

Adaptive hybrid mesh refinement for multiphysics applications

International Nuclear Information System (INIS)

Khamayseh, Ahmed; Almeida, Valmor de

2007-01-01

The accuracy and convergence of computational solutions of mesh-based methods is strongly dependent on the quality of the mesh used. We have developed methods for optimizing meshes that are comprised of elements of arbitrary polygonal and polyhedral type. We present in this research the development of r-h hybrid adaptive meshing technology tailored to application areas relevant to multi-physics modeling and simulation. Solution-based adaptation methods are used to reposition mesh nodes (r-adaptation) or to refine the mesh cells (h-adaptation) to minimize solution error. The numerical methods perform either the r-adaptive mesh optimization or the h-adaptive mesh refinement method on the initial isotropic or anisotropic meshes to equidistribute weighted geometric and/or solution error function. We have successfully introduced r-h adaptivity to a least-squares method with spherical harmonics basis functions for the solution of the spherical shallow atmosphere model used in climate modeling. In addition, application of this technology also covers a wide range of disciplines in computational sciences, most notably, time-dependent multi-physics, multi-scale modeling and simulation

Review of the modified finite particle method and application to incompressible solids

Directory of Open Access Journals (Sweden)

D Asprone

2016-10-01

Full Text Available This paper focuses on the application of the Modified Finite Particle Method (MFPM on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

NLO renormalization in the Hamiltonian truncation

Science.gov (United States)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Relativistic particles coupled to Chern-Simons term-revisited

International Nuclear Information System (INIS)

Chakraborty, B.

1995-01-01

The author considers the model of N relativistic spinless particles coupled to an abelian Chern-Simons term. Rewriting the action in a time reparamaterized form by introducing an arbitary parameter, parameterizing the world line of the particles, the author makes a classical constraint Hamiltonian analysis of the model. Subsequent to gauge fixing by equating the arbitrary parameter with the time the author identifies the Hamiltonian of the system, which agrees with the Hamiltonian obtained by using Banerjee's method of fixing the arbitrary Langrange multiplier by using equations of motion. The author exhibits the Poincare invariance of the model, at the classical level, by constructing spacetime generators using either the canonical or symmetric definition of the energy-momentum tensor. A detailed comparison of the expressions of angular momentum obtained by both methods show that both agree up to a boundary term. In presence of rotationally symmetric vortex configuration this term can be interpreted as an anomalous angular momentum term. The author also heuristically discusses the effect of gauge fixing on the transformation properties. 13 refs

Theoretical issues in quantum computing: Graph isomorphism, PageRank, and Hamiltonian determination

Science.gov (United States)

Rudinger, Kenneth Michael

This thesis explores several theoretical questions pertaining to quantum computing. First we examine several questions regarding multi-particle quantum random walk-based algorithms for the graph isomorphism problem. We find that there exists a non-trivial difference between continuous-time walks of one and two non-interacting particles as compared to non-interacting walks of three or more particles, in that the latter are able to distinguish many strongly regular graphs (SRGs), a class of graphs with many graph pairs that are difficult to distinguish. We demonstrate analytically where this distinguishing power comes from, and we show numerically that three-particle and four-particle non-interacting continuous-time walks can distinguish many pairs of strongly regular graphs. We additionally show that this distinguishing power, while it grows with particle number, is bounded, so that no continuous-time non-interacting walk of fixed particle number can distinguish all strongly regular graphs. We then investigate the relationship between continuous-time and discrete-time walks, in the context of the graph isomorphism problem. While it has been previously demonstrated numerically that discrete-time walks of non-interacting particles can distinguish some SRGs, we demonstrate where this distinguishing power comes from. We also show that while no continuous-time non-interacting walk of fixed particle number can distinguish SRGs, it remains a possibility that such a discrete-time walk could, leaving open the possibility of a non-trivial difference between discrete-time and continuous-time walks. The last piece of our work on graph isomorphism examines limitations on certain kinds of continuous-time walk-based algorithms for distinguishing graphs. We show that a very general class of continuous-time walk algorithms, with a broad class of allowable interactions, cannot distinguish all graphs. We next consider a previously-proposed quantum adiabatic algorithm for computing the

Hamiltonian dynamics for complex food webs

Science.gov (United States)

Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

2016-03-01

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

Energy Technology Data Exchange (ETDEWEB)

De Corato, M., E-mail: marco.decorato@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Slot, J.J.M., E-mail: j.j.m.slot@tue.nl [Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); Hütter, M., E-mail: m.huetter@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); D' Avino, G., E-mail: gadavino@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Maffettone, P.L., E-mail: pierluca.maffettone@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Hulsen, M.A., E-mail: m.a.hulsen@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands)

2016-07-01

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.

Explicit K-symplectic algorithms for charged particle dynamics

International Nuclear Information System (INIS)

He, Yang; Zhou, Zhaoqi; Sun, Yajuan; Liu, Jian; Qin, Hong

2017-01-01

We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.

Explicit K-symplectic algorithms for charged particle dynamics

Energy Technology Data Exchange (ETDEWEB)

He, Yang [School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China); Zhou, Zhaoqi [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China); Sun, Yajuan, E-mail: sunyj@lsec.cc.ac.cn [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Liu, Jian [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 (China); Qin, Hong [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States)

2017-02-12

We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.

Extended hamiltonian formalism and Lorentz-violating lagrangians

Directory of Open Access Journals (Sweden)

Don Colladay

2017-09-01

Full Text Available A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler–Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Extended hamiltonian formalism and Lorentz-violating lagrangians

Science.gov (United States)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Stability and amplitude ranges of two dimensional non-linear oscillations with periodical Hamiltonian applied to betatron oscillations in circular particle accelerators: Part 1 and Part 2

Energy Technology Data Exchange (ETDEWEB)

Hagedorn, R

1957-03-07

A mechanical system of two degrees of freedom is considered which can be described by a system of canonical differential equations. The Hamiltonian is assumed to be explicitly time-dependent with period 2. The aim is to bring this system by a sequence of canonical and periodical transformations into a form where the new Hamiltonian is constant and as simple as possible. The general theory is then brought to a stage where it becomes immediately applicable to given particular cases, particularly to circular particle accelerators. More general results are given on exciting strengths of different subresonance lines of equal order, on symmetry relations and on the one-dimensional case. An example is also given where the theory is overstressed and its predictions become wrong.

Quantum and classical dissipation of charged particles

Energy Technology Data Exchange (ETDEWEB)

Ibarra-Sierra, V.G. [Departamento de Física, Universidad Autónoma Metropolitana at Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Anzaldo-Meneses, A.; Cardoso, J.L.; Hernández-Saldaña, H. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana at Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana at Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Roa-Neri, J.A.E. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana at Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

2013-08-15

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle. •Classical and quantum dynamics of a damped electric charge.

Quantum and classical dissipation of charged particles

International Nuclear Information System (INIS)

Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.; Hernández-Saldaña, H.; Kunold, A.; Roa-Neri, J.A.E.

2013-01-01

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle. •Classical and quantum dynamics of a damped electric charge

Hamiltonian Algorithm Sound Synthesis

OpenAIRE

大矢, 健一

2013-01-01

Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.

Mathematics and computational methods development in U.S. department of energy-sponsored research (nuclear energy research initiative and nuclear engineering education research). 4. Development of an Expert System for Generation of an Effective Mesh Distribution for the SN Method

International Nuclear Information System (INIS)

Patchimpattapong, Apisit; Haghighat, Alireza

2001-01-01

The discrete ordinates (S N ) method is widely used to obtain numerical solutions of the transport equation. The method calls for discretization of spatial, energy, and angular variables. To generate an 'effective' spatial mesh distribution, one has to consider various factors including particle mean free path (mfp), material and source discontinuities, and problem objectives. This becomes more complicated if we consider the effect of numerics such as differencing schemes, parallel processing strategies, and computation resources. As a result, one may often over/under-mesh depending upon limitations on accuracy, computing resources, and time allotted. To overcome the foregoing issues, we are developing an expert system for input preparation of the discrete ordinates (S N ) method. This project is a part of an ongoing project sponsored by Nuclear Engineering Education Research. Our expert system consists of two parts: (a) an algorithm for generation of a mesh distribution for a serial calculation and (b) an algorithm for extension to parallel computing, which accounts for parallelization parameters including granularity, load balancing, parallel algorithms, and possible architectural issues. Thus far, we have developed a stand-alone algorithm for generation of an 'effective' mesh distribution for a serial calculation. The algorithm has been successfully tested with the Parallel Environment Neutral-Particle Transport (PENTRAN) code system. In this paper, we discuss the structure of our algorithm and present its use for simulating the VENUS-3 experimental facility. To date, we have developed and tested part 1 of this system. This part comprises of four steps: creation of a geometric model and coarse meshes, calculation of un-collided flux, selection of differencing schemes, and generation of fine-mesh distribution. For the un-collided flux calculation, we have developed a parallel code called PENFC. It is capable of calculating un-collided and first-collision fluxes

Nonextensive formalism and continuous Hamiltonian systems

International Nuclear Information System (INIS)

Boon, Jean Pierre; Lutsko, James F.

2011-01-01

A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.

Transonic Airfoil Flow Simulation. Part I: Mesh Generation and Inviscid Method

Directory of Open Access Journals (Sweden)

Vladimir CARDOS

2010-06-01

Full Text Available A calculation method for the subsonic and transonic viscous flow over airfoil using thedisplacement surface concept is described. Part I presents a mesh generation method forcomputational grid and a finite volume method for the time-dependent Euler equations. The inviscidsolution is used for the inviscid-viscous coupling procedure presented in the Part II.

On the minimization of Hamiltonians over pure Gaussian states

DEFF Research Database (Denmark)

Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip

2013-01-01

that this procedure eliminates from the Hamiltonian terms of degree 1 and 2 that do not preserve the particle number, and leaves only terms that can be interpreted as quasiparticles excitations. We propose to call this fact Beliaev's Theorem, since to our knowledge it was mentioned for the first time in a paper...

On local Hamiltonians and dissipative systems

Energy Technology Data Exchange (ETDEWEB)

Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)

2006-11-15

We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.

Virtual particle-antiparticle pair formation by a scalar particle bound in an external Coulomb field

International Nuclear Information System (INIS)

Darewych, J.W.; Horbatsch, M.; Lev, B.I.; Shapoval, D.V.

1995-01-01

A Hamiltonian variational Fock-space method is used to describe scalar massive particles in an external Coulomb field with strength f=Zα. The use of an ansatz that includes a three-particle state in addition to a single-particle state built on the field-free vacuum enables one to highlight the role played by particle-antiparticle pair formation. Comparison is made with the Klein-Gordon equation in the Feshbach-Villars representation and it is shown explicitly how the virtual pair contribution corrects an O(f 5 ) deficiency present in the energy spectrum of the naive Schroedinger-type single-particle equation. ((orig.))

Effect of particle size on mixing degree in dispensation.

Science.gov (United States)

Nakamura, Hitoshi; Yanagihara, Yoshitsugu; Sekiguchi, Hiroko; Ohtani, Michiteru; Kariya, Satoru; Uchino, Katsuyoshi; Suzuki, Hiroshi; Iga, Tatsuji

2004-03-01

By using lactose colored with erythrocin, we examined the effect of particle size on mixing degree during the preparation of triturations with a mortar and pestle. We used powders with different distributions of particle sizes, i.e., powder that passed through 32-mesh but was trapped on a 42-mesh sieve (32/42-mesh powder), powder that passed through a 42-mesh sieve but was trapped on a 60-mesh sieve (42/60-mesh powder), powder that passed through a 60-mesh sieve but was trapped on a 100-mesh sieve (60/100-mesh powder), and powder that passes through a 100-mesh sieve (> 100-mesh powder). The mixing degree of colored powder and non-colored powder whose distribution of particle sizes was the same as that of the colored powder was excellent. The coefficient of variation (CV) value of the mixing degree was 6.08% after 40 rotations when colored powder was mixed with non-colored powder that both passed through a 100-mesh sieve. The CV value of the mixing degree was low in the case of mixing of colored and non-colored powders with different particle size distributions. After mixing, about 50% of 42/60-mesh powder had become smaller particles, whereas the distribution of particle sizes was not influenced by the mixing of 60/100-mesh powder. It was suggested that the mixing degree is affected by distribution of particle sizes. It may be important to determine the mixing degrees for drugs with narrow therapeutic ranges.

Application of coarse-mesh methods to fluid dynamics equations

International Nuclear Information System (INIS)

Romstedt, P.; Werner, W.

1977-01-01

An Asymmetric Weighted Residual (ASWR) method for fluid dynamics equations is described. It leads to local operators with a 7-point Finite Difference (FD) structure, which is independent of the degree of the approximating polynomials. An 1-dimensional problem was solved by both this ASWR-method and a commonly used FD-method. The numerical results demonstrate that the ASWR-method combines high accuracy on a coarse computational mesh with short computing time per space point. The posibility of using fewer space points consequently brings about a considerable reduction in total running time for the ASWR-method as compared with conventional FD-methods. (orig.) [de

N=2, D=4 supersymmetric σ-models and Hamiltonian mechanics

International Nuclear Information System (INIS)

Galperin, A.; Ogievetsky, V.

1991-05-01

A deep similarity is established between the Hamiltonian mechanics of point particle and supersymmetric N=2, D=4 σ-models formulated within harmonic superspace. An essential part of the latter, the sphere S 2 , comes out as a counterpart of the time variable. (author). 7 refs

Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

Science.gov (United States)

Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.

2017-04-01

In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the "exact" adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.

Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator

International Nuclear Information System (INIS)

Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.

1984-01-01

Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator

Studies of particles statistics in one and two dimensions, based on the quantization methods of Heisenberg, Schroedinger and Feynman

International Nuclear Information System (INIS)

Myrheim, J.

1993-06-01

The thesis deals with the application of different methods to the quantization problem for system of identical particles in one and two dimensions. The standard method is the analytic quantization method due to Schroedinger, which leads to the concept of fractional statistics in one and two dimensions. Two-dimensional particles with fractional statistics are well known by the name of anyons. Two alternative quantization methods are shown by the author, the algebraic method of Heisenberg and the Feynman path integral method. The Feynman method is closely related to the Schroedinger method, whereas the Heisenberg and Schroedinger methods may give different results. The relation between the Heisenberg and Schroedinger methods is discussed. The Heisenberg method is applied to the equations of motion of vortices in superfluid helium, which have the form of Hamiltonian equations for a one-dimensional system. The same method is also discussed more generally for systems of identical particles in one and two dimensions. An application of the Feynman method to the problem of computing the equation of state for a gas of anyons is presented. 104 refs., 4 figs

Lagrangian Particle Tracking in a Discontinuous Galerkin Method for Hypersonic Reentry Flows in Dusty Environments

Science.gov (United States)

Ching, Eric; Lv, Yu; Ihme, Matthias

2017-11-01

Recent interest in human-scale missions to Mars has sparked active research into high-fidelity simulations of reentry flows. A key feature of the Mars atmosphere is the high levels of suspended dust particles, which can not only enhance erosion of thermal protection systems but also transfer energy and momentum to the shock layer, increasing surface heat fluxes. Second-order finite-volume schemes are typically employed for hypersonic flow simulations, but such schemes suffer from a number of limitations. An attractive alternative is discontinuous Galerkin methods, which benefit from arbitrarily high spatial order of accuracy, geometric flexibility, and other advantages. As such, a Lagrangian particle method is developed in a discontinuous Galerkin framework to enable the computation of particle-laden hypersonic flows. Two-way coupling between the carrier and disperse phases is considered, and an efficient particle search algorithm compatible with unstructured curved meshes is proposed. In addition, variable thermodynamic properties are considered to accommodate high-temperature gases. The performance of the particle method is demonstrated in several test cases, with focus on the accurate prediction of particle trajectories and heating augmentation. Financial support from a Stanford Graduate Fellowship and the NASA Early Career Faculty program are gratefully acknowledged.

Progress in the study of mesh refinement for particle-in-cell plasma simulations and its application to heavy ion fusion

International Nuclear Information System (INIS)

Vay, J.-L.; Friedman, A.; Grote, D.P.

2002-01-01

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and, despite rapid progress in computer power, one must consider the use of the most advanced numerical techniques. One of the difficulties of these simulations resides in the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the Adaptive-Mesh-Refinement (AMR) technique. We follow in this article the progress accomplished in the last few months in the merging of the AMR technique with Particle-In-Cell (PIC) method. This includes a detailed modeling of the Lampel-Tiefenback solution for the one-dimensional diode using novel techniques to suppress undesirable numerical oscillations and an AMR patch to follow the head of the particle distribution. We also report new results concerning the modeling of ion sources using the axisymmetric WARPRZ-AMR prototype showing the utility of an AMR patch resolving the emitter vicinity and the beam edge

The hamiltonian index of a graph and its branch-bonds

NARCIS (Netherlands)

Xiong, Liming; Broersma, Haitze J.; Li, Xueliang; Li, Xueliang; Li, MingChu

2004-01-01

Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G) ≤ 2 is given here. We

Tsallis thermostatistics for finite systems: a Hamiltonian approach

Science.gov (United States)

Adib, Artur B.; Moreira, Andrã© A.; Andrade, José S., Jr.; Almeida, Murilo P.

2003-05-01

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.

On the generating function of Poincare plots defining one dimensional perturbed Hamiltonian systems

International Nuclear Information System (INIS)

Montvai, A.

1989-01-01

A simple numerical method has been devised, for deriving the generating function of an arbitrary, one dimensional Hamiltonian system represented by its Poincare plot. In this case, the plot to be numerically processed is an area preserving transformation of a two-dimensional surface onto itself. Although the method in its present form is capable of treating only this case, there are no principal restrictions excluding the analysis of systems with higher dimensionality as well. As an example, the generating function of the motion of alpha particles in a nonsymmetric, toroidal magnetic field is derived and studied numerically. (orig.)

Boltzmann Solver with Adaptive Mesh in Velocity Space

International Nuclear Information System (INIS)

Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.

2011-01-01

We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.

A Wrapping Method for Inserting Titanium Micro-Mesh Implants in the Reconstruction of Blowout Fractures

Directory of Open Access Journals (Sweden)

Tae Joon Choi

2016-01-01

Full Text Available Titanium micro-mesh implants are widely used in orbital wall reconstructions because they have several advantageous characteristics. However, the rough and irregular marginal spurs of the cut edges of the titanium mesh sheet impede the efficacious and minimally traumatic insertion of the implant, because these spurs may catch or hook the orbital soft tissue, skin, or conjunctiva during the insertion procedure. In order to prevent this problem, we developed an easy method of inserting a titanium micro-mesh, in which it is wrapped with the aseptic transparent plastic film that is used to pack surgical instruments or is attached to one side of the inner suture package. Fifty-four patients underwent orbital wall reconstruction using a transconjunctival or transcutaneous approach. The wrapped implant was easily inserted without catching or injuring the orbital soft tissue, skin, or conjunctiva. In most cases, the implant was inserted in one attempt. Postoperative computed tomographic scans showed excellent placement of the titanium micro-mesh and adequate anatomic reconstruction of the orbital walls. This wrapping insertion method may be useful for making the insertion of titanium micro-mesh implants in the reconstruction of orbital wall fractures easier and less traumatic.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

International Nuclear Information System (INIS)

Longhi, Stefano

2014-01-01

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H -hat (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H -hat (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization

Hamiltonian reduction of SU(2) Yang-Mills field theory

International Nuclear Information System (INIS)

Khvedelidze, A.M.; Pavel, H.-P.

1998-01-01

The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

Science.gov (United States)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

Mesh Processing in Medical Image Analysis

DEFF Research Database (Denmark)

The following topics are dealt with: mesh processing; medical image analysis; interactive freeform modeling; statistical shape analysis; clinical CT images; statistical surface recovery; automated segmentation; cerebral aneurysms; and real-time particle-based representation....

Hamiltonian description and quantization of dissipative systems

Science.gov (United States)

Enz, Charles P.

1994-09-01

Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

Redundancy-free single-particle equation-of-motion method for nuclei. Pt. 1

International Nuclear Information System (INIS)

Rolnick, P.; Goswami, A.; Oregon Univ., Eugene

1986-01-01

The problem of coupling an odd nucleon to the collective states of an even core is considered in the intermediate-coupling limit. It is now well known that such intermediate-coupling calculations in spherical open-shell nuclei necessitate the inclusion of ground-state correlation or backward coupling which gives rise to an overcomplete basic set of states for the diagonalization of the hamiltonian. In a recent letter, we have derived a technique to free the single-particle equation-of-motion method of redundancy. Here we shall apply this redundancy-free equation-of-motion method to intermediate-coupling calculations in two regions of near-spherical odd-mass nuclei where forward coupling alone has not been successful. It is shown that qualitative effects of backward coupling previously reported are not spurious effects of double counting, although they are significantly modified by the removal of redundancy. We also discuss what further modifications of the theory will be needed in order to treat the dynamical interplay of collective and single-particle modes in nuclei self-consistently on the same footing. (orig.)

Complex Hamiltonian Dynamics

CERN Document Server

Bountis, Tassos

2012-01-01

This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems.  The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...

Analysis of solid particles falling down and interacting in a channel with sedimentation using fictitious boundary method

Science.gov (United States)

Usman, K.; Walayat, K.; Mahmood, R.; Kousar, N.

2018-06-01

We have examined the behavior of solid particles in particulate flows. The interaction of particles with each other and with the fluid is analyzed. Solid particles can move freely through a fixed computational mesh using an Eulerian approach. Fictitious boundary method (FBM) is used for treating the interaction between particles and the fluid. Hydrodynamic forces acting on the particle's surface are calculated using an explicit volume integral approach. A collision model proposed by Glowinski, Singh, Joseph and coauthors is used to handle particle-wall and particle-particle interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW. Numerical experiments are performed considering two particles falling and colliding and sedimentation of many particles while interacting with each other. Results for these experiments are presented and compared with the reference values. Effects of the particle-particle interaction on the motion of the particles and on the physical behavior of the fluid-particle system has been analyzed.

SU-D-207-04: GPU-Based 4D Cone-Beam CT Reconstruction Using Adaptive Meshing Method

International Nuclear Information System (INIS)

Zhong, Z; Gu, X; Iyengar, P; Mao, W; Wang, J; Guo, X

2015-01-01

Purpose: Due to the limited number of projections at each phase, the image quality of a four-dimensional cone-beam CT (4D-CBCT) is often degraded, which decreases the accuracy of subsequent motion modeling. One of the promising methods is the simultaneous motion estimation and image reconstruction (SMEIR) approach. The objective of this work is to enhance the computational speed of the SMEIR algorithm using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step is to generate the tetrahedral mesh based on the features of a reference phase 4D-CBCT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. After the mesh generation, the updated motion model and other phases of 4D-CBCT can be obtained by matching the 4D-CBCT projection images at each phase with the corresponding forward projections of the deformed reference phase of 4D-CBCT. The entire process of this 4D-CBCT reconstruction method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its tremendous parallel computing ability. Results: A 4D XCAT digital phantom was used to test the proposed mesh-based image reconstruction algorithm. The image Result shows both bone structures and inside of the lung are well-preserved and the tumor position can be well captured. Compared to the previous voxel-based CPU implementation of SMEIR, the proposed method is about 157 times faster for reconstructing a 10 -phase 4D-CBCT with dimension 256×256×150. Conclusion: The GPU-based parallel 4D CBCT reconstruction method uses the feature-based mesh for estimating motion model and demonstrates equivalent image Result with previous voxel-based SMEIR approach, with significantly improved computational speed

Hamiltonian description of the ideal fluid

International Nuclear Information System (INIS)

Morrison, P.J.

1994-01-01

Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems

Model reduction of port-Hamiltonian systems as structured systems

NARCIS (Netherlands)

Polyuga, R.V.; Schaft, van der A.J.

2010-01-01

The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.

Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

2010-05-15

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

Large-scale stochasticity in Hamiltonian systems

International Nuclear Information System (INIS)

Escande, D.F.

1982-01-01

Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)

Generalized internal long wave equations: construction, hamiltonian structure and conservation laws

International Nuclear Information System (INIS)

Lebedev, D.R.

1982-01-01

Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu

The generalized Mayer theorem in the approximating hamiltonian method

International Nuclear Information System (INIS)

Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.

1982-07-01

With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)

Coarse mesh code development

Energy Technology Data Exchange (ETDEWEB)

Lieberoth, J.

1975-06-15

The numerical solution of the neutron diffusion equation plays a very important role in the analysis of nuclear reactors. A wide variety of numerical procedures has been proposed, at which most of the frequently used numerical methods are fundamentally based on the finite- difference approximation where the partial derivatives are approximated by the finite difference. For complex geometries, typical of the practical reactor problems, the computational accuracy of the finite-difference method is seriously affected by the size of the mesh width relative to the neutron diffusion length and by the heterogeneity of the medium. Thus, a very large number of mesh points are generally required to obtain a reasonably accurate approximate solution of the multi-dimensional diffusion equation. Since the computation time is approximately proportional to the number of mesh points, a detailed multidimensional analysis, based on the conventional finite-difference method, is still expensive even with modern large-scale computers. Accordingly, there is a strong incentive to develop alternatives that can reduce the number of mesh-points and still retain accuracy. One of the promising alternatives is the finite element method, which consists of the expansion of the neutron flux by piecewise polynomials. One of the advantages of this procedure is its flexibility in selecting the locations of the mesh points and the degree of the expansion polynomial. The small number of mesh points of the coarse grid enables to store the results of several of the least outer iterations and to calculate well extrapolated values of them by comfortable formalisms. This holds especially if only one energy distribution of fission neutrons is assumed for all fission processes in the reactor, because the whole information of an outer iteration is contained in a field of fission rates which has the size of all mesh points of the coarse grid.

Divide and conquer method for proving gaps of frustration free Hamiltonians

DEFF Research Database (Denmark)

Kastoryano, Michael J.; Lucia, Angelo

2018-01-01

Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain...... such a bound. We furthermore show that such a condition is necessary and equivalent to a constant spectral gap. Thanks to this equivalence, we can prove that for gapless models in any dimension, the spectral gap on regions of diameter $n$ is at most $o\\left(\\frac{\\log(n)^{2+\\epsilon}}{n}\\right)$ for any...... positive $\\epsilon$....

Seeking new surgical predictors of mesh exposure after transvaginal mesh repair.

Science.gov (United States)

Wu, Pei-Ying; Chang, Chih-Hung; Shen, Meng-Ru; Chou, Cheng-Yang; Yang, Yi-Ching; Huang, Yu-Fang

2016-10-01

The purpose of this study was to explore new preventable risk factors for mesh exposure. A retrospective review of 92 consecutive patients treated with transvaginal mesh (TVM) in the urogynecological unit of our university hospital. An analysis of perioperative predictors was conducted in patients after vaginal repairs using a type 1 mesh. Mesh complications were recorded according to International Urogynecological Association (IUGA) definitions. Mesh-exposure-free durations were calculated by using the Kaplan-Meier method and compared between different closure techniques using log-rank test. Hazard ratios (HR) of predictors for mesh exposure were estimated by univariate and multivariate analyses using Cox proportional hazards regression models. The median surveillance interval was 24.1 months. Two late occurrences were found beyond 1 year post operation. No statistically significant correlation was observed between mesh exposure and concomitant hysterectomy. Exposure risks were significantly higher in patients with interrupted whole-layer closure in univariate analysis. In the multivariate analysis, hematoma [HR 5.42, 95 % confidence interval (CI) 1.26-23.35, P = 0.024), Prolift mesh (HR 5.52, 95 % CI 1.15-26.53, P = 0.033), and interrupted whole-layer closure (HR 7.02, 95 % CI 1.62-30.53, P = 0.009) were the strongest predictors of mesh exposure. Findings indicate the risks of mesh exposure and reoperation may be prevented by avoiding hematoma, large amount of mesh, or interrupted whole-layer closure in TVM surgeries. If these risk factors are prevented, hysterectomy may not be a relative contraindication for TVM use. We also provide evidence regarding mesh exposure and the necessity for more than 1 year of follow-up and preoperative counselling.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

Science.gov (United States)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

A current value Hamiltonian Approach for Discrete time Optimal Control Problems arising in Economic Growth

OpenAIRE

Naz, Rehana

2018-01-01

Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.

Origin of constraints in relativistic classical Hamiltonian dynamics

International Nuclear Information System (INIS)

Mallik, S.; Hugentobler, E.

1979-01-01

We investigate the null-plane or the front form of relativistic classical Hamiltonian dynamics as proposed by Dirac and developed by Leutwyler and Stern. For systems of two spinless particles we show that the algebra of Poincare generators is equivalent to describing dynamics in terms of two covariant constraint equations, the Poisson bracket of the two constraints being weakly zero. The latter condition is solved for certain simple forms of constraints

Lagrangian and hamiltonian algorithms applied to the elar ged DGL model

International Nuclear Information System (INIS)

Batlle, C.; Roman-Roy, N.

1988-01-01

We analyse a model of two interating relativistic particles which is useful to illustrate the equivalence between the Dirac-Bergmann and the geometrical presympletic constraint algorithms. Both the lagrangian and hamiltonian formalisms are deeply analysed and we also find and discuss the equations of motion. (Autor)

Effective low-energy Hamiltonians for interacting nanostructures

Science.gov (United States)

Kinza, Michael; Ortloff, Jutta; Honerkamp, Carsten

2010-10-01

We present a functional renormalization group (fRG) treatment of trigonal graphene nanodisks and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodisks, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications [M. Ezawa, Eur. Phys. J. B 67, 543 (2009)10.1140/epjb/e2009-00041-7]. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodisks the degeneracy of the one-particle-states with zero energy turns out to be protected against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisk. We also discuss a second class of nanostructures, bow-tie-shaped systems, where the zero-energy states are not protected.

On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians

International Nuclear Information System (INIS)

O'Reilly, E.P.; Weaire, D.

1984-01-01

The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)

The application of the mesh-free method in the numerical simulations of the higher-order continuum structures

Energy Technology Data Exchange (ETDEWEB)

Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia [School of Civil Engineering and Architecture, Zhongyuan University of Technology, Zhengzhou (China)

2016-06-08

This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe the special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.

N-body simulations for f(R) gravity using a self-adaptive particle-mesh code

International Nuclear Information System (INIS)

Zhao Gongbo; Koyama, Kazuya; Li Baojiu

2011-01-01

We perform high-resolution N-body simulations for f(R) gravity based on a self-adaptive particle-mesh code MLAPM. The chameleon mechanism that recovers general relativity on small scales is fully taken into account by self-consistently solving the nonlinear equation for the scalar field. We independently confirm the previous simulation results, including the matter power spectrum, halo mass function, and density profiles, obtained by Oyaizu et al.[Phys. Rev. D 78, 123524 (2008)] and Schmidt et al.[Phys. Rev. D 79, 083518 (2009)], and extend the resolution up to k∼20 h/Mpc for the measurement of the matter power spectrum. Based on our simulation results, we discuss how the chameleon mechanism affects the clustering of dark matter and halos on full nonlinear scales.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

International Nuclear Information System (INIS)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.

2015-01-01

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

Energy Technology Data Exchange (ETDEWEB)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

2015-11-15

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families

Science.gov (United States)

Leyvraz, F.

2017-07-01

We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such Hamiltonians can be solved explicitly by a separation of variables ansatz. The method leads in particular to a proof that the so-called "goldfish" Hamiltonian is maximally superintegrable and leads to an elementary identification of a full set of integrals of motion. The Hamiltonians in involution with the "goldfish" Hamiltonian are also explicitly integrated. New integrable Hamiltonians are identified, among which some have the property of being isochronous, that is, all their orbits have the same period. Finally, a peculiar structure is identified in the Poisson brackets between the elementary symmetric functions and the set of Hamiltonians commuting with the "goldfish" Hamiltonian: these can be expressed as products between elementary symmetric functions and Hamiltonians. The structure displays an invariance property with respect to one element and has both a symmetry and a closure property. The meaning of this structure is not altogether clear to the author, but it turns out to be a powerful tool.

An extended discrete gradient formula for oscillatory Hamiltonian systems

International Nuclear Information System (INIS)

Liu Kai; Shi Wei; Wu Xinyuan

2013-01-01

In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)

Effective Hamiltonian theory: recent formal results and non-nuclear applications

International Nuclear Information System (INIS)

Brandow, B.H.

1981-01-01

Effective Hamiltonian theory is discussed from the points of view of the unitary transformation method and degenerate perturbation theory. It is shown that the two approaches are identical term by term. The main features of a formulation of the coupled-cluster method for open-shell systems are outlined. Finally, recent applications of the many-body linked-cluster form of degenerate perturbation theory are described: the derivation of effective spin Hamiltonians in magnetic insulator systems, the derivation and calculation ab initio of effective π-electron Hamiltonians for planar conjugated hydrocarbon molecules, and understanding the so-called valence fluctuation phenomenon exhibited by certain rare earth compounds

The investigation of 1+1 dimensional lattice gauge theories with fermions, gauge bosons and scalar using Hamiltonian Monte-Carlo methods

International Nuclear Information System (INIS)

Ranft, J.

1984-01-01

Hamiltonian lattice models with fermions, gauge bosons and scalar fields are studied in 1+1 dimensions using the local Hamiltonian Monte-Carlo method. Results are presented for the massive Schwinger model with one and two flavors, for a model with interacting Higgs fields, fermions and gauge bosons, where fractionally charged solitons are found as free states of the lattice model, and for Wess-Zumino type models with restricted lattice supersymmetry, where examples for spontaneous breaking of supersymmetry are found

Possibilities of the particle finite element method for fluid-soil-structure interaction problems

Science.gov (United States)

Oñate, Eugenio; Celigueta, Miguel Angel; Idelsohn, Sergio R.; Salazar, Fernando; Suárez, Benjamín

2011-09-01

We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.

Mapping method for generating three-dimensional meshes: past and present

International Nuclear Information System (INIS)

Cook, W.A.; Oakes, W.R.

1982-01-01

Two transformations are derived in this paper. One is a mapping of a unit square onto a surve and the other is a mapping of a unit cube onto a three-dimensional region. Two meshing computer programs are then discussed that use these mappings. The first is INGEN, which has been used to calculate three-dimensional meshes for approximately 15 years. This meshing program uses an index scheme to number boundaries, surfaces, and regions. With such an index scheme, it is possible to control nodal points, elements, and boundary conditions. The second is ESCHER, a meshing program now being developed. Two primary considerations governing development of ESCHER are that meshes graded using quadrilaterals are required and that edge-line geometry defined by Computer-Aided Design/Computer-Aided Manufacturing (CAD/CAM) systems will be a major source of geometry definition. This program separates the processes of nodal-point connectivity generation, computation of nodal-point mapping space coordinates, and mapping of nodal points into model space

Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

Energy Technology Data Exchange (ETDEWEB)

Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

2006-01-01

Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

A Novel Mesh Quality Improvement Method for Boundary Elements

Directory of Open Access Journals (Sweden)

Hou-lin Liu

2012-01-01

Full Text Available In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.

Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods

International Nuclear Information System (INIS)

Baker, A.R.

1982-07-01

A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)

Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

Energy Technology Data Exchange (ETDEWEB)

Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schofield, Samuel P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-06-21

A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.

Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles

International Nuclear Information System (INIS)

Alt, E.O.; Levin, S.B.; Yakovlev, S.L.

2004-01-01

A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the 'Coulomb representation'. Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable

A GPU-Accelerated Parameter Interpolation Thermodynamic Integration Free Energy Method.

Science.gov (United States)

Giese, Timothy J; York, Darrin M

2018-03-13

There has been a resurgence of interest in free energy methods motivated by the performance enhancements offered by molecular dynamics (MD) software written for specialized hardware, such as graphics processing units (GPUs). In this work, we exploit the properties of a parameter-interpolated thermodynamic integration (PI-TI) method to connect states by their molecular mechanical (MM) parameter values. This pathway is shown to be better behaved for Mg 2+ → Ca 2+ transformations than traditional linear alchemical pathways (with and without soft-core potentials). The PI-TI method has the practical advantage that no modification of the MD code is required to propagate the dynamics, and unlike with linear alchemical mixing, only one electrostatic evaluation is needed (e.g., single call to particle-mesh Ewald) leading to better performance. In the case of AMBER, this enables all the performance benefits of GPU-acceleration to be realized, in addition to unlocking the full spectrum of features available within the MD software, such as Hamiltonian replica exchange (HREM). The TI derivative evaluation can be accomplished efficiently in a post-processing step by reanalyzing the statistically independent trajectory frames in parallel for high throughput. We also show how one can evaluate the particle mesh Ewald contribution to the TI derivative evaluation without needing to perform two reciprocal space calculations. We apply the PI-TI method with HREM on GPUs in AMBER to predict p K a values in double stranded RNA molecules and make comparison with experiments. Convergence to under 0.25 units for these systems required 100 ns or more of sampling per window and coupling of windows with HREM. We find that MM charges derived from ab initio QM/MM fragment calculations improve the agreement between calculation and experimental results.

Non-perturbative RPA-method implemented in the Coulomb gauge QCD Hamiltonian: From quarks and gluons to baryons and mesons

Science.gov (United States)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

2018-02-01

Starting from an algebraic model based on the QCD-Hamiltonian and previously applied to study meson states, we have developed an extension of it in order to explore the structure of baryon states. In developing our approach we have adapted concepts taken from group theory and non-perturbative many-body methods to describe states built from effective quarks and anti-quarks degrees of freedom. As a Hamiltonian we have used the QCD Hamiltonian written in the Coulomb Gauge, and expressed it in terms of effective quark-antiquark, di-quarks and di-antiquark excitations. To gain some insights about the relevant interactions of quarks in hadronic states, the Hamiltonian was approximately diagonalized by mapping quark-antiquark pairs and di-quarks (di-antiquarks) onto phonon states. In dealing with the structure of the vacuum of the theory, color-scalar and color-vector states are introduced to account for ground-state correlations. While the use of a purely color-scalar ground state is an obvious choice, so that colorless hadrons contain at least three quarks, the presence of coupled color-vector pairs in the ground state allows for colorless excitations resulting from the action of color objects upon it.

Hamiltonian description of the ideal fluid

International Nuclear Information System (INIS)

Morrison, P.J.

1998-01-01

The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society

Analytic Coarse-Mesh Finite-Difference Method Generalized for Heterogeneous Multidimensional Two-Group Diffusion Calculations

International Nuclear Information System (INIS)

Garcia-Herranz, Nuria; Cabellos, Oscar; Aragones, Jose M.; Ahnert, Carol

2003-01-01

In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations

Parallel adaptive simulations on unstructured meshes

International Nuclear Information System (INIS)

Shephard, M S; Jansen, K E; Sahni, O; Diachin, L A

2007-01-01

This paper discusses methods being developed by the ITAPS center to support the execution of parallel adaptive simulations on unstructured meshes. The paper first outlines the ITAPS approach to the development of interoperable mesh, geometry and field services to support the needs of SciDAC application in these areas. The paper then demonstrates the ability of unstructured adaptive meshing methods built on such interoperable services to effectively solve important physics problems. Attention is then focused on ITAPs' developing ability to solve adaptive unstructured mesh problems on massively parallel computers

On squaring the primary constraints in a generalized Hamiltonian dynamics

International Nuclear Information System (INIS)

Nesterenko, V.V.

1993-01-01

Consideration of the model of the relativistic particle with curvature and torsion in the three-dimensional space-time shows that the squaring of the primary constraints entails a wrong result. The complete set of the Hamiltonian constraints arising here corresponds to another model with an action similar but not identical with the initial action. 16 refs

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun

2012-10-01

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan

2012-01-01

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

Accurate halo-galaxy mocks from automatic bias estimation and particle mesh gravity solvers

Science.gov (United States)

Vakili, Mohammadjavad; Kitaura, Francisco-Shu; Feng, Yu; Yepes, Gustavo; Zhao, Cheng; Chuang, Chia-Hsun; Hahn, ChangHoon

2017-12-01

Reliable extraction of cosmological information from clustering measurements of galaxy surveys requires estimation of the error covariance matrices of observables. The accuracy of covariance matrices is limited by our ability to generate sufficiently large number of independent mock catalogues that can describe the physics of galaxy clustering across a wide range of scales. Furthermore, galaxy mock catalogues are required to study systematics in galaxy surveys and to test analysis tools. In this investigation, we present a fast and accurate approach for generation of mock catalogues for the upcoming galaxy surveys. Our method relies on low-resolution approximate gravity solvers to simulate the large-scale dark matter field, which we then populate with haloes according to a flexible non-linear and stochastic bias model. In particular, we extend the PATCHY code with an efficient particle mesh algorithm to simulate the dark matter field (the FASTPM code), and with a robust MCMC method relying on the EMCEE code for constraining the parameters of the bias model. Using the haloes in the BigMultiDark high-resolution N-body simulation as a reference catalogue, we demonstrate that our technique can model the bivariate probability distribution function (counts-in-cells), power spectrum and bispectrum of haloes in the reference catalogue. Specifically, we show that the new ingredients permit us to reach percentage accuracy in the power spectrum up to k ∼ 0.4 h Mpc-1 (within 5 per cent up to k ∼ 0.6 h Mpc-1) with accurate bispectra improving previous results based on Lagrangian perturbation theory.

A covariant formulation of the relativistic Hamiltonian theory on the light cone (fields with spin)

International Nuclear Information System (INIS)

Atakishiev, N.M.; Mir-Kasimov, R.M.; Nagiyev, Sh.M.

1978-01-01

A Hamiltonian formulation of quantum field theory on the light cone, developed earlier, is extended to the case of particles with spin. The singularities accompanying each field theory in light-front variables are removed by the introduction of an infinite number of counterterms of a new type, which can be included into the interaction Hamiltonian. A three-dimensional diagram technique is formulated, which is applied to calculate the fermion self-energy in the lowest order of perturbation theory

Current achievements and future perspectives on particle simulation technologies for fluid dynamics and heat transfer

International Nuclear Information System (INIS)

Koshizuka, Seiichi

2011-01-01

The Moving Particle Semi-implicit (MPS) method is one of the particle methods in which continuum mechanics is analyzed using the concept of particles. Since meshes are not used, large deformation of free surfaces and material interfaces can be simulated without the problems of mesh distortion. Thus, the MPS method has been applied to multiphase flow analysis in nuclear engineering. The advantages of the particle methods are also useful for applications in other engineering fields: ship engineering, civil engineering, microflow, biomechanics, visualization, etc. In this review, calculation examples are described and classified. Commercial codes have been released and applied in industries. The particle methods are also used in TV programs, movies, and computer games. Combinations of numerical techniques for multiphysics problems, fast calculations, and high-quality visualizations are expected to lead to real-time particle simulations for various new applications in the near future. (author)

General technique to produce isochronous Hamiltonians

International Nuclear Information System (INIS)

Calogero, F; Leyvraz, F

2007-01-01

We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra

Revisiting the use of the immersed-boundary lattice-Boltzmann method for simulations of suspended particles

Science.gov (United States)

Mountrakis, L.; Lorenz, E.; Hoekstra, A. G.

2017-07-01

The immersed-boundary lattice-Boltzmann method (IB-LBM) is increasingly being used in simulations of dense suspensions. These systems are computationally very expensive and can strongly benefit from lower resolutions that still maintain the desired accuracy for the quantities of interest. IB-LBM has a number of free parameters that have to be defined, often without exact knowledge of the tradeoffs, since their behavior in low resolutions is not well understood. Such parameters are the lattice constant Δ x , the number of vertices Nv, the interpolation kernel ϕ , and the LBM relaxation time τ . We investigate the effect of these IB-LBM parameters on a number of straightforward but challenging benchmarks. The systems considered are (a) the flow of a single sphere in shear flow, (b) the collision of two spheres in shear flow, and (c) the lubrication interaction of two spheres. All benchmarks are performed in three dimensions. The first two systems are used for determining two effective radii: the hydrodynamic radius rhyd and the particle interaction radius rinter. The last system is used to establish the numerical robustness of the lubrication forces, used to probe the hydrodynamic interactions in the limit of small gaps. Our results show that lower spatial resolutions result in larger hydrodynamic and interaction radii, while surface densities should be chosen above two vertices per LU2 result to prevent fluid penetration in underresolved meshes. Underresolved meshes also failed to produce the migration of particles toward the center of the domain due to lift forces in Couette flow, mostly noticeable for IBM-kernel ϕ2. Kernel ϕ4, despite being more robust toward mesh resolution, produces a notable membrane thickness, leading to the breakdown of the lubrication forces in larger gaps, and its use in dense suspensions where the mean particle distances are small can result in undesired behavior. rhyd is measured to be different from rinter, suggesting that there is

SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS

OpenAIRE

Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.

2006-01-01

In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.

Obtuse triangle suppression in anisotropic meshes

KAUST Repository

Sun, Feng; Choi, Yi King; Wang, Wen Ping; Yan, Dongming; Liu, Yang; Lé vy, Bruno L.

2011-01-01

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

Obtuse triangle suppression in anisotropic meshes

KAUST Repository

Sun, Feng

2011-12-01

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

Hamiltonian dynamics

CERN Document Server

Vilasi, Gaetano

2001-01-01

This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m

A new general method for transform canonically a Hamiltonian in another one of a given form

International Nuclear Information System (INIS)

Gomez T, A.

2002-01-01

The more general method to perform a canonical transformation of a Hamiltonian into another one of a given form is based on the repeated use of the Hamilton-Jacobi equation. This is usually a tedious technique which leads to some particular solutions of the problem. We present a new general method which does not rely on the Hamilton-Jacobi equation and moreover it gives all the possible solutions. (Author)

Analytical reconstruction schemes for coarse-mesh spectral nodal solution of slab-geometry SN transport problems

International Nuclear Information System (INIS)

Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.

2009-01-01

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)

Simulation of bluff-body flows using iterative penalization in a multiresolution particle-mesh vortex method

DEFF Research Database (Denmark)

Spietz, Henrik Juul; Hejlesen, Mads Mølholm; Walther, Jens Honore

in the oncoming flow. This may lead to structural instability e.g. when the shedding frequency aligns with the natural frequency of the structure. Fluid structure interaction must especially be considered when designing long span bridges. A three dimensional vortex-in-cell method is applied for the direct......The ability to predict aerodynamic forces, due to the interaction of a fluid flow with a solid body, is central in many fields of engineering and is necessary to identify error-prone structural designs. In bluff-body flows the aerodynamic forces oscillate due to vortex shedding and variations...... numerical simulation of the flow past a bodies of arbitrary shape. Vortex methods use a simple formulation where only the trajectories of discrete vortex particles are simulated. The Lagrangian formulation eliminates the CFL type condition that Eulerian methods have to satisfy. This allows vortex methods...

15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics

CERN Document Server

Passante, Roberto; Trapani, Camillo

2016-01-01

This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.

Electrical Conductivity of Charged Particle Systems and Zubarev's Nonequilibrium Statistical Operator Method

Science.gov (United States)

Röpke, G.

2018-01-01

One of the fundamental problems in physics that are not yet rigorously solved is the statistical mechanics of nonequilibrium processes. An important contribution to describing irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev, who invented the method of the nonequilibrium statistical operator. We discuss this approach, in particular, the extended von Neumann equation, and as an example consider the electrical conductivity of a system of charged particles. We consider the selection of the set of relevant observables. We show the relation between kinetic theory and linear response theory. Using thermodynamic Green's functions, we present a systematic treatment of correlation functions, but the convergence needs investigation. We compare different expressions for the conductivity and list open questions.

Simulation of transients with space-dependent feedback by coarse mesh flux expansion method

International Nuclear Information System (INIS)

Langenbuch, S.; Maurer, W.; Werner, W.

1975-01-01

For the simulation of the time-dependent behaviour of large LWR-cores, even the most efficient Finite-Difference (FD) methods require a prohibitive amount of computing time in order to achieve results of acceptable accuracy. Static CM-solutions computed with a mesh-size corresponding to the fuel element structure (about 20 cm) are at least as accurate as FD-solutions computed with about 5 cm mesh-size. For 3d-calculations this results in a reduction of storage requirements by a factor 60 and of computing costs by a factor 40, relative to FD-methods. These results have been obtained for pure neutronic calculations, where feedback is not taken into account. In this paper it is demonstrated that the method retains its accuracy also in kinetic calculations, even in the presence of strong space dependent feedback. (orig./RW) [de

Effectively semi-relativistic Hamiltonians of nonrelativistic form

International Nuclear Information System (INIS)

Lucha, W.; Schoeberl, F.F.; Moser, M.

1993-12-01

We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even in relativistic regions. (authors)

Opfront: mesh

DEFF Research Database (Denmark)

2015-01-01

Mesh generation and visualization software based on the CGAL library. Folder content: drawmesh Visualize slices of the mesh (surface/volumetric) as wireframe on top of an image (3D). drawsurf Visualize surfaces of the mesh (surface/volumetric). img2mesh Convert isosurface in image to volumetric m...... mesh (medit format). img2off Convert isosurface in image to surface mesh (off format). off2mesh Convert surface mesh (off format) to volumetric mesh (medit format). reduce Crop and resize 3D and stacks of images. data Example data to test the library on...

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

Science.gov (United States)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Solution of the neutron transport equation by the Method of Characteristics using a linear representation of the source within a mesh

International Nuclear Information System (INIS)

Mazumdar, Tanay; Degweker, S.B.

2017-01-01

Highlights: • In Method of Characteristics, the neutron source within a mesh is expanded up to linear term. • This expansion reduces the number of meshes as compared to flat source assumption. • Poor representation of circular geometry with coarser meshes is corrected. • Few benchmark problems are solved to show the advantages of linear expansion of source. • The advantage of the present formalism is quite visible in problems with large flux gradient. - Abstract: A common assumption in the solution of the neutron transport equation by the Method of Characteristics (MOC) is that the source (or flux) is constant within a mesh. This assumption is adequate provided the meshes are small enough so that the spatial variation of flux within a mesh may be ignored. Whether a mesh is small enough or not depends upon the flux gradient across a mesh, which in turn depends on factors like the presence of strong absorbers, localized sources or vacuum boundaries. The flat flux assumption often requires a very large number of meshes for solving the neutron transport equation with acceptable accuracy as was observed in our earlier work on the subject. A significant reduction in the required number of meshes is attainable by using a higher order representation of the flux within a mesh. In this paper, we expand the source within a mesh up to first order (linear) terms, which permits the use of larger sized (and therefore fewer) meshes and thereby reduces the computation time without compromising the accuracy of calculation. Since the division of the geometry into meshes is through an automatic triangulation procedure using the Bowyer-Watson algorithm, representation of circular objects (cylindrical fuel rods) with coarse meshes is poorer and causes geometry related errors. A numerical recipe is presented to make a correction to the automatic triangulation process and thereby eliminate this source of error. A number of benchmark problems are analyzed to emphasize the

Hamiltonian formalism for perfect fluids in general relativity

International Nuclear Information System (INIS)

Demaret, J.; Moncrief, V.

1980-01-01

Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = γ < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models

Development of three-dimensional ENRICHED FREE MESH METHOD and its application to crack analysis

International Nuclear Information System (INIS)

Suzuki, Hayato; Matsubara, Hitoshi; Ezawa, Yoshitaka; Yagawa, Genki

2010-01-01

In this paper, we describe a method for three-dimensional high accurate analysis of a crack included in a large-scale structure. The Enriched Free Mesh Method (EFMM) is a method for improving the accuracy of the Free Mesh Method (FMM), which is a kind of meshless method. First, we developed an algorithm of the three-dimensional EFMM. The elastic problem was analyzed using the EFMM and we find that its accuracy compares advantageously with the FMM, and the number of CG iterations is smaller. Next, we developed a method for calculating the stress intensity factor by employing the EFMM. The structure with a crack was analyzed using the EFMM, and the stress intensity factor was calculated by the developed method. The analysis results were very well in agreement with reference solution. It was shown that the proposed method is very effective in the analysis of the crack included in a large-scale structure. (author)

Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

Directory of Open Access Journals (Sweden)

Krzysztof Andrzejewski

2014-12-01

Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

Documentation for MeshKit - Reactor Geometry (&mesh) Generator

Energy Technology Data Exchange (ETDEWEB)

Jain, Rajeev [Argonne National Lab. (ANL), Argonne, IL (United States); Mahadevan, Vijay [Argonne National Lab. (ANL), Argonne, IL (United States)

2015-09-30

This report gives documentation for using MeshKit’s Reactor Geometry (and mesh) Generator (RGG) GUI and also briefly documents other algorithms and tools available in MeshKit. RGG is a program designed to aid in modeling and meshing of complex/large hexagonal and rectilinear reactor cores. RGG uses Argonne’s SIGMA interfaces, Qt and VTK to produce an intuitive user interface. By integrating a 3D view of the reactor with the meshing tools and combining them into one user interface, RGG streamlines the task of preparing a simulation mesh and enables real-time feedback that reduces accidental scripting mistakes that could waste hours of meshing. RGG interfaces with MeshKit tools to consolidate the meshing process, meaning that going from model to mesh is as easy as a button click. This report is designed to explain RGG v 2.0 interface and provide users with the knowledge and skills to pilot RGG successfully. Brief documentation of MeshKit source code, tools and other algorithms available are also presented for developers to extend and add new algorithms to MeshKit. RGG tools work in serial and parallel and have been used to model complex reactor core models consisting of conical pins, load pads, several thousands of axially varying material properties of instrumentation pins and other interstices meshes.

Renormalization of Hamiltonian QCD

International Nuclear Information System (INIS)

Andrasi, A.; Taylor, John C.

2009-01-01

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

Wire-mesh capped deposition sensors: Novel passive tool for coarse fraction flux estimation of radon thoron progeny in indoor environments

International Nuclear Information System (INIS)

Mayya, Y.S.; Mishra, Rosaline; Prajith, Rama; Sapra, B.K.; Kushwaha, H.S.

2010-01-01

Deposition-based 222 Rn and 220 Rn progeny sensors act as unique, passive tools for determining the long time-averaged progeny deposition fluxes in the environment. The use of these deposition sensors as progeny concentration monitors was demonstrated in typical indoor environments as conceptually superior alternatives to gas-based indirect monitoring methods. In the present work, the dependency of these deposition monitors on various environmental parameters is minimized by capping the deposition sensor with a suitable wire mesh. These wire-mesh capped deposition sensors measure the coarse fraction deposition flux, which is less dependent on the change in environmental parameters like ventilation rate and turbulence. The calibration of these wire-mesh capped coarse fraction progeny sensors was carried out by laboratory controlled experiments. These sensors were deployed both in indoor and in occupational environments having widely different ventilation rates. The obtained coarse fraction deposition velocities were fairly constant in these environments, which further confirmed that the signal on the wire-mesh capped sensors show the least dependency on the change in environmental parameters. This technique has the potential to serve as a passive particle sizer in the general context of nanoparticles using progeny species as surrogates. On the whole, there exists a strong case for developing a passive system that responds only to coarse fraction for providing alternative tools for dosimetry and environmental fine particle research. - Research highlights: → Wire-mesh capped deposition sensor measures the coarse fraction deposition flux → Coarse fraction deposition flux less dependent on environmental conditions → Wire-mesh capped deposition sensor as passive particle sizer

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

Science.gov (United States)

Ilias, Miroslav; Saue, Trond

2007-02-14

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations

International Nuclear Information System (INIS)

Sczaniecki, L.

1981-02-01

A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Science.gov (United States)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Three-dimensional dynamic rupture simulation with a high-order discontinuous Galerkin method on unstructured tetrahedral meshes

KAUST Repository

Pelties, Christian

2012-02-18

Accurate and efficient numerical methods to simulate dynamic earthquake rupture and wave propagation in complex media and complex fault geometries are needed to address fundamental questions in earthquake dynamics, to integrate seismic and geodetic data into emerging approaches for dynamic source inversion, and to generate realistic physics-based earthquake scenarios for hazard assessment. Modeling of spontaneous earthquake rupture and seismic wave propagation by a high-order discontinuous Galerkin (DG) method combined with an arbitrarily high-order derivatives (ADER) time integration method was introduced in two dimensions by de la Puente et al. (2009). The ADER-DG method enables high accuracy in space and time and discretization by unstructured meshes. Here we extend this method to three-dimensional dynamic rupture problems. The high geometrical flexibility provided by the usage of tetrahedral elements and the lack of spurious mesh reflections in the ADER-DG method allows the refinement of the mesh close to the fault to model the rupture dynamics adequately while concentrating computational resources only where needed. Moreover, ADER-DG does not generate spurious high-frequency perturbations on the fault and hence does not require artificial Kelvin-Voigt damping. We verify our three-dimensional implementation by comparing results of the SCEC TPV3 test problem with two well-established numerical methods, finite differences, and spectral boundary integral. Furthermore, a convergence study is presented to demonstrate the systematic consistency of the method. To illustrate the capabilities of the high-order accurate ADER-DG scheme on unstructured meshes, we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes curved faults, fault branches, and surface topography. Copyright 2012 by the American Geophysical Union.

Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas

International Nuclear Information System (INIS)

Becoulet, A.; Gambier, D.J.; Samain, A.

1990-03-01

The question of heating a tokamak plasma by means of electromagnetic waves in the Ion Cyclotron Range of Frequency (ICRF) is considered in the perspective of large RF powers and in the low collisionality regime. In such case the Quasi Linear Theory (QLT) is validated by the Hamiltonian dynamics of the wave particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows to derive the RF diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. Then the Fokker Planck equation is given a variational from which a solution is derived in the form of a semi analytical trial function of three parameters: the percentage of resonant particle contained in the tail; an isotropic width ΔT and an anisotropic one ΔP. This solution is successfully tested against real experimental observations. Practically it is shown that in the case of JET the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that of a bounce averaged prediction. This may actually be an advantage for machines like JET considering the energy range required to simulate the α-particle behaviour in a relevant fusion reactor

Redesign of the DFT/MRCI Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)

2016-01-21

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.

An algorithm for finding a similar subgraph of all Hamiltonian cycles

Science.gov (United States)

Wafdan, R.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

Short term post-operative morphing of sacrocolpopexy mesh measured by magnetic resonance imaging.

Science.gov (United States)

Sindhwani, Nikhil; Callewaert, Geertje; Deprest, Thomas; Housmans, Susanne; Van Beckevoort, Dirk; Deprest, Jan

2018-04-01

Sacrocolpopexy (SC) involves suspension of the vaginal vault or cervix to the sacrum using a mesh. Following insertion, the meshes have been observed to have undergone dimensional changes. To quantify dimensional changes of meshes following implantation and characterize their morphology in-vivo. 24 patients underwent SC using PolyVinyliDeneFluoride mesh loaded with Fe 3 O 4 particles. Tailored anterior and posterior mesh flaps were sutured to the respective vaginal walls, uniting at the apex. The posterior flap continued to the sacrum and was attached there. Meshes were visualized on magnetic resonance (MR) imaging at 12 [3-12] (median [range]) months postoperatively and 3D models of the mesh were generated. Dynamic MR sequences were acquired during valsalva to record mesh mobility. The area of the vagina effectively supported by the mesh (Effective Support Area (ESA)) was calculated. The 3D models' wall thickness map was analyzed to identify the locations of mesh folding. Intraclass correlation (ICC) was calculated to test the reliability of the methods. To measure the laxity and flatness of the mesh, the curvature and the ellipticity of the sacral flap were calculated. The ESA calculation methodology had ICC = 0.97. A reduction of 75.49 [61.55-78.67] % (median [IQR]) in area, 47.64 [38.07-59.81] % in anterior flap, and of 23.95 [10.96-27.21] % in the posterior flap was measured. The mesh appeared thicker near its attachment at the sacral promontory (n = 19) and near the vaginal apex (n = 22). The laxity of the mesh was 1.13 [1.10-1.16] and 60.55 [49.76-76.25] % of the sacral flap was flat. We could not reliably measure mesh mobility (ICC = 0.16). A methodology for complete 3D characterization of SC meshes using MR images was presented. After implantation, the supported area is much lower than what is prepared prior to implantation. We propose this happened during the surgery itself. Copyright © 2018 Elsevier Ltd. All rights reserved.

Geometry of Hamiltonian chaos

DEFF Research Database (Denmark)

Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

2007-01-01

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

Magnetic field line Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1984-03-01

The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained

Mesh refinement for particle-in-cell plasma simulations: Applications to - and benefits for HIF (heavy ion fusion)

International Nuclear Information System (INIS)

Vay, J.L.; Colella, P.; McCorquodale, P.; Van Straalen, B.; Friedman, A.; Grote, D.P.

2002-01-01

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and simulation of the power plant as a whole, or even of the drive,r is not yet possible. Despite the rapid progress in computer power, past and anticipated, one must consider the use of the most advanced numerical techniques, if they are to reach the goal expeditiously. One of the difficulties of these simulations resides in the disparity of scales, in time and in space, which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. They discuss the challenges posed by the implementation of this technique into plasma simulations (due to the presence of particles and electromagnetic waves). They will present the prospects for and projected benefits of its application to heavy ion fusion, in particular to the simulation of the ion source and the final beam propagation in the chamber

Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

International Nuclear Information System (INIS)

Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

2005-01-01

In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

Classical mechanics Hamiltonian and Lagrangian formalism

CERN Document Server

Deriglazov, Alexei

2016-01-01

This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.

Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes

Science.gov (United States)

Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian

2013-09-01

In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.

On functional relations between reduced distribution functions and entropy production by non-Hamiltonian perturbations

International Nuclear Information System (INIS)

Dobbertin, R.

1976-01-01

Functional relations are derived which link the reduced distribution functions of a classical N-particle system through the entropy production due to microscopic deviations from hamiltonian dynamics. These relations have been used in an earlier paper for the closure of the BBGKY-hierarchy and may be useful for the establishment of collective particle models in particular and the understanding of irreversibility in general. (Auth.)

Production and transfer of energy and information in Hamiltonian systems.

Directory of Open Access Journals (Sweden)

Chris G Antonopoulos

Full Text Available We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an "experimental" implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented.

Magnetic moments of light nuclei within the framework of reduced Hamiltonian method

CERN Document Server

Deveikis, A

1998-01-01

A new procedure for evaluation of magnetic dipole moments of light atomic nuclei has been developed. The procedure presented obeys the principles of antisymmetry and translational invariance and is based on the reduced Hamiltonian method. The theoretical formulation has been illustrated by calculation of magnetic dipole moments for 2 sup H , 3 sup H , 3 sup H e, 4 sup H e, 5 sup H e, 5 sup L i, 11 sup L i, and 6 sup L i nuclei. The calculations were performed in a complete 0(h/2 pi)omega basis. The obtained results are in good agreement with the experimental data. (author)

N-body simulations for f(R) gravity using a self-adaptive particle-mesh code

Science.gov (United States)

Zhao, Gong-Bo; Li, Baojiu; Koyama, Kazuya

2011-02-01

We perform high-resolution N-body simulations for f(R) gravity based on a self-adaptive particle-mesh code MLAPM. The chameleon mechanism that recovers general relativity on small scales is fully taken into account by self-consistently solving the nonlinear equation for the scalar field. We independently confirm the previous simulation results, including the matter power spectrum, halo mass function, and density profiles, obtained by Oyaizu [Phys. Rev. DPRVDAQ1550-7998 78, 123524 (2008)10.1103/PhysRevD.78.123524] and Schmidt [Phys. Rev. DPRVDAQ1550-7998 79, 083518 (2009)10.1103/PhysRevD.79.083518], and extend the resolution up to k˜20h/Mpc for the measurement of the matter power spectrum. Based on our simulation results, we discuss how the chameleon mechanism affects the clustering of dark matter and halos on full nonlinear scales.

Mapping the electron correlation onto a model Hamiltonian for Cs/GaAs(110): a Mott-Hubbard insulator at quarter filling

CERN Document Server

Chen Chang Feng

1998-01-01

We have constructed an effective model Hamiltonian in the Hubbard formalism for the Cs/GaAs(110) surface at quarter-monolayer coverage with all of the parameters extracted from constrained local-density-approximation (LDA) pseudopotential calculations. The single-particle excitation spectrum of the model has been calculated using an exact-diagonalization technique to help determine the relevant interaction terms. It is shown that the intersite interaction between the nearest-neighbour Ga sites plays the key role in determining the insulating nature of the system and must be included in the model, in contrast to suggestions of some previous work. Our results show that a reliable mapping of LDA results onto an effective model Hamiltonian can be achieved by combining constrained LDA calculations for the Hamiltonian parameters and many-body calculations of the single-particle excitation spectrum for identifying relevant interaction terms. (author)

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

Science.gov (United States)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

Science.gov (United States)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Canonical transformations and hamiltonian path integrals

International Nuclear Information System (INIS)

Prokhorov, L.V.

1982-01-01

Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms

GPUs, a new tool of acceleration in CFD: efficiency and reliability on smoothed particle hydrodynamics methods.

Directory of Open Access Journals (Sweden)

Alejandro C Crespo

Full Text Available Smoothed Particle Hydrodynamics (SPH is a numerical method commonly used in Computational Fluid Dynamics (CFD to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs or Graphics Processor Units (GPUs, a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability.

Fragmentation of Millimeter-Size Hypervelocity Projectiles on Combined Mesh-Plate Bumpers

Directory of Open Access Journals (Sweden)

Aleksandr Cherniaev

2017-01-01

Full Text Available This numerical study evaluates the concept of a combined mesh-plate bumper as a shielding system protecting unmanned spacecraft from small (1 mm orbital debris impacts. Two-component bumpers consisting of an external layer of woven mesh (aluminum or steel directly applied to a surface of the aluminum plate are considered. Results of numerical modeling with a projectile velocity of 7 km/s indicate that, in comparison to the steel mesh-combined bumper, the combination of aluminum mesh and aluminum plate provides better fragmentation of small hypervelocity projectiles. At the same time, none of the combined mesh/plate bumpers provide a significant increase of ballistic properties as compared to an aluminum plate bumper. This indicates that the positive results reported in the literature for bumpers with metallic meshes and large projectiles are not scalable down to millimeter-sized particles. Based on this investigation’s results, a possible modification of the combined mesh/plate bumper is proposed for the future study.

Perspective: Quantum Hamiltonians for optical interactions

Science.gov (United States)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Quantum Hamiltonian Physics with Supercomputers

International Nuclear Information System (INIS)

Vary, James P.

2014-01-01

The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed

Quantum Hamiltonian Physics with Supercomputers

Energy Technology Data Exchange (ETDEWEB)

Vary, James P.

2014-06-15

The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

Hamiltonian mechanics and divergence-free fields

International Nuclear Information System (INIS)

Boozer, A.H.

1986-08-01

The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space

Cache-Oblivious Mesh Layouts

International Nuclear Information System (INIS)

Yoon, S; Lindstrom, P; Pascucci, V; Manocha, D

2005-01-01

We present a novel method for computing cache-oblivious layouts of large meshes that improve the performance of interactive visualization and geometric processing algorithms. Given that the mesh is accessed in a reasonably coherent manner, we assume no particular data access patterns or cache parameters of the memory hierarchy involved in the computation. Furthermore, our formulation extends directly to computing layouts of multi-resolution and bounding volume hierarchies of large meshes. We develop a simple and practical cache-oblivious metric for estimating cache misses. Computing a coherent mesh layout is reduced to a combinatorial optimization problem. We designed and implemented an out-of-core multilevel minimization algorithm and tested its performance on unstructured meshes composed of tens to hundreds of millions of triangles. Our layouts can significantly reduce the number of cache misses. We have observed 2-20 times speedups in view-dependent rendering, collision detection, and isocontour extraction without any modification of the algorithms or runtime applications

Notch filters for port-Hamiltonian systems

NARCIS (Netherlands)

Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.

2012-01-01

In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the

Energy mesh optimization for multi-level calculation schemes

International Nuclear Information System (INIS)

Mosca, P.; Taofiki, A.; Bellier, P.; Prevost, A.

2011-01-01

The industrial calculations of third generation nuclear reactors are based on sophisticated strategies of homogenization and collapsing at different spatial and energetic levels. An important issue to ensure the quality of these calculation models is the choice of the collapsing energy mesh. In this work, we show a new approach to generate optimized energy meshes starting from the SHEM 281-group library. The optimization model is applied on 1D cylindrical cells and consists of finding an energy mesh which minimizes the errors between two successive collision probability calculations. The former is realized over the fine SHEM mesh with Livolant-Jeanpierre self-shielded cross sections and the latter is performed with collapsed cross sections over the energy mesh being optimized. The optimization is done by the particle swarm algorithm implemented in the code AEMC and multigroup flux solutions are obtained from standard APOLLO2 solvers. By this new approach, a set of new optimized meshes which encompass from 10 to 50 groups has been defined for PWR and BWR calculations. This set will allow users to adapt the energy detail of the solution to the complexity of the calculation (assembly, multi-assembly, two-dimensional whole core). Some preliminary verifications, in which the accuracy of the new meshes is measured compared to a direct 281-group calculation, show that the 30-group optimized mesh offers a good compromise between simulation time and accuracy for a standard 17 x 17 UO 2 assembly with and without control rods. (author)

Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states

Energy Technology Data Exchange (ETDEWEB)

Mannheim, Philip D., E-mail: philip.mannheim@uconn.edu

2016-02-10

We extend the CPT theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time-independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an antilinear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter two requirements then force this antilinear symmetry to be CPT, while forcing the Hamiltonian to be real rather than Hermitian. Our work justifies the use of the CPT theorem in establishing the equality of the lifetimes of unstable particles that are charge conjugates of each other. We show that the Euclidean time path integrals of a CPT-symmetric theory must always be real. In the quantum-mechanical limit the key results of the PT symmetry program of Bender and collaborators are recovered, with the C-operator of the PT symmetry program being identified with the linear component of the charge conjugation operator.

Evolution operators and transformation of states under uniform and an/or elastic forces into free particle states

International Nuclear Information System (INIS)

Dattoli, G.; Torre, A.

1999-01-01

In this paper are exploited the techniques, associated with the evolution operator method, to prove the existence of a one-to one correspondence between the wave function of a free particle and those of a particle ruled by a quadratic Hamiltonian [it

Hamiltonian truncation approach to quenches in the Ising field theory

Directory of Open Access Journals (Sweden)

T. Rakovszky

2016-10-01

Full Text Available In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

Science.gov (United States)

Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.

2014-01-01

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

Theory of collective Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Zhang Qingying

1982-02-01

Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

Simulating non-Newtonian flows with the moving particle semi-implicit method with an SPH kernel

International Nuclear Information System (INIS)

Xiang, Hao; Chen, Bin

2015-01-01

The moving particle semi-implicit (MPS) method and smoothed particle hydrodynamics (SPH) are commonly used mesh-free particle methods for free surface flows. The MPS method has superiority in incompressible flow simulation and simple programing. However, the crude kernel function is not accurate enough for the discretization of the divergence of the shear stress tensor by the particle inconsistency when the MPS method is extended to non-Newtonian flows. This paper presents an improved MPS method with an SPH kernel to simulate non-Newtonian flows. To improve the consistency of the partial derivative, the SPH cubic spline kernel and the Taylor series expansion are combined with the MPS method. This approach is suitable for all non-Newtonian fluids that can be described with τ  = μ(|γ|) Δ (where τ is the shear stress tensor, μ is the viscosity, |γ| is the shear rate, and Δ is the strain tensor), e.g., the Casson and Cross fluids. Two examples are simulated including the Newtonian Poiseuille flow and container filling process of the Cross fluid. The results of Poiseuille flow are more accurate than the traditional MPS method, and different filling processes are obtained with good agreement with previous results, which verified the validation of the new algorithm. For the Cross fluid, the jet fracture length can be correlated with We 0.28 Fr 0.78 (We is the Weber number, Fr is the Froude number). (paper)

Can model Hamiltonians describe the electron–electron interaction in π-conjugated systems?: PAH and graphene

International Nuclear Information System (INIS)

Chiappe, G; Louis, E; San-Fabián, E; Vergés, J A

2015-01-01

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser–Parr–Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree–Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree–Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The

Mesh Excision: Is Total Mesh Excision Necessary?

Science.gov (United States)

Wolff, Gillian F; Winters, J Christian; Krlin, Ryan M

2016-04-01

Nearly 29% of women will undergo a secondary, repeat operation for pelvic organ prolapse (POP) symptom recurrence following a primary repair, as reported by Abbott et al. (Am J Obstet Gynecol 210:163.e1-163.e1, 2014). In efforts to decrease the rates of failure, graft materials have been utilized to augment transvaginal repairs. Following the success of using polypropylene mesh (PPM) for stress urinary incontinence (SUI), the use of PPM in the transvaginal repair of POP increased. However, in recent years, significant concerns have been raised about the safety of PPM mesh. Complications, some specific to mesh, such as exposures, erosion, dyspareunia, and pelvic pain, have been reported with increased frequency. In the current literature, there is not substantive evidence to suggest that PPM has intrinsic properties that warrant total mesh removal in the absence of complications. There are a number of complications that can occur after transvaginal mesh placement that do warrant surgical intervention after failure of conservative therapy. In aggregate, there are no high-quality controlled studies that clearly demonstrate that total mesh removal is consistently more likely to achieve pain reduction. In the cases of obstruction and erosion, it seems clear that definitive removal of the offending mesh is associated with resolution of symptoms in the majority of cases and reasonable practice. There are a number of complications that can occur with removal of mesh, and patients should be informed of this as they formulate a choice of treatment. We will review these considerations as we examine the clinical question of whether total versus partial removal of mesh is necessary for the resolution of complications following transvaginal mesh placement.

Root-cause analysis of the better performance of the coarse-mesh finite-difference method for CANDU-type reactors

International Nuclear Information System (INIS)

Shen, W.

2012-01-01

Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, three benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)

Root-cause analysis of the better performance of the coarse-mesh finite-difference method for CANDU-type reactors

Energy Technology Data Exchange (ETDEWEB)

Shen, W. [Candu Energy Inc., 2285 Speakman Dr., Mississauga, ON L5B 1K (Canada)

2012-07-01

Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, three benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)

On the domain of the Nelson Hamiltonian

Science.gov (United States)

Griesemer, M.; Wünsch, A.

2018-04-01

The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

Hubbard-U corrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations

DEFF Research Database (Denmark)

Patrick, Christopher; Thygesen, Kristian Sommer

2016-01-01

In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we...... investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transitionmetal compounds ZnS, TiO2, and NiO.We find that the RPA lattice constants are essentially independent of U, despite large changes...... in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U. Our RPA calculations find the rutile phase of TiO2 to be more stable than anatase independent of U, a result which is consistent with experiments...

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

Science.gov (United States)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Interactive Terascale Particle Visualization

Science.gov (United States)

Ellsworth, David; Green, Bryan; Moran, Patrick

2004-01-01

This paper describes the methods used to produce an interactive visualization of a 2 TB computational fluid dynamics (CFD) data set using particle tracing (streaklines). We use the method introduced by Bruckschen et al. [2001] that pre-computes a large number of particles, stores them on disk using a space-filling curve ordering that minimizes seeks, and then retrieves and displays the particles according to the user's command. We describe how the particle computation can be performed using a PC cluster, how the algorithm can be adapted to work with a multi-block curvilinear mesh, and how the out-of-core visualization can be scaled to 296 billion particles while still achieving interactive performance on PG hardware. Compared to the earlier work, our data set size and total number of particles are an order of magnitude larger. We also describe a new compression technique that allows the lossless compression of the particles by 41% and speeds the particle retrieval by about 30%.

Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics - Monte Carlo Canonical Propagation Algorithm.

Science.gov (United States)

Chen, Yunjie; Kale, Seyit; Weare, Jonathan; Dinner, Aaron R; Roux, Benoît

2016-04-12

A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method.

Users manual for Opt-MS : local methods for simplicial mesh smoothing and untangling.

Energy Technology Data Exchange (ETDEWEB)

Freitag, L.

1999-07-20

Creating meshes containing good-quality elements is a challenging, yet critical, problem facing computational scientists today. Several researchers have shown that the size of the mesh, the shape of the elements within that mesh, and their relationship to the physical application of interest can profoundly affect the efficiency and accuracy of many numerical approximation techniques. If the application contains anisotropic physics, the mesh can be improved by considering both local characteristics of the approximate application solution and the geometry of the computational domain. If the application is isotropic, regularly shaped elements in the mesh reduce the discretization error, and the mesh can be improved a priori by considering geometric criteria only. The Opt-MS package provides several local node point smoothing techniques that improve elements in the mesh by adjusting grid point location using geometric, criteria. The package is easy to use; only three subroutine calls are required for the user to begin using the software. The package is also flexible; the user may change the technique, function, or dimension of the problem at any time during the mesh smoothing process. Opt-MS is designed to interface with C and C++ codes, ad examples for both two-and three-dimensional meshes are provided.

Weak KAM for commuting Hamiltonians

International Nuclear Information System (INIS)

Zavidovique, M

2010-01-01

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)

Local unitary transformation method for large-scale two-component relativistic calculations. II. Extension to two-electron Coulomb interaction.

Science.gov (United States)

Seino, Junji; Nakai, Hiromi

2012-10-14

The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X(2) and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.

Passivation controller design for turbo-generators based on generalised Hamiltonian system theory

NARCIS (Netherlands)

Cao, M.; Shen, T.L.; Song, Y.H.

2002-01-01

A method of pre-feedback to formulate the generalised forced Hamiltonian system model for speed governor control systems is proposed. Furthermore, passivation controllers are designed based on the scheme of Hamiltonian structure for single machne infinite bus and multimachine power systems. In

Lagrangian and Hamiltonian Formulation of Transmission Line Systems with Boundary Energy Flow

NARCIS (Netherlands)

Jeltsema, Dimitri; Schaft, Arjan J. van der

The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems

Multidimensional Hamiltonian chaos. Mnogomernyj gamil'tonovskij khaos

Energy Technology Data Exchange (ETDEWEB)

Zaslavskij, G M; Zakharov, M Yu; Nejshtadt, A I; Sagdeev, P Z; Usikov, D A; Chernikov, A A [AN SSSR, Moscow (USSR). Inst. Kosmicheskikh Issledovanij

1989-01-01

In hamiltonian systems, which are close to nondegenerate integrable systems, Arnold diffusion does not arise in the case of two degrees freedom; for a larger number of gegrees of freedom the diffusion is, generally speaking, exponentially slow. If a nonperturbed system is degenerate, diffusion proceeding according to a stochastic pattern may arise, even in the case of two degrees of freedom. The results pertain to the 21/2 degree of freedom problem of the motion of a charged particle in a magnetic field or in the field of a wave propagating at angle with respect to the magnetic field.

Reaction Hamiltonian and state-to-state description of chemical reactions

International Nuclear Information System (INIS)

Ruf, B.A.; Kresin, V.Z.; Lester, W.A. Jr.

1985-08-01

A chemical reaction is treated as a quantum transition from reactants to products. A specific reaction Hamiltonian (in second quantization formalism) is introduced. The approach leads to Franck-Condon-like factor, and adiabatic method in the framework of the nuclear motion problems. The influence of reagent vibrational state on the product energy distribution has been studied following the reaction Hamiltonian method. Two different cases (fixed available energy and fixed translational energy) are distinguished. Results for several biomolecular reactions are presented. 40 refs., 5 figs

Magnetic field line Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1985-02-01

The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined

New procedure for criticality search using coarse mesh nodal methods

International Nuclear Information System (INIS)

Pereira, Wanderson F.; Silva, Fernando C. da; Martinez, Aquilino S.

2011-01-01

The coarse mesh nodal methods have as their primary goal to calculate the neutron flux inside the reactor core. Many computer systems use a specific form of calculation, which is called nodal method. In classical computing systems that use the criticality search is made after the complete convergence of the iterative process of calculating the neutron flux. In this paper, we proposed a new method for the calculation of criticality, condition which will be over very iterative process of calculating the neutron flux. Thus, the processing time for calculating the neutron flux was reduced by half compared with the procedure developed by the Nuclear Engineering Program of COPPE/UFRJ (PEN/COPPE/UFRJ). (author)

New procedure for criticality search using coarse mesh nodal methods

Energy Technology Data Exchange (ETDEWEB)

Pereira, Wanderson F.; Silva, Fernando C. da; Martinez, Aquilino S., E-mail: wneto@con.ufrj.b, E-mail: fernando@con.ufrj.b, E-mail: Aquilino@lmp.ufrj.b [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear

2011-07-01

The coarse mesh nodal methods have as their primary goal to calculate the neutron flux inside the reactor core. Many computer systems use a specific form of calculation, which is called nodal method. In classical computing systems that use the criticality search is made after the complete convergence of the iterative process of calculating the neutron flux. In this paper, we proposed a new method for the calculation of criticality, condition which will be over very iterative process of calculating the neutron flux. Thus, the processing time for calculating the neutron flux was reduced by half compared with the procedure developed by the Nuclear Engineering Program of COPPE/UFRJ (PEN/COPPE/UFRJ). (author)

Hamiltonian closures in fluid models for plasmas

Science.gov (United States)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

Multi-phase Volume Segmentation with Tetrahedral Mesh

DEFF Research Database (Denmark)

Nguyen Trung, Tuan; Dahl, Vedrana Andersen; Bærentzen, Jakob Andreas

Volume segmentation is efficient for reconstructing material structure, which is important for several analyses, e.g. simulation with finite element method, measurement of quantitative information like surface area, surface curvature, volume, etc. We are concerned about the representations of the 3......D volumes, which can be categorized into two groups: fixed voxel grids [1] and unstructured meshes [2]. Among these two representations, the voxel grids are more popular since manipulating a fixed grid is easier than an unstructured mesh, but they are less efficient for quantitative measurements....... In many cases, the voxel grids are converted to explicit meshes, however the conversion may reduce the accuracy of the segmentations, and the effort for meshing is also not trivial. On the other side, methods using unstructured meshes have difficulty in handling topology changes. To reduce the complexity...

Hamiltonian derivation of the nonhydrostatic pressure-coordinate model

Science.gov (United States)

Salmon, Rick; Smith, Leslie M.

1994-07-01

In 1989, the Miller-Pearce (MP) model for nonhydrostatic fluid motion governed by equations written in pressure coordinates was extended by removing the prescribed reference temperature, T(sub s)(p), while retaining the conservation laws and other desirable properties. It was speculated that this extension of the MP model had a Hamiltonian structure and that a slick derivation of the Ertel property could be constructed if the relevant Hamiltonian were known. In this note, the extended equations are derived using Hamilton's principle. The potential vorticity law arises from the usual particle-relabeling symmetry of the Lagrangian, and even the absence of sound waves is anticipated from the fact that the pressure inside the free energy G(p, theta) in the derived equation is hydrostatic and thus G is insensitive to local pressure fluctuations. The model extension is analogous to the semigeostrophic equations for nearly geostrophic flow, which do not incorporate a prescribed reference state, while the earlier MP model is analogous to the quasigeostrophic equations, which become highly inaccurate when the flow wanders from a prescribed state with nearly flat isothermal surfaces.

Hamiltonian partial differential equations and applications

CERN Document Server

Nicholls, David; Sulem, Catherine

2015-01-01

This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

A new method for simplification and compression of 3D meshes

OpenAIRE

Attene, Marco

2001-01-01

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply-connected regions, called triangloids. We compute a new mesh M'. Each triangle of M' is a close approximation of a pseudo-triangle of M. By construction, the connectivity of M' is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M' ...

Velocity width of the resonant domain in wave-particle interaction

International Nuclear Information System (INIS)

Firpo, Marie-Christine; Doveil, Fabrice

2002-01-01

Wave-particle interaction is a ubiquitous physical mechanism exhibiting locality in velocity space. A single-wave Hamiltonian provides a rich model by which to study the self-consistent interaction between one electrostatic wave and N quasiresonant particles. For the simplest nonintegrable Hamiltonian coupling two particles to one wave, we analytically derive the particle velocity borders separating quasi-integrable motions from chaotic ones. These estimates are fully retrieved through computation of the largest Lyapunov exponent. For the large-N particle self-consistent case, we numerically investigate the localization of stochasticity in velocity space and test a qualitative estimate of the borders of chaos

The Hamiltonian of QED. Zero mode

International Nuclear Information System (INIS)

Zastavenko, L.G.

1990-01-01

We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs

Simulation of the Beam-Beam Effects in e+e- Storage Rings with a Method of Reducing the Region of Mesh

Energy Technology Data Exchange (ETDEWEB)

Cai, Yunhai

2000-08-31

A highly accurate self-consistent particle code to simulate the beam-beam collision in e{sup +}e{sup -} storage rings has been developed. It adopts a method of solving the Poisson equation with an open boundary. The method consists of two steps: assigning the potential on a finite boundary using the Green's function, and then solving the potential inside the boundary with a fast Poisson solver. Since the solution of the Poisson's equation is unique, the authors solution is exactly the same as the one obtained by simply using the Green's function. The method allows us to select much smaller region of mesh and therefore increase the resolution of the solver. The better resolution makes more accurate the calculation of the dynamics in the core of the beams. The luminosity simulated with this method agrees quantitatively with the measurement for the PEP-II B-factory ring in the linear and nonlinear beam current regimes, demonstrating its predictive capability in detail.

Streaming Compression of Hexahedral Meshes

Energy Technology Data Exchange (ETDEWEB)

Isenburg, M; Courbet, C

2010-02-03

We describe a method for streaming compression of hexahedral meshes. Given an interleaved stream of vertices and hexahedral our coder incrementally compresses the mesh in the presented order. Our coder is extremely memory efficient when the input stream documents when vertices are referenced for the last time (i.e. when it contains topological finalization tags). Our coder then continuously releases and reuses data structures that no longer contribute to compressing the remainder of the stream. This means in practice that our coder has only a small fraction of the whole mesh in memory at any time. We can therefore compress very large meshes - even meshes that do not file in memory. Compared to traditional, non-streaming approaches that load the entire mesh and globally reorder it during compression, our algorithm trades a less compact compressed representation for significant gains in speed, memory, and I/O efficiency. For example, on the 456k hexahedra 'blade' mesh, our coder is twice as fast and uses 88 times less memory (only 3.1 MB) with the compressed file increasing about 3% in size. We also present the first scheme for predictive compression of properties associated with hexahedral cells.

Advanced Variance Reduction Strategies for Optimizing Mesh Tallies in MAVRIC

International Nuclear Information System (INIS)

Peplow, Douglas E.; Blakeman, Edward D; Wagner, John C

2007-01-01

More often than in the past, Monte Carlo methods are being used to compute fluxes or doses over large areas using mesh tallies (a set of region tallies defined on a mesh that overlays the geometry). For problems that demand that the uncertainty in each mesh cell be less than some set maximum, computation time is controlled by the cell with the largest uncertainty. This issue becomes quite troublesome in deep-penetration problems, and advanced variance reduction techniques are required to obtain reasonable uncertainties over large areas. The CADIS (Consistent Adjoint Driven Importance Sampling) methodology has been shown to very efficiently optimize the calculation of a response (flux or dose) for a single point or a small region using weight windows and a biased source based on the adjoint of that response. This has been incorporated into codes such as ADVANTG (based on MCNP) and the new sequence MAVRIC, which will be available in the next release of SCALE. In an effort to compute lower uncertainties everywhere in the problem, Larsen's group has also developed several methods to help distribute particles more evenly, based on forward estimates of flux. This paper focuses on the use of a forward estimate to weight the placement of the source in the adjoint calculation used by CADIS, which we refer to as a forward-weighted CADIS (FW-CADIS)

Canonical harmonic tracking of charged particles in circular accelerators

International Nuclear Information System (INIS)

Kvardakov, V.; Levichev, E.

2006-01-01

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed

Canonical harmonic tracking of charged particles in circular accelerators

Science.gov (United States)

Kvardakov, V.; Levichev, E.

2006-03-01

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed.

A singular position-dependent mass particle in an infinite potential well

International Nuclear Information System (INIS)

Mustafa, Omar; Mazharimousavi, S. Habib

2009-01-01

An unusual singular position-dependent-mass particle in an infinite potential well is considered. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian and a Poeschl-Teller type reference Hamiltonian is obtained. New ordering ambiguity parametric setting are suggested

Refficientlib: an efficient load-rebalanced adaptive mesh refinement algorithm for high-performance computational physics meshes

OpenAIRE

Baiges Aznar, Joan; Bayona Roa, Camilo Andrés

2017-01-01

No separate or additional fees are collected for access to or distribution of the work. In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. The proposed method is developed for nodally based parallel domain partitions where the nodes of the mesh belong to a single processor, whereas the elements can belong to multiple processors. Some of the main features of the algorithm presented in this paper a...

Dirac equation in low dimensions: The factorization method

Energy Technology Data Exchange (ETDEWEB)

Sánchez-Monroy, J.A., E-mail: antosan@if.usp.br [Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP (Brazil); Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, Bogotá, D. C. (Colombia); CIF, Bogotá (Colombia)

2014-11-15

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.

Control by Interconnection and Energy-Shaping Methods of Port Hamiltonian Models. Application to the Shallow Water Equations

OpenAIRE

Hamroun , Boussad; Dimofte , Alexandru; Lefevre , Laurent; Mendes , Eduardo

2010-01-01

International audience; — In this paper a control algorithm for the reduced port-Controlled Hamiltonian model (PCH) of the shallow water equations (PDEs) is developed. This control is developed using the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) method on the reduced PCH model without the natural dissipation. It allows to assign desired structure and energy function to the closed loop system. The same control law is then derived using an energy shaping method ba...

Dissipative systems and Bateman's Hamiltonian

International Nuclear Information System (INIS)

Pedrosa, I.A.; Baseia, B.

1983-01-01

It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt

Relativistic Model of Hamiltonian Renormalization for Bound States and Scattering Amplitudes

International Nuclear Information System (INIS)

Serafin, Kamil

2017-01-01

We test the renormalization group procedure for effective particles on a model of fermion–scalar interaction based on the Yukawa theory. The model is obtained by truncating the Yukawa theory to just two Fock sectors in the Dirac front form of Hamiltonian dynamics, a fermion, and a fermion and a boson, for the purpose of simple analytic calculation that exhibits steps of the procedure. (author)

r-Adaptive mesh generation for shell finite element analysis

International Nuclear Information System (INIS)

Cho, Maenghyo; Jun, Seongki

2004-01-01

An r-adaptive method or moving grid technique relocates a grid so that it becomes concentrated in the desired region. This concentration improves the accuracy and efficiency of finite element solutions. We apply the r-adaptive method to computational mesh of shell surfaces, which is initially regular and uniform. The r-adaptive method, given by Liao and Anderson [Appl. Anal. 44 (1992) 285], aggregate the grid in the region with a relatively high weight function without any grid-tangling. The stress error estimator is calculated in the initial uniform mesh for a weight function. However, since the r-adaptive method is a method that moves the grid, shell surface geometry error such as curvature error and mesh distortion error will increase. Therefore, to represent the exact geometry of a shell surface and to prevent surface geometric errors, we use the Naghdi's shell theory and express the shell surface by a B-spline patch. In addition, using a nine-node element, which is relatively less sensitive to mesh distortion, we try to diminish mesh distortion error in the application of an r-adaptive method. In the numerical examples, it is shown that the values of the error estimator for a cylinder, hemisphere, and torus in the overall domain can be reduced effectively by using the mesh generated by the r-adaptive method. Also, the reductions of the estimated relative errors are demonstrated in the numerical examples. In particular, a new functional is proposed to construct an adjusted mesh configuration by considering a mesh distortion measure as well as the stress error function. The proposed weight function provides a reliable mesh adaptation method after a parameter value in the weight function is properly chosen

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

KAUST Repository

Almarouf, Mohamad Abdulilah Alhusain Alali

2017-02-25

We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

KAUST Repository

Almarouf, Mohamad Abdulilah Alhusain Alali; Samtaney, Ravi

2017-01-01

We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

Numerical homogenization of concrete microstructures without explicit meshes

International Nuclear Information System (INIS)

Sanahuja, Julien; Toulemonde, Charles

2011-01-01

Life management of electric hydro or nuclear power plants requires to estimate long-term concrete properties on facilities, for obvious safety and serviceability reasons. Decades-old structures are foreseen to be operational for several more decades. As a large number of different concrete formulations are found in EDF facilities, empirical models based on many experiments cannot be an option for a large fleet of power plant buildings. To build predictive models, homogenization techniques offer an appealing alternative. To properly upscale creep, especially at long term, a rather precise description of the microstructure is required. However, the complexity of the morphology of concrete poses several challenges. In particular, concrete is formulated to maximize the packing density of the granular skeleton, leading to aggregates spanning several length scales with small inter particle spacings. Thus, explicit meshing of realistic concrete microstructures is either out of reach of current meshing algorithms or would produce a number of degrees of freedom far higher than the current generic FEM codes capabilities. This paper proposes a method to deal with complex matrix-inclusions microstructures such as the ones encountered at the mortar or concrete scales, without explicitly meshing them. The microstructure is superimposed to an independent mesh, which is a regular Cartesian grid. This inevitably yields so called 'gray elements', spanning across multiple phases. As the reliability of the estimate of the effective properties highly depends on the behavior affected to these gray elements, special attention is paid to them. As far as the question of the solvers is concerned, generic FEM codes are found to lack efficiency: they cannot reach high enough levels of discretization with classical free meshes, and they do not take advantage of the regular structure of the mesh. Thus, a specific finite differences/finite volumes solver has been developed. At first, generic off

Squeezed states from a quantum deformed oscillator Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)

2016-03-11

The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.

Notes on the Mesh Handler and Mesh Data Conversion

International Nuclear Information System (INIS)

Lee, Sang Yong; Park, Chan Eok

2009-01-01

At the outset of the development of the thermal-hydraulic code (THC), efforts have been made to utilize the recent technology of the computational fluid dynamics. Among many of them, the unstructured mesh approach was adopted to alleviate the restriction of the grid handling system. As a natural consequence, a mesh handler (MH) has been developed to manipulate the complex mesh data from the mesh generator. The mesh generator, Gambit, was chosen at the beginning of the development of the code. But a new mesh generator, Pointwise, was introduced to get more flexible mesh generation capability. An open source code, Paraview, was chosen as a post processor, which can handle unstructured as well as structured mesh data. Overall data processing system for THC is shown in Figure-1. There are various file formats to save the mesh data in the permanent storage media. A couple of dozen of file formats are found even in the above mentioned programs. A competent mesh handler should have the capability to import or export mesh data as many as possible formats. But, in reality, there are two aspects that make it difficult to achieve the competence. The first aspect to consider is the time and efforts to program the interface code. And the second aspect, which is even more difficult one, is the fact that many mesh data file formats are proprietary information. In this paper, some experience of the development of the format conversion programs will be presented. File formats involved are Gambit neutral format, Ansys-CFX grid file format, VTK legacy file format, Nastran format and CGNS

AUTOMATIC MESH GENERATION OF 3-D GEOMETRIC MODELS

Institute of Scientific and Technical Information of China (English)

刘剑飞

2003-01-01

In this paper the presentation of the ball-packing method is reviewed,and a scheme to generate mesh for complex 3-D geometric models is given,which consists of 4 steps:(1)create nodes in 3-D models by ball-packing method,(2)connect nodes to generate mesh by 3-D Delaunay triangulation,(3)retrieve the boundary of the model after Delaunay triangulation,(4)improve the mesh.

Functional integral and effective Hamiltonian t-J-V model of strongly correlated electron system

International Nuclear Information System (INIS)

Belinicher, V.I.; Chertkov, M.V.

1990-09-01

The functional integral representation for the generating functional of t-J-V model is obtained. In the case close to half filling this functional integral representation reduces the conventional Hamiltonian of t-J-V model to the Hamiltonian of the system containing holes and spins 1/2 at each lattice size. This effective Hamiltonian coincides with that one obtained one of the authors by different method. This Hamiltonian and its dynamical variables can be used for description of different magnetic phases of t-J-V model. (author). 16 refs

Feature-Sensitive Tetrahedral Mesh Generation with Guaranteed Quality

OpenAIRE

Wang, Jun; Yu, Zeyun

2012-01-01

Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is prov...

Mesh Adaptation and Shape Optimization on Unstructured Meshes, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — In this SBIR CRM proposes to implement the entropy adjoint method for solution adaptive mesh refinement into the Loci/CHEM unstructured flow solver. The scheme will...

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

Science.gov (United States)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Quantum Hamiltonian reduction in superspace formalism

International Nuclear Information System (INIS)

Madsen, J.O.; Ragoucy, E.

1994-02-01

Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs

Discrete Hamiltonian evolution and quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

Optimal mesh hierarchies in Multilevel Monte Carlo methods

KAUST Repository

Von Schwerin, Erik

2016-01-01

I will discuss how to choose optimal mesh hierarchies in Multilevel Monte Carlo (MLMC) simulations when computing the expected value of a quantity of interest depending on the solution of, for example, an Ito stochastic differential equation or a partial differential equation with stochastic data. I will consider numerical schemes based on uniform discretization methods with general approximation orders and computational costs. I will compare optimized geometric and non-geometric hierarchies and discuss how enforcing some domain constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. I will also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. This talk presents joint work with N.Collier, A.-L.Haji-Ali, F. Nobile, and R. Tempone.

Optimal mesh hierarchies in Multilevel Monte Carlo methods

KAUST Repository

Von Schwerin, Erik

2016-01-08

I will discuss how to choose optimal mesh hierarchies in Multilevel Monte Carlo (MLMC) simulations when computing the expected value of a quantity of interest depending on the solution of, for example, an Ito stochastic differential equation or a partial differential equation with stochastic data. I will consider numerical schemes based on uniform discretization methods with general approximation orders and computational costs. I will compare optimized geometric and non-geometric hierarchies and discuss how enforcing some domain constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. I will also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. This talk presents joint work with N.Collier, A.-L.Haji-Ali, F. Nobile, and R. Tempone.

Hamiltonian Monte Carlo study of the N=1 Wess-Zumino model on the lattice in 1+1 dimensions

International Nuclear Information System (INIS)

Schiller, A.

1984-01-01

1+1 dimensional models with restricted supersymmetry are studied. The problems of formulating supersymmetric models on the lattice are overcome by working in the Hamiltonian lattice formulation and using restricted supersymmetry algebra involving only the Hamiltonian. For the two-dimensional Wess-Zumino model a lattice Hamiltonian suitable for the local Hamiltonian method is obtained. Using this method field theoretical models with fermions and scalar Higgs fields are investigated. Emphasis is laid on supersymmetry breaking and soliton formation

A characteristic based multiple balance approach for SN on arbitrary polygonal meshes

International Nuclear Information System (INIS)

Grove, R.E.; Pevey, R.E.

1995-01-01

The authors introduce a new approach for characteristic based S n transport on arbitrary polygonal meshes in XY geometry. They approximate a general surface as an arbitrary polygon and rotate to a coordinate system aligned with the direction of particle travel. They use exact moment balance equations on whole cells and subregions called slices and close the system by analytically solving the characteristic equation. The authors assume spatial functions for boundary conditions and cell sources and formulate analogous functions for outgoing edge and cell angular fluxes which exactly preserve spatial moments of the analytic solution. In principle, their approach provides the framework to extend characteristic methods formulated on rectangular grids to arbitrary polygonal meshes. The authors derive schemes based on step and linear spatial approximations. Their step characteristic scheme is mathematically equivalent to the Extended Step Characteristic (ESC) method but their approach and scheme differ in the geometry rotation and in the solution form. Their solutions are simple and permit edge-based transport sweep ordering

An adaptive mesh refinement approach for average current nodal expansion method in 2-D rectangular geometry

International Nuclear Information System (INIS)

Poursalehi, N.; Zolfaghari, A.; Minuchehr, A.

2013-01-01

Highlights: ► A new adaptive h-refinement approach has been developed for a class of nodal method. ► The resulting system of nodal equations is more amenable to efficient numerical solution. ► The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. ► Spatially adaptive approach greatly enhances the accuracy of the solution. - Abstract: The aim of this work is to develop a spatially adaptive coarse mesh strategy that progressively refines the nodes in appropriate regions of domain to solve the neutron balance equation by zeroth order nodal expansion method. A flux gradient based a posteriori estimation scheme has been utilized for checking the approximate solutions for various nodes. The relative surface net leakage of nodes has been considered as an assessment criterion. In this approach, the core module is called in by adaptive mesh generator to determine gradients of node surfaces flux to explore the possibility of node refinements in appropriate regions and directions of the problem. The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. For this purpose, a computer program ANRNE-2D, Adaptive Node Refinement Nodal Expansion, has been developed to solve neutron diffusion equation using average current nodal expansion method for 2D rectangular geometries. Implementing the adaptive algorithm confirms its superiority in enhancing the accuracy of the solution without using fine nodes throughout the domain and increasing the number of unknown solution. Some well-known benchmarks have been investigated and improvements are reported

Generalized oscillator representations for Calogero Hamiltonians

International Nuclear Information System (INIS)

Tyutin, I V; Voronov, B L

2013-01-01

This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)

A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

OpenAIRE

Ngwane, F. F.; Jator, S. N.

2017-01-01

In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one...

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Direct numerical simulations of agglomeration of circular colloidal particles in two-dimensional shear flow

International Nuclear Information System (INIS)

Choi, Young Joon; Djilali, Ned

2016-01-01

Colloidal agglomeration of nanoparticles in shear flow is investigated by solving the fluid-particle and particle-particle interactions in a 2D system. We use an extended finite element method in which the dynamics of the particles is solved in a fully coupled manner with the flow, allowing an accurate description of the fluid-particle interfaces without the need of boundary-fitted meshes or of empirical correlations to account for the hydrodynamic interactions between the particles. Adaptive local mesh refinement using a grid deformation method is incorporated with the fluid-structure interaction algorithm, and the particle-particle interaction at the microscopic level is modeled using the Lennard-Jones potential. Motivated by the process used in fabricating fuel cell catalysts from a colloidal ink, the model is applied to investigate agglomeration of colloidal particles under external shear flow in a sliding bi-periodic Lees-Edwards frame with varying shear rates and particle fraction ratios. Both external shear and particle fraction are found to have a crucial impact on the structure formation of colloidal particles in a suspension. Segregation intensity and graph theory are used to analyze the underlying agglomeration patterns and structures, and three agglomeration regimes are identified

Meshes optimized for discrete exterior calculus (DEC).

Energy Technology Data Exchange (ETDEWEB)

Mousley, Sarah C. [Univ. of Illinois, Urbana-Champaign, IL (United States); Deakin, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knupp, Patrick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-12-01

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.

Constructing Dense Graphs with Unique Hamiltonian Cycles

Science.gov (United States)

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

New finite volume methods for approximating partial differential equations on arbitrary meshes

International Nuclear Information System (INIS)

Hermeline, F.

2008-12-01

This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

Science.gov (United States)

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Analysis of ultrasonically rotating droplet using moving particle semi-implicit and distributed point source methods

Science.gov (United States)

Wada, Yuji; Yuge, Kohei; Tanaka, Hiroki; Nakamura, Kentaro

2016-07-01

Numerical analysis of the rotation of an ultrasonically levitated droplet with a free surface boundary is discussed. The ultrasonically levitated droplet is often reported to rotate owing to the surface tangential component of acoustic radiation force. To observe the torque from an acoustic wave and clarify the mechanism underlying the phenomena, it is effective to take advantage of numerical simulation using the distributed point source method (DPSM) and moving particle semi-implicit (MPS) method, both of which do not require a calculation grid or mesh. In this paper, the numerical treatment of the viscoacoustic torque, which emerges from the viscous boundary layer and governs the acoustical droplet rotation, is discussed. The Reynolds stress traction force is calculated from the DPSM result using the idea of effective normal particle velocity through the boundary layer and input to the MPS surface particles. A droplet levitated in an acoustic chamber is simulated using the proposed calculation method. The droplet is vertically supported by a plane standing wave from an ultrasonic driver and subjected to a rotating sound field excited by two acoustic sources on the side wall with different phases. The rotation of the droplet is successfully reproduced numerically and its acceleration is discussed and compared with those in the literature.

Numerical simulation of a flow-like landslide using the particle finite element method

Science.gov (United States)

Zhang, Xue; Krabbenhoft, Kristian; Sheng, Daichao; Li, Weichao

2015-01-01

In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained.

Automatic mesh generation with QMESH program

International Nuclear Information System (INIS)

Ise, Takeharu; Tsutsui, Tsuneo

1977-05-01

Usage of the two-dimensional self-organizing mesh generation program, QMESH, is presented together with the descriptions and the experience, as it has recently been converted and reconstructed from the NEACPL version to the FACOM. The program package consists of the QMESH code to generate quadrilaterial meshes with smoothing techniques, the QPLOT code to plot the data obtained from the QMESH on the graphic COM, and the RENUM code to renumber the meshes by using a bandwidth minimization procedure. The technique of mesh reconstructuring coupled with smoothing techniques is especially useful when one generates the meshes for computer codes based on the finite element method. Several typical examples are given for easy access to the QMESH program, which is registered in the R.B-disks of JAERI for users. (auth.)

A Reconfigurable Mesh-Ring Topology for Bluetooth Sensor Networks

Directory of Open Access Journals (Sweden)

Ben-Yi Wang

2018-05-01

Full Text Available In this paper, a Reconfigurable Mesh-Ring (RMR algorithm is proposed for Bluetooth sensor networks. The algorithm is designed in three stages to determine the optimal configuration of the mesh-ring network. Firstly, a designated root advertises and discovers its neighboring nodes. Secondly, a scatternet criterion is built to compute the minimum number of piconets and distributes the connection information for piconet and scatternet. Finally, a peak-search method is designed to determine the optimal mesh-ring configuration for various sizes of networks. To maximize the network capacity, the research problem is formulated by determining the best connectivity of available mesh links. During the formation and maintenance phases, three possible configurations (including piconet, scatternet, and hybrid are examined to determine the optimal placement of mesh links. The peak-search method is a systematic approach, and is implemented by three functional blocks: the topology formation block generates the mesh-ring topology, the routing efficiency block computes the routing performance, and the optimum decision block introduces a decision-making criterion to determine the optimum number of mesh links. Simulation results demonstrate that the optimal mesh-ring configuration can be determined and that the scatternet case achieves better overall performance than the other two configurations. The RMR topology also outperforms the conventional ring-based and cluster-based mesh methods in terms of throughput performance for Bluetooth configurable networks.

Optimization of gold ore Sumbawa separation using gravity method: Shaking table

Science.gov (United States)

Ferdana, Achmad Dhaefi; Petrus, Himawan Tri Bayu Murti; Bendiyasa, I. Made; Prijambada, Irfan Dwidya; Hamada, Fumio; Sachiko, Takahi

2018-04-01

Most of artisanal small gold mining in Indonesia has been using amalgamation method, which caused negative impact to the environment around ore processing area due to the usage of mercury. One of the more environmental-friendly method for gold processing is gravity method. Shaking table is one of separation equipment of gravity method used to increase concentrate based on difference of specific gravity. The optimum concentration result is influenced by several variables, such as rotational speed shaking, particle size and deck slope. In this research, the range of rotational speed shaking was between 100 rpm and 200 rpm, the particle size was between -100 + 200 mesh and -200 + 300 mesh and deck slope was between 3° and 7°. Gold concentration in concentrate was measured by EDX. The result shows that the optimum condition is obtained at a shaking speed of 200 rpm, with a slope of 7° and particle size of -100 + 200 mesh.